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Well you can always make a group for that.

There is option of 'invite only' in the giveaway creation page

You can create such a giveaway. In giveaway creation page tick whitelist and don't set a contributor limit. It will show up for all those users on the front page with a heart icon.

I think what he wants is to be able create a public or group GA with a high CV (or level I suppose now) which wouldn't apply to his whitelist.

Would be very useful, and for group giveaways too.

Is there any way to make it so people view a giveaway that you've set to just your group only so they join it?

Well that's some super saiyan way to dodge the implemented system. Ask cg to code a ring 0 list.