Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 3. #10604733 | C2 | semidirect |
| 4. #10604727 | C2 | semidirect |
| 5. #10598769 | C2 | semidirect |
| 6. C22×C5×M16 | C4 | semidirect |
| 13. #65496 | C4 | semidirect |
| 19. #65391 | C4 | semidirect |
| 20. #65390 | C4 | semidirect |
| 128. C22×M16 | AGL(1,𝔽5) | semidirect |
| 344. C5 | #12806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615487 | 2 |
| #10604887 | 2 |
| #10604733 | 2 |
| #10604727 | 2 |
| #10598769 | 2 |
| #12806 | 5 |