Does every closed subgroup of an abelian variety have a direct complement?

Question

Consider A is an Abelian variety over $\mathbb{C}$ and B is a closed subgroup of A. I think there is an Abelian variety $C$ such that $A$ and $B\oplus C$ are isogenic. But I can't find a reference for this fact or if it's false a counter example. Any help is appreciated.