Problem plotting hasse diagram with xypic

Problem plotting hasse diagram with xypic

I need to plot the following hasse diagrams: 1)
2)
I tried using xypic. For the first I worte the following code
\xymatrix{
&{G}\ar@{-}[dr]\ar@{-}[dl] \\
{\mathbb{Z}_p}\ar@{-}[dr] & & \mathbb{Z}_q}\ar@{-}[dl]}\\
{{e}} \\
}
but it displays nothing. About second one, I don't really know from where
to start. I can write also this wrong code:
\xymatrix{
& {HK}\ar@{-}[dr]\ar@{=}[dl]\\
H@\ar{=}[dr] & K@\ar{-}[dl]\\
{H\cap K}
}
How can I plot them both? Where is my mistake?