Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. C2×#3950 | C2 | semidirect |
| 5. C2×#3948 | C2 | semidirect |
| 6. C2×#3948 | C2 | semidirect |
| 7. #64771 | C2 | semidirect |
| 227. C5 | #2036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4070 | 2 |
| C2×C5×C22⋊C8 | 2 |
| #65501 | 2 |
| C2×#3950 | 2 |
| C2×#3948 | 2 |
| #64771 | 2 |
| #2036 | 5 |