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×C3×Dic5 | C2 | semidirect |
| 3. C2×C3×C4×D5 | C2 | semidirect |
| 4. C3×C5×C22⋊C4 | C2 | semidirect |
| 5. C3×#685 | C2 | semidirect |
| 6. C3×#683 | C2 | semidirect |
| 7. C3×C4×Dic5 | C2 | semidirect |
| 8. #4027 | C3 | direct (N × H) |
| 13. C3×C22⋊D5 | C4 | semidirect |
| 21. C22×Dic5 | C2×C3 | semidirect |
| 22. C2×C4×D5 | C2×C3 | semidirect |
| 23. C5×C22⋊C4 | C2×C3 | semidirect |
| 24. #685 | C2×C3 | semidirect |
| 25. #683 | C2×C3 | semidirect |
| 26. C4×Dic5 | C2×C3 | semidirect |
| 29. C22×C3×C5 | C2×C4 | semidirect |
| 33. C2×C3×D5 | C2×C4 | semidirect |
| 37. C3×Dic5 | C2×C4 | semidirect |
| 38. C3×Dic5 | D4 | semidirect |
| 44. C3×C22⋊C4 | D5 | semidirect |
| 50. C22⋊D5 | C3×C4 | semidirect |
| 74. C22×C5 | C2×C3×C4 | semidirect |
| 78. C2×D5 | C2×C3×C4 | semidirect |
| 82. Dic5 | C2×C3×C4 | semidirect |
| 83. Dic5 | C3×D4 | semidirect |
| 89. C22⋊C4 | C3×D5 | semidirect |
| 91. C3×C5 | C4×D4 | semidirect |
| 97. C22×C3 | C4×D5 | semidirect |
| 124. C5 | C3×C4×D4 | semidirect |
| 130. C22 | C3×C4×D5 | semidirect |
| 137. C3 | #4027 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊D5 | 2 |
| C22×C3×Dic5 | 2 |
| C2×C3×C4×D5 | 2 |
| C3×C5×C22⋊C4 | 2 |
| C3×#685 | 2 |
| C3×#683 | 2 |
| C3×C4×Dic5 | 2 |
| #4027 | 3 |
| C3×C4×D4 | 5 |