Sending Alvar to Azhar for tutelage turned out to be a losing decision for the Major House. Due to his presence there they got embroiled in a conflict that none of them wanted. Fortunately they eventually managed to turn the situation into a profitable one, as after the war they became one of the larges food exporters to Azhar.
While they lost important family members, House Helheim gained quite a lot of good reputation for defeating a Bene Tleilax plot, rescuing an entire planet from famine afterwards and their overlords from Hala granted them several boons in exchange for assisting Aeolus in the transfer of power from the previous rulers, Draco.