Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
936 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 148 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. #10604872 | C2 | semidirect |
| 3. C2×C22⋊#674 | C2 | semidirect |
| 4. C2×#64898 | C2 | semidirect |
| 15. C2×#3998 | C22 | semidirect |
| 16. C22×#674 | C22 | semidirect |
| 224. C22×C5 | #350 | semidirect |
| 340. C5 | #12683 | semidirect |
| 353. C22 | #64898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4053 | 2 |
| #10604872 | 2 |
| C2×C22⋊#674 | 2 |
| C2×#64898 | 2 |
| #12683 | 5 |