Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1098 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 139 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. #10602932 | C2 | semidirect |
| 3. C2×#64765 | C2 | semidirect |
| 4. C2×#64761 | C2 | semidirect |
| 5. C22×C5×#41 | C4 | semidirect |
| 9. C2×C5×C4⋊Q8 | C4 | semidirect |
| 11. C2×C5×#124 | C4 | semidirect |
| 15. C22×C42×C5 | C4 | semidirect |
| 128. C22×#41 | Dic5 | semidirect |
| 132. C2×C4⋊Q8 | Dic5 | semidirect |
| 134. C2×#124 | Dic5 | semidirect |
| 138. C22×C42 | Dic5 | semidirect |
| 373. C5 | #12695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#532 | 2 |
| #10602932 | 2 |
| C2×#64765 | 2 |
| C2×#64761 | 2 |
| #12695 | 5 |