I was trying to get some insight into the definition of composition series and I'll appreciate it if someone verifies my understanding.
I am comprehending that if we were to draw the lattice of a group there will always be a normal subgroup in the immediate next "level" of the lattice. By the 4th isomorphism the composition factor $G_{i+1} /G_i$ is simple. This will continue until we reach the trivial subgroup of G.
Is this correct?
Thank you.