Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
878 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 111 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. #10614035 | C2 | semidirect |
| 3. #10602922 | C2 | semidirect |
| 4. #10602395 | C2 | semidirect |
| 5. #10598117 | C2 | semidirect |
| 49. C2×#681 | D4 | semidirect |
| 175. C2×C4×C5 | #100 | semidirect |
| 349. C2×C4 | #3965 | semidirect |
| 355. C5 | #9504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2408 | 2 |
| #10614035 | 2 |
| #10602922 | 2 |
| #10602395 | 2 |
| #10598117 | 2 |
| #9504 | 5 |