Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 62 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. C2×#1200 | C2 | semidirect |
| 3. C2×D5×Dic3 | C2 | semidirect |
| 4. #6714 | C2 | semidirect |
| 5. C4×C5×Dic3 | C2 | semidirect |
| 6. C3×#685 | C2 | semidirect |
| 7. Dic3⋊Dic5 | C2 | semidirect |
| 16. #1202 | C4 | semidirect |
| 25. #685 | D3 | semidirect |
| 30. C2×D15 | C2×C4 | semidirect |
| 33. C2×C3×D5 | C2×C4 | semidirect |
| 37. C5×Dic3 | C2×C4 | semidirect |
| 38. C5×Dic3 | D4 | semidirect |
| 45. C4×Dic3 | D5 | semidirect |
| 78. C2×D5 | C4×D3 | semidirect |
| 91. C3×C5 | C4×D4 | semidirect |
| 102. Dic3 | C4×D5 | semidirect |
| 103. Dic3 | D20 | semidirect |
| 124. C5 | #67⋊C4 | semidirect |
| 137. C3 | C4×D20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1202 | 2 |
| C2×#1200 | 2 |
| C2×D5×Dic3 | 2 |
| #6714 | 2 |
| C4×C5×Dic3 | 2 |
| C3×#685 | 2 |
| Dic3⋊Dic5 | 2 |
| C4×D20 | 3 |
| #67⋊C4 | 5 |