Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10603932 | C2 | semidirect |
| 5. #10598578 | C2 | semidirect |
| 7. C2×#4131 | C4 | semidirect |
| 11. #65776 | C4 | semidirect |
| 15. #65682 | C4 | semidirect |
| 16. C4×D5⋊C8 | C4 | semidirect |
| 21. C5×#355 | C4 | semidirect |
| 22. #64762 | C4 | semidirect |
| 23. #64698 | C4 | semidirect |
| 123. #355 | AGL(1,𝔽5) | semidirect |
| 290. C5 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617309 | 2 |
| #10604545 | 2 |
| #10603932 | 2 |
| #10599958 | 2 |
| #10598578 | 2 |
| #12633 | 5 |