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* [[Weaker than::Homomorph-containing subgroup]]

* [[Weaker than::Subhomomorph-containing subgroup]]

* [[Weaker than::Variety-containing subgroup]]

===Weaker properties===

* [[Stronger than::Intermediately characteristic subgroup]]

* [[Stronger than::Characteristic subgroup]]

==Metaproperties==

{{intransitive}}

An intermediately fully characteristic subgroup of an intermediately fully characteristic subgroup need not be intermediately fully characteristic. {{proofat|[[Intermediate full characteristicity is not transitive]]}}

{{join-closed}}

An arbitrary join of intermediately fully characteristic subgroups is intermediately fully characteristic. This follows from the fact that the intermediately operator preserves the property of being closed under joins. {{proofat|[[Intermediate full characteristicity is strongly join-closed]]}}

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