Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. C5×#1362 | C2 | semidirect |
| 5. #10598284 | C2 | semidirect |
| 6. #10598055 | C2 | semidirect |
| 7. #10597966 | C2 | semidirect |
| 59. #1362 | D5 | semidirect |
| 236. C5 | #11954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613523 | 2 |
| #10600068 | 2 |
| D5×#335 | 2 |
| C5×#1362 | 2 |
| #10598284 | 2 |
| #10598055 | 2 |
| #10597966 | 2 |
| #11954 | 5 |