Finite Group DatabasebetaFinite Group DatabasebetaOrder 31707.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C13×C271 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | C13×C271 | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | #14578512 | — | 13 | 1 | no | maximal, Hall |
| 4 | C3×C271 | C13⋊C3 | 1 | 1 | yes | characteristic |
| 5 | C271 | C13⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C13⋊C9 | — | 271 | 1 | no | maximal, Hall |
| 7 | C3×C13 | C271⋊C3 | 1 | 1 | yes | characteristic |
| 8 | C13 | #14578512 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C9 | — | 3523 | 1 | no | Sylow |
| 10 | C3 | #24902294 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #24902294 |
| commutator, hypocenter | C13×C271 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C13×C271 | C3 |
| LCS | G ▷ C13×C271 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×C271 | C9 | semidirect |
| 5. C271 | C13⋊C9 | semidirect |
| 8. C13 | #14578512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C13×C271 | 3 |
| #14578512 | 13 |
| C13⋊C9 | 271 |