Determine the order of each of the following elements in the respective quotient groups. ($D_{20}$ denotes the dihedral group of order $40$ ).

coset	quotient group	order
$6$ + $\langle 16 \pmod{28} \rangle$	$\mathbb{Z}_{28}/\langle 16 \pmod{28}\rangle$
$8$ $\langle 27 \pmod{37} \rangle$	$U(37) /\langle 27 \pmod{37}\rangle$
$a^{5} \langle a^{11} \rangle$	$D_{20}/\langle a^{11} \rangle$
$a^{5} b \langle a^{11} \rangle$	$D_{20}/\langle a^{11} \rangle$
$-j\langle k \rangle$	$Q_8/ \langle k \rangle$