Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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. #10599859 | C2 | semidirect |
| 4. C5×#1422 | C2 | semidirect |
| 5. #10598096 | C2 | semidirect |
| 38. #1422 | D5 | semidirect |
| 144. C5 | #13693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10600167 | 2 |
| #10599860 | 2 |
| #10599859 | 2 |
| C5×#1422 | 2 |
| #10598096 | 2 |
| #13693 | 5 |