Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
782 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 782 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×#65529 | C2 | semidirect |
| 3. #10602932 | C2 | semidirect |
| 4. C2×#64765 | C2 | semidirect |
| 5. #10598132 | C2 | semidirect |
| 8. C2×C5×#124 | C4 | semidirect |
| 9. C2×C5×#121 | C4 | semidirect |
| 13. C5×#391 | C4 | semidirect |
| 17. C4×C5×C22⋊C4 | C4 | semidirect |
| 70. #3966 | D4 | semidirect |
| 153. C2×#124 | Dic5 | semidirect |
| 154. C2×#121 | Dic5 | semidirect |
| 163. #391 | Dic5 | semidirect |
| 168. C4×C22⋊C4 | Dic5 | semidirect |
| 481. C5 | #13089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2431 | 2 |
| C2×#65529 | 2 |
| #10602932 | 2 |
| C2×#64765 | 2 |
| #10598132 | 2 |
| #13089 | 5 |