Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10605363 | C2 | semidirect |
| 3. C5×#1980 | C2 | semidirect |
| 4. #10602606 | C2 | semidirect |
| 5. #10600653 | C2 | semidirect |
| 6. #10598157 | C2 | semidirect |
| 7. #10598112 | C2 | semidirect |
| 14. #65378 | C4 | semidirect |
| 15. #65363 | C4 | semidirect |
| 37. C5×C4⋊Q8 | C2×C4 | semidirect |
| 38. C5×#127 | C2×C4 | semidirect |
| 79. #3935 | C2×C4 | semidirect |
| 82. #1980 | D5 | semidirect |
| 225. C4⋊Q8 | C4×D5 | semidirect |
| 226. #127 | C4×D5 | semidirect |
| 408. C5 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615037 | 2 |
| #10605363 | 2 |
| C5×#1980 | 2 |
| #10602606 | 2 |
| #10600653 | 2 |
| #10598157 | 2 |
| #10598112 | 2 |
| #9381 | 5 |