Some theorems are proved which exhibit the impossibility of constructing nontrivial products of the 3+2 de Sitter group with internal-symmetry groups (under physically reasonable assumptions). It is shown that either mass degeneracy, $[{E}_{\ensuremath{\alpha}},{P}_{\ensuremath{\mu}}]=0$, or simultaneous measurement of internal quantum numbers and momentum, $[{\mathrm{H}}_{l},{P}_{\ensuremath{\mu}}]=0$, is alone sufficient to imply a direct product relationship. In this sense, the combination of internal symmetry and de Sitter symmetry in a closed system is even less reasonable physically than a combination of internal symmetry and Lorentz invariance (or Galilean invariance).