do you understand what H_T does?it suffices to show that H_T is a subgroup of S_n. or do you know that and are wondering how to do it?

you must show that H_T is nonempty. (consider the identity function)

then show that it is closed under the composition of functions

then show that each element has an inverse

which of these do you have problems with?

H_T leaves the elements in T fixed and permutes the other elements. how many ways can we permute the remaining elements?What is the order of H_T