Finite Group DatabasebetaFinite Group DatabasebetaOrder 10246.
8 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C47×C109 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D109 | — | 47 | 1 | no | maximal, Hall |
| 3 | C109 | D47 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 4 | D47 | — | 109 | 1 | no | maximal, Hall |
| 5 | C47 | D109 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C2 | — | 5123 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C47×C109 | C2 |
| LCS | G ▷ C47×C109 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C47×C109 | C2 | semidirect |
| 3. C109 | D47 | semidirect |
| 5. C47 | D109 | semidirect |