Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
152 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 47 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×#689 | C2 | semidirect |
| 3. C2×#687 | C2 | semidirect |
| 4. #4070 | C2 | semidirect |
| 5. #3967 | C2 | semidirect |
| 6. #3964 | C2 | semidirect |
| 7. C22⋊#168 | C2 | semidirect |
| 102. C5 | #452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#41 | 2 |
| C2×#689 | 2 |
| C2×#687 | 2 |
| #4070 | 2 |
| #3967 | 2 |
| #3964 | 2 |
| C22⋊#168 | 2 |
| #452 | 5 |