Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 67 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. #10602177 | C2 | semidirect |
| 3. #10600089 | C2 | semidirect |
| 5. C5×#1365 | C2 | semidirect |
| 7. #10597963 | C2 | semidirect |
| 57. #1365 | D5 | semidirect |
| 226. C5 | #12398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613678 | 2 |
| #10602177 | 2 |
| #10600089 | 2 |
| #10599372 | 2 |
| C5×#1365 | 2 |
| #10598047 | 2 |
| #10597963 | 2 |
| #12398 | 5 |