Complex forms of nitrogen are of interest for their potential as high-energy materials, but many all-nitrogen systems lack the stability for practical high-energy applications. Inclusion of carbon atoms in an otherwise all-nitrogen structure can increase stability. Nitrogen cages are known for energetically preferring cylindrical structures with triangular endcaps, but carbon cages prefer the pentagon-hexagon structure of the fullerenes. Previous calculations on N22C2have shown that carbon inclusion narrows the gap between triangular and fullerene-like structures. In the current study, three isomers of N24are used as frameworks for carbon substitution. Theoretical calculations are carried out on isomers of N20C4, N18C6, and N16C8, with the goal of determining what level of carbon substitution causes the carbon fullerene-like structures to become energetically preferred.