Rank the top 5 entries in different criteria - excel

Question

I have a table that I want to find the top X people in each of the different groups.
Unique Names Number Group
a 30 1
b 4 2
c 19 3
d 40 2
e 1 1
f 9 2
g 15 3
I've ranked the top 5 people by number by using =index($A$2:$A$8,match(large($B$2:$B$8,1),$B$2:$B$8,0)). The 1 in the LARGE function I linked to a ranked range so that when I dragged down it changed up the number.
What I would like to do next is rank the top x number of people in each group. So top 3 in group 1.
I tried =index($A$2:$A$8,match("1"&large($B$2:$B$8,1),$C$2:$C$8&$B$2:$B$8,0)) but it didn't seem to work.
Thanks
EDIT: After looking at the answers below I have realised why they are not working for me. My actual data that I want to use the formula with have multiple entries of numbers. I have adjusted the example data to show this. The problem I have is that if there are duplicate numbers then it returns both of the names even if one is not in the group.
Unique Names Number Group
a 30 1
b 30 2
c 19 3
d 40 2
e 1 1
f 30 2
g 15 3

Answer 1

Proof of Concept
Use the following formula in the example above in cell F2 and copy down and to the right as needed.
=IFERROR(INDEX($A$2:$A$8,MATCH(AGGREGATE(14,6,($C$2:$C$8=F$1)*($B$2:$B$8),ROW($A2)-1),$B$2:$B$8,0)),"")
In the header row provide the group numbers. or come up with a formula to augment and reset the group number as you copy down based on your X number in your question.
Explanation:
The AGGREGATE function unlike the large function is an array function without the need to use CSE. As such we can add criteria to what we want to use. In this case only 1 criteria was used and that was the group number. in the formula it was the following part:
($C$2:$C$8=F$1)
If there were multiple criteria we would use either an + operator as an OR or we would use an * operator as an AND.
The 6 option in the aggregate function allows us to ignore errors. This is useful when trying to get the small. It is also useful for dealing with other information that may cause errors that do not need to be worried about.
As this is technically an array operation avoid using full column/row references as they can bog down your system.
The basics of what the over all formula is doing is building a list that match the group number you are interested in. After filtering your numbers, it then determines which is the largest, second largest etc by what row you have copied down to. It then determine what row the nth largest number occurs in through the match function, and finally it returns to the corresponding name to that row with the index function.

Answer 2

Building on all the other great answers.
Because you have the possibilities of duplicate values in each group we need to do this with two formulas.
First we need to get the numbers in order. I used the Aggregate, but this could be done with the array LARGE(IF()) also:
=IFERROR(AGGREGATE(14,6,$B$2:$B$8/($C$2:$C$8=E$1),ROW(1:1)),"")
Then using that number and order we can reference, we can use a modified version of #ForwardEd's formula, using COUNTIF() to ensure we get the correct name in return.
=IFERROR(INDEX($A$2:$A$8,AGGREGATE(15,6,(ROW($B$2:$B$8)-ROW($B$2)+1)/(($C$2:$C$8=F$1)*($B$2:$B$8=E3)),COUNTIF(E$2:E2,E3)+1)),"")
This will count the number in the results returned and then bring in the correct name.

Answer 3

You could also solve this with array formulas - to filter a group whose name is stored in E1, your code
=INDEX($A$2:$A$8,MATCH(LARGE($B$2:$B$8,1),$B$2:$B$8,0))
would then be adapted to
=INDEX($A$2:$A$8,MATCH(LARGE(IF($C$2:$C$8<>E1,-1,$B$2:$B$8),1),$B$2:$B$8,0))
Note: After entering an array formula, you have press CTRL+SHIFT+ENTER.

Answer 4

Thank you to everyone who offered help but for some reason none of your methods worked for me, which I am sure was to do with the quality of my data. I used an alternate method in the end which is slightly convoluted but seemed to work.
=IF($C2="1",RANK($B2,$B$2:$B$8,1)+ROW()/10000,-1)
Essentially using the rank function and adding a fraction to separate out duplicate values.