# Finding subgroup summand

Hi everyone, Let (G,.) be group with two subgroup H and K, I want to know when HK=G? $HK={h.k | h\in H ,k\in K}$ I try this

```
D= CyclicPermutationGroup(9)
H=D.subgroups()
for i in H:
for j in H:
i*j=K
if(K==G)
```

I have no idea how define " * "

http://www.gap-system.org/Manuals/doc/ref/chap49_mj.html suggests this isn't possible even in GAP.