diff --git a/CHANGELOG.md b/CHANGELOG.md
index c3d8c2a7a826..cba0ea43ec25 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -11,6 +11,7 @@
 * [#5630](https://github.com/bbatsov/rubocop/issues/5630): Fix false positive for `Style/FormatStringToken` when using placeholder arguments in `format` method. ([@koic][])
 * [#5651](https://github.com/bbatsov/rubocop/pull/5651): Fix NoMethodError when specified config file that does not exist. ([@onk][])
 * [#5647](https://github.com/bbatsov/rubocop/pull/5647): Fix encoding method of RuboCop::MagicComment::SimpleComment. ([@htwroclau][])
+* [#5619](https://github.com/bbatsov/rubocop/issues/5619): Do not register an offense in `Style/InverseMethods` when comparing constants with `<`, `>`, `<=`, or `>=`. If the code is being used to determine class hierarchy, the correction might not be accurate. ([@rrosenblum][])
 
 ### Changes
 
diff --git a/lib/rubocop/cop/style/inverse_methods.rb b/lib/rubocop/cop/style/inverse_methods.rb
index 1a57b1c11983..7709cd126a01 100644
--- a/lib/rubocop/cop/style/inverse_methods.rb
+++ b/lib/rubocop/cop/style/inverse_methods.rb
@@ -27,18 +27,21 @@ module Style
       #   foo != bar
       #   foo == bar
       #   !!('foo' =~ /^\w+$/)
+      #   !(foo.class < Numeric) # Checking class hierarchy is allowed
       class InverseMethods < Cop
         include IgnoredNode
 
         MSG = 'Use `%<inverse>s` instead of inverting `%<method>s`.'.freeze
+        CLASS_COMPARISON_METHODS = %i[<= >= < >].freeze
         EQUALITY_METHODS = %i[== != =~ !~ <= >= < >].freeze
         NEGATED_EQUALITY_METHODS = %i[!= !~].freeze
+        CAMEL_CASE = /[A-Z]+[a-z]+/
 
         def_node_matcher :inverse_candidate?, <<-PATTERN
           {
-            (send $(send (...) $_ ...) :!)
-            (send (block $(send (...) $_) ...) :!)
-            (send (begin $(send (...) $_ ...)) :!)
+            (send $(send $(...) $_ $...) :!)
+            (send (block $(send $(...) $_) $...) :!)
+            (send (begin $(send $(...) $_ $...)) :!)
           }
         PATTERN
 
@@ -52,8 +55,9 @@ class InverseMethods < Cop
 
         def on_send(node)
           return if part_of_ignored_node?(node)
-          inverse_candidate?(node) do |_method_call, method|
+          inverse_candidate?(node) do |_method_call, lhs, method, rhs|
             return unless inverse_methods.key?(method)
+            return if possible_class_hierarchy_check?(lhs, rhs, method)
             return if negated?(node)
 
             add_offense(node,
@@ -78,7 +82,7 @@ def on_block(node)
         end
 
         def autocorrect(node)
-          method_call, method = inverse_candidate?(node)
+          method_call, _lhs, method, _rhs = inverse_candidate?(node)
 
           if method_call && method
             lambda do |corrector|
@@ -143,6 +147,19 @@ def end_parentheses(node, method_call)
                                     method_call.loc.expression.end_pos,
                                     node.loc.expression.end_pos)
         end
+
+        # When comparing classes, `!(Integer < Numeric)` is not the same as
+        # `Integer > Numeric`.
+        def possible_class_hierarchy_check?(lhs, rhs, method)
+          CLASS_COMPARISON_METHODS.include?(method) &&
+            (camel_case_constant?(lhs) ||
+             (rhs.size == 1 &&
+              camel_case_constant?(rhs.first)))
+        end
+
+        def camel_case_constant?(node)
+          node.const_type? && node.source =~ CAMEL_CASE
+        end
       end
     end
   end
diff --git a/manual/cops_style.md b/manual/cops_style.md
index da62289c1044..0e6b66f5c62d 100644
--- a/manual/cops_style.md
+++ b/manual/cops_style.md
@@ -2508,6 +2508,7 @@ foo.any? { |f| f.even? }
 foo != bar
 foo == bar
 !!('foo' =~ /^\w+$/)
+!(foo.class < Numeric) # Checking class hierarchy is allowed
 ```
 
 ### Configurable attributes
diff --git a/spec/rubocop/cop/style/inverse_methods_spec.rb b/spec/rubocop/cop/style/inverse_methods_spec.rb
index 3d403020b4d5..f30e173376a8 100644
--- a/spec/rubocop/cop/style/inverse_methods_spec.rb
+++ b/spec/rubocop/cop/style/inverse_methods_spec.rb
@@ -150,6 +150,36 @@
     end
   end
 
+  it 'allows comparing camel case constants on the right' do
+    expect_no_offenses(<<-RUBY.strip_indent)
+      klass = self.class
+      !(klass < BaseClass)
+    RUBY
+  end
+
+  it 'allows comparing camel case constants on the left' do
+    expect_no_offenses(<<-RUBY.strip_indent)
+      klass = self.class
+      !(BaseClass < klass)
+    RUBY
+  end
+
+  it 'registers an offense for comparing snake case constants on the right' do
+    expect_offense(<<-RUBY.strip_indent)
+      klass = self.class
+      !(klass < FOO_BAR)
+      ^^^^^^^^^^^^^^^^^^ Use `>=` instead of inverting `<`.
+    RUBY
+  end
+
+  it 'registers an offense for comparing snake case constants on the left' do
+    expect_offense(<<-RUBY.strip_indent)
+      klass = self.class
+      !(FOO_BAR < klass)
+      ^^^^^^^^^^^^^^^^^^ Use `>=` instead of inverting `<`.
+    RUBY
+  end
+
   context 'inverse blocks' do
     { select: :reject,
       reject: :select,