Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
434 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10604733 | C2 | semidirect |
| 3. #10604727 | C2 | semidirect |
| 5. #10598791 | C2 | semidirect |
| 7. C22×C8×D5 | C4 | semidirect |
| 13. C5×#405 | C4 | semidirect |
| 15. #65415 | C4 | semidirect |
| 16. #65288 | C4 | semidirect |
| 141. #405 | AGL(1,𝔽5) | semidirect |
| 345. C5 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610284 | 2 |
| #10604733 | 2 |
| #10604727 | 2 |
| #10604381 | 2 |
| #10598791 | 2 |
| #12805 | 5 |