The isospin effects of projectile fragmentation at intermediate energies are investigated using an isospin-dependent Boltzmann-Langevin model. The collisions of mass-symmetric reactions including ⁵⁸Fe, ⁵⁸Ni + ⁵⁸Fe, and ⁵⁸Ni at intermediate energies, in the 30 to 100 MeV/A range, are studied for different symmetry energies. Yield ratios of the isotopic, isobaric, and isotonic pairs of fragments from the intermediate-mass region using three symmetry energies are extracted as functions of the N/Z ratio of the composite systems in the entrance channel and the incident energies. It is found that the yield ratios are sensitive to symmetry energies, especially for neutron-rich systems, and the calculations using soft symmetry energy are closer to the experimental data. The isospin effect is stronger for the soft symmetry energy, owing to the competition of the repulsive Coulomb force and the symmetry energy attractive force on the proton. For the first time, the splits are presented, revealing a transition from the isospin equilibrium at lower energies to translucency at intermediate energies. The results show a degree of transparency in that intermediate mass fragments undergo a transition from dependence on the composite systems in the entrance channel to reliance on the projectile and target nuclei.