Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
378 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 378 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 |
|---|---|---|
| 1. #10611641 | C2 | semidirect |
| 2. C5×#1668 | C2 | semidirect |
| 3. #10602086 | C2 | semidirect |
| 4. #10602083 | C2 | semidirect |
| 5. Q8⋊#672 | C2 | semidirect |
| 6. #10597964 | C2 | semidirect |
| 7. #10597962 | C2 | semidirect |
| 58. #1668 | D5 | semidirect |
| 120. C5×Q8 | D16 | semidirect |
| 243. Q8 | #3958 | semidirect |
| 272. C5 | #12328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611641 | 2 |
| C5×#1668 | 2 |
| #10602086 | 2 |
| #10602083 | 2 |
| Q8⋊#672 | 2 |
| #10597964 | 2 |
| #10597962 | 2 |
| #12328 | 5 |