Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
314 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. #10611349 | C2 | semidirect |
| 2. C5×#2206 | C2 | semidirect |
| 3. #10602082 | C2 | semidirect |
| 4. #10602076 | C2 | semidirect |
| 5. #10598253 | C2 | semidirect |
| 6. #10598054 | C2 | semidirect |
| 7. #10598048 | C2 | semidirect |
| 64. #2206 | D5 | semidirect |
| 280. C5 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611349 | 2 |
| C5×#2206 | 2 |
| #10602082 | 2 |
| #10602076 | 2 |
| #10598253 | 2 |
| #10598054 | 2 |
| #10598048 | 2 |
| #12348 | 5 |