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v t e Groups
Basic notions	Subgroup Normal subgroup Commutator subgroup Quotient group Group homomorphism (Semi-) direct product direct sum
Types of groups	Finite groups Abelian groups Cyclic groups Infinite group Simple groups Solvable groups Symmetry group Space group Point group Wallpaper group Trivial group
Discrete groups	Classification of finite simple groups Cyclic group Z_n Alternating group A_n Sporadic groups Mathieu group M_11..12,M_22..24 Conway group Co_1..3 Janko groups J₁, J₂, J₃, J₄ Fischer group F_22..24 Baby monster group B Monster group M Other finite groups Symmetric group S_n Dihedral group D_n Rubik's Cube group
Lie groups	General linear group GL(n) Special linear group SL(n) Orthogonal group O(n) Special orthogonal group SO(n) Unitary group U(n) Special unitary group SU(n) Symplectic group Sp(n) Exceptional Lie groups G₂ F₄ E₆ E₇ E₈ Circle group Lorentz group Poincaré group Quaternion group
Infinite dimensional groups	Conformal group Diffeomorphism group Loop group Quantum group O(∞) SU(∞) Sp(∞)
History Applications Abstract algebra

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