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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{12}=c^{2}=d^{10}=[a,b]=[a,c]=[a,d]=[c,d]=1, c^{b}=d^{5}, d^{b}=cd^{3} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_2\times A_4\times F_5$ 1A $1$ $1$ $C_2\times A_4\times F_5$ 1A 1A 1A $1$
$C_2\times A_4\times F_5$ 2A $2$ $1$ $C_2\times A_4\times F_5$ 1A 2A 2A $a$
$C_2\times A_4\times F_5$ 2B $2$ $3$ $C_2^3\times F_5$ 1A 2B 2B $d^{5}$
$C_2\times A_4\times F_5$ 2C $2$ $3$ $C_2^3\times F_5$ 1A 2C 2C $ad^{5}$
$C_2\times A_4\times F_5$ 2D $2$ $5$ $C_2^3:C_{12}$ 1A 2D 2D $b^{6}d^{8}$
$C_2\times A_4\times F_5$ 2E $2$ $5$ $C_2^3:C_{12}$ 1A 2E 2E $ab^{6}$
$C_2\times A_4\times F_5$ 2F $2$ $15$ $C_2^3\times C_4$ 1A 2F 2F $b^{6}d$
$C_2\times A_4\times F_5$ 2G $2$ $15$ $C_2^3\times C_4$ 1A 2G 2G $ab^{6}d$
$C_2\times A_4\times F_5$ 3A1 $3$ $4$ $C_6\times F_5$ 3A-1 1A 3A-1 $b^{4}$
$C_2\times A_4\times F_5$ 3A-1 $3$ $4$ $C_6\times F_5$ 3A1 1A 3A1 $b^{8}$
$C_2\times A_4\times F_5$ 4A1 $4$ $5$ $C_2^3:C_{12}$ 2D 4A-1 4A1 $b^{3}$
$C_2\times A_4\times F_5$ 4A-1 $4$ $5$ $C_2^3:C_{12}$ 2D 4A1 4A-1 $b^{9}$
$C_2\times A_4\times F_5$ 4B1 $4$ $5$ $C_2^3:C_{12}$ 2D 4B-1 4B1 $ab^{3}$
$C_2\times A_4\times F_5$ 4B-1 $4$ $5$ $C_2^3:C_{12}$ 2D 4B1 4B-1 $ab^{9}$
$C_2\times A_4\times F_5$ 4C1 $4$ $15$ $C_2^3\times C_4$ 2D 4C-1 4C1 $b^{3}d$
$C_2\times A_4\times F_5$ 4C-1 $4$ $15$ $C_2^3\times C_4$ 2D 4C1 4C-1 $b^{9}d$
$C_2\times A_4\times F_5$ 4D1 $4$ $15$ $C_2^3\times C_4$ 2D 4D-1 4D1 $ab^{3}d$
$C_2\times A_4\times F_5$ 4D-1 $4$ $15$ $C_2^3\times C_4$ 2D 4D1 4D-1 $ab^{9}d$
$C_2\times A_4\times F_5$ 5A $5$ $4$ $C_{10}\times A_4$ 5A 5A 1A $d^{2}$
$C_2\times A_4\times F_5$ 6A1 $6$ $4$ $C_6\times F_5$ 3A1 2A 6A-1 $ab^{8}$
$C_2\times A_4\times F_5$ 6A-1 $6$ $4$ $C_6\times F_5$ 3A-1 2A 6A1 $ab^{4}$
$C_2\times A_4\times F_5$ 6B1 $6$ $20$ $C_2\times C_{12}$ 3A1 2E 6B-1 $ab^{2}$
$C_2\times A_4\times F_5$ 6B-1 $6$ $20$ $C_2\times C_{12}$ 3A-1 2E 6B1 $ab^{10}$
$C_2\times A_4\times F_5$ 6C1 $6$ $20$ $C_2\times C_{12}$ 3A1 2D 6C-1 $b^{2}$
$C_2\times A_4\times F_5$ 6C-1 $6$ $20$ $C_2\times C_{12}$ 3A-1 2D 6C1 $b^{10}$
$C_2\times A_4\times F_5$ 10A $10$ $4$ $C_{10}\times A_4$ 5A 10A 2A $ad^{6}$
$C_2\times A_4\times F_5$ 10B $10$ $12$ $C_2^2\times C_{10}$ 5A 10B 2B $d$
$C_2\times A_4\times F_5$ 10C $10$ $12$ $C_2^2\times C_{10}$ 5A 10C 2C $ad$
$C_2\times A_4\times F_5$ 12A1 $12$ $20$ $C_2\times C_{12}$ 6C1 4A1 12A5 $b$
$C_2\times A_4\times F_5$ 12A-1 $12$ $20$ $C_2\times C_{12}$ 6C-1 4A-1 12A-5 $b^{11}$
$C_2\times A_4\times F_5$ 12A5 $12$ $20$ $C_2\times C_{12}$ 6C-1 4A1 12A1 $b^{5}$
$C_2\times A_4\times F_5$ 12A-5 $12$ $20$ $C_2\times C_{12}$ 6C1 4A-1 12A-1 $b^{7}$
$C_2\times A_4\times F_5$ 12B1 $12$ $20$ $C_2\times C_{12}$ 6C1 4B1 12B5 $ab$
$C_2\times A_4\times F_5$ 12B-1 $12$ $20$ $C_2\times C_{12}$ 6C-1 4B-1 12B-5 $ab^{11}$
$C_2\times A_4\times F_5$ 12B5 $12$ $20$ $C_2\times C_{12}$ 6C-1 4B1 12B1 $ab^{5}$
$C_2\times A_4\times F_5$ 12B-5 $12$ $20$ $C_2\times C_{12}$ 6C1 4B-1 12B-1 $ab^{7}$
$C_2\times A_4\times F_5$ 15A1 $15$ $16$ $C_{30}$ 15A-1 5A 3A1 $b^{8}d^{4}$
$C_2\times A_4\times F_5$ 15A-1 $15$ $16$ $C_{30}$ 15A1 5A 3A-1 $b^{4}d^{6}$
$C_2\times A_4\times F_5$ 30A1 $30$ $16$ $C_{30}$ 15A1 10A 6A1 $ab^{4}d^{2}$
$C_2\times A_4\times F_5$ 30A-1 $30$ $16$ $C_{30}$ 15A-1 10A 6A-1 $ab^{8}d^{2}$
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