Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
498 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 96 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. C2×#64903 | C2 | semidirect |
| 4. C4×#3993 | C2 | semidirect |
| 5. #10603827 | C2 | semidirect |
| 13. C5×#495 | C4 | semidirect |
| 14. #65470 | C4 | semidirect |
| 16. #65440 | C4 | semidirect |
| 18. #64985 | C4 | semidirect |
| 59. #3993 | D4 | semidirect |
| 129. #495 | AGL(1,𝔽5) | semidirect |
| 236. Dic5 | #360 | semidirect |
| 332. C5 | #13255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613551 | 2 |
| C2×#64907 | 2 |
| C2×#64903 | 2 |
| C4×#3993 | 2 |
| #10603827 | 2 |
| #13255 | 5 |