Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 4. C2×#64733 | C2 | semidirect |
| 5. #10601456 | C2 | semidirect |
| 6. #10598302 | C2 | semidirect |
| 7. #10598217 | C2 | semidirect |
| 20. C5×#357 | C4 | semidirect |
| 44. C2×C5×C16 | C2×C4 | semidirect |
| 45. C5×#107 | C2×C4 | semidirect |
| 117. #357 | Dic5 | semidirect |
| 169. C2×C16 | C2×Dic5 | semidirect |
| 172. #107 | C2×Dic5 | semidirect |
| 267. C5 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65441 | 2 |
| C5×#2140 | 2 |
| C2×#64783 | 2 |
| C2×#64733 | 2 |
| #10601456 | 2 |
| #10598302 | 2 |
| #10598217 | 2 |
| #12956 | 5 |