Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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×#4072 | C2 | semidirect |
| 3. C4×C5×C22⋊C4 | C2 | semidirect |
| 5. #65242 | C2 | semidirect |
| 6. C4×#685 | C2 | semidirect |
| 7. C4×C4⋊Dic5 | C2 | semidirect |
| 8. #64966 | C2 | semidirect |
| 9. #64963 | C2 | semidirect |
| 10. #64950 | C2 | semidirect |
| 11. #64948 | C2 | semidirect |
| 80. C4×C22⋊C4 | D5 | semidirect |
| 243. C5 | #2395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D5 | 2 |
| C2×#4072 | 2 |
| C4×C5×C22⋊C4 | 2 |
| #65250 | 2 |
| #65242 | 2 |
| C4×#685 | 2 |
| C4×C4⋊Dic5 | 2 |
| #64966 | 2 |
| #64963 | 2 |
| #64950 | 2 |
| #64948 | 2 |
| #2395 | 5 |