Analytic curves are classified w.r.t. their symmetry under a given regular and separately analytic Lie group action G×M→M on an analytic manifold. We show that a non-constant analytic curve γ:D→M is either free or exponential – i.e., up to analytic reparametrization of the form t↦exp(t⋅g→)⋅x. The vector g→∈g is additionally proven to be unique up to (non-zero scalation and) addition of elements in the Lie algebra of the stabilizer Gγ≡{g∈G|g⋅γ=γ} of the curve γ. We furthermore prove that in the free case, γ splits into countably many immersive subcurves – each of them discretely generated by G. This means that each such subcurve δ:D⊇(ι′,ι)→M is build up countably many G-translates of a symmetry free building block δ|Δ, whereby three different cases can occur:−In the shift case, the building blocks are continuously distributed in δ, with Δ always compact. Then, δ is created by iterated shifts of δ|Δ by some g∈G and its inverse; whereby the class [e]≠[g]∈G/Gγ is uniquely determined, as well as the same for each possible decomposition.−In the flip case, there exist countably many building blocks – each of them defined on a compact interval, and contained in the one and only decomposition that exists in this case. Here, δ is created by iterated flips at the boundary points of these building blocks, whereby the occurring transformations are generated by two non-trivial classes in G/Gγ.−In the mirror case, there exists exactly one symmetry (flipping) point δ(τ), as well as one translation class [e]≠[g]∈G/Gγ. The one and only decomposition of δ is thus given by δ|(i′,τ], δ|[τ,i), whereby δ|(i′,τ] is flipped into δ|[τ,i) or vice versa (or both). We finally extend the classification result to the analytic 1-submanifold case. Specifically, we show that an analytic 1-submanifold of M is either free or (exponential, i.e.) analytically diffeomorphic to U(1) or to an interval via the exponential map. The corresponding decomposition results in the free case are outlined in this paper, but proven in a separate one.