Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
328 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×D3 |
| commutator, cosocle | C2×C3 | C24×C5 |
| Frattini | C2 | C23×C5×D3 |
| Fitting | C3×C5×#41 | C2 |
| socle | C2×C3×C5 | C24 |
| hypercenter | C5×#41 | D3 |
| hypocenter | C3 | C2×C5×#41 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4×C5 ◁ C5×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#41 | C2 | semidirect |
| 2. C5×#239 | C2 | semidirect |
| 3. C5×D3×Q8 | C2 | semidirect |
| 4. C5×#237 | C2 | semidirect |
| 5. C5×D3×D4 | C2 | semidirect |
| 6. C5×#235 | C2 | semidirect |
| 7. C2×C4×C5×D3 | C2 | semidirect |
| 10. C3×C5×Q8 | C22 | semidirect |
| 11. C3×C5×D4 | C22 | semidirect |
| 12. C2×C3×C4×C5 | C22 | semidirect |
| 13. C5×#67 | C22 | semidirect |
| 14. C2×C5×Dic3 | C22 | semidirect |
| 15. C5×D12 | C22 | semidirect |
| 18. C4×C5×D3 | C22 | semidirect |
| 19. C4×C5×D3 | C22 | semidirect |
| 20. C5×Dic6 | C22 | semidirect |
| 21. D3×#41 | C5 | direct (N × H) |
| 25. C5×#41 | D3 | direct (N × H) |
| 37. C3×#41 | C2×C5 | semidirect |
| 38. #239 | C2×C5 | semidirect |
| 39. D3×Q8 | C2×C5 | semidirect |
| 40. #237 | C2×C5 | semidirect |
| 41. D3×D4 | C2×C5 | semidirect |
| 42. #235 | C2×C5 | semidirect |
| 43. C2×C4×D3 | C2×C5 | semidirect |
| 46. C5×Q8 | C2×D3 | semidirect |
| 49. C5×D4 | C2×D3 | semidirect |
| 55. C2×C4×C5 | C2×D3 | semidirect |
| 60. C5×D3 | #41 | direct (N × H) |
| 62. C3×Q8 | C22×C5 | semidirect |
| 63. C3×D4 | C22×C5 | semidirect |
| 64. C2×C3×C4 | C22×C5 | semidirect |
| 65. #67 | C22×C5 | semidirect |
| 66. C2×Dic3 | C22×C5 | semidirect |
| 67. D12 | C22×C5 | semidirect |
| 70. C4×D3 | C22×C5 | semidirect |
| 71. C4×D3 | C22×C5 | semidirect |
| 72. Dic6 | C22×C5 | semidirect |
| 84. #41 | C5×D3 | direct (N × H) |
| 88. C3×C5 | C2×#41 | semidirect |
| 103. Q8 | C2×C5×D3 | semidirect |
| 106. D4 | C2×C5×D3 | semidirect |
| 112. C2×C4 | C2×C5×D3 | semidirect |
| 116. D3 | C5×#41 | direct (N × H) |
| 117. C5 | D3×#41 | direct (N × H) |
| 126. C3 | C2×C5×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#41 | 2 |
| C5×#239 | 2 |
| C5×D3×Q8 | 2 |
| C5×#237 | 2 |
| C5×D3×D4 | 2 |
| C5×#235 | 2 |
| C2×C4×C5×D3 | 2 |
| C2×C5×#41 | 3 |
| D3×#41 | 5 |