PSL(3,5): |P| = 372000, k = 31, |Q| = 12000, |phibar(Q)| = 120, M = 800  [2s]
point stabiliser P_x: order 12000, 132 classes of subgroups (13640 subgroups); classes of order > M: 10  [22s]
   |S| =  12000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 12000, 120, False), (30, 400, 20, False)]
   |S| =   6000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 6000, 60, False), (30, 200, 20, False)]
   |S| =   3000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 3000, 60, False), (30, 100, 20, False)]
   |S| =   2400  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 2400, 24, False), (30, 80, 20, False)]
   |S| =   2000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 2000, 20, False), (5, 400, 20, False), (25, 80, 20, False)]
   |S| =   1200  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 1200, 12, False), (30, 40, 20, False)]
   |S| =   1200  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 1200, 12, False), (30, 40, 20, False)]
   |S| =   1000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 1000, 20, False), (5, 200, 10, False), (25, 40, 20, False)]
   |S| =   1000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 1000, 20, False), (5, 200, 20, False), (25, 40, 10, False)]
   |S| =   1000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 1000, 10, False), (5, 200, 20, False), (25, 40, 20, False)]
line stabiliser P_l: order 12000, 132 classes of subgroups (13640 subgroups); classes of order > M: 10  [44s]
   |S| =  12000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(6, 2000, 20, False), (25, 480, 120, False)]
   |S| =   6000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(6, 1000, 20, False), (25, 240, 60, False)]
   |S| =   3000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(6, 500, 20, False), (25, 120, 60, False)]
   |S| =   2400  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(6, 400, 20, False), (25, 96, 24, False)]
   |S| =   2000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 2000, 20, False), (5, 400, 20, False), (25, 80, 20, False)]
   |S| =   1200  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(6, 200, 20, False), (25, 48, 12, False)]
   |S| =   1200  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(6, 200, 20, False), (25, 48, 12, False)]
   |S| =   1000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 1000, 20, False), (5, 200, 10, False), (25, 40, 20, False)]
   |S| =   1000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 1000, 10, False), (5, 200, 20, False), (25, 40, 20, False)]
   |S| =   1000  good = False  orbits (length, |S_d|, |image|, fixes t != 1): [(1, 1000, 20, False), (5, 200, 20, False), (25, 40, 10, False)]
RESULT: largest order of a good subgroup among the subgroups of order > M of the two parabolic subgroups: none; M = 800; hence (with the list of maximal subgroups) M_G = M = 800  [44s]
