From the little study I have done on this matter, I get the impression that the different sects at the time were in a sense at war with each other. Or at least greatly disliked each other.
You have all the priestly classes who had a position of power that Jesus was threatening. The Pharisees who wanted to have an earthly kingdom and were concerned with their own piety and the rebels who desired to overthrow roman rule. They all despised Jesus or wanted to use him for different ends. In one sense we get a picture of why he was crucified in terms of human opposition to his message at that time.
I am wondering since the Jewish religion rejected Jesus as the hoped for Messiah they are obviously awaiting a messianic appearance of some sort and how did this diverge into greater schools of Jewish thought.
It is true to say that there were several different Jewish factions, some of which rubbed along together, and some were daggers drawn with each other.
All Jewish groups accepted the main tenets of Judaism, such as monotheism, the Laws of Moses and circumcision, but there were deep splits over more minor religious issues such as life after death, the coming of the Messiah, and attitudes to the ruling Roman regime.
Most Christians will recognise some of these groups. The most famous, of course are the Pharisees and Sadducees, but most Christians will know that Jesus’s disciple, Simon, was a Zealot (Matt 10 4).
Less well recognised are other groups, such as the Scribes, the Herodians, the Essenes, John’s disciples, the Levites and Priests, and also those recognised as “elders” by the people, each of which had different religious or political emphases.
Then, of course, came the disciples of Jesus, with a whole new set of values, which turned most of the contemporary culture on its head.
The Pharisees lived by their own strict interpretation of Old Testament Law and their own gradual accumulation of traditions.
The Sadducees (lit the “righteous ones”) rejected the newer traditions and some aspects of religious thought, most famously, the resurrection of the dead.
The Essenes were a sect which lived in the Judean desert at Qumran. They rejected the official priesthood as coming from the wrong part of the Levitical tribe. They expected two Messiahs, one coming as a king and one as a priest.
The Zealots were a fierce group who opposed Roman rule, and therefore opposed the semi-Jewish Herodian family who were the puppet-rulers on behalf of the Roman Empire.
The Herodians, conversely, were a group who supported the Herodian family, and the Roman rule, particularly people who had a vested financial interest in the status quo.
The Priests and High Priests, were the religious leaders of Temple worship and sacrifice, and so were very influential in both the religious and social life of the nation.
Scribes were specially trained in writing. They were involved in copying the scriptures for synagogue use and therefore had extensive knowledge of the scriptures and the fine details of Jewish Law. They usually lined up with the Pharisees, and most of them, with a few exceptions, were vigorously opposed to Jesus.
Most of John’s disciples switched to follow Jesus, but it is said that some refused to change, and even after John’s death, continued to believe that he, rather than Jesus, was God’s chosen one.
Most of these groups lasted only a few centuries, and disappeared with the dispersion of the Jews by the Romans after AD 130.
Modern Jewish life encompasses many diverse groups, which share sometimes only superficial theological similarities. These range from ultra-liberals, sometimes rejecting the idea of a deity, and practicing only cultural aspects of Judaism, to ultra-conservatives, very strict, exclusive, and often Messianic in nature.
Of course these are the extremes, the “middle of the road” Jews are by far the greatest proportion, practicing sometimes nominal forms of Jewish religion and culture.
These groups, and their synagogues, often are described by names such as Liberal, Reform, and Conservative.
I hope that starts it off for you, Let me know if you think I haven’t covered something.