Finite Group DatabasebetaFinite Group DatabasebetaOrder 36075.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C52×C13×C37 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C52⋊(C37⋊C3) | — | 13 | 1 | no | maximal, Hall |
| 3 | C5×C13×C37 | — | 3 | 2 | no | — |
| 4 | #13089650 | — | 25 | 1 | no | maximal, Hall |
| 5 | C13⋊(C52⋊C3) | — | 37 | 1 | no | maximal, Hall |
| 6 | C52×C37 | C13⋊C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C13×C37 | C52⋊C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C52×C13 | C37⋊C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C5×C37 | — | 3 | 2 | no | — |
| 10 | C37⋊C3 | — | 325 | 1 | no | Hall |
| 11 | C52⋊C3 | — | 481 | 1 | no | Hall |
| 12 | C5×C13 | — | 3 | 2 | no | — |
| 13 | C13⋊C3 | — | 925 | 1 | no | Hall |
| 14 | C37 | C13⋊(C52⋊C3) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | C52 | #13089650 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C13 | C52⋊(C37⋊C3) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 17 | C5 | — | 3 | 2 | no | — |
| 18 | C3 | — | 12025 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13×C37 | C3 |
| LCS | G ▷ C52×C13×C37 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×C13×C37 | C3 | semidirect |
| 6. C52×C37 | C13⋊C3 | semidirect |
| 7. C13×C37 | C52⋊C3 | semidirect |
| 8. C52×C13 | C37⋊C3 | semidirect |
| 14. C37 | C13⋊(C52⋊C3) | semidirect |
| 15. C52 | #13089650 | semidirect |
| 16. C13 | C52⋊(C37⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C13×C37 | 3 |
| C52⋊(C37⋊C3) | 13 |
| #13089650 | 25 |
| C13⋊(C52⋊C3) | 37 |