Lie groups with co-dimension 1 sub groups

Question

I know very little about Lie groups but it would greatly benefit me to know some with co-dimension one sub groups which are not products of one dimensional groups with other things. Do these exist?

Answer 1

Consider the subgroup of $\mathrm{GL}(2,\mathbb{R})$ whose elements are the matrices$$\begin{pmatrix}a&b\\0&a^{-1}\end{pmatrix}$$($a>0$ and $b\in\mathbb R$). Then, consider the subgroup of those matrices such that $a=1$. Its codimension is $1$.