Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10602192 | C2 | semidirect |
| 5. #10601499 | C2 | semidirect |
| 6. #10598298 | C2 | semidirect |
| 7. #10598226 | C2 | semidirect |
| 20. #64785 | C4 | semidirect |
| 21. #64783 | C4 | semidirect |
| 262. C5 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#359 | 2 |
| #10602879 | 2 |
| #10602874 | 2 |
| #10602192 | 2 |
| #10601499 | 2 |
| #10598298 | 2 |
| #10598226 | 2 |
| #13146 | 5 |