Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
490 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 2. #21424560 | C2 | semidirect |
| 3. #21424532 | C2 | semidirect |
| 4. #21424303 | C2 | semidirect |
| 5. #21422455 | C2 | semidirect |
| 6. #21422002 | C2 | semidirect |
| 7. C59×#1519 | C2 | semidirect |
| 220. #1519 | D59 | semidirect |
| 253. C59 | #10560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434893 | 2 |
| #21424560 | 2 |
| #21424532 | 2 |
| #21424303 | 2 |
| #21422455 | 2 |
| #21422002 | 2 |
| C59×#1519 | 2 |
| #10560 | 59 |