The person who usually organizes things deserves an invitation they did not have to create.

In most groups one person does the arranging: picks the date, books the table, chases the replies. Because they always start it, everyone else gets a full social life while that person gets an administrative task. They also never receive the small pleasure of being thought of, which is most of what an invitation actually is. Being included and being invited are not quite the same.

Think of whoever usually organises things around you. Invite them to something you have arranged completely, with the date already chosen, and let their only job be turning up.