Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 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×C5×C22⋊C8 | C2 | semidirect |
| 3. C2×C22⋊#168 | C2 | semidirect |
| 4. C2×#3952 | C2 | semidirect |
| 5. C2×#3952 | C2 | semidirect |
| 6. C2×#3947 | C2 | semidirect |
| 7. C2×#3946 | C2 | semidirect |
| 55. C2×C5×C8 | D4 | semidirect |
| 66. C2×#168 | D4 | semidirect |
| 72. C2×C22⋊C8 | D5 | semidirect |
| 201. C2×C8 | C22⋊D5 | semidirect |
| 262. C5 | #1955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D5 | 2 |
| C2×C5×C22⋊C8 | 2 |
| C2×C22⋊#168 | 2 |
| C2×#3952 | 2 |
| C2×#3947 | 2 |
| C2×#3946 | 2 |
| #1955 | 5 |