Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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. #64972 | C2 | semidirect |
| 4. #64714 | C2 | semidirect |
| 5. #64683 | C2 | semidirect |
| 90. C5 | #2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#443 | 2 |
| #64972 | 2 |
| #64786 | 2 |
| #64714 | 2 |
| #64683 | 2 |
| #2231 | 5 |