Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
548 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 99 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. C5×#1507 | C2 | semidirect |
| 3. #10602469 | C2 | semidirect |
| 4. #10600775 | C2 | semidirect |
| 5. #10600763 | C2 | semidirect |
| 6. C22⋊C4×#168 | C2 | semidirect |
| 7. #10600237 | C2 | semidirect |
| 9. C22×#686 | C4 | semidirect |
| 14. C2×#3964 | C4 | semidirect |
| 22. C2×#3941 | C4 | semidirect |
| 23. C2×#3939 | C4 | semidirect |
| 83. #1507 | D5 | semidirect |
| 413. C5 | #9815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65327 | 2 |
| C5×#1507 | 2 |
| #10602469 | 2 |
| #10600775 | 2 |
| #10600763 | 2 |
| C22⋊C4×#168 | 2 |
| #10600237 | 2 |
| #9815 | 5 |