Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #10602183 | C2 | semidirect |
| 4. #10602177 | C2 | semidirect |
| 6. #10597967 | C2 | semidirect |
| 7. #10597963 | C2 | semidirect |
| 226. C5 | #12398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611146 | 2 |
| C5×#1675 | 2 |
| #10602183 | 2 |
| #10602177 | 2 |
| D4⋊#672 | 2 |
| #10597967 | 2 |
| #10597963 | 2 |
| #12398 | 5 |