Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
406 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 87 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. #10602233 | C2 | semidirect |
| 3. #10602231 | C2 | semidirect |
| 4. #10601478 | C2 | semidirect |
| 5. #10601457 | C2 | semidirect |
| 6. #10601445 | C2 | semidirect |
| 7. C5×#1389 | C2 | semidirect |
| 69. #1389 | D5 | semidirect |
| 305. C5 | #13404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65186 | 2 |
| #10602233 | 2 |
| #10602231 | 2 |
| #10601478 | 2 |
| #10601457 | 2 |
| #10601445 | 2 |
| C5×#1389 | 2 |
| #13404 | 5 |