Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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×#498 | C2 | semidirect |
| 4. #65383 | C2 | semidirect |
| 5. #65380 | C2 | semidirect |
| 6. #65157 | C2 | semidirect |
| 7. #65156 | C2 | semidirect |
| 8. #65151 | C2 | semidirect |
| 9. #65150 | C2 | semidirect |
| 10. C4×Dic20 | C2 | semidirect |
| 76. #498 | 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 |
| #66064 | 2 |
| C5×#498 | 2 |
| #65383 | 2 |
| #65380 | 2 |
| #65157 | 2 |
| #65156 | 2 |
| #65151 | 2 |
| #65150 | 2 |
| C4×Dic20 | 2 |
| #64977 | 2 |
| #3356 | 5 |