Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 4. #10602222 | C2 | semidirect |
| 5. #10601456 | C2 | semidirect |
| 6. #10598303 | C2 | semidirect |
| 7. #10598218 | C2 | semidirect |
| 20. C5×#360 | C4 | semidirect |
| 119. #360 | Dic5 | semidirect |
| 268. C5 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65486 | 2 |
| C5×#2145 | 2 |
| #10602873 | 2 |
| #10602222 | 2 |
| #10601456 | 2 |
| #10598303 | 2 |
| #10598218 | 2 |
| #12944 | 5 |