Quantum chemical calculations have been performed to gauge the effect of substituents on concerted interactions of pnicogen, chalcogen, and halogen bonds in the X–TAZ···Y complexes (X = CN, F, Cl, Br, H, CH3, OH, and NH2, where TAZ and Y denote s-triazine ring and P, S, and Cl atoms, respectively) at the M06-2X/aug-cc-pVDZ level. The mutual interplay of these interactions is also investigated. The results indicate that diminutive effects are observed when the three kinds of noncovalent interactions pnicogen, chalcogen, and halogen bonds are coexisted in the complexes. These effects are studied in terms of energetic and geometric features of the complexes. In addition, Bader’s theory of “atoms in molecules” is used to analyze their strength of varying electron density at bond critical points. Natural bond orbital (NBO) theory is used to characterize the orbital interactions. The results indicate that the electron-withdrawing/donating substituents decrease/increase the magnitude of the binding energies compared to the unsubstituted X–TAZ···Y (X = H) complex. Good correlations among binding energies, Hammett constants, geometrical, atoms in molecular and NBO parameters are established in X–TAZ···Y complexes. By taking advantage of all the aforementioned computational methods, this study examines how these interactions mutually influence each other.