Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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×#3959 | C2 | semidirect |
| 3. C2×Dic40 | C2 | semidirect |
| 4. #65176 | C2 | semidirect |
| 5. C5×#357 | C2 | semidirect |
| 6. #64727 | C2 | semidirect |
| 7. #64712 | C2 | semidirect |
| 53. #357 | D5 | semidirect |
| 152. C5 | #2189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4058 | 2 |
| C2×#3959 | 2 |
| C2×Dic40 | 2 |
| #65176 | 2 |
| C5×#357 | 2 |
| #64727 | 2 |
| #64712 | 2 |
| #2189 | 5 |