Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2014 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 2014 conjugacy classes of subgroups — too many to draw. Only its 288 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×#65686 | C2 | semidirect |
| 3. #10604988 | C2 | semidirect |
| 5. #10604253 | C2 | semidirect |
| 10. C2×C5×#124 | C4 | semidirect |
| 11. C2×#4093 | C4 | semidirect |
| 12. C2×#4082 | C4 | semidirect |
| 14. C2×#4031 | C4 | semidirect |
| 16. C2×#4021 | C4 | semidirect |
| 106. C42×C5 | C22⋊C4 | semidirect |
| 110. C4×Dic5 | C22⋊C4 | semidirect |
| 111. C4×Dic5 | C22⋊C4 | semidirect |
| 119. C2×#124 | AGL(1,𝔽5) | semidirect |
| 276. C42 | C22⋊AGL(1,𝔽5) | semidirect |
| 326. C5 | #14169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#124 | 2 |
| C2×#65686 | 2 |
| #10604988 | 2 |
| #10604954 | 2 |
| #10604253 | 2 |
| #14169 | 5 |