/*
L2(32):5 presented on its standard generators.
*/

G<x,y>:=Group<x,y|
x^2,
y^5,
// (x*y*x*y^2*x*y*x*y^-1*x*y^2)^2, // redundant.
x*y*x*y*x*y^-2*x*y^-1*x*y^-2*x*y*x*y^-2*x*y^-1*x*y^2*x*y^-2,
(x*y)^4*x*y^-2*(x*y^2)^3*x*y^-2*x*y^2*x*y^-1*x*y*x*y^2
>;

c:=x;d:=y;

// Subgroups 2^5:31:5, 33:10 and 31:10 respectively.
M2:=sub<G|y,x*y*x*y^3*x*y*x>;
M3:=sub<G|x,y^2*x*y^2*x*y*x*y^-1>;
M4:=sub<G|x,y^2*x*y*x*y*x*y^-1>;