In 1986, the second author classified the minimal clones on a finite universe into five types. We extend this classification
to infinite universes and to multiclones. We show that every non-trivial clone contains a “small” clone of one of the five
types. From it we deduce, in part, an earlier result, namely that if $${\mathcal{C}}$$ is a clone on a universe A with at least two elements that contains all constant operations, then all binary idempotent operations are projections and
some m-ary idempotent operation is not a projection for some m ≥ 3 if and only if there is a boolean group G on A for which $${\mathcal{C}}$$ is the set of all operations f(x
1, . . . , x
n
) of the form $$a + {\sum_{i \in I}x_{i}}$$ for $${a \in A}$$ and $${I \subseteq \{1,\,.\,.\,.\,,n\}}$$.