Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
818 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 111 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×#65526 | C2 | semidirect |
| 3. #10602932 | C2 | semidirect |
| 4. C2×#64756 | C2 | semidirect |
| 5. #10598128 | C2 | semidirect |
| 7. C2×C5×#120 | C4 | semidirect |
| 9. C22×C5×C22⋊C4 | C4 | semidirect |
| 15. C5×#386 | C4 | semidirect |
| 17. C5×#381 | C4 | semidirect |
| 70. #3965 | D4 | semidirect |
| 153. C2×#120 | Dic5 | semidirect |
| 155. C22×C22⋊C4 | Dic5 | semidirect |
| 165. #386 | Dic5 | semidirect |
| 168. #381 | Dic5 | semidirect |
| 484. C5 | #13083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2404 | 2 |
| C2×#65526 | 2 |
| #10602932 | 2 |
| C2×#64756 | 2 |
| #10598128 | 2 |
| #13083 | 5 |