Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
230 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 64 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. #65759 | C2 | semidirect |
| 3. C2×C4×#170 | C2 | semidirect |
| 4. Q8⋊#170 | C2 | semidirect |
| 5. #64871 | C2 | semidirect |
| 159. C5 | #1494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65958 | 2 |
| #65759 | 2 |
| C2×C4×#170 | 2 |
| Q8⋊#170 | 2 |
| #64871 | 2 |
| #1494 | 5 |