We investigate the spin-dependent electronic states of antiferromagnetic (AFM) lanthanum chromite (LaCrO), lanthanum manganite (LaMnO), and lanthanum ferrite (LaFeO) using spin-polarized first-principles density functional theory with Hubbard U correction. The band structures are calculated for 15 types of their different AFM structures. It is verified for these structures that there is a very simple rule to identify which wave number [Formula: see text] exhibits spin splitting or degeneracy in the band structure. This rule uses the symmetry operations that map the up-spin atoms onto the down-spin atoms. The resulting spin splitting is very small for the most stable spin configuration of the most stable experimental structure. We discuss a plausible benefit of this characteristic, i.e. the direction-independence of the spin current, in electrode applications.