Hyperspaces which are products

Let X be a continuum, let C(X) be the hyperspace of subcontinua of X. Answering questions by S.B. Nadler Jr, we prove that C(X) is a finite-dimensional product of two nondegenerate continua if and only if X is an arc or a circle. We also give an example of a nonlocally connected continuum Z such that C(Z) is homeomorphic to Z × I.