Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #21434478 | C2 | semidirect |
| 4. #21422821 | C2 | semidirect |
| 6. #21421989 | C2 | semidirect |
| 7. C59×#1506 | C2 | semidirect |
| 180. #1506 | D59 | semidirect |
| 210. C59 | #10098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435095 | 2 |
| #21434478 | 2 |
| #21430032 | 2 |
| #21422821 | 2 |
| #21422695 | 2 |
| #21421989 | 2 |
| C59×#1506 | 2 |
| #10098 | 59 |