Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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. C5×#475 | C2 | semidirect |
| 4. #65368 | C2 | semidirect |
| 5. C4×#689 | C2 | semidirect |
| 6. #65151 | C2 | semidirect |
| 7. #65150 | C2 | semidirect |
| 8. #65139 | C2 | semidirect |
| 10. #65105 | C2 | semidirect |
| 11. #65103 | C2 | semidirect |
| 80. #475 | D5 | semidirect |
| 213. C5 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66066 | 2 |
| #65913 | 2 |
| C5×#475 | 2 |
| #65368 | 2 |
| C4×#689 | 2 |
| #65151 | 2 |
| #65150 | 2 |
| #65139 | 2 |
| #65127 | 2 |
| #65105 | 2 |
| #65103 | 2 |
| #3356 | 5 |