Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
292 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 19. ΓL(1,𝔽81) | C4 | semidirect |
| 20. #64847 | C4 | semidirect |
| 21. #64846 | C4 | semidirect |
| 22. #64846 | C4 | semidirect |
| 23. C5×#368 | C4 | semidirect |
| 24. #64726 | C4 | semidirect |
| 25. #64713 | C4 | semidirect |
| 26. #64713 | C4 | semidirect |
| 111. #368 | AGL(1,𝔽5) | semidirect |
| 236. C5 | #12678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604104 | 2 |
| C2×#64846 | 2 |
| #10604090 | 2 |
| #10604086 | 2 |
| #10600153 | 2 |
| #10598632 | 2 |
| #10598630 | 2 |
| #12678 | 5 |