We study the difference between quandles that arise from conjugation in groups and those which do not. As a result, we define conjugation subquandles, and show that not all quandles or keis are in this class of examples. We investigate coloring by keis which are not conjugation subquandles. And we investigate the relationship between decomposable quandles or keis and link colorings. Subsequently, we analyze what kinds of quandles or keis can be homomorphic images of a knot quandle.