Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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. #64689 | C2 | semidirect |
| 5. #64688 | C2 | semidirect |
| 36. C2×C22⋊D5 | C8 | semidirect |
| 57. C2×C22⋊C8 | D5 | semidirect |
| 71. C22×D5 | C2×C8 | semidirect |
| 90. C2×Dic5 | C2×C8 | semidirect |
| 211. C5 | #1459 | 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 |
| #64689 | 2 |
| #64688 | 2 |
| #1459 | 5 |