Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
496 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 113 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. #10602238 | C2 | semidirect |
| 5. #10601503 | C2 | semidirect |
| 6. #10598306 | C2 | semidirect |
| 7. #10598220 | C2 | semidirect |
| 18. C2×#3959 | C4 | semidirect |
| 48. C2×Dic20 | C2×C4 | semidirect |
| 64. C2×#672 | C2×C4 | semidirect |
| 300. C5 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615554 | 2 |
| C22×#3959 | 2 |
| C2×C5×#361 | 2 |
| #10602238 | 2 |
| #10601503 | 2 |
| #10598306 | 2 |
| #10598220 | 2 |
| #13019 | 5 |