Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
474 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 121 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×#65473 | C2 | semidirect |
| 5. C2×#64785 | C2 | semidirect |
| 6. #10598307 | C2 | semidirect |
| 7. #10598302 | C2 | semidirect |
| 13. C2×C5×Q32 | C4 | semidirect |
| 14. C2×C5×SD32 | C4 | semidirect |
| 129. C2×Q32 | Dic5 | semidirect |
| 130. C2×SD32 | Dic5 | semidirect |
| 319. C5 | #13038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#510 | 2 |
| C2×#65473 | 2 |
| #10602878 | 2 |
| C2×#64786 | 2 |
| C2×#64785 | 2 |
| #10598307 | 2 |
| #10598302 | 2 |
| #13038 | 5 |