Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
602 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C2×#64761 | C2 | semidirect |
| 4. #10602412 | C2 | semidirect |
| 5. C4×#3966 | C2 | semidirect |
| 7. C2×C5×#124 | C4 | semidirect |
| 12. C5×#391 | C4 | semidirect |
| 13. C5×#390 | C4 | semidirect |
| 16. C4×C5×C4⋊C4 | C4 | semidirect |
| 131. C2×#124 | Dic5 | semidirect |
| 138. #391 | Dic5 | semidirect |
| 139. #390 | Dic5 | semidirect |
| 143. C4×C4⋊C4 | Dic5 | semidirect |
| 406. C5 | #13225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2544 | 2 |
| C2×#64765 | 2 |
| C2×#64761 | 2 |
| #10602412 | 2 |
| C4×#3966 | 2 |
| #13225 | 5 |