Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
980 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#65500 | C2 | semidirect |
| 3. #10602919 | C2 | semidirect |
| 4. C2×#64757 | C2 | semidirect |
| 5. #10598115 | C2 | semidirect |
| 7. C2×C5×#121 | C4 | semidirect |
| 13. C5×#380 | C4 | semidirect |
| 51. #3963 | D4 | semidirect |
| 112. C2×#121 | Dic5 | semidirect |
| 121. #380 | Dic5 | semidirect |
| 364. C5 | #9158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2847 | 2 |
| C2×#65500 | 2 |
| #10602919 | 2 |
| C2×#64757 | 2 |
| #10598115 | 2 |
| #9158 | 5 |