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Let $G$ be a group. Identify which of the following subgroups $H$ of $G$ are normal in general. Select ALL that apply.

Center of $G$: $Z(G)=\{z\in G: zg=gz \textrm{ for all $g\in G$}\}$

Centralizer of a subset $S$ of $G$: $C_G(S)=\{g\in G: gs=sg \textrm{ for all $s\in S$}\}$

Normalizer of a subset $S$ of $G$: $N_G(S)=\{g\in G: gS=Sg \}$

Stabilizer of the element $x$ of $G$: $G_x=\{g\in G: gx=x\}$

None of the above.