Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 67 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. C5×#2252 | C2 | semidirect |
| 3. #10602183 | C2 | semidirect |
| 5. #10598293 | C2 | semidirect |
| 6. #10597996 | C2 | semidirect |
| 54. #2252 | D5 | semidirect |
| 226. C5 | #12398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613678 | 2 |
| C5×#2252 | 2 |
| #10602183 | 2 |
| #10602165 | 2 |
| #10598293 | 2 |
| #10597996 | 2 |
| #10597994 | 2 |
| #12398 | 5 |