Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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. C5×#123 | C2 | semidirect |
| 3. #4075 | C2 | semidirect |
| 4. #3966 | C2 | semidirect |
| 5. #3938 | C2 | semidirect |
| 7. C22×C4×C5 | C22 | semidirect |
| 15. C5×C22⋊C4 | C22 | semidirect |
| 16. C22⋊Dic5 | C22 | semidirect |
| 40. #123 | D5 | semidirect |
| 62. C22×C4 | C2×D5 | semidirect |
| 68. C22⋊C4 | C2×D5 | semidirect |
| 92. C5 | #458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4144 | 2 |
| C5×#123 | 2 |
| #4075 | 2 |
| #3966 | 2 |
| #3938 | 2 |
| #458 | 5 |