Let \(\Gamma =\mathrm {Cay}(G,S)\) be a Cayley graph on a finite group G. A perfect code in \(\Gamma \) is a subset C of G such that every vertex in \(G\setminus C\) is adjacent to exactly one vertex in C and vertices of C are not adjacent to each other. In Zhang and Zhou (Eur J Comb 91:103228, 2021) it is proved that if H is a subgroup of G whose Sylow 2-subgroup is a perfect code of G, then H is a perfect code of G. Also they proved that if G is a metabelian group and H is a normal subgroup of G, then H is a perfect code of G if and only if a Sylow 2-subgroup of H is a perfect code of G. As a generalization, we prove that this result holds for each finite group G. Also they proved that if G is a nilpotent group and H is a subgroup of G, then H is a perfect code of G if and only if the Sylow 2-subgroup of H is a perfect code of G. We generalize this result by proving that the same result holds for every group with a normal Sylow 2-subgroup. In the rest of the paper, we classify groups whose set of all subgroup perfect codes forms a chain of subgroups and also we determine groups with exactly two proper non-trivial subgroup perfect codes.

令\(\Gamma =\mathrm {Cay}(G,S)\)是有限群G上的凯莱图。\(\Gamma \)中的完美代码是G的子集C，使得\(G\setminus C\)中的每个顶点都与C中的一个顶点恰好相邻，并且C的顶点彼此不相邻。在 Zhang 和 Zhou (Eur J Comb 91:103228, 2021) 中证明了如果H是G的子群，其 Sylow 2-子群是G的完美码，则H是G的完美码。他们还证明了如果G是一个 metabelian 群并且H是G的正规子群，则H是G的完美码当且仅当H的 Sylow 2-子群是G的完美码。作为概括，我们证明这个结果对每个有限群G成立。他们还证明了如果G是幂零群且H是G的子群，则H是G的完美码当且仅当H的 Sylow 2-子群是G的完美码. 我们通过证明对于具有正常 Sylow 2-子组的每个组都成立相同的结果来推广该结果。在本文的其余部分，我们对所有子群完美代码的集合形成子群链的群进行分类，并且我们确定具有恰好两个适当非平凡子群完美代码的群。