Symmetry can enforce entanglement in maximally mixed states. This study explores how symmetry influences entanglement in quantum many-body systems, particularly in maximally mixed invariant states (MMIS). For unital quantum channels with strong symmetry, the MMIS can be highly entangled. The MMIS is separable for Abelian symmetries and entangled for non-Abelian ones. For non-Abelian continuous symmetries like SU(2), the bipartite entanglement of the MMIS scales logarithmically with the number of qudits, N. The MMIS is a mixture of all pure states in the invariant sector of the symmetry group. It is shown that the entanglement of formation and distillation are equal for any bipartition of the MMIS. The MMIS is also robust against local perturbations and can be prepared with a certain depth of quantum circuits. The study also shows that the MMIS exhibits long-range entanglement, which is not present in the Gibbs state of local Hamiltonians at high temperatures. The results highlight the role of symmetry in generating entanglement in mixed states and provide a framework for understanding the entanglement structure of symmetric quantum systems.Symmetry can enforce entanglement in maximally mixed states. This study explores how symmetry influences entanglement in quantum many-body systems, particularly in maximally mixed invariant states (MMIS). For unital quantum channels with strong symmetry, the MMIS can be highly entangled. The MMIS is separable for Abelian symmetries and entangled for non-Abelian ones. For non-Abelian continuous symmetries like SU(2), the bipartite entanglement of the MMIS scales logarithmically with the number of qudits, N. The MMIS is a mixture of all pure states in the invariant sector of the symmetry group. It is shown that the entanglement of formation and distillation are equal for any bipartition of the MMIS. The MMIS is also robust against local perturbations and can be prepared with a certain depth of quantum circuits. The study also shows that the MMIS exhibits long-range entanglement, which is not present in the Gibbs state of local Hamiltonians at high temperatures. The results highlight the role of symmetry in generating entanglement in mixed states and provide a framework for understanding the entanglement structure of symmetric quantum systems.