Small monoids generating varieties with uncountably many subvarieties

An algebra that generates a variety with uncountably many subvarieties is said to be of type \(2^{\aleph _0}\) $2^{{\aleph }_0}$ . We show that the Rees quotient monoid M(aabb) of order ten is of type \(2^{\aleph _0}\) $2^{{\aleph }_0}$ , thereby affirmatively answering a recent question of Glasson. As a corollary, we exhibit a new example of type \(2^{\aleph _0}\) $2^{{\aleph }_0}$ monoid of order six, which turns out to be the minimal possible cardinality and the first of its kind that is finitely based.