Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1870 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 1870 conjugacy classes of subgroups — too many to draw. Only its 256 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×#65757 | C2 | semidirect |
| 3. #10604927 | C2 | direct (N × H) |
| 4. C2×#64925 | C2 | semidirect |
| 17. #65757 | C22 | semidirect |
| 18. C2×#4004 | C22 | semidirect |
| 20. #64925 | C22 | semidirect |
| 57. #4004 | C23 | semidirect |
| 276. C2×C5 | #1555 | semidirect |
| 320. C5 | C2×#1555 | semidirect |
| 344. C2 | #10604927 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4086 | 2 |
| C2×#65757 | 2 |
| #10604927 | 2 |
| C2×#64925 | 2 |
| C2×#1555 | 5 |