Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1958 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1958 conjugacy classes of subgroups — too many to draw. Only its 587 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×#65273 | C2 | semidirect |
| 5. #10609825 | C2 | direct (N × H) |
| 6. C2×C5⋊#401 | C2 | semidirect |
| 18. #65273 | C22 | semidirect |
| 21. C5⋊#401 | C22 | semidirect |
| 172. C2×C5 | #2834 | semidirect |
| 199. C5 | C2×#2834 | semidirect |
| 215. C2 | #10609825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#399 | 2 |
| C2×#65273 | 2 |
| C2×#65242 | 2 |
| C2×#65235 | 2 |
| #10609825 | 2 |
| C2×C5⋊#401 | 2 |
| C2×#2834 | 5 |