Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
378 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10603845 | C2 | semidirect |
| 3. #10603829 | C2 | semidirect |
| 4. #10598805 | C2 | semidirect |
| 5. #10598611 | C2 | semidirect |
| 8. C4×C5×D8 | C4 | semidirect |
| 10. #65440 | C4 | semidirect |
| 13. #65163 | C4 | semidirect |
| 16. C4×D40 | C4 | semidirect |
| 109. C4×D8 | AGL(1,𝔽5) | semidirect |
| 288. C5 | #11856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611329 | 2 |
| #10603845 | 2 |
| #10603829 | 2 |
| #10598805 | 2 |
| #10598611 | 2 |
| #11856 | 5 |