Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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×#354 | C2 | semidirect |
| 3. C2×#64762 | C2 | semidirect |
| 4. #10598036 | C2 | semidirect |
| 5. #10598035 | C2 | semidirect |
| 9. #65811 | C4 | semidirect |
| 12. #65349 | C4 | semidirect |
| 16. #65347 | C4 | semidirect |
| 18. C4×#681 | C4 | semidirect |
| 51. #4020 | C2×C4 | semidirect |
| 53. #4015 | C2×C4 | semidirect |
| 58. #3935 | C2×C4 | semidirect |
| 59. #3935 | C2×C4 | semidirect |
| 63. C2×#354 | D5 | semidirect |
| 325. C5 | #13578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614674 | 2 |
| C2×C5×#354 | 2 |
| C2×#64762 | 2 |
| #10598036 | 2 |
| #10598035 | 2 |
| #13578 | 5 |