Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
204 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 1. C2×#64877 | C2 | semidirect |
| 2. C22×#3928 | C2 | semidirect |
| 4. C22⋊#3928 | C2 | semidirect |
| 5. C22⋊#3928 | C2 | semidirect |
| 6. C4⋊#3928 | C2 | semidirect |
| 7. #10598535 | C2 | semidirect |
| 40. #3928 | D4 | semidirect |
| 122. C22×C5 | M64 | semidirect |
| 172. C5 | #13645 | semidirect |
| 178. C22 | #64877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64877 | 2 |
| C22×#3928 | 2 |
| D4×#672 | 2 |
| C22⋊#3928 | 2 |
| C4⋊#3928 | 2 |
| #10598535 | 2 |
| #13645 | 5 |