Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×#64889 | C2 | semidirect |
| 3. #10604687 | C2 | semidirect |
| 4. #10598623 | C2 | semidirect |
| 17. #64889 | C22 | semidirect |
| 19. C8×#170 | C22 | semidirect |
| 30. C2×Dic20 | C8 | semidirect |
| 33. #4050 | C8 | semidirect |
| 35. C2×D40 | C8 | semidirect |
| 262. C5 | #11602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65184 | 2 |
| C2×#64889 | 2 |
| #10604687 | 2 |
| #10598623 | 2 |
| #11602 | 5 |