Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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. #65517 | C2 | semidirect |
| 5. #65340 | C2 | semidirect |
| 6. #65339 | C2 | semidirect |
| 7. #65333 | C2 | semidirect |
| 8. #65259 | C2 | semidirect |
| 20. C2×#689 | C22 | semidirect |
| 28. #3967 | C22 | semidirect |
| 31. #3942 | C22 | semidirect |
| 32. #3939 | C22 | semidirect |
| 77. C23×C5 | Q16 | semidirect |
| 188. C23 | #689 | semidirect |
| 215. C5 | #3189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C22⋊Q8 | 2 |
| C2×#4070 | 2 |
| #65517 | 2 |
| C2×C22⋊#168 | 2 |
| #65340 | 2 |
| #65339 | 2 |
| #65333 | 2 |
| #65259 | 2 |
| #3189 | 5 |