Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1526 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1526 conjugacy classes of subgroups — too many to draw. Only its 360 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 |
|---|---|---|
| 3. C2×#64918 | C2 | semidirect |
| 4. #10604229 | C2 | direct (N × H) |
| 16. #64918 | C22 | semidirect |
| 187. C2×C5 | #1818 | semidirect |
| 218. C5 | C2×#1818 | semidirect |
| 235. C2 | #10604229 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4023 | 2 |
| C22×C22⋊#170 | 2 |
| C2×#64918 | 2 |
| #10604229 | 2 |
| C2×#1818 | 5 |