Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
336 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. C2×#4002 | C2 | semidirect |
| 4. C2×C4×#170 | C2 | semidirect |
| 5. #64918 | C2 | semidirect |
| 17. #4003 | C4 | semidirect |
| 163. C5 | #1750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4038 | 2 |
| C2×#4003 | 2 |
| C2×#4002 | 2 |
| C2×C4×#170 | 2 |
| #64918 | 2 |
| #1750 | 5 |