My program starts by reading in paragraph mode, then chomping. Only groups with more than 1 line can have 1 or more newlines.

#!/usr/bin/perl
use strict;
use warnings;
use 5.014;

{
    local $/ = "";
    while (<DATA>) {
        chomp;
        print "$_\n" if tr/\n//; # if 1 or more newlines   
    }   
}

__DATA__
Group 1

Group 2

Group 3
Group 3

Group 4

Group 5
Group 5
Group 5
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prints:

Group 3
Group 3
Group 5
Group 5
Group 5
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