Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
590 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 148 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. #10604948 | C2 | semidirect |
| 3. C2×D4⋊#170 | C2 | semidirect |
| 4. C2×#64881 | C2 | semidirect |
| 5. C2×#64879 | C2 | semidirect |
| 28. C2×C5×D8 | C8 | semidirect |
| 134. C5×C8 | C22⋊C8 | semidirect |
| 140. C2×D8 | #170 | semidirect |
| 256. C8 | C22⋊#170 | semidirect |
| 257. C5 | #9659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×Dic5 | 2 |
| #10604948 | 2 |
| C2×D4⋊#170 | 2 |
| C2×#64881 | 2 |
| C2×#64879 | 2 |
| #9659 | 5 |