Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
538 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 538 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 |
|---|---|---|
| 1. C2×#65731 | C2 | semidirect |
| 3. #10604798 | C2 | semidirect |
| 4. C2×#64906 | C2 | semidirect |
| 5. C2×#64903 | C2 | semidirect |
| 6. #10598663 | C2 | semidirect |
| 7. #10598660 | C2 | semidirect |
| 20. C2×C5×D16 | C4 | semidirect |
| 21. C2×#3959 | C4 | semidirect |
| 22. C2×#3958 | C4 | semidirect |
| 25. C2×#3932 | C4 | semidirect |
| 41. C2×C5×D8 | C2×C4 | semidirect |
| 52. C2×Dic20 | C2×C4 | semidirect |
| 68. C2×C5×C16 | C2×C4 | semidirect |
| 71. C2×#672 | C2×C4 | semidirect |
| 144. C2×D16 | AGL(1,𝔽5) | semidirect |
| 217. C2×D8 | C2×AGL(1,𝔽5) | semidirect |
| 236. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 377. C5 | #13037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65731 | 2 |
| C2×#65200 | 2 |
| #10604798 | 2 |
| C2×#64906 | 2 |
| C2×#64903 | 2 |
| #10598663 | 2 |
| #10598660 | 2 |
| #13037 | 5 |