Why can't the vue route show the component on the right?

Why does the page jump when I click on each option instead of displaying the relevant components on the right side of the current page?

import Vue from "vue"
import Router from "vue-router"
import Index from "@/components/Index"
import Product from "@/components/Product"
import Work from "@/components/Work"
import Contact from "@/components/Contact"

Vue.use(Router)

export default new Router({
  mode: "history",
  routes: [
    {
      path: "/",
      name: "Index",
      component: Index
    },
    {
      path: "/product",
      name: "Product",
      component: Product
    },
    {
      path: "/work",
      name: "Work",
      component: Work
    },
    {
      path: "/contact",
      name: "Contact",
      component: Contact
    }
  ]
})

index.vue

<template>
  <div>
  <div id="left">
    <router-link class="list-group-item  router-link-active" to="/product">product</router-link>
    <router-link class="list-group-item" to="/work">work</router-link>
    <router-link class="list-group-item" to="/contact">contact</router-link>
  </div>
  <div id="right">
    <router-view></router-view>
  </div>
  </div>
</template>

<script>
export default {
  name: "Index",
  data () {
  }
}
</script>

<style scoped>
</style>
May.25,2021

write a sub-route under the root route: children: [], put those sub-routes into children and try

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