  We consider theories with one gauge group (SU, SO or Sp) and one scalar in a
two-index representation. The renormalizable action often has accidental
symmetries (such as global U(1) or unusual group parities) that lead to one or
more stable states, providing Dark Matter candidates. We discuss the confined
phase(s) of each theory and compute the two Higgs phases, finding no generic
dualities among them. Discrete gauge symmetries can arise and accidental
symmetries can be broken, possibly giving pseudo-Goldstone Dark Matter. Dark
Matter candidates can have a complicated sub-structure characteristic of each
group and can be accompanied by extra dark radiation.
