Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. #66159 | C2 | semidirect |
| 3. C2×#4097 | C2 | semidirect |
| 4. C2×#4094 | C2 | semidirect |
| 5. #65522 | C2 | semidirect |
| 6. #65341 | C2 | semidirect |
| 7. #65340 | C2 | semidirect |
| 8. #65331 | C2 | semidirect |
| 9. #65330 | C2 | semidirect |
| 10. C2×#3942 | C2 | semidirect |
| 11. #65253 | C2 | semidirect |
| 80. #681 | D4 | semidirect |
| 261. C5 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#537 | 2 |
| #66159 | 2 |
| C2×#4097 | 2 |
| C2×#4094 | 2 |
| #65522 | 2 |
| #65341 | 2 |
| #65340 | 2 |
| #65331 | 2 |
| #65330 | 2 |
| C2×#3942 | 2 |
| #65253 | 2 |
| #3063 | 5 |