Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
| 4. C4×Dic10 | C2 | semidirect |
| 5. #3967 | C2 | semidirect |
| 7. C4⋊#168 | C2 | semidirect |
| 87. C5 | #464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#124 | 2 |
| C2×#689 | 2 |
| C2×#687 | 2 |
| C4×Dic10 | 2 |
| #3967 | 2 |
| #3964 | 2 |
| C4⋊#168 | 2 |
| #464 | 5 |