subgroups by index from canonical classes: {1: 1, 6: 12, 7: 28, 8: 16, 10: 20}
subgroups by index from plain low-index  : {1: 1, 6: 12, 7: 28, 8: 16, 10: 20}
find_X vs brute force: cases 336 x 4 roles, total solutions 335 , mismatches 0
SELFTEST PASSED
