Function restriction formalism chart

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Subgroup property Expression Endo-invariance Balanced Invariance Left-inner -

Normal subgroup || Inner Aut, Inner Function || Yes || No || Yes || Yes || Yes |- Characteristic subgroup || Aut Aut, Aut Function || Yes || Yes || Yes || No || No |- Strictly characteristic subgroup || Surj. End Function, Surj. End. End. || Yes || No || Yes || No || Yes |- |}