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 |
|---|---|---|
| 1. C2×C5×D12 | C2 | semidirect |
| 2. C2×C5×D12 | C2 | semidirect |
| 3. C2×C4×C5×D3 | C2 | semidirect |
| 4. C3×C5×C4⋊C4 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 15. #895 | C5 | direct (N × H) |
| 19. C5×C4⋊C4 | D3 | semidirect |
| 27. C2×C5×D3 | D4 | semidirect |
| 29. C3×C4×C5 | D4 | semidirect |
| 31. C2×D12 | C2×C5 | semidirect |
| 32. C2×D12 | C2×C5 | semidirect |
| 33. C2×C4×D3 | C2×C5 | semidirect |
| 34. C3×C4⋊C4 | C2×C5 | semidirect |
| 35. (C2×D3)⋊C4 | C2×C5 | semidirect |
| 67. C4×C5 | D12 | semidirect |
| 71. C4⋊C4 | C5×D3 | semidirect |
| 73. C3×C5 | #121 | semidirect |
| 80. C2×D3 | C5×D4 | semidirect |
| 82. C3×C4 | C5×D4 | semidirect |
| 102. C5 | #895 | direct (N × H) |
| 112. C4 | C5×D12 | semidirect |
| 113. C3 | C5×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D12 | 2 |
| C2×C4×C5×D3 | 2 |
| C3×C5×C4⋊C4 | 2 |
| C5×(C2×D3)⋊C4 | 2 |
| C5×#121 | 3 |
| #895 | 5 |