Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×C5×#365 | C2 | semidirect |
| 3. #10602243 | C2 | semidirect |
| 4. #10602231 | C2 | semidirect |
| 5. #10601512 | C2 | semidirect |
| 6. #10601480 | C2 | semidirect |
| 7. #10598212 | C2 | semidirect |
| 54. C5×M32 | D4 | semidirect |
| 69. C2×#365 | D5 | semidirect |
| 210. M32 | D20 | semidirect |
| 333. C5 | #13400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610851 | 2 |
| C2×C5×#365 | 2 |
| #10602243 | 2 |
| #10602231 | 2 |
| #10601512 | 2 |
| #10601480 | 2 |
| #10598212 | 2 |
| #13400 | 5 |