Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10605482 | C2 | semidirect |
| 3. C5×#1980 | C2 | semidirect |
| 4. #10602605 | C2 | semidirect |
| 5. #10600648 | C2 | semidirect |
| 6. #10598156 | C2 | semidirect |
| 7. #10598112 | C2 | semidirect |
| 14. #65373 | C4 | semidirect |
| 15. #65361 | C4 | semidirect |
| 35. C5×C4⋊Q8 | C2×C4 | semidirect |
| 36. C5×#127 | C2×C4 | semidirect |
| 70. C4⋊#168 | C2×C4 | semidirect |
| 75. #1980 | D5 | semidirect |
| 187. D20 | #104 | semidirect |
| 200. C4⋊Q8 | C4×D5 | semidirect |
| 201. #127 | C4×D5 | semidirect |
| 361. C5 | #9325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615031 | 2 |
| #10605482 | 2 |
| C5×#1980 | 2 |
| #10602605 | 2 |
| #10600648 | 2 |
| #10598156 | 2 |
| #10598112 | 2 |
| #9325 | 5 |