Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 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. C22×C3×C4×C5 | C2 | semidirect |
| 2. C2×C3×C22⋊D5 | C2 | semidirect |
| 3. C3×#709 | C2 | direct (N × H) |
| 4. C2×C3×D20 | C2 | semidirect |
| 5. C2×C3×C4×D5 | C2 | semidirect |
| 6. C2×C3×Dic10 | C2 | semidirect |
| 7. C2×#709 | C3 | direct (N × H) |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 13. C3×C22⋊D5 | C22 | semidirect |
| 15. C3×D20 | C22 | semidirect |
| 16. C3×C4×D5 | C22 | semidirect |
| 17. C3×Dic10 | C22 | semidirect |
| 19. C22×C4×C5 | C2×C3 | semidirect |
| 20. C2×C22⋊D5 | C2×C3 | semidirect |
| 21. #709 | C2×C3 | direct (N × H) |
| 22. C2×D20 | C2×C3 | semidirect |
| 23. C2×C4×D5 | C2×C3 | semidirect |
| 24. C2×Dic10 | C2×C3 | semidirect |
| 38. C22×C3×C4 | D5 | semidirect |
| 43. C2×C4×C5 | C22×C3 | semidirect |
| 44. C22⋊D5 | C22×C3 | semidirect |
| 46. D20 | C22×C3 | semidirect |
| 47. C4×D5 | C22×C3 | semidirect |
| 48. Dic10 | C22×C3 | semidirect |
| 51. C2×C3×C5 | #41 | semidirect |
| 63. C2×C3×C4 | C2×D5 | semidirect |
| 77. C22×C4 | C3×D5 | semidirect |
| 78. C3×C5 | C2×#41 | semidirect |
| 88. C2×C5 | C3×#41 | semidirect |
| 100. C2×C4 | C2×C3×D5 | semidirect |
| 103. C2×C3 | #709 | direct (N × H) |
| 105. C5 | C2×C3×#41 | semidirect |
| 114. C3 | C2×#709 | direct (N × H) |
| 117. C2 | C3×#709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C5 | 2 |
| C2×C3×C22⋊D5 | 2 |
| C3×#709 | 2 |
| C2×C3×D20 | 2 |
| C2×C3×C4×D5 | 2 |
| C2×C3×Dic10 | 2 |
| C2×#709 | 3 |
| C2×C3×#41 | 5 |