Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
264 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 100 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. C22×Dic15 | C2 | semidirect |
| 3. C22×C3×Dic5 | C2 | semidirect |
| 4. (C2×D3)⋊Dic5 | C2 | direct (N × H) |
| 9. C22×C5×D3 | C4 | semidirect |
| 12. C2×Dic15 | C22 | semidirect |
| 14. C2×C3×Dic5 | C22 | semidirect |
| 18. C22×Dic5 | D3 | semidirect |
| 27. C2×C5×D3 | C2×C4 | semidirect |
| 42. C2×Dic5 | C2×D3 | semidirect |
| 44. C2×C3×C5 | C22⋊C4 | semidirect |
| 52. C22×D3 | Dic5 | semidirect |
| 72. C3×C5 | C2×C22⋊C4 | semidirect |
| 80. C2×D3 | C2×Dic5 | semidirect |
| 84. C2×C5 | (C2×D3)⋊C4 | semidirect |
| 97. C2×C3 | C22⋊Dic5 | semidirect |
| 102. C5 | C2×(C2×D3)⋊C4 | semidirect |
| 113. C3 | C2×C22⋊Dic5 | semidirect |
| 115. C2 | (C2×D3)⋊Dic5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D3 | 2 |
| C22×Dic15 | 2 |
| C22×C3×Dic5 | 2 |
| (C2×D3)⋊Dic5 | 2 |
| C2×C22⋊Dic5 | 3 |
| C2×(C2×D3)⋊C4 | 5 |