Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #10602155 | C2 | semidirect |
| 5. #10598293 | C2 | semidirect |
| 6. #10598056 | C2 | semidirect |
| 7. #10598046 | C2 | semidirect |
| 57. C5×D8 | Q16 | semidirect |
| 149. D8 | #689 | semidirect |
| 190. C5 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2226 | 2 |
| #10602155 | 2 |
| #10601680 | 2 |
| D8×#168 | 2 |
| #10598293 | 2 |
| #10598056 | 2 |
| #10598046 | 2 |
| #12447 | 5 |