Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 154 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. #65708 | C2 | semidirect |
| 4. #65706 | C2 | semidirect |
| 5. #65684 | C2 | semidirect |
| 6. #65683 | C2 | semidirect |
| 7. C4×#700 | C2 | semidirect |
| 8. #65676 | C2 | semidirect |
| 187. C5 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#713 | 2 |
| #65787 | 2 |
| #65708 | 2 |
| #65706 | 2 |
| #65684 | 2 |
| #65683 | 2 |
| C4×#700 | 2 |
| #65676 | 2 |
| #2923 | 5 |