Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
160 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 94 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. C4⋊#674 | C2 | semidirect |
| 4. C4×#674 | C2 | semidirect |
| 36. C2×C4×C5 | C16 | semidirect |
| 88. C2×C4 | #674 | semidirect |
| 99. C5 | #2162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#168 | 2 |
| C22⋊#674 | 2 |
| C4⋊#674 | 2 |
| C4×#674 | 2 |
| #2162 | 5 |