Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
710 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 3. #10604897 | C2 | semidirect |
| 4. C4×C22⋊#170 | C2 | semidirect |
| 5. #10598821 | C2 | semidirect |
| 21. #64933 | C4 | semidirect |
| 407. C5 | #8155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65233 | 2 |
| C2×#64933 | 2 |
| #10604897 | 2 |
| C4×C22⋊#170 | 2 |
| #10598821 | 2 |
| #8155 | 5 |