Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
302 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 107 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×C5×#366 | C2 | semidirect |
| 3. C2×#64719 | C2 | semidirect |
| 4. #10598069 | C2 | semidirect |
| 5. #10598068 | C2 | semidirect |
| 11. #65193 | C4 | semidirect |
| 34. Dic40 | C2×C4 | semidirect |
| 37. D80 | C2×C4 | semidirect |
| 41. C2×#366 | D5 | semidirect |
| 173. C5 | #13616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65193 | 2 |
| C2×C5×#366 | 2 |
| C2×#64719 | 2 |
| #10598069 | 2 |
| #10598068 | 2 |
| #13616 | 5 |