On Day 10, we continued to talk about subgroups and generators. After going over the basic definition more formally than the last time and cleaning up our notation, we worked out more examples of subgroups of cyclic groups and practiced applying Lagrange’s theorem to find the orders of possible subgroups. We concluded with finding subgroups of D₃, from which the takeaway was that there could be multiple instances of a subgroup of the same order. It was not particularly exciting day, but it solidified students’ understanding of the basic concepts. And we also had tea.