Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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×#117 | C2 | semidirect |
| 3. #4072 | C2 | semidirect |
| 4. #3938 | C2 | semidirect |
| 11. C2×D20 | C4 | semidirect |
| 12. C2×C4×D5 | C4 | semidirect |
| 13. C2×Dic10 | C4 | semidirect |
| 42. #117 | D5 | semidirect |
| 96. C5 | #410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| C5×#117 | 2 |
| #4072 | 2 |
| #3938 | 2 |
| #410 | 5 |