Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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×C3×Dic5 | C2 | semidirect |
| 3. C2×D3×Dic5 | C2 | semidirect |
| 4. #6719 | C2 | semidirect |
| 5. Dic3⋊Dic5 | C2 | semidirect |
| 6. (C2×D3)⋊Dic5 | C2 | semidirect |
| 7. Dic3×Dic5 | C2 | semidirect |
| 13. C5×#67 | C4 | semidirect |
| 22. C22×Dic5 | D3 | semidirect |
| 29. C22×C3×C5 | C2×C4 | semidirect |
| 33. C2×C5×D3 | C2×C4 | semidirect |
| 37. C3×Dic5 | D4 | semidirect |
| 38. C5×Dic3 | C2×C4 | semidirect |
| 67. #67 | Dic5 | direct (N × H) |
| 77. C22×C5 | C4×D3 | semidirect |
| 83. Dic5 | #67 | direct (N × H) |
| 91. C3×C5 | C4×D4 | semidirect |
| 94. C22×C3 | C2×Dic5 | semidirect |
| 98. C2×D3 | C2×Dic5 | semidirect |
| 103. Dic3 | C2×Dic5 | semidirect |
| 124. C5 | C4×#67 | semidirect |
| 130. C22 | D3×Dic5 | semidirect |
| 137. C3 | D4×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#67 | 2 |
| C22×C3×Dic5 | 2 |
| C2×D3×Dic5 | 2 |
| #6719 | 2 |
| Dic3⋊Dic5 | 2 |
| (C2×D3)⋊Dic5 | 2 |
| Dic3×Dic5 | 2 |
| D4×Dic5 | 3 |
| C4×#67 | 5 |