Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
368 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 89 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. #65501 | C2 | semidirect |
| 4. C2×#3953 | C2 | semidirect |
| 5. C2×#3953 | C2 | semidirect |
| 6. C2×#3950 | C2 | semidirect |
| 7. #64771 | C2 | semidirect |
| 53. C2×C5×C8 | D4 | semidirect |
| 66. C2×C22⋊C8 | D5 | semidirect |
| 186. C2×C8 | C22⋊D5 | semidirect |
| 248. C5 | #2033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4076 | 2 |
| C2×C5×C22⋊C8 | 2 |
| #65501 | 2 |
| C2×#3953 | 2 |
| C2×#3950 | 2 |
| #64771 | 2 |
| #2033 | 5 |