Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
292 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 292 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. #10600088 | C2 | semidirect |
| 4. #10599839 | C2 | semidirect |
| 6. #10598056 | C2 | semidirect |
| 7. #10597996 | C2 | semidirect |
| 230. C5 | #12394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611146 | 2 |
| #10601645 | 2 |
| #10600088 | 2 |
| #10599839 | 2 |
| C5×D4⋊C16 | 2 |
| #10598056 | 2 |
| #10597996 | 2 |
| #12394 | 5 |