Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 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×Q8×Dic5 | C2 | semidirect |
| 4. #65519 | C2 | semidirect |
| 6. #65240 | C2 | semidirect |
| 7. #65239 | C2 | semidirect |
| 8. #65224 | C2 | semidirect |
| 9. #65221 | C2 | semidirect |
| 13. C5×#124 | C4 | semidirect |
| 34. C2×C5×Q8 | C2×C4 | semidirect |
| 48. C5×C22⋊C4 | C2×C4 | semidirect |
| 49. C42×C5 | C2×C4 | semidirect |
| 100. #124 | Dic5 | semidirect |
| 138. C2×Q8 | C2×Dic5 | semidirect |
| 158. C22⋊C4 | C2×Dic5 | semidirect |
| 162. C42 | C2×Dic5 | semidirect |
| 198. C5 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#124 | 2 |
| C2×Q8×Dic5 | 2 |
| C2×D4×Dic5 | 2 |
| #65519 | 2 |
| #65510 | 2 |
| #65240 | 2 |
| #65239 | 2 |
| #65224 | 2 |
| #65221 | 2 |
| #2326 | 5 |