Finite Group DatabasebetaFinite Group DatabasebetaOrder 10134.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C32×C563 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C3×D563 | C3 | 1 | 4 | yes | maximal, direct product factor |
| 3 | C3×C563 | C2×C3 | 1 | 4 | yes | complemented |
| 4 | D563 | C32 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 5 | C563 | C2×C32 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C2×C32 | — | 563 | 1 | no | maximal, Hall |
| 7 | C32 | D563 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 8 | C2×C3 | — | 563 | 4 | no | — |
| 9 | C3 | C3×D563 | 1 | 4 | yes | direct product factor |
| 10 | C2 | — | 563 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D563 |
| commutator, cosocle, hypocenter | C563 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C563 | C2 |
| LCS | G ▷ C563 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C563 | C2 | semidirect |
| 2. C3×D563 | C3 | direct (N × H) |
| 3. C3×C563 | C2×C3 | semidirect |
| 4. D563 | C32 | direct (N × H) |
| 5. C563 | C2×C32 | semidirect |
| 7. C32 | D563 | direct (N × H) |
| 9. C3 | C3×D563 | direct (N × H) |