Finite Group DatabasebetaFinite Group DatabasebetaOrder 8540.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C7×C61⋊C5 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×C61⋊C5 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | Dic427 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 4 | Dic61⋊C5 | — | 7 | 1 | no | maximal, Hall |
| 5 | C2×C7×C61 | C2×C5 | 1 | 1 | yes | characteristic |
| 6 | C2×C61⋊C5 | D7 | 1 | 1 | yes | characteristic |
| 7 | C7×C61 | C4×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C61⋊C5 | Dic7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | Dic61 | — | 7 | 1 | no | Hall |
| 10 | C5×Dic7 | — | 61 | 1 | no | maximal, Hall |
| 11 | C2×C61 | C5×D7 | 1 | 1 | yes | characteristic |
| 12 | C2×C5×C7 | — | 61 | 1 | no | — |
| 13 | C61 | C5×Dic7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C5×C7 | — | 61 | 1 | no | Hall |
| 15 | Dic7 | — | 61 | 1 | no | Hall |
| 16 | C4×C5 | — | 427 | 1 | no | Hall |
| 17 | C2×C7 | D61⋊C5 | 1 | 1 | yes | characteristic |
| 18 | C2×C5 | — | 61 | 1 | no | — |
| 19 | C7 | Dic61⋊C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 20 | C5 | — | 61 | 1 | no | Sylow |
| 21 | C4 | — | 427 | 1 | no | Sylow |
| 22 | C2 | C7⋊(D61⋊C5) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(D61⋊C5) |
| commutator, hypocenter | C7×C61 | C4×C5 |
| Fitting, socle | C2×C7×C61 | C2×C5 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×C61⋊C5 | C4 | semidirect |
| 3. Dic427 | C5 | semidirect |
| 7. C7×C61 | C4×C5 | semidirect |
| 8. C61⋊C5 | Dic7 | semidirect |
| 13. C61 | C5×Dic7 | semidirect |
| 19. C7 | Dic61⋊C5 | semidirect |