Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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. #10598858 | C2 | semidirect |
| 4. #10597967 | C2 | semidirect |
| 5. #10597931 | C2 | semidirect |
| 44. C5×D8 | Q16 | semidirect |
| 121. D8 | Dic20 | semidirect |
| 157. C5 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C8×D8 | 2 |
| #10601680 | 2 |
| #10598858 | 2 |
| #10597967 | 2 |
| #10597931 | 2 |
| #12447 | 5 |