Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
338 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 338 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. #10602174 | C2 | semidirect |
| 4. #10602171 | C2 | semidirect |
| 5. #10598254 | C2 | semidirect |
| 6. #10598051 | C2 | semidirect |
| 7. #10598049 | C2 | semidirect |
| 55. #2226 | D5 | semidirect |
| 249. C5 | #12384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611309 | 2 |
| C5×#2226 | 2 |
| #10602174 | 2 |
| #10602171 | 2 |
| #10598254 | 2 |
| #10598051 | 2 |
| #10598049 | 2 |
| #12384 | 5 |