Perimeter search with a maximum of 1 item of a specific group

Question

I have a table of shops with some chains among them. When I do a proximity search, I want only the closest shop of each chain to be included in the result. However, I want all shops from the non-chains to be found.

My idea is to assign a group to the chain shops and then filter them in the SQL - but how?

shop_id	shop	shop_lat	shop_lon	chaingroup
1	SHOP1	55.8	9.4	NULL
2	SHOP2	55.9	9.5	2
3	SHOP3	55.1	9.6	NULL
4	SHOP4	55.2	9.7	3
5	SHOP5	55.3	9.8	NULL
6	SHOP6	55.4	9.9	2
7	SHOP7	55.5	10.0	NULL
8	SHOP8	55.6	10.1	5
9	SHOP9	55.7	10.2	NULL
10	SHOP10	55.8	10.3	5

My SQL:

SELECT shop, ((ACOS(SIN(53.58393 * PI() / 180) * SIN(shop_lat * PI() / 180) + COS(53.58393 * PI() / 180) * COS(shop_lat * PI() / 180) * COS((10.01413 - shop_lon) * PI() / 180)) * 180 / PI()) * 60 * 1.150779448 * 1.609344) as distance, chaingroup
FROM shops
GROUP BY shop_id
HAVING distance <= 10 
ORDER BY distance ASC

Result should be:

shop	distance	chaingroup
SHOP1	1.0	NULL
SHOP2	2.0	2
SHOP3	3.0	NULL
SHOP4	4.0	3
SHOP5	5.0	NULL
SHOP7	7.0	NULL
SHOP8	8.0	5
SHOP9	9.0	NULL

As you can see, SHOP10 is not listed because SHOP8 from chain no. 5 has already been found.

Any suggestions?