Finite Group DatabasebetaFinite Group DatabasebetaOrder 15730.
28 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C13×#10597245 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C11×C13×D11 | — | 5 | 1 | no | maximal, Hall |
| 3 | C112×C13 | D5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | #11925890 | C13 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 5 | C13×C11⋊C5 | — | 22 | 1 | no | — |
| 6 | #10597245 | C2×C13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C2×C11×C13 | — | 55 | 1 | no | — |
| 8 | C13×D11 | — | 5 | 1 | no | — |
| 9 | C11×D11 | — | 5 | 1 | no | Hall |
| 10 | C11×C13 | — | 2 | 1 | no | — |
| 11 | C11×C13 | — | 5 | 1 | no | — |
| 12 | C11×C13 | — | 5 | 1 | no | — |
| 13 | D5×C13 | — | 121 | 1 | no | maximal, Hall |
| 14 | C112 | D5×C13 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | C5×C13 | — | 121 | 1 | no | Hall |
| 16 | C11⋊C5 | — | 22 | 1 | no | — |
| 17 | C2×C13 | — | 55 | 1 | no | Hall |
| 18 | C2×C11 | — | 55 | 1 | no | — |
| 19 | D11 | — | 5 | 1 | no | — |
| 20 | C13 | #11925890 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 21 | C11 | — | 2 | 1 | no | — |
| 22 | C11 | — | 5 | 1 | no | — |
| 23 | C11 | — | 5 | 1 | no | — |
| 24 | D5 | — | 121 | 1 | no | Hall |
| 25 | C5 | — | 121 | 1 | no | Sylow |
| 26 | C2 | — | 55 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #11925890 |
| commutator, cosocle, hypocenter | #10597245 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C112×C13 | D5 |
| LCS | G ▷ #10597245 | |
| UCS | C1 ◁ C13 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#10597245 | C2 | semidirect |
| 3. C112×C13 | D5 | semidirect |
| 4. #11925890 | C13 | direct (N × H) |
| 6. #10597245 | C2×C13 | semidirect |
| 14. C112 | D5×C13 | semidirect |
| 20. C13 | #11925890 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#10597245 | 2 |
| C11×C13×D11 | 5 |
| #11925890 | 13 |
| D5×C13 | 121 |