Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
278 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 278 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 |
|---|---|---|
| 2. #10602178 | C2 | semidirect |
| 3. #10601704 | C2 | semidirect |
| 5. #10598292 | C2 | semidirect |
| 6. #10598256 | C2 | semidirect |
| 226. C5 | #12397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3342 | 2 |
| #10602178 | 2 |
| #10601704 | 2 |
| #10601646 | 2 |
| #10598292 | 2 |
| #10598256 | 2 |
| D4⋊#672 | 2 |
| #12397 | 5 |