Quiz:Subgroup structure of symmetric group:S5

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See subgroup structure of symmetric group:S5 for background information and more details.

Basic stuff

Summary table on the structure of subgroups: [SHOW MORE]

1 For which of the following divisors of 120 does there not exist a subgroup of the symmetric group of degree five with that as order?

12
20
24
30
60

2 What is the smallest possible order of a group that is not isomorphic to any subgroup of the symmetric group of degree five?

5
6
7
8
9

3 What is the smallest possible order of a group that is isomorphic to subgroups in two distinct conjugacy classes of subgroups in the symmetric group of degree five?

2
3
4
5
6