Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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×#2127 | C2 | semidirect |
| 3. #10602655 | C2 | semidirect |
| 4. #10598035 | C2 | semidirect |
| 5. #10598034 | C2 | semidirect |
| 7. #65869 | C4 | semidirect |
| 12. #65362 | C4 | semidirect |
| 14. #65360 | C4 | semidirect |
| 18. #65289 | C4 | semidirect |
| 42. #4020 | C2×C4 | semidirect |
| 44. #4016 | C2×C4 | semidirect |
| 55. #3935 | C2×C4 | semidirect |
| 56. C4×#168 | C2×C4 | semidirect |
| 59. #2127 | D5 | semidirect |
| 288. C5 | #13605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615119 | 2 |
| C5×#2127 | 2 |
| #10602655 | 2 |
| #10598035 | 2 |
| #10598034 | 2 |
| #13605 | 5 |