Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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×#3967 | C2 | semidirect |
| 4. #65225 | C2 | semidirect |
| 5. C2×C4×#168 | C2 | semidirect |
| 9. C5×#124 | C4 | semidirect |
| 70. #124 | Dic5 | semidirect |
| 138. C5 | #1958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#124 | 2 |
| C2×#3967 | 2 |
| C2×#3964 | 2 |
| #65225 | 2 |
| C2×C4×#168 | 2 |
| #1958 | 5 |