Finite Group DatabasebetaFinite Group DatabasebetaOrder 60.
9 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | A4 | — | 5 | 1 | no | maximal, Hall |
| 2 | D5 | — | 6 | 1 | no | maximal |
| 3 | D3 | — | 10 | 1 | no | maximal |
| 4 | C5 | — | 6 | 1 | no | Sylow |
| 5 | C22 | — | 5 | 1 | no | Sylow |
| 6 | C3 | — | 10 | 1 | no | Sylow |
| 7 | C2 | — | 15 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4 | 5 |
| D5 | 6 |
| D3 | 10 |