Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. C2×#4015 | C2 | semidirect |
| 3. #65358 | C2 | semidirect |
| 4. #65349 | C2 | semidirect |
| 5. #65339 | C2 | semidirect |
| 7. #65320 | C2 | semidirect |
| 8. #65308 | C2 | semidirect |
| 9. #65215 | C2 | semidirect |
| 208. C5 | #3218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#529 | 2 |
| C2×#4015 | 2 |
| #65358 | 2 |
| #65349 | 2 |
| #65339 | 2 |
| #65329 | 2 |
| #65320 | 2 |
| #65308 | 2 |
| #65215 | 2 |
| #3218 | 5 |