Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21435298 | C2 | semidirect |
| 5. #21422451 | C2 | semidirect |
| 6. #21421968 | C2 | semidirect |
| 7. C59×#1485 | C2 | semidirect |
| 178. #1485 | D59 | semidirect |
| 211. C59 | #10123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435298 | 2 |
| #21435294 | 2 |
| #21434497 | 2 |
| #21422566 | 2 |
| #21422451 | 2 |
| #21421968 | 2 |
| C59×#1485 | 2 |
| #10123 | 59 |