Exact sequences of $SU(N)$ and $SO(N)$

Question

We know that the spin group $Spin(N)$ has a short exact sequence of Lie groups

$$1 \to Z_2 \to Spin(N) \to SO(N) \to 1\textrm{.}$$

I wonder whether there are some examples for $SU(N)$ and $SO(N)$ groups

such that there exists an exact sequence as

Q1. $$1 \to ? \to SU(N) \to ? \to 1$$

-

Q2. $$1 \to ? \to SO(N) \to ? \to 1$$

Here I am interested to know the case where the question marks are nontrivial non-Abelian Lie groups.

In particular, I am interested to know when

$SU(N)$ is $SU(4)$ and $SU(5)$

and when

$SO(N)$ is $SO(8)$, $SO(9)$, and $SO(10)$.

Reference is very welcome. Thank you. :-)