Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
610 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10604953 | C2 | semidirect |
| 3. #10604926 | C2 | semidirect |
| 4. #10604697 | C2 | semidirect |
| 5. C8×#704 | C2 | semidirect |
| 86. #704 | D8 | semidirect |
| 159. C5×C8 | #100 | semidirect |
| 161. #168 | #100 | semidirect |
| 301. C8 | #4013 | semidirect |
| 302. C5 | #9802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65440 | 2 |
| #10604953 | 2 |
| #10604926 | 2 |
| #10604697 | 2 |
| C8×#704 | 2 |
| #9802 | 5 |