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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{6}=c^{40}=[a,b]=1, a^{4}=c^{20}, c^{a}=b^{3}c^{29}, c^{b}=c^{21} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$(C_5\times \OD_{16}):C_{12}$ 1A $1$ $1$ $(C_5\times \OD_{16}):C_{12}$ 1A 1A 1A $1$
$(C_5\times \OD_{16}):C_{12}$ 2A $2$ $1$ $(C_5\times \OD_{16}):C_{12}$ 1A 2A 2A $c^{20}$
$(C_5\times \OD_{16}):C_{12}$ 2B $2$ $2$ $(C_2\times C_{20}):C_{12}$ 1A 2B 2B $a^{2}b^{3}c^{30}$
$(C_5\times \OD_{16}):C_{12}$ 2C $2$ $2$ $\OD_{16}\times C_{30}$ 1A 2C 2C $a^{2}c^{10}$
$(C_5\times \OD_{16}):C_{12}$ 2D $2$ $2$ $C_{30}:\OD_{16}$ 1A 2D 2D $b^{3}$
$(C_5\times \OD_{16}):C_{12}$ 3A1 $3$ $1$ $(C_5\times \OD_{16}):C_{12}$ 3A-1 1A 3A-1 $b^{2}$
$(C_5\times \OD_{16}):C_{12}$ 3A-1 $3$ $1$ $(C_5\times \OD_{16}):C_{12}$ 3A1 1A 3A1 $b^{4}$
$(C_5\times \OD_{16}):C_{12}$ 4A1 $4$ $1$ $(C_5\times \OD_{16}):C_{12}$ 2A 4A-1 4A1 $a^{2}c^{20}$
$(C_5\times \OD_{16}):C_{12}$ 4A-1 $4$ $1$ $(C_5\times \OD_{16}):C_{12}$ 2A 4A1 4A-1 $a^{2}$
$(C_5\times \OD_{16}):C_{12}$ 4B $4$ $2$ $(C_2\times C_{20}):C_{12}$ 2A 4B 4B $b^{3}c^{30}$
$(C_5\times \OD_{16}):C_{12}$ 4C $4$ $2$ $C_{30}:\OD_{16}$ 2A 4C 4C $a^{2}b^{3}c^{20}$
$(C_5\times \OD_{16}):C_{12}$ 4D $4$ $2$ $\OD_{16}\times C_{30}$ 2A 4D 4D $c^{30}$
$(C_5\times \OD_{16}):C_{12}$ 4E1 $4$ $20$ $C_4\times C_{12}$ 2B 4E-1 4E1 $a^{3}b^{3}c^{11}$
$(C_5\times \OD_{16}):C_{12}$ 4E-1 $4$ $20$ $C_4\times C_{12}$ 2B 4E1 4E-1 $ac$
$(C_5\times \OD_{16}):C_{12}$ 4F1 $4$ $20$ $C_4\times C_{12}$ 2B 4F-1 4F1 $a^{3}b^{3}c^{13}$
$(C_5\times \OD_{16}):C_{12}$ 4F-1 $4$ $20$ $C_4\times C_{12}$ 2B 4F1 4F-1 $ac^{3}$
$(C_5\times \OD_{16}):C_{12}$ 5A1 $5$ $2$ $\OD_{16}\times C_{30}$ 5A2 5A2 1A $c^{32}$
$(C_5\times \OD_{16}):C_{12}$ 5A2 $5$ $2$ $\OD_{16}\times C_{30}$ 5A1 5A1 1A $c^{24}$
$(C_5\times \OD_{16}):C_{12}$ 6A1 $6$ $1$ $(C_5\times \OD_{16}):C_{12}$ 3A-1 2A 6A-1 $b^{2}c^{20}$
$(C_5\times \OD_{16}):C_{12}$ 6A-1 $6$ $1$ $(C_5\times \OD_{16}):C_{12}$ 3A1 2A 6A1 $b^{4}c^{20}$
$(C_5\times \OD_{16}):C_{12}$ 6B1 $6$ $2$ $(C_2\times C_{20}):C_{12}$ 3A1 2B 6B-1 $a^{2}bc^{30}$
$(C_5\times \OD_{16}):C_{12}$ 6B-1 $6$ $2$ $(C_2\times C_{20}):C_{12}$ 3A-1 2B 6B1 $a^{2}b^{5}c^{30}$
$(C_5\times \OD_{16}):C_{12}$ 6C1 $6$ $2$ $\OD_{16}\times C_{30}$ 3A1 2C 6C-1 $a^{2}b^{4}c^{10}$
$(C_5\times \OD_{16}):C_{12}$ 6C-1 $6$ $2$ $\OD_{16}\times C_{30}$ 3A-1 2C 6C1 $a^{2}b^{2}c^{10}$
$(C_5\times \OD_{16}):C_{12}$ 6D1 $6$ $2$ $C_{30}:\OD_{16}$ 3A-1 2D 6D-1 $b^{5}$
$(C_5\times \OD_{16}):C_{12}$ 6D-1 $6$ $2$ $C_{30}:\OD_{16}$ 3A1 2D 6D1 $b$
$(C_5\times \OD_{16}):C_{12}$ 8A1 $8$ $4$ $C_2\times C_{120}$ 4D 8A-1 8A1 $c^{15}$
$(C_5\times \OD_{16}):C_{12}$ 8A-1 $8$ $4$ $C_2\times C_{120}$ 4D 8A1 8A-1 $c^{25}$
$(C_5\times \OD_{16}):C_{12}$ 8B1 $8$ $4$ $C_2\times C_{120}$ 4D 8B-1 8B1 $a^{2}c^{35}$
$(C_5\times \OD_{16}):C_{12}$ 8B-1 $8$ $4$ $C_2\times C_{120}$ 4D 8B1 8B-1 $a^{2}c^{25}$
$(C_5\times \OD_{16}):C_{12}$ 8C1 $8$ $20$ $C_2\times C_{24}$ 4A1 8C-1 8C1 $a^{3}$
$(C_5\times \OD_{16}):C_{12}$ 8C-1 $8$ $20$ $C_2\times C_{24}$ 4A-1 8C1 8C-1 $ac^{20}$
$(C_5\times \OD_{16}):C_{12}$ 8D1 $8$ $20$ $C_2\times C_{24}$ 4A1 8D-1 8D1 $a^{3}c^{2}$
$(C_5\times \OD_{16}):C_{12}$ 8D-1 $8$ $20$ $C_2\times C_{24}$ 4A-1 8D1 8D-1 $ac^{22}$
$(C_5\times \OD_{16}):C_{12}$ 10A1 $10$ $2$ $\OD_{16}\times C_{30}$ 5A2 10A3 2A $c^{28}$
$(C_5\times \OD_{16}):C_{12}$ 10A3 $10$ $2$ $\OD_{16}\times C_{30}$ 5A1 10A1 2A $c^{4}$
$(C_5\times \OD_{16}):C_{12}$ 10B1 $10$ $2$ $\OD_{16}\times C_{30}$ 5A1 10B3 2C $a^{2}c^{26}$
$(C_5\times \OD_{16}):C_{12}$ 10B-1 $10$ $2$ $\OD_{16}\times C_{30}$ 5A1 10B-3 2C $a^{2}c^{34}$
$(C_5\times \OD_{16}):C_{12}$ 10B3 $10$ $2$ $\OD_{16}\times C_{30}$ 5A2 10B-1 2C $a^{2}c^{18}$
$(C_5\times \OD_{16}):C_{12}$ 10B-3 $10$ $2$ $\OD_{16}\times C_{30}$ 5A2 10B1 2C $a^{2}c^{2}$
$(C_5\times \OD_{16}):C_{12}$ 10C1 $10$ $4$ $C_2^2\times C_{60}$ 5A1 10C3 2D $b^{3}c^{24}$
$(C_5\times \OD_{16}):C_{12}$ 10C3 $10$ $4$ $C_2^2\times C_{60}$ 5A2 10C1 2D $b^{3}c^{32}$
$(C_5\times \OD_{16}):C_{12}$ 10D1 $10$ $4$ $C_2^2\times C_{60}$ 5A1 10D3 2B $a^{2}b^{3}c^{26}$
$(C_5\times \OD_{16}):C_{12}$ 10D3 $10$ $4$ $C_2^2\times C_{60}$ 5A2 10D1 2B $a^{2}b^{3}c^{18}$
$(C_5\times \OD_{16}):C_{12}$ 12A1 $12$ $1$ $(C_5\times \OD_{16}):C_{12}$ 6A1 4A1 12A5 $a^{2}b^{4}$
$(C_5\times \OD_{16}):C_{12}$ 12A-1 $12$ $1$ $(C_5\times \OD_{16}):C_{12}$ 6A-1 4A-1 12A-5 $a^{2}b^{2}c^{20}$
$(C_5\times \OD_{16}):C_{12}$ 12A5 $12$ $1$ $(C_5\times \OD_{16}):C_{12}$ 6A-1 4A1 12A1 $a^{2}b^{2}$
$(C_5\times \OD_{16}):C_{12}$ 12A-5 $12$ $1$ $(C_5\times \OD_{16}):C_{12}$ 6A1 4A-1 12A-1 $a^{2}b^{4}c^{20}$
$(C_5\times \OD_{16}):C_{12}$ 12B1 $12$ $2$ $(C_2\times C_{20}):C_{12}$ 6A-1 4B 12B-1 $b^{5}c^{10}$
$(C_5\times \OD_{16}):C_{12}$ 12B-1 $12$ $2$ $(C_2\times C_{20}):C_{12}$ 6A1 4B 12B1 $bc^{30}$
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