Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
356 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 166 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. #65788 | C2 | semidirect |
| 3. Q8×#170 | C2 | semidirect |
| 5. #65707 | C2 | semidirect |
| 41. #700 | Q8 | semidirect |
| 163. C5 | #2962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| #65788 | 2 |
| Q8×#170 | 2 |
| #65708 | 2 |
| #65707 | 2 |
| #65701 | 2 |
| D5⋊(C4⋊C8) | 2 |
| C4×#700 | 2 |
| #2962 | 5 |