Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 3. #65382 | C2 | semidirect |
| 4. #65381 | C2 | semidirect |
| 6. #65320 | C2 | semidirect |
| 71. C2×C4×C5 | Q16 | semidirect |
| 159. C2×C4 | #689 | semidirect |
| 167. C5 | #3209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#533 | 2 |
| C2×#4015 | 2 |
| #65382 | 2 |
| #65381 | 2 |
| #65339 | 2 |
| #65320 | 2 |
| #65214 | 2 |
| #3209 | 5 |