Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
264 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 114 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×C4×C5 | C2 | semidirect |
| 3. C22×C3×Dic5 | C2 | semidirect |
| 4. C3×#685 | C2 | direct (N × H) |
| 5. C2×#685 | C3 | direct (N × H) |
| 9. C22×C3×D5 | C4 | semidirect |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 14. C2×C3×Dic5 | C22 | semidirect |
| 17. C22×C4×C5 | C2×C3 | semidirect |
| 18. C22×Dic5 | C2×C3 | semidirect |
| 19. #685 | C2×C3 | direct (N × H) |
| 27. C2×C3×D5 | C2×C4 | semidirect |
| 32. C22×C3×C4 | D5 | semidirect |
| 37. C22×D5 | C3×C4 | semidirect |
| 40. C2×C4×C5 | C22×C3 | semidirect |
| 42. C2×Dic5 | C22×C3 | semidirect |
| 44. C2×C3×C5 | C22⋊C4 | semidirect |
| 57. C2×C3×C4 | C2×D5 | semidirect |
| 65. C2×D5 | C2×C3×C4 | semidirect |
| 70. C22×C4 | C3×D5 | semidirect |
| 72. C3×C5 | C2×C22⋊C4 | semidirect |
| 83. C2×C5 | C3×C22⋊C4 | semidirect |
| 96. C2×C4 | C2×C3×D5 | semidirect |
| 98. C2×C3 | #685 | direct (N × H) |
| 102. C5 | C2×C3×C22⋊C4 | semidirect |
| 113. C3 | C2×#685 | direct (N × H) |
| 115. C2 | C3×#685 | 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 |
| C22×C3×C4×C5 | 2 |
| C22×C3×Dic5 | 2 |
| C3×#685 | 2 |
| C2×#685 | 3 |
| C2×C3×C22⋊C4 | 5 |