Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
394 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 4. #10602582 | C2 | semidirect |
| 5. #10602567 | C2 | semidirect |
| 6. #10601541 | C2 | semidirect |
| 7. #10598234 | C2 | semidirect |
| 294. C5 | #10489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3206 | 2 |
| #10602603 | 2 |
| #10602594 | 2 |
| #10602582 | 2 |
| #10602567 | 2 |
| #10601541 | 2 |
| #10598234 | 2 |
| #10489 | 5 |