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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{16}=b^{5}=1, b^{a}=b^{4} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P
$C_5:C_{16}$ 1A $1$ $1$ $C_5:C_{16}$ 1A 1A $1$
$C_5:C_{16}$ 2A $2$ $1$ $C_5:C_{16}$ 1A 2A $a^{8}$
$C_5:C_{16}$ 4A1 $4$ $1$ $C_5:C_{16}$ 2A 4A1 $a^{4}$
$C_5:C_{16}$ 4A-1 $4$ $1$ $C_5:C_{16}$ 2A 4A-1 $a^{12}$
$C_5:C_{16}$ 5A1 $5$ $2$ $C_{40}$ 5A2 1A $b^{3}$
$C_5:C_{16}$ 5A2 $5$ $2$ $C_{40}$ 5A1 1A $b$
$C_5:C_{16}$ 8A1 $8$ $1$ $C_5:C_{16}$ 4A1 8A-3 $a^{2}$
$C_5:C_{16}$ 8A-1 $8$ $1$ $C_5:C_{16}$ 4A-1 8A3 $a^{14}$
$C_5:C_{16}$ 8A3 $8$ $1$ $C_5:C_{16}$ 4A-1 8A-1 $a^{6}$
$C_5:C_{16}$ 8A-3 $8$ $1$ $C_5:C_{16}$ 4A1 8A1 $a^{10}$
$C_5:C_{16}$ 10A1 $10$ $2$ $C_{40}$ 5A1 2A $a^{8}b^{4}$
$C_5:C_{16}$ 10A3 $10$ $2$ $C_{40}$ 5A2 2A $a^{8}b^{2}$
$C_5:C_{16}$ 16A1 $16$ $5$ $C_{16}$ 8A1 16A5 $a$
$C_5:C_{16}$ 16A-1 $16$ $5$ $C_{16}$ 8A-1 16A-5 $a^{15}$
$C_5:C_{16}$ 16A3 $16$ $5$ $C_{16}$ 8A3 16A-1 $a^{3}$
$C_5:C_{16}$ 16A-3 $16$ $5$ $C_{16}$ 8A-3 16A1 $a^{13}$
$C_5:C_{16}$ 16A5 $16$ $5$ $C_{16}$ 8A-3 16A-7 $a^{5}$
$C_5:C_{16}$ 16A-5 $16$ $5$ $C_{16}$ 8A3 16A7 $a^{11}$
$C_5:C_{16}$ 16A7 $16$ $5$ $C_{16}$ 8A-1 16A3 $a^{7}$
$C_5:C_{16}$ 16A-7 $16$ $5$ $C_{16}$ 8A1 16A-3 $a^{9}$
$C_5:C_{16}$ 20A1 $20$ $2$ $C_{40}$ 10A1 4A1 $a^{4}b^{2}$
$C_5:C_{16}$ 20A-1 $20$ $2$ $C_{40}$ 10A1 4A-1 $a^{12}b^{3}$
$C_5:C_{16}$ 20A3 $20$ $2$ $C_{40}$ 10A3 4A-1 $a^{12}b$
$C_5:C_{16}$ 20A-3 $20$ $2$ $C_{40}$ 10A3 4A1 $a^{4}b^{4}$
$C_5:C_{16}$ 40A1 $40$ $2$ $C_{40}$ 20A1 8A-3 $a^{2}b$
$C_5:C_{16}$ 40A-1 $40$ $2$ $C_{40}$ 20A-1 8A3 $a^{14}b$
$C_5:C_{16}$ 40A3 $40$ $2$ $C_{40}$ 20A3 8A-1 $a^{6}b^{2}$
$C_5:C_{16}$ 40A-3 $40$ $2$ $C_{40}$ 20A-3 8A1 $a^{10}b^{2}$
$C_5:C_{16}$ 40A7 $40$ $2$ $C_{40}$ 20A3 8A3 $a^{14}b^{2}$
$C_5:C_{16}$ 40A-7 $40$ $2$ $C_{40}$ 20A-3 8A-3 $a^{2}b^{2}$
$C_5:C_{16}$ 40A11 $40$ $2$ $C_{40}$ 20A-1 8A-1 $a^{6}b$
$C_5:C_{16}$ 40A-11 $40$ $2$ $C_{40}$ 20A1 8A1 $a^{10}b$
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