Is there an example of a periodic variety $\mathbf{V}$ of groups that satisfies all of the following properties?

- $\mathbf{V}$ is finitely based
- $\mathbf{V}$ contains finitely many subvarieties
- $\mathbf{V}$ is not finitely generated

Recall that a variety of groups is *periodic* if it satisfies the identity $x^n = 1$ for some $n \geq 1$; *finitely based* if all its identities are deducible from some finite set of its identities; *non-finitely generated* if it cannot be generated by a single finite group.