Finite Group DatabasebetaFinite Group DatabasebetaOrder 37620.
176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D33⋊D95 |
| commutator, cosocle, hypocenter | C3×C5×C11×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C11×C19 | C22 |
| LCS | G ▷ C3×C5×C11×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×D1045 | C2 | semidirect |
| 2. C3×C5×C19×D33 | C2 | semidirect |
| 3. C3×C11×D285 | C2 | semidirect |
| 4. D33⋊D95 | C3 | direct (N × H) |
| 6. C32×C5×C11×C19 | C22 | semidirect |
| 8. C11×D285 | C2×C3 | semidirect |
| 9. C5×C19×D33 | C2×C3 | semidirect |
| 11. C3×D1045 | D3 | semidirect |
| 12. C3×D1045 | C2×C3 | semidirect |
| 16. C3×C19×D33 | D5 | semidirect |
| 21. C3×C5×C11×C19 | C2×D3 | semidirect |
| 22. C3×C5×C11×C19 | C22×C3 | semidirect |
| 25. D1045 | C3×D3 | semidirect |
| 29. C32×C11×C19 | C2×D5 | semidirect |
| 30. C3×D285 | D11 | semidirect |
| 33. C19×D33 | C3×D5 | semidirect |
| 42. C5×C11×C19 | C2×C3×D3 | semidirect |
| 44. C3×C5×D33 | D19 | semidirect |
| 46. C32×C5×C19 | C2×D11 | semidirect |
| 52. C3×C11×C19 | D3×D5 | semidirect |
| 53. C3×C11×C19 | C2×C3×D5 | semidirect |
| 55. D285 | C3×D11 | semidirect |
| 61. C32×C5×C11 | C2×D19 | semidirect |
| 71. C5×D33 | C3×D19 | semidirect |
| 78. C3×C5×C19 | D3×D11 | semidirect |
| 79. C3×C5×C19 | C2×C3×D11 | semidirect |
| 83. C11×C19 | C3×D3×D5 | semidirect |
| 84. C3×D33 | D95 | semidirect |
| 91. C32×C19 | D5×D11 | semidirect |
| 93. C3×C5×C11 | D3×D19 | semidirect |
| 94. C3×C5×C11 | C2×C3×D19 | semidirect |
| 107. C32×C11 | C2×D95 | semidirect |
| 108. C5×C19 | C3×D3×D11 | semidirect |
| 114. D33 | C3×D95 | semidirect |
| 123. C3×C19 | C3×D5×D11 | semidirect |
| 124. C3×C19 | D15⋊D11 | semidirect |
| 125. C5×C11 | C3×D3×D19 | semidirect |
| 126. C32×C5 | D11×D19 | semidirect |
| 133. C3×C11 | D3×D95 | semidirect |
| 134. C3×C11 | C2×C3×D95 | semidirect |
| 146. C19 | C3×D15⋊D11 | semidirect |
| 151. C3×C5 | C3×D11×D19 | semidirect |
| 152. C3×C5 | D33⋊D19 | semidirect |
| 155. C11 | C3×D3×D95 | semidirect |
| 159. C32 | D11×D95 | semidirect |
| 167. C5 | C3×D33⋊D19 | semidirect |
| 170. C3 | C3×D11×D95 | semidirect |
| 171. C3 | D33⋊D95 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D1045 | 2 |
| C3×C5×C19×D33 | 2 |
| C3×C11×D285 | 2 |
| D33⋊D95 | 3 |
| C3×D11×D95 | 3 |
| C3×D33⋊D19 | 5 |
| C3×D3×D95 | 11 |
| C3×D15⋊D11 | 19 |