Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
954 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 264 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 |
|---|---|---|
| 9. #65686 | C4 | semidirect |
| 10. C42×AGL(1,𝔽5) | C4 | semidirect |
| 11. C2×C5×#97 | C4 | semidirect |
| 12. C2×C8×Dic5 | C4 | semidirect |
| 13. C2×#3935 | C4 | semidirect |
| 15. #64895 | C4 | semidirect |
| 60. C4×AGL(1,𝔽5) | C42 | semidirect |
| 63. C2×C5×C8 | C42 | semidirect |
| 73. C2×#168 | C42 | semidirect |
| 80. C2×#97 | AGL(1,𝔽5) | semidirect |
| 146. Dic5 | H(3,ℤ/4) | semidirect |
| 167. C2×C8 | C4×AGL(1,𝔽5) | semidirect |
| 208. C5 | C4×H(3,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#4130 | 2 |
| C2×#64996 | 2 |
| C2×#64895 | 2 |
| C4×H(3,ℤ/4) | 5 |