Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
216 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 58 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. #65683 | C2 | semidirect |
| 3. C4×#700 | C2 | semidirect |
| 4. #64927 | C2 | semidirect |
| 5. #64870 | C2 | semidirect |
| 159. C5 | #1529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65914 | 2 |
| #65683 | 2 |
| C4×#700 | 2 |
| #64927 | 2 |
| #64870 | 2 |
| #1529 | 5 |