Four possible isomers of the Ti2C80 metallofullerene are discussed in detail at the B3LYP DFT level of theory: two isomers in Ti2@C80 formula with two Ti atoms encapsulated inside a C80 cage and the other two in Ti2C2@C78 formula with a Ti2C2 cluster involved inside a C78 cage. In the encaged Ti2C2 cluster, there are end-on and side-on C2 bridging modes into the two Ti atoms. The optimized end-on cluster has a linear Ti-C-C-Ti array, whereas the side-on cluster has a butterfly-like structure where the two Ti atoms and the C2 unit do not lie in a plane. DFT calculations show that the Ti2C2@C78 molecule with the end-on Ti2C2 cluster is energetically most favorable in the four isomers. Stabilities of the Ti2C80 molecules are essentially dominated by Ti binding sites inside fullerene cages. The Ti atoms bind over the hexagon rings in preference to a junction between hexagon and pentagon rings. In the Ti2C2@C78 molecules, orbital interactions between the Ti2C2 cluster and the outer cage play a significant role in determining the C2 bridging modes into the dititanium center and their relative stabilities.