Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
484 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 3. #65711 | C2 | semidirect |
| 5. #65689 | C2 | semidirect |
| 6. #65688 | C2 | semidirect |
| 7. C4×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 14. C5×#117 | C4 | semidirect |
| 15. #4072 | C4 | semidirect |
| 16. #4038 | C4 | semidirect |
| 19. #4023 | C4 | semidirect |
| 20. #4018 | C4 | semidirect |
| 21. #4018 | C4 | semidirect |
| 106. #117 | AGL(1,𝔽5) | semidirect |
| 213. C5 | #2314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#117 | 2 |
| #65765 | 2 |
| #65711 | 2 |
| #65700 | 2 |
| #65689 | 2 |
| #65688 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 2 |
| #2314 | 5 |