Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 294 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×#1674 | C2 | semidirect |
| 4. #10602175 | C2 | semidirect |
| 5. Q8⋊#672 | C2 | semidirect |
| 6. #10597965 | C2 | semidirect |
| 56. #1674 | D5 | semidirect |
| 234. C5 | #12383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611643 | 2 |
| C5×#1674 | 2 |
| #10602180 | 2 |
| #10602175 | 2 |
| Q8⋊#672 | 2 |
| #10597965 | 2 |
| #10597962 | 2 |
| #12383 | 5 |