Long, long ago, Tama-yori-hime, daughter of the Sea God, had a child with Hiko-nagisa-ta u-gaya-fuki-ahezu no Mikoto. They named him Kami-Yamato-Ihare-Biko. He was the first Emperor of Japan or Tenno, under the name of Jimmu. Here is his lineage.

Early Periods

The dates for the first emperors should not be taken too seriously. Consider how long most of the reigns are.

Emperor Jimmu          660-585 BC
Emperor Suizei         581-549 BC
Emperor Annei          549-511 BC
Emperor Itoku          510-477 BC
Emperor Kosho          475-393 BC
Emperor Koan           392-291 BC
Emperor Korei          290-215 BC
Emperor Kogen          214-158 BC
Emperor Kaika          158-98  BC
Emperor Sujin           97-30  BC
Emperor Suinin          29 BC-70 AD
Emperor Keiko           71-130       
Emperor Seimu          131-190      
Emperor Chuai          192-200      
Regent  Jingu          201-269      
Emperor Ojin           270-310       
Emperor Nintoku        313-399    
Emperor Richu          400-405      
Emperor Hanzei         406-410     
Emperor Ingyo          412-453      
Emperor Anko           453-456       
Emperor Yuryaku        456-479    
Emperor Seinei         480-484     
Emperor Kenzo          485-487      
Emperor Ninken         488-498     
Emperor Buretsu        498-506    
Emperor Keitai         507-531     
Emperor Ankan          531-535      
Emperor Senka          535-539      
Emperor Kimmei         539-571     
Emperor Bidatsu        572-585    
Emperor Yomei          585-587      
Emperor Sushun         587-592     
Empress Suiko          592-628      
Emperor Jomei          629-641      
Empress Kogyoku        642-645    
Emperor Kotoku         645-654     
Empress Saimei         655-661     
Emperor Tenji          662-671      
Emperor Kobun          671-672      
Emperor Temmu          673-686      
Empress Jito           690-697          
Emperor Mommu          697-707         
Empress Gemmei         707-715        

Nara period

Empress Gensho         715-724        
Emperor Shomu          724-749         
Empress Koken          749-758         
Emperor Junnin         758-764        
Empress Shotoku        764-770       
Emperor Konin          770-781         
Emperor Kammu          781-806

Heian period

Emperor Heizei         806-809        
Emperor Saga           809-823          
Emperor Junna          823-833         
Emperor Nimmyo         833-850        
Emperor Montoku        850-858       
Emperor Seiwa          858-876         
Emperor Yozei          876-884         
Emperor Koko           884-887          
Emperor Uda            887-897           
Emperor Daigo          897-930         
Emperor Suzaku         930-946        
Emperor Murakami       946-967      
Emperor Reizei         967-969        
Emperor Enyu           969-984         
Emperor Kazan          984-986         
Emperor Ichijo         986-1011       
Emperor Sanjo         1011-1016       
Emperor Go-Ichijo     1016-1036   
Emperor Go-Suzaku     1036-1045   
Emperor Go-Reizei     1045-1068   
Emperor Go-Sanjo      1068-1072    
Emperor Shirakawa     1072-1086   
Emperor Horikawa      1086-1107    
Emperor Toba          1107-1123        
Emperor Sutoku        1123-1141      
Emperor Konoe         1141-1155       
Emperor Go-Shirakawa  1155-1158
Emperor Nijo          1158-1165        
Emperor Rokujo        1165-1168      
Emperor Takakura      1168-1180    
Emperor Antoku        1180-1183      

Kamakura period

As the Heike Monogatari says, Emperor Antoku died at the battle of Dan-no-ura, which ended the Heike wars. Then Go-Toba, who was a 4-year-old child, became emperor. He appointed Yoritomo as Shogun. The relationship between the emperors, the retired emperors and the shoguns were very complex, so the following lists are only approximations.

      Emperors                            Shoguns
                                            
Emperor Go-Toba      1183-1198       Minamoto Yoritomo  1192      
Emperor Tsuchimikado 1198-1210       Minamoto Yoriie   1202   
Emperor Juntoku      1210-1221       Minamoto Sanetomo  1203   
Emperor Chukyo       1221                                     
Emperor Go-Horikawa  1221-1232       Fujiwara Yoritsune 1226  
Emperor Shijo        1232-1242       
Emperor Go-Saga      1242-1246       Fujiwara Yoritsugu 1244
Emperor Go-Fukakusa  1246-1249       Munetaka-Shinno    1252     
Emperor Kameyama     1259-1274       Koreyasu-Shinno    1266     
Emperor Go-Uda       1274-1287       
Emperor Fushimi      1288-1298       Hisaakira-Shinno   1289    
Emperor Go-Fushimi   1298-1301       Morikuni-Shinno    1308     
Emperor Go-Nijo      1301-1308       Morinaga-Shinno    1333     
Emperor Hanazono     1308-1318       Narinaga-Shinno    1334     

Muromachi Period

Go-Daigo, who became emperor in 1318, tried several times to wrest power from the shoguns. He failed, but the Kamakura dynasty collapsed and was replaced by the Ashikaga dynasty, which relocated the shogunal headquarters from Kamakura to Muromachi Avenue in Kyoto. During several decades, there were also two rival emperors.

                  Emperors                             Shoguns

Southern Dynasty           Northern Dynasty              

Go-Daigo    1318-1338      Kogon      1331-1333     Ashikaga Takauji     1338
Go-Murakami 1339-1368      Komyo      1336-1348     Ashikaga Yoshiakira  1358
                           Suko       1348-1351     Ashikaga Yoshimitsu  1367
                           Go-Kogon   1352-1371     Ashikaga Yoshimochi  1395
Chokei      1368-1383      Go-Enyu    1371-1382     Ashikaga Yoshikazu   1423
Go-Kameyama 1383-1392      Go-Komatsu 1382-1392     Ashikaga Yoshinori   1428
                                                    Ashikaga Yoshikatsu  1441
                                                    Ashikaga Yoshimasa   1449
                                                    Ashikaga Yoshihisa   1474
Emperor Go-Komatsu      1392-1412                   Ashikaga Yoshitane   1490
Emperor Shoko           1412-1428                   Ashikaga Yoshizumi   1493
Emperor Go-Hanazono     1429-1464                   Ashikaga Yoshitane   1508
Emperor Go-Tsuchimikado 1465-1500                   Ashikaga Yoshiharu   1510
Emperor Go-Kashiwabara  1500-1526                   Ashikaga Yoshiteru   1545
Emperor Go-Nara         1526-1557                   Ashikaga Yoshihide   1568
Emperor Ogimachi        1557-1586                   Ashikaga Yoshiaki    1568

Azuchi-Momoyama period

Emperor Go-Yozei 1586-1611

Edo period

             
          Emperors                             Shoguns

Emperor Go-Mizunoo     1611-1629            Tokugawa Ieyasu    1603         
Empress Meisho         1630-1643            Tokugawa Hidetada   1605     
Emperor Go-Komyo       1643-1654            Tokugawa Iemitsu   1622     
Emperor Go-Sai         1656-1663            Tokugawa Ietsuna   1651     
Emperor Reigen         1663-1687            Tokugawa Tsunayoshi 1680   
Emperor Higashiyama    1687-1709            Tokugawa Ienobu    1709      
Emperor Nakamikado     1710-1735            Tokugawa Ietsugu   1713     
Emperor Sakuramachi    1735-1747            Tokugawa Yoshimune  1716    
Emperor Momozono       1747-1762            Tokugawa Ieshige   1745     
Empress Go-Sakuramachi 1763-1770            Tokugawa Ieharu    1760      
Emperor Go-Momozono    1771-1779            Tokugawa Ienari    1786      
Emperor Kokaku         1780-1817            Tokugawa Ieyoshi   1837     
Emperor Ninko          1817-1846            Tokugawa Iesada    1853      
Emperor Komei          1847-1866            Tokugawa Iemochi   1858     
Emperor Meiji          1867-1912            Tokugawa Yoshinobu  1866

Modern period

Emperor Taisho           1912-1926
Emperor Hirohito (Showa) 1926-1989
Emperor Akihito (Heisei) 1989

I used http://www.sho-shin.com/soverns.htm, and a couple of other partial sources as well. Thanks to gn0sis and sekicho, and a huge thanks to mauler for numerous helpful corrections.

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