A few connected starting points for studying groups.
- Group Actions — groups as transformations.
- Normal Subgroups — the subgroups that allow quotients.
- Quotient Groups — identifying elements without losing multiplication.
- First Isomorphism Theorem — a homomorphism through its kernel.
- Orbit–Stabilizer Theorem — counting through symmetry.
A small subgroup lattice
The Klein four-group has three subgroups of order two. All its subgroups are normal because the group is abelian.
