I am just a new student in this field.
My question is from the following statement: 

"Let $G$ be a Lie group and $H$ be its subgroup, if $H$ is a smooth manifold, then $H$ is a Lie group." 

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> My question is under such condition, is it possible that $H$ is not a smooth manifold? (I mean if there is no condition "if $H$ is a smooth manifold")
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My question lies in since $G$ is a Lie group, $G$ is a smooth manifold. So all transition functions are differentiable. So for $H$. 

I am not quite sure about this. Could someone point something wrong out?