Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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×#687 | C2 | semidirect |
| 3. #4070 | C2 | semidirect |
| 4. #3964 | C2 | semidirect |
| 5. C22⋊#168 | C2 | semidirect |
| 11. C2×Dic10 | C22 | semidirect |
| 14. C4⋊Dic5 | C22 | semidirect |
| 16. C2×#168 | C22 | semidirect |
| 44. C22×C5 | SD16 | semidirect |
| 81. C5 | #450 | semidirect |
| 88. C22 | #687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D4 | 2 |
| C2×#687 | 2 |
| #4070 | 2 |
| #3964 | 2 |
| C22⋊#168 | 2 |
| #450 | 5 |