Absolute subservience of the interests of the individual to the state and the masses (volk).
Individuals and especially children are the property of the state.
Contempt for democracy in any of its forms.
Workers and labor (Proletariat), through the National Socialist German Workers' Party, were in theory in charge of the means of production. In practice and for practical reasons private management of industry continued but strictly under the direction and with the consent of the Party and its Fuehrer (Leader). "Capital" meant "Jews". "Patriotic" and ethnically pure Aryan capitalists were allowed to exist and even thrived under Nazism but more as a convenience than because Hitler believed in a free market economy.
An armed citizenry? Ganz verboten!
Anyone who evidenced disagreement with this philosophy were silenced on pain of imprisonment and frequently death.
"Right" and "Left" are labels which are routinely and intentionally (or more often ignorantly) misused. Everything about Nazism reeks of anti-Capitalism, anti-Individual Liberty, anti-Christianity, pro-Statism, and pro violent revolution against the Western European and Enlightenment Judeo-Christian ethos. It therefore is also a fair mirror image of today's U.S. Democratic Party and its leadership and philosophy.
Nice summary!
I forgot the shared Socialist love for a disarmed populace - well worth mentioning.
IIRC, the Bolsheviks only had to negotiate with the White Russians while the White Russians retained their weapons. Once they were laid down the ‘cleansing of counter-revolutionary elements’ could take place.
The Communists never forgot that.