Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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×#4097 | C2 | semidirect |
| 3. C2×#4015 | C2 | semidirect |
| 4. #65381 | C2 | semidirect |
| 5. #65365 | C2 | semidirect |
| 6. #65349 | C2 | semidirect |
| 7. C4×#681 | C2 | semidirect |
| 48. #681 | D4 | semidirect |
| 102. C4×C5 | #137 | semidirect |
| 151. C5 | #3152 | semidirect |
| 161. C4 | #4097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#532 | 2 |
| C2×#4097 | 2 |
| C2×#4015 | 2 |
| #65381 | 2 |
| #65365 | 2 |
| #65349 | 2 |
| C4×#681 | 2 |
| #3152 | 5 |