Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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. #65426 | C2 | semidirect |
| 5. #65410 | C2 | semidirect |
| 6. #65140 | C2 | semidirect |
| 7. #65139 | C2 | semidirect |
| 8. #65012 | C2 | semidirect |
| 9. #65010 | C2 | semidirect |
| 10. C4×Dic20 | C2 | semidirect |
| 11. #64969 | C2 | semidirect |
| 213. C5 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65877 | 2 |
| #65876 | 2 |
| C5×#436 | 2 |
| #65426 | 2 |
| #65410 | 2 |
| #65140 | 2 |
| #65139 | 2 |
| #65012 | 2 |
| #65010 | 2 |
| C4×Dic20 | 2 |
| #64969 | 2 |
| #3356 | 5 |