Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 13. #65739 | C4 | semidirect |
| 14. #65739 | C4 | semidirect |
| 22. #64908 | C4 | semidirect |
| 26. C5×#362 | C4 | semidirect |
| 27. #64785 | C4 | semidirect |
| 28. #64737 | C4 | semidirect |
| 29. #64716 | C4 | semidirect |
| 143. #362 | AGL(1,𝔽5) | semidirect |
| 316. C5 | #12648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65739 | 2 |
| #10604832 | 2 |
| #10604114 | 2 |
| #10604090 | 2 |
| D5×#362 | 2 |
| #10598675 | 2 |
| #10598627 | 2 |
| #12648 | 5 |