Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
498 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 2. C2×#64907 | C2 | semidirect |
| 3. C4×#3993 | C2 | semidirect |
| 4. #10603827 | C2 | semidirect |
| 11. C5×#494 | C4 | semidirect |
| 13. #65480 | C4 | semidirect |
| 15. #64984 | C4 | semidirect |
| 47. #3993 | D4 | semidirect |
| 101. #494 | AGL(1,𝔽5) | semidirect |
| 181. C4×C5 | #360 | semidirect |
| 259. C5 | #13255 | semidirect |
| 273. C4 | #64907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613530 | 2 |
| C2×#64907 | 2 |
| C4×#3993 | 2 |
| #10603827 | 2 |
| #13255 | 5 |