Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 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. C5×#2161 | C2 | semidirect |
| 3. C2×#64738 | C2 | semidirect |
| 4. #10602228 | C2 | semidirect |
| 5. #10601513 | C2 | semidirect |
| 6. #10601480 | C2 | semidirect |
| 7. #10598221 | C2 | semidirect |
| 70. #2161 | D5 | semidirect |
| 331. C5 | #13391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610987 | 2 |
| C5×#2161 | 2 |
| C2×#64738 | 2 |
| #10602228 | 2 |
| #10601513 | 2 |
| #10601480 | 2 |
| #10598221 | 2 |
| #13391 | 5 |