Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
736 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 218 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. C2×#4005 | C2 | direct (N × H) |
| 14. #4005 | C22 | direct (N × H) |
| 71. C22×C5 | #101 | semidirect |
| 101. C2×C5 | C2×#101 | semidirect |
| 122. C5 | C22×#101 | semidirect |
| 125. C22 | #4005 | direct (N × H) |
| 135. C2 | C2×#4005 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic10 | 2 |
| C22×#704 | 2 |
| C2×#4005 | 2 |
| C22×#101 | 5 |