/*
U4(2) presented on its (Type I) standard generators.
*/

G<x,y>:=Group<x,y|
x^2,
y^5,
(x*y)^9,
(x,y)^3,
(x,y*x*y)^2
>;
a:=x;b:=y;

// Maximal subgroups.
M1:=sub<G|y,x*y*x*y*x*y^-1*x>;
M2:=sub<G|y,x*y^2*x*y^-2*x>;
M3:=sub<G|x*y,y*x*y*x*y*x>;
M4:=sub<G|x,y*x*y*x*y*x*y^2>;
M5:=sub<G|x,y*x*y^2>;
// 2^4:A5, S6, 3^{1+2}:2"A4, 3^3:S4, 2"(A4 x A4):2.


/*
Demonstration of correctness.
Coset enumeration over trivial subgroup:

print Order(G);
*/