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For an irreducible character $\chi$ of a finite group $G$, the codegree of$\chi$ is defined as $|G:\ker(\chi)|/\chi(1)$. In this paper, we determinefinite nonsolvable groups with exactly three nonlinear irreducible charactercodegrees, and they are $\mathrm{L}_2(2^f)$ for $f\ge 2$, $\mathrm{PGL}_2(q)$for odd $q\ge 5$ or $\mathrm{M}_{10}$.

Nonsolvable groups with three nonlinear irreducible character codegrees