Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. D5×C4⋊Q8 | C2 | semidirect |
| 3. C5×#474 | C2 | semidirect |
| 4. #65376 | C2 | semidirect |
| 5. #65296 | C2 | semidirect |
| 6. #65171 | C2 | semidirect |
| 7. #65163 | C2 | semidirect |
| 8. #65135 | C2 | semidirect |
| 9. #65122 | C2 | semidirect |
| 10. #65063 | C2 | semidirect |
| 11. #65049 | C2 | semidirect |
| 90. #474 | D5 | semidirect |
| 255. C5 | #3226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C4⋊Q8 | 2 |
| #65882 | 2 |
| C5×#474 | 2 |
| #65376 | 2 |
| #65296 | 2 |
| #65171 | 2 |
| #65163 | 2 |
| #65135 | 2 |
| #65122 | 2 |
| #65063 | 2 |
| #65049 | 2 |
| #3226 | 5 |