q=5: |S|=60, 9 classes of subgroups, 59 subgroups in all
  class 1: |X|=5 orders={1: 1, 5: 4} delta-invariant; |N_S(X)|=10 soluble=True; (b1)=False (b2)=False
  class 2: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=4 soluble=True; (b1)=False (b2)=False
  class 3: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=6 soluble=True; (b1)=False (b2)=False
  class 4: |X|=12 orders={1: 1, 2: 3, 3: 8} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 5: |X|=6 orders={1: 1, 2: 3, 3: 2} delta-invariant; |N_S(X)|=6 soluble=True; (b1)=False (b2)=False
  class 6: |X|=10 orders={1: 1, 2: 5, 5: 4} delta-invariant; |N_S(X)|=10 soluble=True; (b1)=False (b2)=False
  class 7: |X|=4 orders={1: 1, 2: 3} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
q=5: 7 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=5, c=delta): 2 [(12, {1: 1, 2: 3, 3: 8}, False, True, 12), (4, {1: 1, 2: 3}, False, True, 12)]
q=5: time 0.0 s
RESULT q=5 (q = +-3 mod 8, control): V and A_4 found: PASS
q=7: |S|=168, 15 classes of subgroups, 179 subgroups in all
  class 1: |X|=7 orders={1: 1, 7: 6} delta-invariant; |N_S(X)|=21 soluble=True; (b1)=False (b2)=False
  class 2: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=6 soluble=True; (b1)=False (b2)=False
  class 3: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=8 soluble=True; (b1)=False (b2)=False
  class 4: |X|=4 orders={1: 1, 2: 1, 4: 2} delta-invariant; |N_S(X)|=8 soluble=True; (b1)=False (b2)=False
  class 7: |X|=8 orders={1: 1, 2: 5, 4: 2} delta-invariant; |N_S(X)|=8 soluble=True; (b1)=False (b2)=False
  class 8: |X|=6 orders={1: 1, 2: 3, 3: 2} delta-invariant; |N_S(X)|=6 soluble=True; (b1)=False (b2)=False
  class 13: |X|=21 orders={1: 1, 3: 14, 7: 6} delta-invariant; |N_S(X)|=21 soluble=True; (b1)=False (b2)=False
q=7: 7 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=7, c=delta): 0 []
q=7: time 0.0 s
RESULT q=7 (q = +-1 mod 8): no witness for (l, delta): PASS
q=9: |S|=360, 22 classes of subgroups, 501 subgroups in all
  class 3: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=8 soluble=True; (b1)=False (b2)=False
  class 4: |X|=4 orders={1: 1, 2: 1, 4: 2} delta-invariant; |N_S(X)|=8 soluble=True; (b1)=False (b2)=False
  class 5: |X|=5 orders={1: 1, 5: 4} delta-invariant; |N_S(X)|=10 soluble=True; (b1)=False (b2)=False
  class 8: |X|=10 orders={1: 1, 2: 5, 5: 4} delta-invariant; |N_S(X)|=10 soluble=True; (b1)=False (b2)=False
  class 9: |X|=36 orders={1: 1, 2: 9, 3: 8, 4: 18} delta-invariant; |N_S(X)|=36 soluble=True; (b1)=False (b2)=False
  class 10: |X|=8 orders={1: 1, 2: 5, 4: 2} delta-invariant; |N_S(X)|=8 soluble=True; (b1)=False (b2)=False
  class 19: |X|=18 orders={1: 1, 2: 9, 3: 8} delta-invariant; |N_S(X)|=36 soluble=True; (b1)=False (b2)=False
  class 20: |X|=9 orders={1: 1, 3: 8} delta-invariant; |N_S(X)|=36 soluble=True; (b1)=False (b2)=False
q=9: 8 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=3, c=delta): 0 []
q=9: time 0.1 s
RESULT q=9 (q = +-1 mod 8): no witness for (l, delta): PASS
q=11: |S|=660, 16 classes of subgroups, 620 subgroups in all
  class 1: |X|=11 orders={1: 1, 11: 10} delta-invariant; |N_S(X)|=55 soluble=True; (b1)=False (b2)=False
  class 2: |X|=5 orders={1: 1, 5: 4} delta-invariant; |N_S(X)|=10 soluble=True; (b1)=False (b2)=False
  class 3: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=False
  class 4: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=False
  class 7: |X|=12 orders={1: 1, 2: 3, 3: 8} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 10: |X|=6 orders={1: 1, 2: 1, 3: 2, 6: 2} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=False
  class 11: |X|=12 orders={1: 1, 2: 7, 3: 2, 6: 2} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=False
  class 12: |X|=10 orders={1: 1, 2: 5, 5: 4} delta-invariant; |N_S(X)|=10 soluble=True; (b1)=False (b2)=False
  class 13: |X|=4 orders={1: 1, 2: 3} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 14: |X|=55 orders={1: 1, 5: 44, 11: 10} delta-invariant; |N_S(X)|=55 soluble=True; (b1)=False (b2)=False
q=11: 10 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=11, c=delta): 2 [(12, {1: 1, 2: 3, 3: 8}, False, True, 12), (4, {1: 1, 2: 3}, False, True, 12)]
q=11: time 0.3 s
RESULT q=11 (q = +-3 mod 8, control): V and A_4 found: PASS
q=13: |S|=1092, 16 classes of subgroups, 942 subgroups in all
  class 1: |X|=13 orders={1: 1, 13: 12} delta-invariant; |N_S(X)|=78 soluble=True; (b1)=False (b2)=False
  class 2: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=False
  class 3: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=False
  class 4: |X|=7 orders={1: 1, 7: 6} delta-invariant; |N_S(X)|=14 soluble=True; (b1)=False (b2)=False
  class 5: |X|=14 orders={1: 1, 2: 7, 7: 6} delta-invariant; |N_S(X)|=14 soluble=True; (b1)=False (b2)=False
  class 6: |X|=26 orders={1: 1, 2: 13, 13: 12} delta-invariant; |N_S(X)|=78 soluble=True; (b1)=False (b2)=False
  class 7: |X|=6 orders={1: 1, 2: 1, 3: 2, 6: 2} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=False
  class 8: |X|=78 orders={1: 1, 2: 13, 3: 26, 6: 26, 13: 12} delta-invariant; |N_S(X)|=78 soluble=True; (b1)=False (b2)=False
  class 9: |X|=4 orders={1: 1, 2: 3} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 11: |X|=12 orders={1: 1, 2: 3, 3: 8} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 12: |X|=12 orders={1: 1, 2: 7, 3: 2, 6: 2} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=False
  class 14: |X|=39 orders={1: 1, 3: 26, 13: 12} delta-invariant; |N_S(X)|=78 soluble=True; (b1)=False (b2)=False
q=13: 12 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=13, c=delta): 2 [(4, {1: 1, 2: 3}, False, True, 12), (12, {1: 1, 2: 3, 3: 8}, False, True, 12)]
q=13: time 0.6 s
RESULT q=13 (q = +-3 mod 8, control): V and A_4 found: PASS
q=17: |S|=2448, 22 classes of subgroups, 2420 subgroups in all
  class 1: |X|=17 orders={1: 1, 17: 16} delta-invariant; |N_S(X)|=136 soluble=True; (b1)=False (b2)=False
  class 2: |X|=8 orders={1: 1, 2: 1, 4: 2, 8: 4} delta-invariant; |N_S(X)|=16 soluble=True; (b1)=False (b2)=False
  class 3: |X|=4 orders={1: 1, 2: 1, 4: 2} delta-invariant; |N_S(X)|=16 soluble=True; (b1)=False (b2)=False
  class 4: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=16 soluble=True; (b1)=False (b2)=False
  class 5: |X|=9 orders={1: 1, 3: 2, 9: 6} delta-invariant; |N_S(X)|=18 soluble=True; (b1)=False (b2)=False
  class 6: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=18 soluble=True; (b1)=False (b2)=False
  class 10: |X|=6 orders={1: 1, 2: 3, 3: 2} delta-invariant; |N_S(X)|=6 soluble=True; (b1)=False (b2)=False
  class 12: |X|=18 orders={1: 1, 2: 9, 3: 2, 9: 6} delta-invariant; |N_S(X)|=18 soluble=True; (b1)=False (b2)=False
  class 13: |X|=34 orders={1: 1, 2: 17, 17: 16} delta-invariant; |N_S(X)|=136 soluble=True; (b1)=False (b2)=False
  class 14: |X|=136 orders={1: 1, 2: 17, 4: 34, 8: 68, 17: 16} delta-invariant; |N_S(X)|=136 soluble=True; (b1)=False (b2)=False
  class 15: |X|=68 orders={1: 1, 2: 17, 4: 34, 17: 16} delta-invariant; |N_S(X)|=136 soluble=True; (b1)=False (b2)=False
  class 19: |X|=16 orders={1: 1, 2: 9, 4: 2, 8: 4} delta-invariant; |N_S(X)|=16 soluble=True; (b1)=False (b2)=False
q=17: 12 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=17, c=delta): 0 []
q=17: time 4.0 s
RESULT q=17 (q = +-1 mod 8): no witness for (l, delta): PASS
q=19: |S|=3420, 19 classes of subgroups, 2912 subgroups in all
  class 1: |X|=19 orders={1: 1, 19: 18} delta-invariant; |N_S(X)|=171 soluble=True; (b1)=False (b2)=False
  class 2: |X|=9 orders={1: 1, 3: 2, 9: 6} delta-invariant; |N_S(X)|=18 soluble=True; (b1)=False (b2)=False
  class 3: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=18 soluble=True; (b1)=False (b2)=False
  class 4: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=20 soluble=True; (b1)=False (b2)=False
  class 5: |X|=5 orders={1: 1, 5: 4} delta-invariant; |N_S(X)|=20 soluble=True; (b1)=False (b2)=False
  class 9: |X|=10 orders={1: 1, 2: 1, 5: 4, 10: 4} delta-invariant; |N_S(X)|=20 soluble=True; (b1)=False (b2)=False
  class 11: |X|=20 orders={1: 1, 2: 11, 5: 4, 10: 4} delta-invariant; |N_S(X)|=20 soluble=True; (b1)=False (b2)=False
  class 12: |X|=18 orders={1: 1, 2: 9, 3: 2, 9: 6} delta-invariant; |N_S(X)|=18 soluble=True; (b1)=False (b2)=False
  class 13: |X|=6 orders={1: 1, 2: 3, 3: 2} delta-invariant; |N_S(X)|=6 soluble=True; (b1)=False (b2)=False
  class 14: |X|=12 orders={1: 1, 2: 3, 3: 8} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 15: |X|=4 orders={1: 1, 2: 3} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 16: |X|=57 orders={1: 1, 3: 38, 19: 18} delta-invariant; |N_S(X)|=171 soluble=True; (b1)=False (b2)=False
  class 17: |X|=171 orders={1: 1, 3: 38, 9: 114, 19: 18} delta-invariant; |N_S(X)|=171 soluble=True; (b1)=False (b2)=False
q=19: 13 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=19, c=delta): 2 [(12, {1: 1, 2: 3, 3: 8}, False, True, 12), (4, {1: 1, 2: 3}, False, True, 12)]
q=19: time 6.3 s
RESULT q=19 (q = +-3 mod 8, control): V and A_4 found: PASS
q=23: |S|=6072, 23 classes of subgroups, 5915 subgroups in all
  class 1: |X|=23 orders={1: 1, 23: 22} delta-invariant; |N_S(X)|=253 soluble=True; (b1)=False (b2)=False
  class 2: |X|=11 orders={1: 1, 11: 10} delta-invariant; |N_S(X)|=22 soluble=True; (b1)=False (b2)=False
  class 3: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=24 soluble=True; (b1)=False (b2)=False
  class 4: |X|=4 orders={1: 1, 2: 1, 4: 2} delta-invariant; |N_S(X)|=24 soluble=True; (b1)=False (b2)=False
  class 5: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=24 soluble=True; (b1)=False (b2)=False
  class 10: |X|=12 orders={1: 1, 2: 1, 3: 2, 4: 2, 6: 2, 12: 4} delta-invariant; |N_S(X)|=24 soluble=True; (b1)=False (b2)=False
  class 13: |X|=6 orders={1: 1, 2: 1, 3: 2, 6: 2} delta-invariant; |N_S(X)|=24 soluble=True; (b1)=False (b2)=False
  class 16: |X|=24 orders={1: 1, 2: 13, 3: 2, 4: 2, 6: 2, 12: 4} delta-invariant; |N_S(X)|=24 soluble=True; (b1)=False (b2)=False
  class 17: |X|=8 orders={1: 1, 2: 5, 4: 2} delta-invariant; |N_S(X)|=8 soluble=True; (b1)=False (b2)=False
  class 18: |X|=22 orders={1: 1, 2: 11, 11: 10} delta-invariant; |N_S(X)|=22 soluble=True; (b1)=False (b2)=False
  class 21: |X|=253 orders={1: 1, 11: 230, 23: 22} delta-invariant; |N_S(X)|=253 soluble=True; (b1)=False (b2)=False
q=23: 11 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=23, c=delta): 0 []
q=23: time 26.9 s
RESULT q=23 (q = +-1 mod 8): no witness for (l, delta): PASS
ALL CHECKS PASSED
