Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
264 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 264 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 |
|---|---|---|
| 2. C2×C3×C4×D5 | C2 | semidirect |
| 3. C3×C5×C22⋊C4 | C2 | semidirect |
| 4. C3×C22⋊Dic5 | C2 | semidirect |
| 5. C3×#685 | C2 | semidirect |
| 6. D5×C22⋊C4 | C3 | direct (N × H) |
| 9. C22×C3×D5 | C4 | semidirect |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 13. C2×C3×Dic5 | C22 | semidirect |
| 17. C2×C4×D5 | C2×C3 | semidirect |
| 18. C5×C22⋊C4 | C2×C3 | semidirect |
| 19. C22⋊Dic5 | C2×C3 | semidirect |
| 20. #685 | C2×C3 | semidirect |
| 22. C22×C3×C5 | C2×C4 | semidirect |
| 27. C2×C3×D5 | C2×C4 | semidirect |
| 35. C3×C22⋊C4 | D5 | direct (N × H) |
| 38. C22×D5 | C3×C4 | semidirect |
| 41. C2×C4×C5 | C22×C3 | semidirect |
| 42. C2×Dic5 | C22×C3 | semidirect |
| 49. C3×D5 | C22⋊C4 | direct (N × H) |
| 57. C2×C3×C4 | C2×D5 | semidirect |
| 59. C22×C5 | C2×C3×C4 | semidirect |
| 64. C2×D5 | C2×C3×C4 | semidirect |
| 72. C22⋊C4 | C3×D5 | direct (N × H) |
| 73. C3×C5 | C2×C22⋊C4 | semidirect |
| 80. C22×C3 | C4×D5 | semidirect |
| 88. D5 | C3×C22⋊C4 | direct (N × H) |
| 96. C2×C4 | C2×C3×D5 | semidirect |
| 102. C5 | C2×C3×C22⋊C4 | semidirect |
| 109. C22 | C3×C4×D5 | semidirect |
| 113. C3 | D5×C22⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D5 | 2 |
| C2×C3×C4×D5 | 2 |
| C3×C5×C22⋊C4 | 2 |
| C3×C22⋊Dic5 | 2 |
| C3×#685 | 2 |
| D5×C22⋊C4 | 3 |
| C2×C3×C22⋊C4 | 5 |