Partial orders

Reflexive. $A\subseteq A$.

Antisymmetric. $A\subseteq B$ and $B\subseteq A$ implies $A=B$.

Transitive. $A\subseteq B\subseteq C\Rightarrow A\subseteq C$.

Not total. For $X=\{1,2\}$: $\{1\}\not\subseteq\{2\}$ and $\{2\}\not\subseteq\{1\}$.

Conclusion. $(\mathcal{P}(X),\subseteq)$ is a partial order, not total (for $|X|\ge2$).