Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
494 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 11. C5×#494 | C4 | semidirect |
| 13. #65470 | C4 | semidirect |
| 15. #64988 | C4 | semidirect |
| 103. #494 | AGL(1,𝔽5) | semidirect |
| 178. C4×C5 | #358 | semidirect |
| 183. Dic5 | #358 | semidirect |
| 256. C5 | #13253 | semidirect |
| 269. C4 | #64908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#494 | 2 |
| C2×#64908 | 2 |
| C4×#3994 | 2 |
| D5⋊(C4⋊C16) | 2 |
| #13253 | 5 |