Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3798 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 555 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. #10615817 | C2 | semidirect |
| 3. C2×#65529 | C2 | semidirect |
| 4. #10602935 | C2 | semidirect |
| 6. C5×#585 | C4 | semidirect |
| 12. C2×#4072 | C22 | semidirect |
| 13. C22×C4×Dic5 | C22 | semidirect |
| 17. #65509 | C22 | semidirect |
| 18. C2×#3966 | C22 | semidirect |
| 75. C2×C5×Q8 | C22⋊C4 | semidirect |
| 84. C2×C5×D4 | C22⋊C4 | semidirect |
| 92. C22×C4×C5 | C22⋊C4 | semidirect |
| 108. #585 | Dic5 | semidirect |
| 221. C2×Q8 | C22⋊Dic5 | semidirect |
| 230. C2×D4 | C22⋊Dic5 | semidirect |
| 241. C22×C4 | C22⋊Dic5 | semidirect |
| 291. C5 | #20608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#585 | 2 |
| #10615817 | 2 |
| C2×#65529 | 2 |
| #10602935 | 2 |
| #20608 | 5 |