For each of the following subgroups $H$ of the respective groups $G$, determine if it is normal:

$G$	$H$	Answer (Y/N)
$\mathbb{Z}_{24}$	$\langle 13 \pmod{24} \rangle$
$U(24)$	$\langle 13 \pmod{24} \rangle$
$D_{4}$	$\langle a^{16} \rangle$
$D_{4}$	$\langle a^{16} b \rangle$
$D_{4}$	$\langle a^{16}, b \rangle$
$Q_8$	$\langle (-k) \rangle$
$GL_{2}(\mathbb{Q})$	subgroup of upper triangular matrices