Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
104 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 38 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. C3×C5×C22⋊C4 | C2 | semidirect |
| 3. C5×#217 | C2 | semidirect |
| 6. C22×C5×D3 | C4 | semidirect |
| 11. C2×C5×Dic3 | C4 | semidirect |
| 12. #806 | C5 | direct (N × H) |
| 15. C5×C22⋊C4 | D3 | semidirect |
| 26. C3×C22⋊C4 | C2×C5 | semidirect |
| 27. #217 | C2×C5 | semidirect |
| 42. C22×D3 | C4×C5 | semidirect |
| 47. C2×Dic3 | C4×C5 | semidirect |
| 59. C22⋊C4 | C5×D3 | semidirect |
| 60. C3×C5 | #99 | semidirect |
| 87. C5 | #806 | direct (N × H) |
| 97. C3 | C5×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#67 | 2 |
| C3×C5×C22⋊C4 | 2 |
| C5×#217 | 2 |
| C5×#99 | 3 |
| #806 | 5 |