Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
364 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
| 4. #65709 | C2 | semidirect |
| 6. #65703 | C2 | semidirect |
| 45. D5⋊C8 | Q8 | semidirect |
| 171. C5 | #2960 | 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 |
| #65709 | 2 |
| #65708 | 2 |
| #65703 | 2 |
| #65701 | 2 |
| #65681 | 2 |
| C4×D5⋊C8 | 2 |
| #2960 | 5 |