Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
558 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×#3944 | C2 | semidirect |
| 3. C5×#1808 | C2 | semidirect |
| 4. C2×#64711 | C2 | semidirect |
| 5. #10598213 | C2 | semidirect |
| 12. #65404 | C4 | semidirect |
| 49. C2×#672 | D4 | semidirect |
| 53. #1808 | D5 | semidirect |
| 262. C5 | #13061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65404 | 2 |
| C22×#3944 | 2 |
| C5×#1808 | 2 |
| C2×#64711 | 2 |
| #10598213 | 2 |
| #13061 | 5 |