index match with multiple criteria

Alright. I need some help.
I'm familiar with vlookups, and index,matches but I can not get this to work.

I have a workbook with 2 sheets, Sheet1 and Sheet2.
Sheet 1 has 11 columns. Only 3 that I care about. Name, ID Group, IDmin and IDmax.
Sheet 2 has 6 columns. 3 that I care about aswell... Dept, IDGroup and ID.

What I'm trying to do is match up Name on Sheet1 to Sheet2, according to the IDGroup and ID...
However, the tricky part is, when we enter the ID, we enter them as a range on Sheet1.
So,
Sheet1 looks like this.

Name	GroupID	IDmin	IDmax
Matt	1234	0000	9999
John	1234	0000	9999

Sheet2 looks like this.

Dept	GroupID	ID
1000056	1234	1458
1000056	1234	1854

I want to add a column on Sheet2 called Name, to lookup the IDGroup and ID number to tell me who the ID is. We have several different Group IDs, so that would need to be included.