if H is a subgroup of G..

let N(H)={g belongs to G/ gHg^=H} , show that

1) N(H) is a subgroup of G,

2) H is normal in N(H) ,

3) if H is normal in G iff N(H)=G,

4) if H is a normal subgroup of the subgroup K in G, then K is a subset of or = N(H)

how do we prove? im a beginner in groups...any help would be greatful..