Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1250 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 344 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 |
|---|---|---|
| 3. #10604226 | C2 | semidirect |
| 4. C22⋊C4×#170 | C2 | semidirect |
| 5. #10604224 | C2 | semidirect |
| 9. C2×C22⋊#170 | C4 | semidirect |
| 13. C2×#4002 | C22 | semidirect |
| 14. C2×C4×#170 | C22 | semidirect |
| 20. #64918 | C22 | semidirect |
| 231. C5 | #20528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#170 | 2 |
| #10605548 | 2 |
| #10604226 | 2 |
| C22⋊C4×#170 | 2 |
| #10604224 | 2 |
| #20528 | 5 |