Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D59 |
| commutator, socle, cosocle | C23×C59 | C25 |
| Fitting | C59×#2840 | C2 |
| hypercenter | #2840 | D59 |
| hypocenter | C59 | #36675 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21432287 | C2 | semidirect |
| 2. #21432180 | C2 | semidirect |
| 3. #21432093 | C2 | semidirect |
| 4. #21427378 | C2 | semidirect |
| 5. #21427313 | C2 | semidirect |
| 6. #21426595 | C2 | semidirect |
| 7. C59×#2840 | C2 | semidirect |
| 8. C22×#11745689 | C22 | semidirect |
| 11. C2×Q8×Dic59 | C22 | semidirect |
| 13. #16837344 | C22 | semidirect |
| 14. #16837329 | C22 | semidirect |
| 16. #16837321 | C22 | semidirect |
| 17. #16837320 | C22 | semidirect |
| 19. #16837313 | C22 | semidirect |
| 24. #16837249 | C22 | semidirect |
| 25. #16837247 | C22 | semidirect |
| 57. C24×C59 | #41 | semidirect |
| 126. #2840 | D59 | semidirect |
| 159. C59 | #36675 | semidirect |
| 189. C24 | #11745689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432287 | 2 |
| #21432180 | 2 |
| #21432093 | 2 |
| #21427378 | 2 |
| #21427313 | 2 |
| #21426595 | 2 |
| C59×#2840 | 2 |
| #36675 | 59 |