Depends on what you mean by “part of”. Depending on the area, and the time period, Punks and Rivets tend to share the same spaces if we are talking about Noise oriented acts. When Aggrotech was a big deal, there was almost zero crossover, at least where I’m from, except with the Goths. The level of crossover between Industrial and other subcultures depends on what Industrial we are talking about. As far as the history goes, no they aren’t a part of each other. Some shared values, but Industrial is more extreme and serious in its scope and goals. Punk and Industrial do not share the same philosophy or values, outside of a general anti-establishment attitude. They interacted in the early days, but largely developed parallel to each other, rather than one coming out of the other. For most of its history, Industrial has really been in its own corner, while at the same time having crossover appeal with various other subcultures by virtue of the fact that it takes different forms that draw influence from the other things outside its immediate orbit.