Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
290 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 65 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. #21426323 | C2 | semidirect |
| 4. #21422150 | C2 | semidirect |
| 5. #21422060 | C2 | semidirect |
| 7. C59×#2209 | C2 | semidirect |
| 126. #2209 | D59 | semidirect |
| 152. C59 | #12345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436528 | 2 |
| #21426323 | 2 |
| #21423458 | 2 |
| #21422150 | 2 |
| #21422060 | 2 |
| #21422050 | 2 |
| C59×#2209 | 2 |
| #12345 | 59 |