Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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×C5×Dic3 | C2 | semidirect |
| 3. C2×C4×C5×D3 | C2 | semidirect |
| 4. C3×C5×C22⋊C4 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C5×Dic3⋊C4 | C2 | semidirect |
| 7. C4×C5×Dic3 | C2 | semidirect |
| 13. C5×#67 | C4 | semidirect |
| 19. #67⋊C4 | C5 | direct (N × H) |
| 25. C5×C22⋊C4 | D3 | semidirect |
| 29. C22×C3×C5 | C2×C4 | semidirect |
| 33. C2×C5×D3 | C2×C4 | semidirect |
| 37. C5×Dic3 | C2×C4 | semidirect |
| 38. C5×Dic3 | D4 | semidirect |
| 40. C22×Dic3 | C2×C5 | semidirect |
| 41. C2×C4×D3 | C2×C5 | semidirect |
| 42. C3×C22⋊C4 | C2×C5 | semidirect |
| 43. (C2×D3)⋊C4 | C2×C5 | semidirect |
| 44. Dic3⋊C4 | C2×C5 | semidirect |
| 45. C4×Dic3 | C2×C5 | semidirect |
| 66. #67 | C4×C5 | semidirect |
| 77. C22×C5 | C4×D3 | semidirect |
| 89. C22⋊C4 | C5×D3 | semidirect |
| 91. C3×C5 | C4×D4 | semidirect |
| 94. C22×C3 | C2×C4×C5 | semidirect |
| 98. C2×D3 | C2×C4×C5 | semidirect |
| 102. Dic3 | C2×C4×C5 | semidirect |
| 103. Dic3 | C5×D4 | semidirect |
| 124. C5 | #67⋊C4 | direct (N × H) |
| 130. C22 | C4×C5×D3 | semidirect |
| 137. C3 | C4×C5×D4 | 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×C5×Dic3 | 2 |
| C2×C4×C5×D3 | 2 |
| C3×C5×C22⋊C4 | 2 |
| C5×(C2×D3)⋊C4 | 2 |
| C5×Dic3⋊C4 | 2 |
| C4×C5×Dic3 | 2 |
| C4×C5×D4 | 3 |
| #67⋊C4 | 5 |