Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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. #65382 | C2 | semidirect |
| 4. #65365 | C2 | semidirect |
| 5. #65329 | C2 | semidirect |
| 6. #65308 | C2 | semidirect |
| 7. #65214 | C2 | semidirect |
| 76. C2×C4×C5 | SD16 | semidirect |
| 172. C2×C4 | #687 | semidirect |
| 180. C5 | #3206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#532 | 2 |
| C2×#4015 | 2 |
| #65382 | 2 |
| #65365 | 2 |
| #65329 | 2 |
| #65308 | 2 |
| #65214 | 2 |
| #3206 | 5 |