Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
104 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 34 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. #6719 | C2 | semidirect |
| 3. C5×#217 | C2 | semidirect |
| 6. C22×C3×D5 | C4 | semidirect |
| 11. C2×C3×Dic5 | C4 | semidirect |
| 27. #217 | D5 | semidirect |
| 29. C22×D5 | Dic3 | semidirect |
| 34. C2×Dic5 | Dic3 | semidirect |
| 60. C3×C5 | #99 | semidirect |
| 87. C5 | #834 | semidirect |
| 97. C3 | #3938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊D5 | 2 |
| #6719 | 2 |
| C5×#217 | 2 |
| #3938 | 3 |
| #834 | 5 |