Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1038 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 167 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×#2112 | C2 | semidirect |
| 3. #10602756 | C2 | semidirect |
| 4. C2×#64734 | C2 | semidirect |
| 13. C2×C5×M32 | C22 | semidirect |
| 14. C2×#3944 | C22 | semidirect |
| 52. #2112 | D5 | semidirect |
| 104. C2×M32 | C2×D5 | semidirect |
| 176. C22×C5 | #349 | semidirect |
| 270. C5 | #12681 | semidirect |
| 280. C22 | #64734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#676 | 2 |
| C5×#2112 | 2 |
| #10602756 | 2 |
| C2×#64734 | 2 |
| #12681 | 5 |