The problem of determining (up to lattice isomorphism) the lattices that are sublattices of free lattices is in general an extremely difficult and an unsolved problem. A notable result towards solving this problem was established by Galvin and Jónsson when they classified (up to lattice isomorphism) all of the distributive sublattices of free lattices in 1959. In this paper, we weaken the requirement that a sublattice of a free lattice be distributive to requiring that a such a lattice belongs in the variety of lattices generated by the pentagon \(N_5\). Specifically, we use McKenzie’s list of join-irreducible covers of the variety generated by \(N_5\) to extend Galvin and Jónsson’s results by proving that all sublattices of a free lattice that belong to the variety generated by \(N_5\) satisfy three structural properties. Afterwards, we explain how the results in this paper can be partially extended to lattices from seven known infinite sequences of semidistributive lattice varieties.

确定（直至晶格同构）作为自由晶格的子晶格的晶格的问题通常是极其困难且尚未解决的问题。Galvin和Jónsson在1959年分类（直到晶格同构）所有自由晶格的子分布时，得出了解决该问题的显着结果。在本文中，我们削弱了自由晶格的子晶格必须是分布的要求。要求这样的晶格属于由五边形\（N_5 \）生成的各种晶格。具体来说，我们使用McKenzie的\（N_5 \）生成的变体的不可约合覆盖列表来扩展Galvin和Jónsson的结果，方法是证明自由晶格的所有子格都属于\（N_5 \）满足三个结构特性。之后，我们解释了如何将本文的结果部分扩展到来自七个已知的半分布晶格变体的无限序列的晶格。