Finite Group DatabasebetaFinite Group DatabasebetaOrder 10670.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11⋊C5×C97 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D11×C97 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C11×C97 | C2×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C2×C5×C97 | — | 11 | 1 | no | maximal, Hall |
| 5 | C5×C97 | — | 11 | 1 | no | Hall |
| 6 | C2×C97 | — | 11 | 1 | no | Hall |
| 7 | AGL(1,𝔽11) | C97 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 8 | C97 | AGL(1,𝔽11) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 9 | C11⋊C5 | C2×C97 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | D11 | C5×C97 | 1 | 1 | yes | characteristic, complemented, Hall |
| 11 | C11 | C2×C5×C97 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C2×C5 | — | 11 | 1 | no | Hall |
| 13 | C5 | — | 11 | 1 | no | Sylow |
| 14 | C2 | — | 11 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11 | C2×C5×C97 |
| Frattini | C1 | G |
| Fitting, socle | C11×C97 | C2×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11⋊C5×C97 | C2 | semidirect |
| 2. D11×C97 | C5 | semidirect |
| 3. C11×C97 | C2×C5 | semidirect |
| 7. AGL(1,𝔽11) | C97 | direct (N × H) |
| 8. C97 | AGL(1,𝔽11) | direct (N × H) |
| 9. C11⋊C5 | C2×C97 | semidirect |
| 10. D11 | C5×C97 | semidirect |
| 11. C11 | C2×C5×C97 | semidirect |