Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4009 | C2 | semidirect |
| 4. #65688 | C2 | semidirect |
| 5. #65676 | C2 | semidirect |
| 11. C5×#124 | C4 | semidirect |
| 12. #4093 | C4 | semidirect |
| 13. #4082 | C4 | semidirect |
| 16. #4021 | C4 | semidirect |
| 90. #124 | AGL(1,𝔽5) | semidirect |
| 180. C5 | #1959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#124 | 2 |
| C2×#4009 | 2 |
| C2×#4007 | 2 |
| #65688 | 2 |
| #65676 | 2 |
| #1959 | 5 |