"2-subnormality is not finite-join-closed"
"Automorph-conjugacy is not finite-join-closed"
"Central factor is not finite-join-closed"
"Direct factor is not finite-join-closed"
"Finite-join-closedness is left residual-preserved"
"Intermediately operator preserves join-closedness"
"Procharacteristicity is not finite-join-closed"
"Pronormality is not finite-join-closed"
"Subnormality is not finite-join-closed"
"Transitive normality is not finite-join-closed"