Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
5990 conjugacy classes of subgroups; only the 699 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 699 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×#65496 | C2 | semidirect |
| 3. #10602919 | C2 | semidirect |
| 10. C22×#681 | C22 | semidirect |
| 12. C2×C22⋊#168 | C22 | semidirect |
| 31. C22×#168 | C23 | semidirect |
| 43. C24×C5 | M16 | semidirect |
| 123. C22×C5 | #407 | semidirect |
| 135. C24 | #681 | semidirect |
| 185. C5 | #20579 | semidirect |
| 192. C22 | #65496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4×C5 | 2 |
| C2×#65496 | 2 |
| #10602919 | 2 |
| #20579 | 5 |