Solvability of group of order less than 60 is proved at OrderLt60.lean.
Most cases can be verified by the following criteria:
- p-group is solvable.
- Group of order
$pq$ is solvable. - Group of order
$2p^n$ is solvable. - Group of order
$p^2q$ where$p^2 < q$ is solvable.
Special cases are: 12, 24, 30, 36, 40, 42, 45, 48, 56. Remarkably, 30 and 56 are the most difficult cases.