soluble subgroups of A_5: 58
section types (order, element orders) -> count, |Aut|:
  order 1: count 58, |Aut| = 1
  order 2: count 46, |Aut| = 1
  order 3: count 15, |Aut| = 2
  order 4: count 5, |Aut| = 6
  order 5: count 6, |Aut| = 4
  order 6: count 10, |Aut| = 6
  order 10: count 6, |Aut| = 20
  order 12: count 5, |Aut| = 24
Goursat count of soluble subgroups of A_5 x A_5: 8144
enumerator count of soluble subgroups of A_5 x A_5: 8144 -> agree
