Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
536 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10604731 | C2 | semidirect |
| 3. #10604719 | C2 | semidirect |
| 4. #10604300 | C2 | semidirect |
| 5. #10604258 | C2 | semidirect |
| 6. C22×D40 | C4 | semidirect |
| 14. C2×C5×#107 | C4 | semidirect |
| 15. C2×#3941 | C4 | semidirect |
| 116. C2×#107 | AGL(1,𝔽5) | semidirect |
| 311. C5 | #9818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65172 | 2 |
| #10604731 | 2 |
| #10604719 | 2 |
| #10604300 | 2 |
| #10604258 | 2 |
| #9818 | 5 |