Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
614 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 117 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×#65444 | C2 | semidirect |
| 3. C22×#3959 | C2 | semidirect |
| 4. #10602831 | C2 | semidirect |
| 5. C2×#64782 | C2 | semidirect |
| 6. C2×#64723 | C2 | semidirect |
| 7. #10598295 | C2 | semidirect |
| 369. C5 | #13326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D16 | 2 |
| C2×#65444 | 2 |
| C22×#3959 | 2 |
| #10602831 | 2 |
| C2×#64782 | 2 |
| C2×#64723 | 2 |
| #10598295 | 2 |
| #13326 | 5 |