Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
488 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 4. #64875 | C2 | semidirect |
| 10. C2×C4×AGL(1,𝔽5) | C4 | semidirect |
| 13. D5⋊M16 | C4 | semidirect |
| 16. C5×#117 | C4 | semidirect |
| 17. #4072 | C4 | semidirect |
| 19. D5×C4⋊C4 | C4 | semidirect |
| 44. C4×AGL(1,𝔽5) | C2×C4 | semidirect |
| 46. #700 | C2×C4 | semidirect |
| 48. C5×C4⋊C4 | C2×C4 | semidirect |
| 53. C4⋊Dic5 | C2×C4 | semidirect |
| 103. #117 | AGL(1,𝔽5) | semidirect |
| 152. C4⋊C4 | C2×AGL(1,𝔽5) | semidirect |
| 167. D5 | #339 | semidirect |
| 199. C5 | C2×#339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×AGL(1,𝔽5) | 2 |
| C2×D5⋊M16 | 2 |
| D5×#117 | 2 |
| #64875 | 2 |
| C2×#339 | 5 |