q=25: |S|=7800, 37 classes of subgroups, 9559 subgroups in all
  class 3: |X|=4 orders={1: 1, 2: 1, 4: 2} delta-invariant; |N_S(X)|=24 soluble=True; (b1)=False (b2)=False
  class 4: |X|=2 orders={1: 1, 2: 1} 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 6: |X|=13 orders={1: 1, 13: 12} delta-invariant; |N_S(X)|=26 soluble=True; (b1)=False (b2)=False
  class 7: |X|=26 orders={1: 1, 2: 13, 13: 12} delta-invariant; |N_S(X)|=26 soluble=True; (b1)=False (b2)=False
  class 8: |X|=75 orders={1: 1, 3: 50, 5: 24} delta-invariant; |N_S(X)|=300 soluble=True; (b1)=False (b2)=False
  class 9: |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 10: |X|=300 orders={1: 1, 2: 25, 3: 50, 4: 50, 5: 24, 6: 50, 12: 100} delta-invariant; |N_S(X)|=300 soluble=True; (b1)=False (b2)=False
  class 11: |X|=6 orders={1: 1, 2: 1, 3: 2, 6: 2} delta-invariant; |N_S(X)|=24 soluble=True; (b1)=False (b2)=False
  class 12: |X|=150 orders={1: 1, 2: 25, 3: 50, 5: 24, 6: 50} delta-invariant; |N_S(X)|=300 soluble=True; (b1)=False (b2)=False
  class 23: |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 32: |X|=8 orders={1: 1, 2: 5, 4: 2} delta-invariant; |N_S(X)|=8 soluble=True; (b1)=False (b2)=False
  class 33: |X|=100 orders={1: 1, 2: 25, 4: 50, 5: 24} delta-invariant; |N_S(X)|=300 soluble=True; (b1)=False (b2)=False
  class 34: |X|=50 orders={1: 1, 2: 25, 5: 24} delta-invariant; |N_S(X)|=300 soluble=True; (b1)=False (b2)=False
  class 35: |X|=25 orders={1: 1, 5: 24} delta-invariant; |N_S(X)|=300 soluble=True; (b1)=False (b2)=False
q=25: 15 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=5, c=delta): 0 []
q=25: time 65.2 s
RESULT q=25 (q = +-1 mod 8): no witness for (l, delta): PASS
q=27: |S|=9828, 16 classes of subgroups, 5286 subgroups in all
  class 1: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=27 soluble=True; (b1)=False (b2)=False
  class 2: |X|=13 orders={1: 1, 13: 12} delta-invariant; |N_S(X)|=26 soluble=True; (b1)=False (b2)=False
  class 3: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=28 soluble=True; (b1)=False (b2)=False
  class 4: |X|=7 orders={1: 1, 7: 6} delta-invariant; |N_S(X)|=28 soluble=True; (b1)=False (b2)=False
  class 7: |X|=14 orders={1: 1, 2: 1, 7: 6, 14: 6} delta-invariant; |N_S(X)|=28 soluble=True; (b1)=False (b2)=False
  class 8: |X|=28 orders={1: 1, 2: 15, 7: 6, 14: 6} delta-invariant; |N_S(X)|=28 soluble=True; (b1)=False (b2)=False
  class 9: |X|=12 orders={1: 1, 2: 3, 3: 8} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 10: |X|=26 orders={1: 1, 2: 13, 13: 12} delta-invariant; |N_S(X)|=26 soluble=True; (b1)=False (b2)=False
  class 11: |X|=4 orders={1: 1, 2: 3} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 12: |X|=351 orders={1: 1, 3: 26, 13: 324} delta-invariant; |N_S(X)|=351 soluble=True; (b1)=False (b2)=False
  class 13: |X|=9 orders={1: 1, 3: 8} delta-invariant; |N_S(X)|=27 soluble=True; (b1)=False (b2)=False
  class 14: |X|=27 orders={1: 1, 3: 26} delta-invariant; |N_S(X)|=351 soluble=True; (b1)=False (b2)=False
q=27: 12 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=3, c=delta): 2 [(12, {1: 1, 2: 3, 3: 8}, False, True, 12), (4, {1: 1, 2: 3}, False, True, 12)]
q=27: time 50.3 s
RESULT q=27 (q = +-3 mod 8, control): V and A_4 found: PASS
q=29: |S|=12180, 22 classes of subgroups, 10040 subgroups in all
  class 1: |X|=29 orders={1: 1, 29: 28} delta-invariant; |N_S(X)|=406 soluble=True; (b1)=False (b2)=False
  class 2: |X|=7 orders={1: 1, 7: 6} delta-invariant; |N_S(X)|=28 soluble=True; (b1)=False (b2)=False
  class 3: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=28 soluble=True; (b1)=False (b2)=False
  class 4: |X|=5 orders={1: 1, 5: 4} delta-invariant; |N_S(X)|=30 soluble=True; (b1)=False (b2)=False
  class 5: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=30 soluble=True; (b1)=False (b2)=False
  class 8: |X|=12 orders={1: 1, 2: 3, 3: 8} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 9: |X|=6 orders={1: 1, 2: 3, 3: 2} delta-invariant; |N_S(X)|=6 soluble=True; (b1)=False (b2)=False
  class 10: |X|=15 orders={1: 1, 3: 2, 5: 4, 15: 8} delta-invariant; |N_S(X)|=30 soluble=True; (b1)=False (b2)=False
  class 11: |X|=30 orders={1: 1, 2: 15, 3: 2, 5: 4, 15: 8} delta-invariant; |N_S(X)|=30 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|=58 orders={1: 1, 2: 29, 29: 28} delta-invariant; |N_S(X)|=406 soluble=True; (b1)=False (b2)=False
  class 14: |X|=14 orders={1: 1, 2: 1, 7: 6, 14: 6} delta-invariant; |N_S(X)|=28 soluble=True; (b1)=False (b2)=False
  class 15: |X|=406 orders={1: 1, 2: 29, 7: 174, 14: 174, 29: 28} delta-invariant; |N_S(X)|=406 soluble=True; (b1)=False (b2)=False
  class 16: |X|=4 orders={1: 1, 2: 3} delta-invariant; |N_S(X)|=12 soluble=True; (b1)=False (b2)=True
  class 17: |X|=28 orders={1: 1, 2: 15, 7: 6, 14: 6} delta-invariant; |N_S(X)|=28 soluble=True; (b1)=False (b2)=False
  class 20: |X|=203 orders={1: 1, 7: 174, 29: 28} delta-invariant; |N_S(X)|=406 soluble=True; (b1)=False (b2)=False
q=29: 16 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=29, c=delta): 2 [(12, {1: 1, 2: 3, 3: 8}, False, True, 12), (4, {1: 1, 2: 3}, False, True, 12)]
q=29: time 95.4 s
RESULT q=29 (q = +-3 mod 8, control): V and A_4 found: PASS
q=31: |S|=14880, 29 classes of subgroups, 15413 subgroups in all
  class 1: |X|=31 orders={1: 1, 31: 30} delta-invariant; |N_S(X)|=465 soluble=True; (b1)=False (b2)=False
  class 2: |X|=5 orders={1: 1, 5: 4} delta-invariant; |N_S(X)|=30 soluble=True; (b1)=False (b2)=False
  class 3: |X|=3 orders={1: 1, 3: 2} delta-invariant; |N_S(X)|=30 soluble=True; (b1)=False (b2)=False
  class 4: |X|=2 orders={1: 1, 2: 1} delta-invariant; |N_S(X)|=32 soluble=True; (b1)=False (b2)=False
  class 5: |X|=8 orders={1: 1, 2: 1, 4: 2, 8: 4} delta-invariant; |N_S(X)|=32 soluble=True; (b1)=False (b2)=False
  class 6: |X|=16 orders={1: 1, 2: 1, 4: 2, 8: 4, 16: 8} delta-invariant; |N_S(X)|=32 soluble=True; (b1)=False (b2)=False
  class 7: |X|=4 orders={1: 1, 2: 1, 4: 2} delta-invariant; |N_S(X)|=32 soluble=True; (b1)=False (b2)=False
  class 12: |X|=32 orders={1: 1, 2: 17, 4: 2, 8: 4, 16: 8} delta-invariant; |N_S(X)|=32 soluble=True; (b1)=False (b2)=False
  class 15: |X|=10 orders={1: 1, 2: 5, 5: 4} delta-invariant; |N_S(X)|=10 soluble=True; (b1)=False (b2)=False
  class 18: |X|=6 orders={1: 1, 2: 3, 3: 2} delta-invariant; |N_S(X)|=6 soluble=True; (b1)=False (b2)=False
  class 21: |X|=30 orders={1: 1, 2: 15, 3: 2, 5: 4, 15: 8} delta-invariant; |N_S(X)|=30 soluble=True; (b1)=False (b2)=False
  class 24: |X|=93 orders={1: 1, 3: 62, 31: 30} delta-invariant; |N_S(X)|=465 soluble=True; (b1)=False (b2)=False
  class 25: |X|=15 orders={1: 1, 3: 2, 5: 4, 15: 8} delta-invariant; |N_S(X)|=30 soluble=True; (b1)=False (b2)=False
  class 26: |X|=465 orders={1: 1, 3: 62, 5: 124, 15: 248, 31: 30} delta-invariant; |N_S(X)|=465 soluble=True; (b1)=False (b2)=False
  class 27: |X|=155 orders={1: 1, 5: 124, 31: 30} delta-invariant; |N_S(X)|=465 soluble=True; (b1)=False (b2)=False
q=31: 15 delta-invariant classes of subgroups 1 < X < S tested; witnesses for (p=l=31, c=delta): 0 []
q=31: time 207.3 s
RESULT q=31 (q = +-1 mod 8): no witness for (l, delta): PASS
ALL CHECKS PASSED
