q = 5: |PGL(2,q)| = 120, c_q (brute force) = 8 (formula 8), M = 800  [0s]
subgroup classes of PGL(2,5): 19  [0s]
  |Hbar| =   120 |H cap Z| =   4 |X| =     12000: affine point: |stab| 480, |induced| 120, good False; point (1, 0) of m (orbit 6): |stab| 2000, |induced| 20, good False; line m: |stab| 12000, |induced| 120, good False; affine line, direction (1, 0): |stab| 400, |induced| 20, good False
  |Hbar| =    60 |H cap Z| =   2 |X| =      3000: affine point: |stab| 120, |induced| 60, good False; point (1, 0) of m (orbit 6): |stab| 500, |induced| 20, good False; line m: |stab| 3000, |induced| 60, good False; affine line, direction (1, 0): |stab| 100, |induced| 20, good False
  |Hbar| =    60 |H cap Z| =   4 |X| =      6000: affine point: |stab| 240, |induced| 60, good False; point (1, 0) of m (orbit 6): |stab| 1000, |induced| 20, good False; line m: |stab| 6000, |induced| 60, good False; affine line, direction (1, 0): |stab| 200, |induced| 20, good False
  |Hbar| =    24 |H cap Z| =   4 |X| =      2400: affine point: |stab| 96, |induced| 24, good False; point (1, 0) of m (orbit 6): |stab| 400, |induced| 20, good False; line m: |stab| 2400, |induced| 24, good False; affine line, direction (1, 0): |stab| 80, |induced| 20, good False
  |Hbar| =    20 |H cap Z| =   2 |X| =      1000: affine point: |stab| 40, |induced| 20, good False; point (1, 0) of m (orbit 1): |stab| 1000, |induced| 20, good False; point (1, 1) of m (orbit 5): |stab| 200, |induced| 10, good False; line m: |stab| 1000, |induced| 20, good False; affine line, direction (1, 0): |stab| 200, |induced| 10, good False; affine line, direction (1, 1): |stab| 40, |induced| 20, good False
  |Hbar| =    20 |H cap Z| =   2 |X| =      1000: affine point: |stab| 40, |induced| 20, good False; point (1, 0) of m (orbit 1): |stab| 1000, |induced| 10, good False; point (1, 1) of m (orbit 5): |stab| 200, |induced| 20, good False; line m: |stab| 1000, |induced| 20, good False; affine line, direction (1, 0): |stab| 200, |induced| 20, good False; affine line, direction (1, 1): |stab| 40, |induced| 10, good False
  |Hbar| =    20 |H cap Z| =   4 |X| =      2000: affine point: |stab| 80, |induced| 20, good False; point (1, 0) of m (orbit 1): |stab| 2000, |induced| 20, good False; point (1, 1) of m (orbit 5): |stab| 400, |induced| 20, good False; line m: |stab| 2000, |induced| 20, good False; affine line, direction (1, 0): |stab| 400, |induced| 20, good False; affine line, direction (1, 1): |stab| 80, |induced| 20, good False
  |Hbar| =    12 |H cap Z| =   4 |X| =      1200: affine point: |stab| 48, |induced| 12, good False; point (1, 0) of m (orbit 6): |stab| 200, |induced| 20, good False; line m: |stab| 1200, |induced| 12, good False; affine line, direction (1, 0): |stab| 40, |induced| 20, good False
  |Hbar| =    12 |H cap Z| =   4 |X| =      1200: affine point: |stab| 48, |induced| 12, good False; point (1, 0) of m (orbit 6): |stab| 200, |induced| 20, good False; line m: |stab| 1200, |induced| 12, good False; affine line, direction (1, 0): |stab| 40, |induced| 20, good False
  |Hbar| =    10 |H cap Z| =   4 |X| =      1000: affine point: |stab| 40, |induced| 10, good False; point (1, 0) of m (orbit 1): |stab| 1000, |induced| 20, good False; point (1, 1) of m (orbit 5): |stab| 200, |induced| 20, good False; line m: |stab| 1000, |induced| 10, good False; affine line, direction (1, 0): |stab| 200, |induced| 20, good False; affine line, direction (1, 1): |stab| 40, |induced| 20, good False
RESULT q = 5: 10 subgroups H (|X| = q^2|H| > M = 800) tested; good ones: none  [0s]
