Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
472 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D3×D5 |
| commutator, cosocle | C2×C3×C5 | C24 |
| Frattini | C2 | C22×D3×D5 |
| Fitting | C2×C3×C4×C5 | C22 |
| socle | C22×C3×C5 | C23 |
| hypercenter | C2×C4 | D3×D5 |
| hypocenter | C3×C5 | C22×D4 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D3×D5 | C2 | semidirect |
| 2. C2×C4×D15 | C2 | semidirect |
| 3. C2×C5×D12 | C2 | semidirect |
| 4. C2×C3×D20 | C2 | semidirect |
| 5. C2×#1201 | C2 | semidirect |
| 6. #6777 | C2 | direct (N × H) |
| 9. C22×C5×D3 | C22 | semidirect |
| 10. C22×C3×D5 | C22 | semidirect |
| 12. C2×D3×D5 | C22 | semidirect |
| 13. C2×C3×C4×C5 | C22 | semidirect |
| 14. C2×Dic15 | C22 | semidirect |
| 15. C4×D15 | C22 | semidirect |
| 16. C5×D12 | C22 | semidirect |
| 17. C3×D20 | C22 | semidirect |
| 18. #1201 | C22 | semidirect |
| 24. C2×D20 | D3 | semidirect |
| 27. C2×D15 | D4 | semidirect |
| 30. C2×C5×D3 | C23 | semidirect |
| 32. C2×C3×D5 | C23 | semidirect |
| 34. C3×C4×C5 | C23 | semidirect |
| 35. Dic15 | C23 | semidirect |
| 40. C2×D12 | D5 | semidirect |
| 46. C22×D5 | C2×D3 | semidirect |
| 48. C2×C4×C5 | C2×D3 | semidirect |
| 51. D20 | C2×D3 | semidirect |
| 54. C2×C3×C5 | C2×D4 | semidirect |
| 56. D15 | C2×D4 | semidirect |
| 63. C22×D3 | C2×D5 | semidirect |
| 65. C2×C3×C4 | C2×D5 | semidirect |
| 68. D12 | C2×D5 | semidirect |
| 77. C2×D5 | C22×D3 | semidirect |
| 78. C4×C5 | C22×D3 | semidirect |
| 86. C3×C5 | C22×D4 | semidirect |
| 94. C2×D3 | C22×D5 | semidirect |
| 95. C3×C4 | C22×D5 | semidirect |
| 98. C2×C5 | D3×D4 | semidirect |
| 112. C2×C4 | D3×D5 | semidirect |
| 114. C2×C3 | D4×D5 | semidirect |
| 118. C5 | C2×D3×D4 | semidirect |
| 128. C4 | C2×D3×D5 | semidirect |
| 129. C3 | C2×D4×D5 | semidirect |
| 133. C2 | #6777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×D5 | 2 |
| C2×C4×D15 | 2 |
| C2×C5×D12 | 2 |
| C2×C3×D20 | 2 |
| C2×#1201 | 2 |
| #6777 | 2 |
| C2×D4×D5 | 3 |
| C2×D3×D4 | 5 |