Do single convex and single concave lenses follow the three rules of refraction?

I was learning about convex and concave lenses today, but everything I read primarily focused on double convex and double concave lenses. Do the three rules about the refraction of light (how rays parallel to the principal axis refract, how rays in the direction of the focal point refract, and how rays passing through the center refract) still apply for single lenses? I was thinking that they would, since you can define a lens as converging if it refracts rays parallel to the principal axis such that they pass through the focal point, and you can define a lens as diverging if it refracts rays parallel to the principal axis such that their extensions converge at a focal point. However, I was thinking that the two focal points would not necessarily be equidistant from the lens, as is the case in a double convex or double concave lens, due to the lack of symmetry. Would someone please confirm my thinking, or correct it?