Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
356 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 145 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. C5×#500 | C2 | semidirect |
| 3. #65368 | C2 | semidirect |
| 5. #65167 | C2 | semidirect |
| 7. #64971 | C2 | semidirect |
| 44. C8×D5 | Q8 | semidirect |
| 47. #500 | D5 | semidirect |
| 136. C5 | #3160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| C5×#500 | 2 |
| #65368 | 2 |
| #65169 | 2 |
| #65167 | 2 |
| C4×C8×D5 | 2 |
| #64971 | 2 |
| #3160 | 5 |