Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
356 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 3. C5×#477 | C2 | semidirect |
| 4. #65367 | C2 | semidirect |
| 5. C4×#689 | C2 | semidirect |
| 6. #65173 | C2 | semidirect |
| 7. D5×#107 | C2 | semidirect |
| 8. #65139 | C2 | semidirect |
| 10. #65102 | C2 | semidirect |
| 11. #65098 | C2 | semidirect |
| 80. #477 | D5 | semidirect |
| 99. D20 | Q16 | semidirect |
| 215. C5 | #3338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66064 | 2 |
| #65913 | 2 |
| C5×#477 | 2 |
| #65367 | 2 |
| C4×#689 | 2 |
| #65173 | 2 |
| D5×#107 | 2 |
| #65139 | 2 |
| #65123 | 2 |
| #65102 | 2 |
| #65098 | 2 |
| #3338 | 5 |