PSIGMAL(3,4): |P| = 40320, k = 21, |Q| = 1920, |phibar(Q)| = 120, |Q_t| by o(t): {2: [128], 3: [96], 5: [80]}, M = 128, |P|/M = 315
  [lattice] processed 1/10 classes, closures 9, 0s
  [lattice] processed 11/121 classes, closures 3566, 12s
  [lattice] processed 21/133 classes, closures 5672, 21s
  [lattice] processed 31/138 classes, closures 7487, 28s
  [lattice] processed 41/139 classes, closures 10541, 40s
  [lattice] processed 51/147 classes, closures 12465, 45s
  [lattice] processed 61/147 classes, closures 14491, 56s
  [lattice] processed 71/147 classes, closures 16482, 67s
  [lattice] processed 81/147 classes, closures 18680, 79s
  [lattice] processed 91/148 classes, closures 20411, 87s
  [lattice] processed 101/148 classes, closures 22129, 97s
  [lattice] processed 111/148 classes, closures 24995, 112s
  [lattice] processed 121/148 classes, closures 27110, 125s
  [lattice] processed 131/150 classes, closures 29189, 135s
  [lattice] processed 141/152 classes, closures 30545, 141s
  [lattice] processed 151/152 classes, closures 32067, 150s
  [lattice] processed 152/152 classes, closures 32095, 150s
classes of subgroups: 152; subgroups: 96262; time 150s
normal subgroups (orders): [1, 20160, 40320]
order histogram of classes: {1: 1, 2: 2, 3: 1, 4: 9, 5: 1, 6: 3, 7: 1, 8: 18, 9: 1, 10: 1, 12: 6, 14: 1, 16: 21, 18: 2, 20: 1, 21: 1, 24: 9, 32: 14, 36: 3, 42: 1, 48: 6, 60: 5, 64: 7, 72: 3, 80: 2, 96: 7, 120: 3, 128: 1, 144: 1, 160: 2, 168: 2, 192: 3, 320: 2, 336: 1, 360: 2, 384: 1, 720: 1, 960: 2, 1920: 2, 20160: 1, 40320: 1}

classes with |S| >= M = 128:  (order, conjugates, [(orbit length, |S_d|, induced order on the lines through d, good at d)], good)
   40320      1  [(21, 1920, 120, False)]  not good
   20160      1  [(21, 960, 60, False)]  not good
    1920     21  [(16, 120, 120, False), (5, 384, 24, False)]  not good
    1920     21  [(20, 96, 24, False), (1, 1920, 120, False)]  not good
     960     21  [(20, 48, 12, False), (1, 960, 60, False)]  not good
     960     21  [(5, 192, 12, False), (16, 60, 60, False)]  not good
     720     56  [(15, 48, 12, False), (6, 120, 120, False)]  not good
     384    105  [(16, 24, 24, False), (1, 384, 24, False), (4, 96, 24, False)]  not good
     360    112  [(15, 24, 6, False), (6, 60, 60, False)]  not good
     360     56  [(6, 60, 60, False), (15, 24, 6, False)]  not good
     336    120  [(7, 48, 12, False), (14, 24, 24, False)]  not good
     320    126  [(16, 20, 20, False), (5, 64, 8, True)]  GOOD
     320    126  [(20, 16, 8, True), (1, 320, 20, False)]  GOOD
     192    210  [(16, 12, 12, False), (3, 64, 8, True), (2, 96, 24, False)]  GOOD
     192    210  [(12, 16, 8, True), (8, 24, 24, False), (1, 192, 12, False)]  GOOD
     192    105  [(16, 12, 12, False), (1, 192, 12, False), (4, 48, 12, False)]  not good
     168    120  [(7, 24, 6, False), (14, 12, 12, False)]  not good
     168    240  [(7, 24, 6, False), (14, 12, 12, False)]  not good
     160    126  [(16, 10, 10, False), (5, 32, 4, True)]  GOOD
     160    126  [(20, 8, 4, True), (1, 160, 10, False)]  GOOD
     144    280  [(12, 12, 12, False), (9, 16, 8, True)]  GOOD
     128    315  [(16, 8, 8, True), (1, 128, 8, True), (4, 32, 8, True)]  GOOD

RESULT PSIGMAL(3,4): M = 128; M_G = largest order of a good subgroup over all 152 classes = 320; classes with |S| > M: 21, of which good: 7; good classes of order M: 1; |P|/M = 315, |P|/M_G = 126; strict inequality: True
number of subgroups of order >= M that are good at the base point, by order: {128: 315, 144: 120, 160: 150, 192: 150, 320: 150}
total time 151s
