Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
590 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 85 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. #10615014 | C2 | semidirect |
| 3. #10614711 | C2 | semidirect |
| 4. #10602605 | C2 | semidirect |
| 5. #10602511 | C2 | semidirect |
| 6. #10601616 | C2 | semidirect |
| 7. #10598239 | C2 | semidirect |
| 357. C5 | #10094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3213 | 2 |
| #10615014 | 2 |
| #10614711 | 2 |
| #10602605 | 2 |
| #10602511 | 2 |
| #10601616 | 2 |
| #10598239 | 2 |
| #10094 | 5 |