Finite Group DatabasebetaFinite Group DatabasebetaOrder 4913.
22 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C172 | C17 | 1 | 1 | yes | maximal, characteristic |
| 2 | C289 | C17 | 1 | 17 | yes | maximal, complemented |
| 3 | C17 | — | 17 | 1 | no | — |
| 4 | C17 | C172 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle | C17 | C172 |
| LCS | G ▷ C17 ▷ C1 | |
| UCS | C1 ◁ C17 ◁ G | |
| LECS | G ▷ C17 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C289 | C17 | semidirect |