Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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. #65912 | C2 | semidirect |
| 3. C5×#460 | C2 | semidirect |
| 4. #65460 | C2 | semidirect |
| 5. #65451 | C2 | semidirect |
| 6. #65364 | C2 | semidirect |
| 7. #65309 | C2 | semidirect |
| 8. #65140 | C2 | semidirect |
| 9. D5×C4⋊C8 | C2 | semidirect |
| 10. #65067 | C2 | semidirect |
| 11. #65050 | C2 | semidirect |
| 92. #460 | D5 | semidirect |
| 118. C4×D5 | SD16 | semidirect |
| 250. C5 | #3246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66050 | 2 |
| #65912 | 2 |
| C5×#460 | 2 |
| #65460 | 2 |
| #65451 | 2 |
| #65364 | 2 |
| #65309 | 2 |
| #65140 | 2 |
| D5×C4⋊C8 | 2 |
| #65067 | 2 |
| #65050 | 2 |
| #3246 | 5 |