Inspired by the nice post, I am particularly looking into the exact sequences of SU(N), but I will like to loosen the conditions of the previous post,
Q1. $$1 \to A \to SU(N) \to B \to 1$$
where any of $A$,$B$ can contain finite group or discrete groups.
I am particularly interested in SU(5),
Q2. $$1 \to A \to SU(5) \to B \to 1$$
I wonder whether there is any example such that both $A$ and $B$ contains the same number of generators of continuous part of Lie groups (there can be an additional discrete finite group parts such as additional $\mathbb{Z_N}$)? (for example $SU(5)$ has 24 generators. Is there any example such that $A$ and $B$ have 12 generators for continuous part of Lie groups for each $A$, $B$.) How about $$A=U(1) \times SU(2) \times SU(3)\;\;\; \text{or} \;\;\;A \supset U(1) \times SU(2) \times SU(3)?$$
Or whether there is any example such that $B$ $$B=U(1) \times SU(2) \times SU(3)\;\;\; \text{or} \;\;\;B \supseteq U(1) \times SU(2) \times SU(3)?$$ (there can be an additional discrete finite group parts for $B$ such as additional $\mathbb{Z_N}$.)