Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1102 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 207 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #430×D59 | C2 | semidirect |
| 3. #21425613 | C2 | semidirect |
| 4. #21425612 | C2 | semidirect |
| 5. #21425611 | C2 | semidirect |
| 6. #338×D59 | C2 | semidirect |
| 7. C59×#2091 | C2 | semidirect |
| 11. #16837451 | C22 | semidirect |
| 12. #16837450 | C22 | semidirect |
| 20. C59⋊#338 | C22 | semidirect |
| 21. C59×#430 | C22 | semidirect |
| 23. C59×#338 | C22 | semidirect |
| 162. #2091 | D59 | direct (N × H) |
| 169. D59 | #2091 | direct (N × H) |
| 176. #430 | C2×D59 | semidirect |
| 185. #338 | C2×D59 | semidirect |
| 186. C59 | C2×#2091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #430×D59 | 2 |
| #407×D59 | 2 |
| #21425613 | 2 |
| #21425612 | 2 |
| #21425611 | 2 |
| #338×D59 | 2 |
| C59×#2091 | 2 |
| C2×#2091 | 59 |