Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 3. C4×Dic10 | C2 | semidirect |
| 5. #3942 | C2 | semidirect |
| 6. #3939 | C2 | semidirect |
| 7. #3935 | C2 | semidirect |
| 14. #687 | C4 | semidirect |
| 32. Dic10 | C2×C4 | semidirect |
| 34. #168 | C2×C4 | semidirect |
| 83. C5 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D4 | 2 |
| C2×#687 | 2 |
| C4×Dic10 | 2 |
| #3964 | 2 |
| #3942 | 2 |
| #3939 | 2 |
| #3935 | 2 |
| #440 | 5 |