Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
574 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 131 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. #10614166 | C2 | semidirect |
| 3. C5×#1801 | C2 | semidirect |
| 5. #10598206 | C2 | semidirect |
| 51. #1801 | D5 | semidirect |
| 254. C5 | #9398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614207 | 2 |
| #10614166 | 2 |
| C5×#1801 | 2 |
| #10601295 | 2 |
| #10598206 | 2 |
| #9398 | 5 |