q = 13: |PGL(2,q)| = 2184, c_q (brute force) = 24 (formula 24), M = 48672  [0s]
subgroup classes of PGL(2,13): 30  [1s]
  |Hbar| =  2184 |H cap Z| =   4 |X| =   1476384: affine point: |stab| 8736, |induced| 2184, good False; point (1, 0) of m (orbit 14): |stab| 105456, |induced| 156, good False; line m: |stab| 1476384, |induced| 2184, good False; affine line, direction (1, 0): |stab| 8112, |induced| 156, good False
  |Hbar| =  2184 |H cap Z| =  12 |X| =   4429152: affine point: |stab| 26208, |induced| 2184, good False; point (1, 0) of m (orbit 14): |stab| 316368, |induced| 156, good False; line m: |stab| 4429152, |induced| 2184, good False; affine line, direction (1, 0): |stab| 24336, |induced| 156, good False
  |Hbar| =  1092 |H cap Z| =   2 |X| =    369096: affine point: |stab| 2184, |induced| 1092, good False; point (1, 0) of m (orbit 14): |stab| 26364, |induced| 156, good False; line m: |stab| 369096, |induced| 1092, good False; affine line, direction (1, 0): |stab| 2028, |induced| 156, good False
  |Hbar| =  1092 |H cap Z| =   4 |X| =    738192: affine point: |stab| 4368, |induced| 1092, good False; point (1, 0) of m (orbit 14): |stab| 52728, |induced| 156, good False; line m: |stab| 738192, |induced| 1092, good False; affine line, direction (1, 0): |stab| 4056, |induced| 156, good False
  |Hbar| =  1092 |H cap Z| =   6 |X| =   1107288: affine point: |stab| 6552, |induced| 1092, good False; point (1, 0) of m (orbit 14): |stab| 79092, |induced| 156, good False; line m: |stab| 1107288, |induced| 1092, good False; affine line, direction (1, 0): |stab| 6084, |induced| 156, good False
  |Hbar| =  1092 |H cap Z| =  12 |X| =   2214576: affine point: |stab| 13104, |induced| 1092, good False; point (1, 0) of m (orbit 14): |stab| 158184, |induced| 156, good False; line m: |stab| 2214576, |induced| 1092, good False; affine line, direction (1, 0): |stab| 12168, |induced| 156, good False
  |Hbar| =   156 |H cap Z| =   2 |X| =     52728: affine point: |stab| 312, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 26, good False; line m: |stab| 52728, |induced| 156, good False; affine line, direction (1, 0): |stab| 4056, |induced| 26, good False; affine line, direction (1, 1): |stab| 312, |induced| 156, good False
  |Hbar| =   156 |H cap Z| =   2 |X| =     52728: affine point: |stab| 312, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 78, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 52, good False; line m: |stab| 52728, |induced| 156, good False; affine line, direction (1, 0): |stab| 4056, |induced| 52, good False; affine line, direction (1, 1): |stab| 312, |induced| 78, good False
  |Hbar| =   156 |H cap Z| =   2 |X| =     52728: affine point: |stab| 312, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 78, good False; line m: |stab| 52728, |induced| 156, good False; affine line, direction (1, 0): |stab| 4056, |induced| 78, good False; affine line, direction (1, 1): |stab| 312, |induced| 156, good False
  |Hbar| =   156 |H cap Z| =   2 |X| =     52728: affine point: |stab| 312, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 78, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 156, good False; line m: |stab| 52728, |induced| 156, good False; affine line, direction (1, 0): |stab| 4056, |induced| 156, good False; affine line, direction (1, 1): |stab| 312, |induced| 78, good False
  |Hbar| =   156 |H cap Z| =   2 |X| =     52728: affine point: |stab| 312, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 52, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 78, good False; line m: |stab| 52728, |induced| 156, good False; affine line, direction (1, 0): |stab| 4056, |induced| 78, good False; affine line, direction (1, 1): |stab| 312, |induced| 52, good False
  |Hbar| =   156 |H cap Z| =   2 |X| =     52728: affine point: |stab| 312, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 26, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 156, good False; line m: |stab| 52728, |induced| 156, good False; affine line, direction (1, 0): |stab| 4056, |induced| 156, good False; affine line, direction (1, 1): |stab| 312, |induced| 26, good False
  |Hbar| =   156 |H cap Z| =   3 |X| =     79092: affine point: |stab| 468, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 79092, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 6084, |induced| 39, good False; line m: |stab| 79092, |induced| 156, good False; affine line, direction (1, 0): |stab| 6084, |induced| 39, good False; affine line, direction (1, 1): |stab| 468, |induced| 156, good False
  |Hbar| =   156 |H cap Z| =   3 |X| =     79092: affine point: |stab| 468, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 79092, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 6084, |induced| 78, good False; line m: |stab| 79092, |induced| 156, good False; affine line, direction (1, 0): |stab| 6084, |induced| 78, good False; affine line, direction (1, 1): |stab| 468, |induced| 156, good False
  |Hbar| =   156 |H cap Z| =   3 |X| =     79092: affine point: |stab| 468, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 79092, |induced| 78, good False; point (1, 1) of m (orbit 13): |stab| 6084, |induced| 156, good False; line m: |stab| 79092, |induced| 156, good False; affine line, direction (1, 0): |stab| 6084, |induced| 156, good False; affine line, direction (1, 1): |stab| 468, |induced| 78, good False
  |Hbar| =   156 |H cap Z| =   3 |X| =     79092: affine point: |stab| 468, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 79092, |induced| 39, good False; point (1, 1) of m (orbit 13): |stab| 6084, |induced| 156, good False; line m: |stab| 79092, |induced| 156, good False; affine line, direction (1, 0): |stab| 6084, |induced| 156, good False; affine line, direction (1, 1): |stab| 468, |induced| 39, good False
  |Hbar| =   156 |H cap Z| =   4 |X| =    105456: affine point: |stab| 624, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 105456, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 8112, |induced| 52, good False; line m: |stab| 105456, |induced| 156, good False; affine line, direction (1, 0): |stab| 8112, |induced| 52, good False; affine line, direction (1, 1): |stab| 624, |induced| 156, good False
  |Hbar| =   156 |H cap Z| =   4 |X| =    105456: affine point: |stab| 624, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 105456, |induced| 52, good False; point (1, 1) of m (orbit 13): |stab| 8112, |induced| 156, good False; line m: |stab| 105456, |induced| 156, good False; affine line, direction (1, 0): |stab| 8112, |induced| 156, good False; affine line, direction (1, 1): |stab| 624, |induced| 52, good False
  |Hbar| =   156 |H cap Z| =   4 |X| =    105456: affine point: |stab| 624, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 105456, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 8112, |induced| 156, good False; line m: |stab| 105456, |induced| 156, good False; affine line, direction (1, 0): |stab| 8112, |induced| 156, good False; affine line, direction (1, 1): |stab| 624, |induced| 156, good False
  |Hbar| =   156 |H cap Z| =   6 |X| =    158184: affine point: |stab| 936, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 158184, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 12168, |induced| 78, good False; line m: |stab| 158184, |induced| 156, good False; affine line, direction (1, 0): |stab| 12168, |induced| 78, good False; affine line, direction (1, 1): |stab| 936, |induced| 156, good False
  |Hbar| =   156 |H cap Z| =   6 |X| =    158184: affine point: |stab| 936, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 158184, |induced| 78, good False; point (1, 1) of m (orbit 13): |stab| 12168, |induced| 156, good False; line m: |stab| 158184, |induced| 156, good False; affine line, direction (1, 0): |stab| 12168, |induced| 156, good False; affine line, direction (1, 1): |stab| 936, |induced| 78, good False
  |Hbar| =   156 |H cap Z| =  12 |X| =    316368: affine point: |stab| 1872, |induced| 156, good False; point (1, 0) of m (orbit 1): |stab| 316368, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 24336, |induced| 156, good False; line m: |stab| 316368, |induced| 156, good False; affine line, direction (1, 0): |stab| 24336, |induced| 156, good False; affine line, direction (1, 1): |stab| 1872, |induced| 156, good False
  |Hbar| =    78 |H cap Z| =   4 |X| =     52728: affine point: |stab| 312, |induced| 78, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 52, good False; line m: |stab| 52728, |induced| 78, good False; affine line, direction (1, 0): |stab| 4056, |induced| 52, good False; affine line, direction (1, 1): |stab| 312, |induced| 156, good False
  |Hbar| =    78 |H cap Z| =   4 |X| =     52728: affine point: |stab| 312, |induced| 78, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 52, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 156, good False; line m: |stab| 52728, |induced| 78, good False; affine line, direction (1, 0): |stab| 4056, |induced| 156, good False; affine line, direction (1, 1): |stab| 312, |induced| 52, good False
  |Hbar| =    78 |H cap Z| =   4 |X| =     52728: affine point: |stab| 312, |induced| 78, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 156, good False; line m: |stab| 52728, |induced| 78, good False; affine line, direction (1, 0): |stab| 4056, |induced| 156, good False; affine line, direction (1, 1): |stab| 312, |induced| 156, good False
  |Hbar| =    78 |H cap Z| =   6 |X| =     79092: affine point: |stab| 468, |induced| 78, good False; point (1, 0) of m (orbit 1): |stab| 79092, |induced| 78, good False; point (1, 1) of m (orbit 13): |stab| 6084, |induced| 78, good False; line m: |stab| 79092, |induced| 78, good False; affine line, direction (1, 0): |stab| 6084, |induced| 78, good False; affine line, direction (1, 1): |stab| 468, |induced| 78, good False
  |Hbar| =    78 |H cap Z| =   6 |X| =     79092: affine point: |stab| 468, |induced| 78, good False; point (1, 0) of m (orbit 1): |stab| 79092, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 6084, |induced| 156, good False; line m: |stab| 79092, |induced| 78, good False; affine line, direction (1, 0): |stab| 6084, |induced| 156, good False; affine line, direction (1, 1): |stab| 468, |induced| 156, good False
  |Hbar| =    78 |H cap Z| =  12 |X| =    158184: affine point: |stab| 936, |induced| 78, good False; point (1, 0) of m (orbit 1): |stab| 158184, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 12168, |induced| 156, good False; line m: |stab| 158184, |induced| 78, good False; affine line, direction (1, 0): |stab| 12168, |induced| 156, good False; affine line, direction (1, 1): |stab| 936, |induced| 156, good False
  |Hbar| =    52 |H cap Z| =   6 |X| =     52728: affine point: |stab| 312, |induced| 52, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 78, good False; line m: |stab| 52728, |induced| 52, good False; affine line, direction (1, 0): |stab| 4056, |induced| 78, good False; affine line, direction (1, 1): |stab| 312, |induced| 156, good False
  |Hbar| =    52 |H cap Z| =   6 |X| =     52728: affine point: |stab| 312, |induced| 52, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 78, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 156, good False; line m: |stab| 52728, |induced| 52, good False; affine line, direction (1, 0): |stab| 4056, |induced| 156, good False; affine line, direction (1, 1): |stab| 312, |induced| 78, good False
  |Hbar| =    52 |H cap Z| =  12 |X| =    105456: affine point: |stab| 624, |induced| 52, good False; point (1, 0) of m (orbit 1): |stab| 105456, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 8112, |induced| 156, good False; line m: |stab| 105456, |induced| 52, good False; affine line, direction (1, 0): |stab| 8112, |induced| 156, good False; affine line, direction (1, 1): |stab| 624, |induced| 156, good False
  |Hbar| =    39 |H cap Z| =  12 |X| =     79092: affine point: |stab| 468, |induced| 39, good False; point (1, 0) of m (orbit 1): |stab| 79092, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 6084, |induced| 156, good False; line m: |stab| 79092, |induced| 39, good False; affine line, direction (1, 0): |stab| 6084, |induced| 156, good False; affine line, direction (1, 1): |stab| 468, |induced| 156, good False
  |Hbar| =    28 |H cap Z| =  12 |X| =     56784: affine point: |stab| 336, |induced| 28, good False; point (1, 0) of m (orbit 14): |stab| 4056, |induced| 156, good False; line m: |stab| 56784, |induced| 28, good False; affine line, direction (1, 0): |stab| 312, |induced| 156, good False
  |Hbar| =    26 |H cap Z| =  12 |X| =     52728: affine point: |stab| 312, |induced| 26, good False; point (1, 0) of m (orbit 1): |stab| 52728, |induced| 156, good False; point (1, 1) of m (orbit 13): |stab| 4056, |induced| 156, good False; line m: |stab| 52728, |induced| 26, good False; affine line, direction (1, 0): |stab| 4056, |induced| 156, good False; affine line, direction (1, 1): |stab| 312, |induced| 156, good False
RESULT q = 13: 34 subgroups H (|X| = q^2|H| > M = 48672) tested; good ones: none  [208s]
