Finite Group DatabasebetaFinite Group DatabasebetaOrder 8940.
18 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | A4×C149 | — | 5 | 1 | no | maximal, Hall |
| 2 | D5×C149 | — | 6 | 1 | no | maximal |
| 3 | D3×C149 | — | 10 | 1 | no | maximal |
| 4 | C5×C149 | — | 6 | 1 | no | Hall |
| 5 | C22×C149 | — | 5 | 1 | no | Hall |
| 6 | C3×C149 | — | 10 | 1 | no | Hall |
| 7 | C2×C149 | — | 15 | 1 | no | — |
| 8 | C149 | A5 | 1 | 1 | yes | maximal normal, characteristic, direct product factor, Sylow |
| 9 | A5 | C149 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 10 | A4 | — | 5 | 1 | no | Hall |
| 11 | D5 | — | 6 | 1 | no | — |
| 12 | D3 | — | 10 | 1 | no | — |
| 13 | C5 | — | 6 | 1 | no | Sylow |
| 14 | C22 | — | 5 | 1 | no | Sylow |
| 15 | C3 | — | 10 | 1 | no | Sylow |
| 16 | C2 | — | 15 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C149 | A5 |
| commutator, hypocenter | A5 | C149 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C149 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C149 | A5 | direct (N × H) |
| 9. A5 | C149 | direct (N × H) |