Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
538 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 538 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×#65441 | C2 | semidirect |
| 3. #10602878 | C2 | semidirect |
| 4. C2×#64786 | C2 | semidirect |
| 5. C2×#64783 | C2 | semidirect |
| 6. #10598307 | C2 | semidirect |
| 7. #10598302 | C2 | semidirect |
| 13. C2×C5×SD32 | C4 | semidirect |
| 14. C2×C5×D16 | C4 | semidirect |
| 35. C2×C5×Q16 | C2×C4 | semidirect |
| 41. C2×C5×D8 | C2×C4 | semidirect |
| 56. C2×C5×C16 | C2×C4 | semidirect |
| 130. C2×SD32 | Dic5 | semidirect |
| 131. C2×D16 | Dic5 | semidirect |
| 188. C2×Q16 | C2×Dic5 | semidirect |
| 194. C2×D8 | C2×Dic5 | semidirect |
| 212. C2×C16 | C2×Dic5 | semidirect |
| 332. C5 | #13037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#509 | 2 |
| C2×#65441 | 2 |
| #10602878 | 2 |
| C2×#64786 | 2 |
| C2×#64783 | 2 |
| #10598307 | 2 |
| #10598302 | 2 |
| #13037 | 5 |