Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
304 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10604020 | C2 | semidirect |
| 4. #10604012 | C2 | semidirect |
| 6. #10598592 | C2 | semidirect |
| 7. #10598588 | C2 | semidirect |
| 274. C5 | #9588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604606 | 2 |
| #10604605 | 2 |
| #10604020 | 2 |
| #10604012 | 2 |
| #10599175 | 2 |
| #10598592 | 2 |
| #10598588 | 2 |
| #9588 | 5 |