Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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×D5×Dic3 | C2 | semidirect |
| 3. C4×Dic15 | C2 | semidirect |
| 4. C5×C4⋊Dic3 | C2 | semidirect |
| 5. #6665 | C2 | semidirect |
| 12. C3×D20 | C4 | semidirect |
| 23. C2×C3×D5 | C2×C4 | semidirect |
| 24. C3×C4×C5 | C2×C4 | semidirect |
| 26. Dic15 | D4 | semidirect |
| 31. C4⋊Dic3 | D5 | semidirect |
| 38. D20 | Dic3 | semidirect |
| 55. C2×D5 | C2×Dic3 | semidirect |
| 57. C4×C5 | C2×Dic3 | semidirect |
| 65. C3×C5 | C4×D4 | semidirect |
| 70. C3×C4 | C4×D5 | semidirect |
| 89. C5 | D4×Dic3 | semidirect |
| 97. C4 | D5×Dic3 | semidirect |
| 98. C3 | #4039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D20 | 2 |
| C2×D5×Dic3 | 2 |
| C4×Dic15 | 2 |
| C5×C4⋊Dic3 | 2 |
| #6665 | 2 |
| #4039 | 3 |
| D4×Dic3 | 5 |