Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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. #10602209 | C2 | semidirect |
| 3. C2×Dic80 | C2 | semidirect |
| 4. C2×#64669 | C2 | semidirect |
| 5. C5×C22⋊C32 | C2 | semidirect |
| 6. #10598088 | C2 | semidirect |
| 7. #10598087 | C2 | semidirect |
| 54. C22⋊C32 | D5 | semidirect |
| 202. C5 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65193 | 2 |
| #10602209 | 2 |
| C2×Dic80 | 2 |
| C2×#64669 | 2 |
| C5×C22⋊C32 | 2 |
| #10598088 | 2 |
| #10598087 | 2 |
| #13666 | 5 |