Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C5×#495 | C2 | semidirect |
| 2. C2×#3961 | C2 | semidirect |
| 3. C2×#3960 | C2 | semidirect |
| 4. C2×#3959 | C2 | semidirect |
| 6. #64985 | C2 | semidirect |
| 7. C4×#672 | C2 | semidirect |
| 50. #495 | D5 | semidirect |
| 136. C5 | #2249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#495 | 2 |
| C2×#3961 | 2 |
| C2×#3960 | 2 |
| C2×#3959 | 2 |
| C2×#3958 | 2 |
| #64985 | 2 |
| C4×#672 | 2 |
| #2249 | 5 |