Finite Group DatabasebetaFinite Group DatabasebetaOrder 34430.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×C11×C313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D3443 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 3 | C11×C313 | C2×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C5×D313 | — | 11 | 1 | no | maximal, Hall |
| 5 | C5×C313 | D11 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | D313 | — | 11 | 1 | no | Hall |
| 7 | C313 | C5×D11 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C5×D11 | — | 313 | 1 | no | maximal, Hall |
| 9 | C5×C11 | D313 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | D11 | — | 313 | 1 | no | Hall |
| 11 | C11 | C5×D313 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C2×C5 | — | 3443 | 1 | no | Hall |
| 13 | C5 | D3443 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 14 | C2 | — | 3443 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3443 |
| commutator, cosocle, hypocenter | C11×C313 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C313 | C2 |
| LCS | G ▷ C11×C313 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C11×C313 | C2 | semidirect |
| 2. D3443 | C5 | direct (N × H) |
| 3. C11×C313 | C2×C5 | semidirect |
| 5. C5×C313 | D11 | semidirect |
| 7. C313 | C5×D11 | semidirect |
| 9. C5×C11 | D313 | semidirect |
| 11. C11 | C5×D313 | semidirect |
| 13. C5 | D3443 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C11×C313 | 2 |
| D3443 | 5 |
| C5×D313 | 11 |
| C5×D11 | 313 |