Finite Group DatabasebetaFinite Group DatabasebetaOrder 7260.
34 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×A5 | — | 11 | 2 | no | maximal |
| 2 | PSL(2,𝔽11) | C11 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 3 | C11×C11⋊C5 | — | 12 | 1 | no | maximal, Hall |
| 4 | C2×D3×C11 | — | 55 | 1 | no | maximal |
| 5 | C11×A4 | — | 55 | 1 | no | — |
| 6 | C112 | — | 12 | 1 | no | Sylow |
| 7 | D5×C11 | — | 66 | 1 | no | — |
| 8 | C2×C3×C11 | — | 55 | 1 | no | — |
| 9 | D3×C11 | — | 55 | 2 | no | — |
| 10 | A5 | — | 11 | 2 | no | Hall |
| 11 | C5×C11 | — | 66 | 1 | no | — |
| 12 | C11⋊C5 | — | 12 | 1 | no | — |
| 13 | C22×C11 | — | 55 | 1 | no | — |
| 14 | C3×C11 | — | 55 | 1 | no | — |
| 15 | C2×C11 | — | 55 | 1 | no | — |
| 16 | C2×D3 | — | 55 | 1 | no | Hall |
| 17 | A4 | — | 55 | 1 | no | Hall |
| 18 | C11 | — | 12 | 1 | no | — |
| 19 | C11 | — | 60 | 2 | no | — |
| 20 | C11 | PSL(2,𝔽11) | 1 | 1 | yes | maximal normal, characteristic, direct product factor |
| 21 | D5 | — | 66 | 1 | no | — |
| 22 | C2×C3 | — | 55 | 1 | no | — |
| 23 | D3 | — | 55 | 2 | no | — |
| 24 | C5 | — | 66 | 1 | no | Sylow |
| 25 | C22 | — | 55 | 1 | no | Sylow |
| 26 | C3 | — | 55 | 1 | no | Sylow |
| 27 | C2 | — | 55 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C11 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C11 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C11 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. PSL(2,𝔽11) | C11 | direct (N × H) |
| 20. C11 | PSL(2,𝔽11) | direct (N × H) |