Systematic first-principles calculations were performed for GICs consisting of 54 different intercalants with five reported structures. The formation energy of the GICs, Ef, was compared for different compositions and stacking orderings. Our calculations reproduced the stability of all experimentally reported GICs with negative Ef. We also determined the possibility of synthesizing Sc-, Y-, Fr-, and Ra-GICs, which have not been reported experimentally or computationally as GICs. The Y-, Fr-and Ra-GICs are confirmed to be more stable than Li-GICs and K-GICs, indicating their possible synthesis using the Li-based molten alloy and LiCl-KCl molten salt methods. In addition, Sc-and Y-GIC are considered that they can exhibit superconductivity. In the near future, we expect that the new GICs will be synthesized based on our calculations.