Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
318 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 318 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×#2226 | C2 | semidirect |
| 3. #10602178 | C2 | semidirect |
| 4. #10602165 | C2 | semidirect |
| 5. #10598254 | C2 | semidirect |
| 6. #10598055 | C2 | semidirect |
| 7. #10598047 | C2 | semidirect |
| 55. #2226 | D5 | semidirect |
| 241. C5 | #12396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611345 | 2 |
| C5×#2226 | 2 |
| #10602178 | 2 |
| #10602165 | 2 |
| #10598254 | 2 |
| #10598055 | 2 |
| #10598047 | 2 |
| #12396 | 5 |