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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{8}=c^{20}=[a,b]=1, a^{2}=c^{10}, c^{a}=c^{11}, c^{b}=c^{7} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P
$C_5:C_8\times Q_8$ 1A $1$ $1$ $C_5:C_8\times Q_8$ 1A 1A $1$
$C_5:C_8\times Q_8$ 2A $2$ $1$ $C_5:C_8\times Q_8$ 1A 2A $b^{4}c^{10}$
$C_5:C_8\times Q_8$ 2B $2$ $1$ $C_5:C_8\times Q_8$ 1A 2B $b^{4}$
$C_5:C_8\times Q_8$ 2C $2$ $1$ $C_5:C_8\times Q_8$ 1A 2C $c^{10}$
$C_5:C_8\times Q_8$ 4A $4$ $2$ $C_{20}:C_8$ 2C 4A $c^{5}$
$C_5:C_8\times Q_8$ 4B $4$ $2$ $C_{20}:C_8$ 2C 4B $b^{4}c^{5}$
$C_5:C_8\times Q_8$ 4C $4$ $2$ $C_{20}:C_8$ 2C 4C $a$
$C_5:C_8\times Q_8$ 4D $4$ $2$ $C_{20}:C_8$ 2C 4D $ac^{5}$
$C_5:C_8\times Q_8$ 4E $4$ $2$ $C_{20}:C_8$ 2C 4E $ab^{4}$
$C_5:C_8\times Q_8$ 4F $4$ $2$ $C_{20}:C_8$ 2C 4F $ab^{4}c^{5}$
$C_5:C_8\times Q_8$ 4G1 $4$ $5$ $C_8\times Q_8$ 2B 4G1 $b^{2}c^{10}$
$C_5:C_8\times Q_8$ 4G-1 $4$ $5$ $C_8\times Q_8$ 2B 4G-1 $b^{6}c^{10}$
$C_5:C_8\times Q_8$ 4H1 $4$ $5$ $C_8\times Q_8$ 2B 4H1 $b^{2}$
$C_5:C_8\times Q_8$ 4H-1 $4$ $5$ $C_8\times Q_8$ 2B 4H-1 $b^{6}$
$C_5:C_8\times Q_8$ 4I1 $4$ $10$ $C_4\times C_8$ 2A 4I1 $b^{2}c$
$C_5:C_8\times Q_8$ 4I-1 $4$ $10$ $C_4\times C_8$ 2A 4I-1 $b^{6}c$
$C_5:C_8\times Q_8$ 4J1 $4$ $10$ $C_4\times C_8$ 2A 4J1 $ab^{2}$
$C_5:C_8\times Q_8$ 4J-1 $4$ $10$ $C_4\times C_8$ 2A 4J-1 $ab^{6}$
$C_5:C_8\times Q_8$ 4K1 $4$ $10$ $C_4\times C_8$ 2A 4K1 $ab^{2}c$
$C_5:C_8\times Q_8$ 4K-1 $4$ $10$ $C_4\times C_8$ 2A 4K-1 $ab^{6}c$
$C_5:C_8\times Q_8$ 5A $5$ $4$ $Q_8\times C_{10}$ 5A 1A $c^{8}$
$C_5:C_8\times Q_8$ 8A1 $8$ $5$ $C_8\times Q_8$ 4G1 8A-3 $ab$
$C_5:C_8\times Q_8$ 8A-1 $8$ $5$ $C_8\times Q_8$ 4G-1 8A3 $ab^{7}c^{2}$
$C_5:C_8\times Q_8$ 8A3 $8$ $5$ $C_8\times Q_8$ 4G-1 8A-1 $ab^{3}c^{2}$
$C_5:C_8\times Q_8$ 8A-3 $8$ $5$ $C_8\times Q_8$ 4G1 8A1 $ab^{5}$
$C_5:C_8\times Q_8$ 8B1 $8$ $5$ $C_8\times Q_8$ 4G1 8B-3 $abc^{2}$
$C_5:C_8\times Q_8$ 8B-1 $8$ $5$ $C_8\times Q_8$ 4G-1 8B3 $ab^{7}$
$C_5:C_8\times Q_8$ 8B3 $8$ $5$ $C_8\times Q_8$ 4G-1 8B-1 $ab^{3}$
$C_5:C_8\times Q_8$ 8B-3 $8$ $5$ $C_8\times Q_8$ 4G1 8B1 $ab^{5}c^{2}$
$C_5:C_8\times Q_8$ 8C1 $8$ $10$ $C_4\times C_8$ 4H1 8C-3 $b$
$C_5:C_8\times Q_8$ 8C-1 $8$ $10$ $C_4\times C_8$ 4H-1 8C3 $b^{7}$
$C_5:C_8\times Q_8$ 8C3 $8$ $10$ $C_4\times C_8$ 4H-1 8C-1 $b^{3}$
$C_5:C_8\times Q_8$ 8C-3 $8$ $10$ $C_4\times C_8$ 4H1 8C1 $b^{5}$
$C_5:C_8\times Q_8$ 8D1 $8$ $10$ $C_4\times C_8$ 4H1 8D-3 $bc$
$C_5:C_8\times Q_8$ 8D-1 $8$ $10$ $C_4\times C_8$ 4H-1 8D3 $b^{7}c$
$C_5:C_8\times Q_8$ 8D3 $8$ $10$ $C_4\times C_8$ 4H-1 8D-1 $b^{3}c$
$C_5:C_8\times Q_8$ 8D-3 $8$ $10$ $C_4\times C_8$ 4H1 8D1 $b^{5}c$
$C_5:C_8\times Q_8$ 8E1 $8$ $10$ $C_4\times C_8$ 4H1 8E-3 $abc$
$C_5:C_8\times Q_8$ 8E-1 $8$ $10$ $C_4\times C_8$ 4H-1 8E3 $ab^{7}c$
$C_5:C_8\times Q_8$ 8E3 $8$ $10$ $C_4\times C_8$ 4H-1 8E-1 $ab^{3}c$
$C_5:C_8\times Q_8$ 8E-3 $8$ $10$ $C_4\times C_8$ 4H1 8E1 $ab^{5}c$
$C_5:C_8\times Q_8$ 10A $10$ $4$ $Q_8\times C_{10}$ 5A 2B $b^{4}c^{4}$
$C_5:C_8\times Q_8$ 10B $10$ $4$ $Q_8\times C_{10}$ 5A 2A $b^{4}c^{2}$
$C_5:C_8\times Q_8$ 10C $10$ $4$ $Q_8\times C_{10}$ 5A 2C $c^{2}$
$C_5:C_8\times Q_8$ 20A $20$ $8$ $C_2\times C_{20}$ 10C 4A $c$
$C_5:C_8\times Q_8$ 20B $20$ $8$ $C_2\times C_{20}$ 10C 4B $b^{4}c$
$C_5:C_8\times Q_8$ 20C $20$ $8$ $C_2\times C_{20}$ 10C 4C $ac^{4}$
$C_5:C_8\times Q_8$ 20D $20$ $8$ $C_2\times C_{20}$ 10C 4D $ac$
$C_5:C_8\times Q_8$ 20E $20$ $8$ $C_2\times C_{20}$ 10C 4E $ab^{4}c^{4}$
$C_5:C_8\times Q_8$ 20F $20$ $8$ $C_2\times C_{20}$ 10C 4F $ab^{4}c$
  displayed columns for results