Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
624 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 142 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. C5×#423 | C4 | semidirect |
| 14. #65407 | C4 | semidirect |
| 15. #65407 | C4 | semidirect |
| 16. #65213 | C4 | semidirect |
| 130. #423 | AGL(1,𝔽5) | semidirect |
| 319. C5 | #11245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617409 | 2 |
| #10610779 | 2 |
| #10604771 | 2 |
| D5⋊#338 | 2 |
| C2×#64863 | 2 |
| #11245 | 5 |