Given a prime \(p\), a \(p\)-local group is a module over the ring of integers localized at \(p\). The class of simply presented \(p\)-local torsion groups consists precisely of the totally projective \(p\)-groups. These groups were characterized by Paul Hill in an unpublished paper (ca. 1970) in terms of certain collections of subgroups which he termed Axiom 3 systems. In contrast to totally projective \(p\)-groups, direct summands of simply presented \(p\)-local mixed groups need not be simply presented; these direct summands are the \(p\)-local Warfield groups. P. Hill and C. Megibben gave an Axiom 3 characterization of local Warfield groups [Trans. Am. Math. Soc. 295, 715-734 (1986; Zbl 0597.20048)] which the authors used to prove that local Warfield groups are weakly transitive [J. Algebra 208, No. 2, 644-661 (1998; Zbl 0916.20039)]. Recently, Hill, Megibben and Ullery extended this result to certain isotype subgroups of local Warfield groups raising the question of when an isotype subgroup of a local Warfield group is again a local Warfield group. The present article gives a complete solution to this problem, again involving an Axiom 3 type characterization.