Finite Group DatabasebetaFinite Group DatabasebetaOrder 5452.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C29×C47 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C29×C47 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | Dic47 | C29 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 4 | C4×C29 | — | 47 | 1 | no | maximal, Hall |
| 5 | C2×C47 | C2×C29 | 1 | 1 | yes | characteristic |
| 6 | C2×C29 | D47 | 1 | 1 | yes | characteristic |
| 7 | C47 | C4×C29 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C29 | Dic47 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 9 | C4 | — | 47 | 1 | no | Sylow |
| 10 | C2 | C29×D47 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D47 |
| commutator, hypocenter | C47 | C4×C29 |
| Frattini | C2 | C29×D47 |
| Fitting, socle | C2×C29×C47 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C2×C29 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×C47 | C4 | semidirect |
| 3. Dic47 | C29 | direct (N × H) |
| 7. C47 | C4×C29 | semidirect |
| 8. C29 | Dic47 | direct (N × H) |