using System;

using System.Collections.Generic;

using System.Linq;

public class Program

{

    public class Test

    {

        public string property { get; set; }

        public string name { get; set; }

    }

    public static void Main()

    {

        var items = new List<Test>()

        {

            new Test{ property = "1", name = "1" },

                new Test{ property = "1", name = "2" },

                new Test{ property = "2", name = "3" },

                new Test{ property = "2", name = "4" },

                new Test{ property = "", name = "5" },

                new Test{ property = "", name = "6" }

        };

        var result = items

                .GroupBy(x => x.property == "")

                .SelectMany(x => 

                    !x.Key ? 

                        x.GroupBy(y => y.property).Select(y => y.ToList()).ToList() : 

                        x.Select(y => new List<Test> { y }).ToList() 

                    ).ToList();

        foreach(var res in result)

        {

            Console.WriteLine("Group " + res.First().property + ":");

            foreach (var item in res)           

                Console.WriteLine(item.name);           

        }

    }

}