The older painters，most of whom were born before 1835，practiced in a mode often self-taught and monopolized by landscape subject matter and were securely established in and fostered by the reigning American art organization, the National Academy of Design.
(The older painters…practiced in a mode…and were securely established and fostered by…为句子主干)
老一代画家大多数出生于1835年以前，他们以一种经常是自学的方式和以风景画题材为主的形式作画。这些老画家是由当时美国艺坛上占统治地位的国家设计学院培养出来的，而且他们也在那里确立了自己的地位。
解析：
主句1：The older painters practiced in a mode often self-taught
主句2：monopolized by landscape subject matter
主句3：were securely established in
主句4：fostered by the reigning American art organization
从句1：most of whom were born before 1835
修饰结构1：the National Academy of Design
主句1，2，3，4是并列关系，用and并列
从句1修饰主句1的painters
修饰结构1是主句4中的American art organization的同位语
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