の下で/の下に => under; with ~ N2
ば~のに/たら~のに => would have; should have; if only ~ N3
のうちに => Within... N3
Limit
でも~のに => Even... also..., then... N2
Demonstrate by example
~のに      => to (do something); in order to ~ N4
Purpose, nominalization
のに => although, in spite of, even though ~ N4
いかのように => As below N4
Description
...のに => to (do something); in order to ~ N4
Purpose, target
かのようだ/かのように/かのような => as if; just like ~ N2
~には~の~がある      => has its own~ N3
Characteristic
というのに => even though,despite,when N2
Beyond expectations
かのうちに => right after; as soon as N2
Simultaneously