PSIGMAL(3,4): |P| = 40320, k = 21, |Q| = 1920, M = 128; mode all; part 0/1
subgroups of Q up to Q-conjugacy: 129 classes, 5406 subgroups (2s)
subgroups R to treat (|R|*k >= M): 106
R#10: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 60, |A| = 128, family 3, closures 324, members of order >= M: {}  (0.1s)
R#11: |R| = 8, |phibar(R)| = 2, good, Q-conjugates 60, |A| = 32, family 3, closures 341, members of order >= M: {}  (0.1s)
R#12: |R| = 8, |phibar(R)| = 2, good, Q-conjugates 120, |A| = 32, family 3, closures 341, members of order >= M: {}  (0.1s)
R#14: |R| = 10, |phibar(R)| = 10, not good, Q-conjugates 96, |A| = 300, family 5, closures 232, members of order >= M: {160: 1}  (0.1s)
R#16: |R| = 24, |phibar(R)| = 6, not good, Q-conjugates 40, |A| = 480, family 3, closures 55, members of order >= M: {168: 1, 360: 1}  (0.1s)
R#17: |R| = 160, |phibar(R)| = 10, not good, Q-conjugates 6, |A| = 0, family 1, closures 5, members of order >= M: {160: 1}  (0.0s)
R#19: |R| = 24, |phibar(R)| = 6, not good, Q-conjugates 80, |A| = 480, family 3, closures 55, members of order >= M: {168: 1, 360: 1}  (0.1s)
R#20: |R| = 12, |phibar(R)| = 12, not good, Q-conjugates 80, |A| = 384, family 8, closures 180, members of order >= M: {192: 1}  (0.1s)
R#21: |R| = 12, |phibar(R)| = 12, not good, Q-conjugates 160, |A| = 204, family 4, closures 162, members of order >= M: {168: 1}  (0.1s)
R#22: |R| = 12, |phibar(R)| = 12, not good, Q-conjugates 80, |A| = 216, family 5, closures 169, members of order >= M: {168: 1}  (0.1s)
R#23: |R| = 60, |phibar(R)| = 60, not good, Q-conjugates 16, |A| = 900, family 2, closures 15, members of order >= M: {960: 1}  (0.0s)
R#24: |R| = 60, |phibar(R)| = 60, not good, Q-conjugates 16, |A| = 300, family 2, closures 15, members of order >= M: {360: 1}  (0.0s)
R#25: |R| = 60, |phibar(R)| = 60, not good, Q-conjugates 32, |A| = 300, family 2, closures 15, members of order >= M: {360: 1}  (0.0s)
R#27: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 0, family 1, closures 96, members of order >= M: {}  (0.1s)
R#28: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 0, family 1, closures 96, members of order >= M: {}  (0.1s)
R#32: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 60, |A| = 416, family 7, closures 373, members of order >= M: {}  (0.2s)
R#33: |R| = 32, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 0, family 1, closures 29, members of order >= M: {}  (0.0s)
R#34: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 0, family 1, closures 329, members of order >= M: {}  (0.2s)
R#35: |R| = 8, |phibar(R)| = 8, good, Q-conjugates 120, |A| = 624, family 17, closures 501, members of order >= M: {128: 2}  (0.3s)
R#36: |R| = 64, |phibar(R)| = 8, good, Q-conjugates 15, |A| = 512, family 3, closures 17, members of order >= M: {320: 2}  (0.0s)
R#37: |R| = 8, |phibar(R)| = 8, good, Q-conjugates 120, |A| = 80, family 5, closures 349, members of order >= M: {}  (0.2s)
R#38: |R| = 20, |phibar(R)| = 20, not good, Q-conjugates 96, |A| = 400, family 3, closures 66, members of order >= M: {320: 1}  (0.0s)
R#39: |R| = 320, |phibar(R)| = 20, not good, Q-conjugates 6, |A| = 0, family 1, closures 2, members of order >= M: {320: 1}  (0.0s)
R#40: |R| = 16, |phibar(R)| = 8, good, Q-conjugates 60, |A| = 608, family 7, closures 118, members of order >= M: {320: 2}  (0.1s)
R#41: |R| = 12, |phibar(R)| = 12, not good, Q-conjugates 160, |A| = 420, family 7, closures 202, members of order >= M: {144: 1, 192: 1}  (0.1s)
R#42: |R| = 48, |phibar(R)| = 12, not good, Q-conjugates 40, |A| = 960, family 3, closures 26, members of order >= M: {336: 1, 720: 1}  (0.0s)
R#43: |R| = 120, |phibar(R)| = 120, not good, Q-conjugates 16, |A| = 1800, family 2, closures 7, members of order >= M: {1920: 1}  (0.0s)
R#44: |R| = 120, |phibar(R)| = 120, not good, Q-conjugates 16, |A| = 600, family 2, closures 7, members of order >= M: {720: 1}  (0.0s)
R#45: |R| = 192, |phibar(R)| = 12, not good, Q-conjugates 10, |A| = 0, family 1, closures 4, members of order >= M: {192: 1}  (0.0s)
R#46: |R| = 1920, |phibar(R)| = 120, not good, Q-conjugates 1, |A| = 38400, family 2, closures 2, members of order >= M: {1920: 1, 40320: 1}  (0.0s)
R#47: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 0, family 1, closures 97, members of order >= M: {}  (0.1s)
R#48: |R| = 32, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 0, family 1, closures 29, members of order >= M: {}  (0.0s)
R#49: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 60, |A| = 16, family 3, closures 334, members of order >= M: {}  (0.2s)
R#50: |R| = 16, |phibar(R)| = 2, good, Q-conjugates 30, |A| = 0, family 1, closures 85, members of order >= M: {}  (0.1s)
R#51: |R| = 8, |phibar(R)| = 2, good, Q-conjugates 15, |A| = 0, family 1, closures 320, members of order >= M: {}  (0.2s)
R#52: |R| = 96, |phibar(R)| = 6, not good, Q-conjugates 10, |A| = 0, family 1, closures 9, members of order >= M: {}  (0.0s)
R#53: |R| = 48, |phibar(R)| = 12, not good, Q-conjugates 20, |A| = 0, family 1, closures 15, members of order >= M: {}  (0.0s)
R#54: |R| = 960, |phibar(R)| = 60, not good, Q-conjugates 1, |A| = 19200, family 2, closures 3, members of order >= M: {960: 1, 20160: 1}  (0.0s)
R#55: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 60, |A| = 128, family 3, closures 324, members of order >= M: {}  (0.1s)
R#56: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 5, |A| = 0, family 1, closures 85, members of order >= M: {}  (0.1s)
R#57: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 256, family 5, closures 376, members of order >= M: {}  (0.2s)
R#58: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 60, |A| = 0, family 1, closures 329, members of order >= M: {}  (0.2s)
R#59: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 0, family 1, closures 320, members of order >= M: {}  (0.1s)
R#60: |R| = 64, |phibar(R)| = 8, good, Q-conjugates 15, |A| = 0, family 1, closures 10, members of order >= M: {}  (0.0s)
R#61: |R| = 32, |phibar(R)| = 8, good, Q-conjugates 30, |A| = 0, family 1, closures 26, members of order >= M: {}  (0.0s)
R#62: |R| = 32, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 0, family 1, closures 30, members of order >= M: {}  (0.0s)
R#63: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 0, family 1, closures 85, members of order >= M: {}  (0.1s)
R#64: |R| = 16, |phibar(R)| = 2, good, Q-conjugates 15, |A| = 0, family 1, closures 85, members of order >= M: {}  (0.1s)
R#65: |R| = 8, |phibar(R)| = 2, good, Q-conjugates 30, |A| = 0, family 1, closures 320, members of order >= M: {}  (0.2s)
R#66: |R| = 48, |phibar(R)| = 12, not good, Q-conjugates 40, |A| = 0, family 1, closures 15, members of order >= M: {}  (0.0s)
R#67: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 10, |A| = 0, family 1, closures 85, members of order >= M: {}  (0.1s)
R#68: |R| = 32, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 0, family 1, closures 26, members of order >= M: {}  (0.0s)
R#69: |R| = 32, |phibar(R)| = 8, good, Q-conjugates 30, |A| = 0, family 1, closures 30, members of order >= M: {}  (0.0s)
R#70: |R| = 16, |phibar(R)| = 8, good, Q-conjugates 60, |A| = 256, family 3, closures 98, members of order >= M: {144: 2}  (0.1s)
R#71: |R| = 16, |phibar(R)| = 8, good, Q-conjugates 60, |A| = 0, family 1, closures 85, members of order >= M: {}  (0.1s)
R#72: |R| = 64, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 0, family 1, closures 10, members of order >= M: {}  (0.0s)
R#73: |R| = 12, |phibar(R)| = 3, good, Q-conjugates 40, |A| = 96, family 3, closures 154, members of order >= M: {}  (0.1s)
R#74: |R| = 12, |phibar(R)| = 3, good, Q-conjugates 80, |A| = 96, family 3, closures 154, members of order >= M: {}  (0.1s)
R#75: |R| = 12, |phibar(R)| = 3, good, Q-conjugates 80, |A| = 48, family 2, closures 151, members of order >= M: {}  (0.1s)
R#77: |R| = 24, |phibar(R)| = 6, not good, Q-conjugates 40, |A| = 192, family 3, closures 54, members of order >= M: {}  (0.0s)
R#78: |R| = 96, |phibar(R)| = 6, not good, Q-conjugates 10, |A| = 0, family 1, closures 7, members of order >= M: {}  (0.0s)
R#79: |R| = 24, |phibar(R)| = 6, not good, Q-conjugates 80, |A| = 96, family 2, closures 51, members of order >= M: {}  (0.0s)
R#80: |R| = 24, |phibar(R)| = 24, not good, Q-conjugates 80, |A| = 528, family 5, closures 62, members of order >= M: {192: 1, 384: 1}  (0.0s)
R#81: |R| = 384, |phibar(R)| = 24, not good, Q-conjugates 5, |A| = 1536, family 2, closures 4, members of order >= M: {384: 1, 1920: 1}  (0.0s)
R#82: |R| = 96, |phibar(R)| = 24, not good, Q-conjugates 20, |A| = 0, family 1, closures 7, members of order >= M: {}  (0.0s)
R#83: |R| = 96, |phibar(R)| = 24, not good, Q-conjugates 20, |A| = 1920, family 4, closures 17, members of order >= M: {192: 1, 384: 1, 1920: 1}  (0.0s)
R#84: |R| = 24, |phibar(R)| = 24, not good, Q-conjugates 80, |A| = 408, family 4, closures 59, members of order >= M: {336: 1}  (0.0s)
R#86: |R| = 24, |phibar(R)| = 6, good, Q-conjugates 40, |A| = 0, family 1, closures 45, members of order >= M: {}  (0.0s)
R#87: |R| = 96, |phibar(R)| = 6, good, Q-conjugates 10, |A| = 0, family 1, closures 5, members of order >= M: {}  (0.0s)
R#88: |R| = 80, |phibar(R)| = 5, good, Q-conjugates 6, |A| = 0, family 1, closures 5, members of order >= M: {}  (0.0s)
R#92: |R| = 8, |phibar(R)| = 2, good, Q-conjugates 60, |A| = 0, family 1, closures 329, members of order >= M: {}  (0.2s)
R#93: |R| = 16, |phibar(R)| = 2, good, Q-conjugates 30, |A| = 0, family 1, closures 85, members of order >= M: {}  (0.1s)
R#95: |R| = 8, |phibar(R)| = 2, good, Q-conjugates 30, |A| = 0, family 1, closures 320, members of order >= M: {}  (0.2s)
R#96: |R| = 8, |phibar(R)| = 2, good, Q-conjugates 60, |A| = 0, family 1, closures 329, members of order >= M: {}  (0.2s)
R#97: |R| = 32, |phibar(R)| = 2, good, Q-conjugates 15, |A| = 0, family 1, closures 33, members of order >= M: {}  (0.0s)
R#98: |R| = 16, |phibar(R)| = 2, good, Q-conjugates 15, |A| = 0, family 1, closures 104, members of order >= M: {}  (0.1s)
R#99: |R| = 192, |phibar(R)| = 12, not good, Q-conjugates 5, |A| = 768, family 2, closures 7, members of order >= M: {192: 1, 960: 1}  (0.0s)
R#100: |R| = 32, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 384, family 5, closures 54, members of order >= M: {160: 2}  (0.1s)
R#101: |R| = 32, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 0, family 1, closures 29, members of order >= M: {}  (0.0s)
R#102: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 60, |A| = 64, family 3, closures 114, members of order >= M: {}  (0.1s)
R#103: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 60, |A| = 0, family 1, closures 92, members of order >= M: {}  (0.1s)
R#104: |R| = 128, |phibar(R)| = 8, good, Q-conjugates 15, |A| = 0, family 1, closures 6, members of order >= M: {128: 1}  (0.0s)
R#105: |R| = 16, |phibar(R)| = 2, good, Q-conjugates 30, |A| = 0, family 1, closures 104, members of order >= M: {}  (0.1s)
R#106: |R| = 32, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 0, family 1, closures 29, members of order >= M: {}  (0.0s)
R#107: |R| = 64, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 0, family 1, closures 12, members of order >= M: {}  (0.0s)
R#108: |R| = 64, |phibar(R)| = 8, good, Q-conjugates 15, |A| = 256, family 3, closures 20, members of order >= M: {192: 2}  (0.0s)
R#109: |R| = 8, |phibar(R)| = 2, good, Q-conjugates 15, |A| = 0, family 1, closures 360, members of order >= M: {}  (0.2s)
R#110: |R| = 48, |phibar(R)| = 12, not good, Q-conjugates 20, |A| = 1008, family 5, closures 36, members of order >= M: {192: 1, 960: 1}  (0.1s)
R#111: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 60, |A| = 480, family 19, closures 505, members of order >= M: {160: 2}  (0.3s)
R#112: |R| = 8, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 352, family 17, closures 513, members of order >= M: {}  (0.3s)
R#113: |R| = 32, |phibar(R)| = 8, good, Q-conjugates 30, |A| = 320, family 7, closures 66, members of order >= M: {128: 2}  (0.1s)
R#114: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 0, family 1, closures 105, members of order >= M: {}  (0.1s)
R#115: |R| = 16, |phibar(R)| = 8, good, Q-conjugates 60, |A| = 352, family 7, closures 128, members of order >= M: {192: 2}  (0.1s)
R#116: |R| = 64, |phibar(R)| = 8, good, Q-conjugates 15, |A| = 0, family 1, closures 11, members of order >= M: {}  (0.0s)
R#117: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 0, family 1, closures 85, members of order >= M: {}  (0.1s)
R#118: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 30, |A| = 0, family 1, closures 94, members of order >= M: {}  (0.1s)
R#119: |R| = 32, |phibar(R)| = 8, good, Q-conjugates 30, |A| = 0, family 1, closures 26, members of order >= M: {}  (0.0s)
R#120: |R| = 48, |phibar(R)| = 3, good, Q-conjugates 10, |A| = 0, family 1, closures 15, members of order >= M: {}  (0.0s)
R#121: |R| = 8, |phibar(R)| = 1, good, Q-conjugates 15, |A| = 0, family 1, closures 320, members of order >= M: {}  (0.2s)
R#122: |R| = 32, |phibar(R)| = 2, good, Q-conjugates 10, |A| = 0, family 1, closures 26, members of order >= M: {}  (0.0s)
R#123: |R| = 8, |phibar(R)| = 2, good, Q-conjugates 10, |A| = 0, family 1, closures 356, members of order >= M: {}  (0.2s)
R#124: |R| = 16, |phibar(R)| = 2, good, Q-conjugates 30, |A| = 0, family 1, closures 94, members of order >= M: {}  (0.1s)
R#125: |R| = 64, |phibar(R)| = 4, good, Q-conjugates 5, |A| = 0, family 1, closures 16, members of order >= M: {}  (0.0s)
R#126: |R| = 32, |phibar(R)| = 4, good, Q-conjugates 15, |A| = 0, family 1, closures 38, members of order >= M: {}  (0.0s)
R#127: |R| = 16, |phibar(R)| = 4, good, Q-conjugates 5, |A| = 1216, family 45, closures 722, members of order >= M: {}  (0.5s)
R#128: |R| = 16, |phibar(R)| = 1, good, Q-conjugates 1, |A| = 0, family 1, closures 85, members of order >= M: {}  (0.1s)

TOTALS PSIGMAL(3,4) mode all part 0/1:
  subgroups S with |S| >= M, by order (all conjugates counted): {128: 315, 144: 280, 160: 252, 168: 360, 192: 525, 320: 252, 336: 120, 360: 168, 384: 105, 720: 56, 960: 42, 1920: 42, 20160: 1, 40320: 1}
  of these, good at the base point: {128: 315, 144: 120, 160: 150, 192: 150, 320: 150}
  largest order of a subgroup good at the base point found: 320  (M = 128)
  good subgroups of order > M: 570
  saved 51 subgroups of order > M; every subgroup of P of order > M is conjugate under Q to at least one of them
total time 11s
