Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
878 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 16. C5×#494 | C4 | semidirect |
| 17. #65470 | C4 | semidirect |
| 18. #65381 | C4 | semidirect |
| 19. #64988 | C4 | semidirect |
| 98. #494 | AGL(1,𝔽5) | semidirect |
| 229. C5 | #23200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617434 | 2 |
| D5×#494 | 2 |
| #10604852 | 2 |
| #10604670 | 2 |
| #10603851 | 2 |
| #23200 | 5 |