GMM EM algorithm complexity per iteration

I was fitting GMM clusters with diagonal covariance on my data using EM with $n$ (=5e6) points, each having $m$ (=160) dimensions. I wanted to get around $k$ (=400) clusters. But this is taking a lot of time.

My question are:

• What is the per iteration complexity of GMM EM given $n$, $m$ and $k$?
• Which parameters might help me the most in reducing the runtime most while giving useful clusters?
• Also what is the suggested number of iterations required for EM to converge given this metadata? I'm currently working iterating 100 times.
• How is this affected by going from diagonal covariance to other covariances(tied covariance or full covariance)?