Finite Group DatabasebetaFinite Group DatabasebetaOrder 5672.
8 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4×C709 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C709 | C4 | 1 | 1 | yes | characteristic |
| 3 | C709 | C8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 4 | C8 | — | 709 | 1 | no | maximal, Sylow |
| 5 | C4 | D709 | 1 | 1 | yes | characteristic |
| 6 | C2 | Dic709 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D709 |
| commutator, hypocenter | C709 | C8 |
| Fitting | C4×C709 | C2 |
| socle | C2×C709 | C4 |
| LCS | G ▷ C709 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C709 | C8 | semidirect |