Integer Sequences Realized by the Subgroup Pattern of the Symmetric   Group
  The subgroup pattern of a finite group $G$ is the table of marks of $G$ together with a list of representatives of the conjugacy classes of subgroups of $G$. In this article we describe a collection of sequences realized by the subgroup pattern of the symmetric group. 
Liam Naughton, Goetz Pfeiffer
math.GR