Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 9. #65788 | C4 | semidirect |
| 10. Q8×#170 | C4 | semidirect |
| 26. C5×#333 | C4 | semidirect |
| 27. #64766 | C4 | semidirect |
| 28. #64706 | C4 | semidirect |
| 29. #64702 | C4 | semidirect |
| 131. #333 | AGL(1,𝔽5) | semidirect |
| 300. C5 | #8256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617374 | 2 |
| #10604623 | 2 |
| #10604034 | 2 |
| #10604010 | 2 |
| #10599274 | 2 |
| #10598597 | 2 |
| #10598594 | 2 |
| #8256 | 5 |