Finite Group DatabasebetaFinite Group DatabasebetaOrder 23123.
4 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C1217 | C19 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C19 | — | 1217 | 1 | no | maximal, Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1217 | C19 |
| LCS | G ▷ C1217 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C1217 | C19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C1217 | 19 |
| C19 | 1217 |