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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{6}=b^{5}=c^{5}=d^{15}=[b,c]=[b,d]=[c,d]=1, b^{a}=c^{4}, c^{a}=bc, d^{a}=b^{2}c^{2}d^{14} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_5^2:(C_3\times D_{15})$ 1A $1$ $1$ $C_5^2:(C_3\times D_{15})$ 1A 1A 1A $1$
$C_5^2:(C_3\times D_{15})$ 2A $2$ $375$ $C_6$ 1A 2A 2A $a^{3}bc^{3}d^{3}$
$C_5^2:(C_3\times D_{15})$ 3A $3$ $2$ $C_5^3:C_3^2$ 3A 1A 3A $d^{5}$
$C_5^2:(C_3\times D_{15})$ 3B1 $3$ $25$ $C_3\times D_{15}$ 3B-1 1A 3B-1 $a^{4}c^{3}$
$C_5^2:(C_3\times D_{15})$ 3B-1 $3$ $25$ $C_3\times D_{15}$ 3B1 1A 3B1 $a^{2}b^{2}$
$C_5^2:(C_3\times D_{15})$ 3C1 $3$ $50$ $C_3\times C_{15}$ 3C-1 1A 3C-1 $a^{4}bc^{3}d^{5}$
$C_5^2:(C_3\times D_{15})$ 3C-1 $3$ $50$ $C_3\times C_{15}$ 3C1 1A 3C1 $a^{2}b^{3}cd^{10}$
$C_5^2:(C_3\times D_{15})$ 5A1 $5$ $2$ $C_5^3:C_3^2$ 5A2 5A2 1A $b^{3}cd^{3}$
$C_5^2:(C_3\times D_{15})$ 5A2 $5$ $2$ $C_5^3:C_3^2$ 5A1 5A1 1A $bc^{2}d^{6}$
$C_5^2:(C_3\times D_{15})$ 5B1 $5$ $6$ $C_5^2\times C_{15}$ 5B2 5B2 1A $d^{3}$
$C_5^2:(C_3\times D_{15})$ 5B2 $5$ $6$ $C_5^2\times C_{15}$ 5B1 5B1 1A $d^{6}$
$C_5^2:(C_3\times D_{15})$ 5C1 $5$ $6$ $C_5^2\times C_{15}$ 5C2 5C2 1A $c^{3}d^{3}$
$C_5^2:(C_3\times D_{15})$ 5C2 $5$ $6$ $C_5^2\times C_{15}$ 5C1 5C1 1A $cd^{6}$
$C_5^2:(C_3\times D_{15})$ 5D1 $5$ $6$ $C_5^2\times C_{15}$ 5D2 5D2 1A $b^{3}d^{3}$
$C_5^2:(C_3\times D_{15})$ 5D2 $5$ $6$ $C_5^2\times C_{15}$ 5D1 5D1 1A $bd^{6}$
$C_5^2:(C_3\times D_{15})$ 5E1 $5$ $6$ $C_5^2\times C_{15}$ 5E2 5E2 1A $cd^{3}$
$C_5^2:(C_3\times D_{15})$ 5E2 $5$ $6$ $C_5^2\times C_{15}$ 5E1 5E1 1A $c^{2}d^{6}$
$C_5^2:(C_3\times D_{15})$ 5F1 $5$ $6$ $C_5^2\times C_{15}$ 5F2 5F2 1A $b^{3}d^{6}$
$C_5^2:(C_3\times D_{15})$ 5F2 $5$ $6$ $C_5^2\times C_{15}$ 5F1 5F1 1A $bd^{12}$
$C_5^2:(C_3\times D_{15})$ 5G1 $5$ $6$ $C_5^2\times C_{15}$ 5G2 5G2 1A $c^{4}d^{6}$
$C_5^2:(C_3\times D_{15})$ 5G2 $5$ $6$ $C_5^2\times C_{15}$ 5G1 5G1 1A $c^{3}d^{12}$
$C_5^2:(C_3\times D_{15})$ 5H1 $5$ $6$ $C_5^2\times C_{15}$ 5H2 5H2 1A $b^{4}d^{6}$
$C_5^2:(C_3\times D_{15})$ 5H2 $5$ $6$ $C_5^2\times C_{15}$ 5H1 5H1 1A $b^{3}d^{12}$
$C_5^2:(C_3\times D_{15})$ 5I1 $5$ $6$ $C_5^2\times C_{15}$ 5I2 5I2 1A $c^{3}$
$C_5^2:(C_3\times D_{15})$ 5I2 $5$ $6$ $C_5^2\times C_{15}$ 5I1 5I1 1A $c$
$C_5^2:(C_3\times D_{15})$ 5J1 $5$ $6$ $C_5^2\times C_{15}$ 5J2 5J2 1A $bc^{3}d^{3}$
$C_5^2:(C_3\times D_{15})$ 5J2 $5$ $6$ $C_5^2\times C_{15}$ 5J1 5J1 1A $b^{2}cd^{6}$
$C_5^2:(C_3\times D_{15})$ 5K1 $5$ $6$ $C_5^2\times C_{15}$ 5K2 5K2 1A $b^{3}c$
$C_5^2:(C_3\times D_{15})$ 5K2 $5$ $6$ $C_5^2\times C_{15}$ 5K1 5K1 1A $bc^{2}$
$C_5^2:(C_3\times D_{15})$ 6A1 $6$ $375$ $C_6$ 3B1 2A 6A-1 $a^{5}b^{4}c^{3}d^{3}$
$C_5^2:(C_3\times D_{15})$ 6A-1 $6$ $375$ $C_6$ 3B-1 2A 6A1 $abd^{3}$
$C_5^2:(C_3\times D_{15})$ 15A1 $15$ $2$ $C_5^3:C_3^2$ 15A2 5A1 3A $bc^{2}d$
$C_5^2:(C_3\times D_{15})$ 15A2 $15$ $2$ $C_5^3:C_3^2$ 15A4 5A2 3A $b^{2}c^{4}d^{2}$
$C_5^2:(C_3\times D_{15})$ 15A4 $15$ $2$ $C_5^3:C_3^2$ 15A7 5A1 3A $bc^{2}d^{11}$
$C_5^2:(C_3\times D_{15})$ 15A7 $15$ $2$ $C_5^3:C_3^2$ 15A1 5A2 3A $b^{3}cd^{8}$
$C_5^2:(C_3\times D_{15})$ 15B1 $15$ $6$ $C_5^2\times C_{15}$ 15B2 5B1 3A $d$
$C_5^2:(C_3\times D_{15})$ 15B2 $15$ $6$ $C_5^2\times C_{15}$ 15B4 5B2 3A $d^{2}$
$C_5^2:(C_3\times D_{15})$ 15B4 $15$ $6$ $C_5^2\times C_{15}$ 15B7 5B1 3A $d^{4}$
$C_5^2:(C_3\times D_{15})$ 15B7 $15$ $6$ $C_5^2\times C_{15}$ 15B1 5B2 3A $d^{7}$
$C_5^2:(C_3\times D_{15})$ 15C1 $15$ $6$ $C_5^2\times C_{15}$ 15C2 5C1 3A $cd$
$C_5^2:(C_3\times D_{15})$ 15C2 $15$ $6$ $C_5^2\times C_{15}$ 15C4 5C2 3A $c^{2}d^{2}$
$C_5^2:(C_3\times D_{15})$ 15C4 $15$ $6$ $C_5^2\times C_{15}$ 15C7 5C1 3A $cd^{11}$
$C_5^2:(C_3\times D_{15})$ 15C7 $15$ $6$ $C_5^2\times C_{15}$ 15C1 5C2 3A $c^{2}d^{7}$
$C_5^2:(C_3\times D_{15})$ 15D1 $15$ $6$ $C_5^2\times C_{15}$ 15D2 5D1 3A $bd$
$C_5^2:(C_3\times D_{15})$ 15D2 $15$ $6$ $C_5^2\times C_{15}$ 15D4 5D2 3A $b^{2}d^{2}$
$C_5^2:(C_3\times D_{15})$ 15D4 $15$ $6$ $C_5^2\times C_{15}$ 15D7 5D1 3A $bd^{11}$
$C_5^2:(C_3\times D_{15})$ 15D7 $15$ $6$ $C_5^2\times C_{15}$ 15D1 5D2 3A $b^{2}d^{7}$
$C_5^2:(C_3\times D_{15})$ 15E1 $15$ $6$ $C_5^2\times C_{15}$ 15E2 5E1 3A $c^{2}d$
$C_5^2:(C_3\times D_{15})$ 15E2 $15$ $6$ $C_5^2\times C_{15}$ 15E4 5E2 3A $c^{4}d^{2}$
$C_5^2:(C_3\times D_{15})$ 15E4 $15$ $6$ $C_5^2\times C_{15}$ 15E7 5E1 3A $c^{3}d^{4}$
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