Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
774 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 204 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. C2×#4133 | C2 | semidirect |
| 3. #65776 | C2 | semidirect |
| 4. #65756 | C2 | semidirect |
| 5. D5⋊(C22⋊C8) | C2 | semidirect |
| 15. C2×#700 | C22 | semidirect |
| 16. C2×D5⋊C8 | C22 | semidirect |
| 17. C22⋊#170 | C22 | semidirect |
| 18. C22⋊#170 | C22 | semidirect |
| 98. C2×D5 | #131 | semidirect |
| 155. C5 | #2880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#41 | 2 |
| C2×#4133 | 2 |
| #65776 | 2 |
| #65756 | 2 |
| D5⋊(C22⋊C8) | 2 |
| #2880 | 5 |