Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
184 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C3×C5×C4⋊C4 | C2 | semidirect |
| 4. C5×C4⋊Dic3 | C2 | semidirect |
| 5. C5×Dic3⋊C4 | C2 | semidirect |
| 13. C4×C5×D3 | C4 | semidirect |
| 14. D3×C4⋊C4 | C5 | direct (N × H) |
| 19. C5×C4⋊C4 | D3 | direct (N × H) |
| 25. C3×C4×C5 | C2×C4 | semidirect |
| 27. C5×Dic3 | C2×C4 | semidirect |
| 30. C3×C4⋊C4 | C2×C5 | semidirect |
| 31. C4⋊Dic3 | C2×C5 | semidirect |
| 32. Dic3⋊C4 | C2×C5 | semidirect |
| 44. C5×D3 | C4⋊C4 | direct (N × H) |
| 51. C4×D3 | C4×C5 | semidirect |
| 59. C4×C5 | C4×D3 | semidirect |
| 64. C4⋊C4 | C5×D3 | direct (N × H) |
| 65. C3×C5 | C2×C4⋊C4 | semidirect |
| 71. C3×C4 | C2×C4×C5 | semidirect |
| 73. Dic3 | C2×C4×C5 | semidirect |
| 88. D3 | C5×C4⋊C4 | direct (N × H) |
| 89. C5 | D3×C4⋊C4 | direct (N × H) |
| 97. C4 | C4×C5×D3 | semidirect |
| 98. C3 | C2×C5×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D3 | 2 |
| C3×C5×C4⋊C4 | 2 |
| C5×C4⋊Dic3 | 2 |
| C5×Dic3⋊C4 | 2 |
| C2×C5×C4⋊C4 | 3 |
| D3×C4⋊C4 | 5 |