  A symmetry analysis is presented for the three-dimensional nonrelativistic
motion of charged particles in arbitrary stationary electromagnetic fields. The
general form of the Lie point symmetries is found along with the fields that
respect them, considering non-trivial cases of physical interest. The
restrictions placed upon the electromagnetic field yield five classes of
solutions, expressed in terms of the vector and scalar potential. The Noether
type symmetries are also investigated and their corresponding invariants are
found. A second integral of motion, besides the Hamiltonian, results in three
general cases. Finally, a relation between the symmetries of the charged
particle motion and the symmetries of the magnetic field lines is established.
