Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 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. #4023 | C2 | semidirect |
| 3. C5×#99 | C2 | semidirect |
| 4. #3966 | C2 | semidirect |
| 5. #3938 | C2 | semidirect |
| 7. C2×C22⋊D5 | C4 | semidirect |
| 9. C22×Dic5 | C4 | semidirect |
| 13. C2×C4×D5 | C4 | semidirect |
| 14. C2×Dic10 | C4 | semidirect |
| 43. #99 | D5 | semidirect |
| 95. C5 | #410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#711 | 2 |
| #4023 | 2 |
| C5×#99 | 2 |
| #3966 | 2 |
| #3938 | 2 |
| #410 | 5 |