All subgroups of index up to 10782720 (order at least 1940400) are shown, as well as all normal subgroups of any index.
| Order 20922789888000: $S_{16}$ |
| Order 10461394944000: $A_{16}$ |
| Order 1307674368000: $S_{15}$ |
| Order 653837184000: $A_{15}$ |
| Order 174356582400: $C_2.S_{14}$ |
| Order 87178291200: $S_{14}$ x 2, $C_2.A_{14}$ |
| Order 43589145600: $A_{14}$ |
| Order 37362124800: $S_3\times S_{13}$ |
| Order 18681062400: $C_3.S_{13}$, $C_3.S_{13}$, $A_{13}\times S_3$ |
| Order 12454041600: $C_2\times S_{13}$ |
| Order 11496038400: $S_{12}\times S_4$ |
| Order 9340531200: $C_3\times A_{13}$ |
| Order 6227020800: $S_{13}$ x 2, $C_2\times A_{13}$ |
| Order 5748019200: $A_4.A_{12}.C_2$ x 2, $S_4.A_{12}$ |
| Order 4790016000: $S_5\times S_{11}$ |
| Order 3832012800: $D_4.A_{12}.C_2$ |
| Order 3251404800: $S_8\wr C_2$ |
| Order 3113510400: $A_{13}$ |
| Order 2874009600: $A_4.A_{12}$, $S_3\times S_{12}$ |
| Order 2612736000: $S_6\times S_{10}$ |
| Order 2395008000: $A_{11}.S_5$ x 2, $A_{11}.A_5.C_2$ |
| Order 1916006400: $C_2^2.A_{12}.C_2$ x 3, $C_4.A_{12}.C_2$ x 2, $D_4.A_{12}$, $C_2^2\times S_{12}$ |
| Order 1828915200: $S_7\times S_9$ |
| Order 1625702400: $A_8.A_8.C_2^2$, $A_8^2.C_2^2$, $A_8^2.C_4$ |
| Order 1437004800: $C_3.S_{12}$, $C_3\times S_{12}$, $S_3\times A_{12}$ |
| Order 1306368000: $A_{10}.A_6.C_2$ x 3 |
| Order 1197504000: $A_{11}\times A_5$ |
| Order 958003200: $C_2\times S_{12}$ x 5, $C_2^2.A_{12}$ x 2, $C_4.A_{12}$, $C_2.A_{12}.C_2$, $S_4\times S_{11}$ |
| Order 914457600: $A_9.A_7.C_2$ x 3 |
| Order 812851200: $A_8.A_8.C_2$ x 2, $A_8\wr C_2$ |
| Order 798336000: $F_5.A_{11}.C_2$ |
| Order 718502400: $C_3\times A_{12}$ |
| Order 653184000: $A_6\times A_{10}$ |
| Order 479001600: $S_{12}$ x 3, $C_2\times A_{12}$ x 2, $D_6.A_{11}.C_2$, $A_4.S_{11}$, $A_4\times S_{11}$, $S_4\times A_{11}$ |
| Order 457228800: $A_9\times A_7$ |
| Order 435456000: $S_5\times S_{10}$ x 2 |
| Order 406425600: $A_8^2$ |
| Order 399168000: $D_5.A_{11}.C_2$ x 2, $F_5\times A_{11}$ |
| Order 319334400: $D_4\times S_{11}$ |
| Order 261273600: $S_{10}\times S_3\wr C_2$, $S_6\times S_9$ |
| Order 239500800: $S_3\times S_{11}$ x 4, $C_6.A_{11}.C_2$ x 2, $D_6.A_{11}$, $A_4\times A_{11}$, $A_{12}$ |
| Order 217728000: $S_5\times A_{10}$ x 2, $A_5.S_{10}$ x 2, $A_5\times S_{10}$ x 2 |
| Order 203212800: $S_7\times S_8$ |
| Order 199584000: $D_5.A_{11}$, $C_5\times S_{11}$, $C_5.A_{11}.C_2$ |
| Order 174182400: $(C_2\times S_4).A_{10}.C_2$ x 2 |
| Order 159667200: $C_2^2\times S_{11}$ x 2, $C_2^2.S_{11}$ x 2, $C_4\times S_{11}$, $C_4.S_{11}$, $A_{11}\times D_4$ |
| Order 130636800: $S_3^2.A_{10}.C_2$ x 4, $C_3:S_3.C_2.A_{10}.C_2$ x 2, $A_{10}\times S_3\wr C_2$, $A_6.S_9$, $S_6\times A_9$, $A_6\times S_9$ |
| Order 119750400: $C_3.S_{11}$ x 2, $C_3\times S_{11}$ x 2, $S_3\times A_{11}$ x 2, $C_6.A_{11}$ |
| Order 108864000: $A_5\times A_{10}$ x 2 |
| Order 101606400: $S_7\times A_8$, $A_7.S_8$, $A_7\times S_8$, $S_7^2.C_2^2$ |
| Order 99792000: $C_5\times A_{11}$ |
| Order 87091200: $S_4\times S_{10}$ x 8, $(C_2\times A_4).A_{10}.C_2$ x 4, $C_2\times S_4\times A_{10}$, $C_2\times S_4.A_{10}$, $C_2.A_9.S_5.C_2$ |
| Order 79833600: $C_2\times S_{11}$ x 5, $C_2^2\times A_{11}$ x 2, $C_4\times A_{11}$, $C_2.S_{11}$ |
| Order 72576000: $F_5\times S_{10}$ |
| Order 65318400: $C_3:S_3.A_{10}.C_2$ x 4, $(C_3\times S_3).A_{10}.C_2$ x 4, $S_3^2.A_{10}$ x 2, $C_3:S_3.C_2.A_{10}$, $A_6\times A_9$ |
| Order 60963840: $S_9\times \PSL(2,7)$ |
| Order 59875200: $C_3\times A_{11}$ |
| Order 58060800: $C_2.A_8.A_6.C_2^2$, $(C_2\times D_4).A_{10}.C_2$ |
| Order 54190080: $C_2^3.\PSL(2,7).A_8.C_2$ |
| Order 52254720: $S_3\times S_4\times S_9$ |
| Order 50803200: $S_7\wr C_2$ x 4, $C_2.A_7.A_7.C_2^2$, $A_7\times A_8$, $A_7^2.C_2^3$, $C_2\times A_7^2.C_4$ |
| Order 46448640: $A_4^2.D_4.A_8.C_2$ |
| Order 43545600: $S_5\times S_9$ x 5, $A_4.S_{10}$ x 4, $A_4\times S_{10}$ x 4, $S_4\times A_{10}$ x 4, $C_2.A_9.S_5$ x 2, $(C_2\times A_4).A_{10}$ x 2, $D_6.S_{10}$ x 2, $C_2.A_9.A_5.C_2$ |
| Order 39916800: $S_{11}$ x 3, $C_2\times A_{11}$ x 2 |
| Order 36288000: $F_5\times A_{10}$, $D_5.S_{10}$, $D_5\times S_{10}$ |
| Order 32659200: $C_3^2.A_{10}.C_2$ x 4, $(C_3\times S_3).A_{10}$ x 2, $C_3:S_3.A_{10}$ |
| Order 30481920: $A_9\times \PSL(2,7)$ |
| Order 29030400: $S_{10}\times D_4$ x 8, $C_2^3.A_{10}.C_2$ x 4, $S_6\times S_8$ x 4, $C_2.A_8.A_6.C_2$ x 3, $(C_2\times C_4).A_{10}.C_2$ x 2, $(S_3\times A_5).A_8.C_2^2$, $(C_2\times D_4).A_{10}$ |
| Order 27095040: $C_2^3.\PSL(2,7)\times A_8$ |
| Order 26127360: $C_3:S_4.A_9.C_2$ x 2, $(S_3\times A_4).A_9.C_2$ x 2, $(C_3\times S_4).A_9.C_2$ x 2, $(S_3\times S_4).A_9$, $S_9\times \SOPlus(4,2)$ |
| Order 25401600: $S_7^2$ x 3, $A_7^2.C_2^2$ x 3, $C_2.A_7.A_7.C_2$ x 2, $A_7^2.C_4$ x 2, $A_7^2.C_2^2$ |
| Order 24883200: $S_4.A_6^2.D_4$ |
| Order 23224320: $A_4^2.C_2^2.A_8.C_2$ x 4, $A_4^2.C_4.A_8.C_2$ x 2, $A_4^2.D_4.A_8$ |
| Order 21772800: $S_3\times S_{10}$ x 8, $A_5.S_9$ x 3, $A_5\times S_9$ x 3, $S_5\times A_9$ x 3, $C_6.S_{10}$ x 2, $D_6.A_{10}$ x 2, $C_6\times S_{10}$ x 2, $A_4\times A_{10}$ x 2, $S_3.A_6.A_7.C_2^2$, $C_2.A_9.A_5$ |
| Order 20736000: $A_6.A_5^2.C_2^3.C_2$ |
| Order 19958400: $A_{11}$ |
| Order 18144000: $D_5\times A_{10}$, $C_5\times S_{10}$, $C_5.S_{10}$ |
| Order 17418240: $C_2\times S_4\times S_9$ x 2, $(S_3\times D_4).A_9.C_2$ |
| Order 16329600: $C_3^2.A_{10}$ |
| Order 15482880: $C_2\wr A_4.C_2.A_8.C_2$ |
| Order 15240960: $F_7.A_9.C_2$ |
| Order 14515200: $C_2^2\times S_{10}$ x 11, $C_2^2.S_{10}$ x 8, $(C_3\times A_5).A_8.C_2^2$ x 4, $C_4.S_{10}$ x 4, $C_4\times S_{10}$ x 4, $A_{10}\times D_4$ x 4, $(S_3\times A_5).A_8.C_2$ x 3, $C_2^3.A_{10}$ x 2, $A_6\times S_8$ x 2, $A_6.S_8$ x 2, $S_6\times A_8$ x 2, $S_4.A_7.A_5.C_2^2$, $C_2^2.A_{10}.C_2$, $C_2.A_8.A_6$, $(C_2\times F_5).A_9.C_2$, $(C_2\times C_4).A_{10}$ |
| Order 13547520: $\PSL(2,7).A_8.C_2^2$ |
| Order 13063680: $(C_3\times A_4).A_9.C_2$ x 4, $S_3^2.S_9$ x 2, $S_9\times S_3^2$ x 2, $C_3:S_4.A_9$, $(S_3\times A_4).A_9$, $(C_3\times S_4).A_9$, $A_9\times S_3\wr C_2$, $A_9.\SOPlus(4,2)$, $C_3^2.(C_4\times S_9)$ |
| Order 12700800: $A_7\times S_7$ x 2, $A_7.S_7$ x 2, $A_7\wr C_2$ x 2, $C_2.A_7.A_7$ |
| Order 12441600: $A_4.A_6^2.D_4$ x 4, $S_4.A_6^2.C_4$, $S_4.A_6^2.C_2^2$, $S_4.A_6.A_6.C_2^2$ |
| Order 11612160: $\PSOPlusPlus(4,3).A_8.C_2$ x 4, $A_4^2.C_2^2.A_8$ x 2, $A_4\wr C_2.A_8.C_2$ x 2, $(A_4\times S_4).A_8.C_2$ x 2, $A_4^2.C_4.A_8$ |
| Order 10886400: $C_3.A_6.A_7.C_2^2$ x 4, $S_3\times A_{10}$ x 4, $C_3.S_{10}$ x 4, $C_3\times S_{10}$ x 4, $S_3.A_6.A_7.C_2$ x 3, $C_6\times A_{10}$ x 2, $A_5\times A_9$ x 2 |
| Order 10368000: $A_6.A_5^2.D_4$ x 4, $A_6.A_5^2.C_4.C_2$, $A_6.A_5^2.C_2^3$, $A_5.A_5.A_6.C_2^3$, $S_5^3.S_3$ |
| Order 10321920: $C_2^8.S_8$ |
| Order 9676800: $C_2\times S_5\times S_8$ x 2 |
| Order 9072000: $C_5\times A_{10}$ |
| Order 8709120: $S_4\times S_9$ x 9, $C_3:D_4.A_9.C_2$ x 4, $(C_2^2\times S_3).A_9.C_2$ x 4, $D_{12}.A_9.C_2$ x 2, $(C_4\times S_3).A_9.C_2$ x 2, $(C_3\times D_4).A_9.C_2$ x 2, $C_2\times A_9\times S_4$ x 2, $(C_2\times A_4).S_9$ x 2, $C_2\times S_9\times A_4$ x 2, $(S_3\times D_4).A_9$ |
| Order 8294400: $D_4.A_6^2.D_4$ |
| Order 7962624: $C_2^8.S_3\wr S_4$ |
| Order 7741440: $C_2^3:S_4.A_8.C_2$ x 2, $C_2^3:A_4:C_2.A_8.C_2$ x 2, $C_2\wr A_4.A_8.C_2$ x 2, $C_2^2:S_4:C_2.A_8.C_2$, $C_2\wr A_4.C_2.A_8$, $(D_4\times S_4).A_8.C_2$ |
| Order 7620480: $C_7:C_3.A_9.C_2$ x 2, $\SL(2,8).C_3\times S_7$, $F_7\times A_9$ |
| Order 7257600: $C_2\times S_{10}$ x 12, $(C_3\times A_5).A_8.C_2$ x 6, $C_2^2\times A_{10}$ x 5, $A_4.A_7.S_5.C_2$ x 4, $F_5\times S_9$ x 4, $S_4.A_7.S_5$ x 2, $D_{10}.A_9.C_2$ x 2, $C_2.S_{10}$ x 2, $C_4\times A_{10}$ x 2, $S_4.A_7.A_5.C_2$, $(S_3\times A_5).A_8$, $(C_2\times F_5).A_9$, $A_6\times A_8$, $C_2\times S_6\times S_7$ |
| Order 6773760: $\PSL(2,7).A_8.C_2$ x 2, $S_8\times \PSL(2,7)$ x 2, $F_8:C_3.A_8.C_2$, $S_7\times C_2^3:\GL(3,2)$ |
| Order 6531840: $S_3^2\times A_9$ x 2, $A_9.S_3^2$ x 2, $C_3\times S_9\times S_3$ x 2, $A_9.S_3^2$ x 2, $C_3^3:C_2^2.D_6.A_7.C_2$, $C_3\times A_4.A_9$, $C_3^2.(C_4\times A_9)$, $C_3:S_3\times S_9$, $(C_3^2\times A_9).C_4$ |
| Order 6350400: $A_7^2$ |
| Order 6220800: $A_4.A_6^2.C_2^2$ x 3, $S_4.A_6.A_6.C_2$ x 2, $A_4.A_6^2.C_4$ x 2, $A_4.A_6.A_6.C_2^2$ x 2, $S_6\times A_4.A_6.C_2$, $S_4.A_6^2.C_2$, $S_6^2.D_6$ |
| Order 5806080: $A_4^2.A_8.C_2$ x 3, $\PSOPlusPlus(4,3).A_8$, $A_8\times A_4\wr C_2$, $A_4\times A_4.A_8.C_2$, $(C_2\times S_3\wr C_2).A_8.C_2$, $(A_4\times S_4).A_8$, $S_3\times S_4\times S_8$, $C_2\times S_9\times D_4$, $S_7\times S_4\wr C_2$ |
| Order 5443200: $C_3.A_6.A_7.C_2$ x 6, $C_3\times A_{10}$ x 2, $S_3.A_6.A_7$ |
| Order 5184000: $A_5.A_5.A_6.C_2^2$ x 5, $A_6.A_5^2.C_2^2$ x 4, $A_6.A_5^2.C_4$ x 2, $S_5\wr C_3$, $A_5^3.S_4$, $A_5^3.S_4$ |
| Order 5160960: $D_4^2.C_2.A_8.C_2$, $C_2^7.S_8$, $C_2^7.S_8$, $C_2^8.A_8$ |
| Order 5080320: $D_7.A_9.C_2$ |
| Order 4838400: $S_5\times S_8$ x 8, $C_2\times A_8.S_5$ x 2, $C_2\times A_8\times S_5$ x 2, $C_2\times A_5\times S_8$ x 2, $D_4.A_7.S_5.C_2$, $(S_3\times F_5).A_8.C_2$ |
| Order 4354560: $D_6.S_9$ x 12, $(C_2\times C_6).A_9.C_2$ x 8, $D_6.A_9.C_2$ x 5, $A_4.S_9$ x 5, $A_4\times S_9$ x 5, $S_4\times A_9$ x 5, $C_{12}.A_9.C_2$ x 4, $C_3:C_4.A_9.C_2$ x 4, $C_3:D_4.A_9$ x 2, $(C_2^2\times S_3).A_9$ x 2, $C_2\times A_9\times A_4$ x 2, $D_{12}.A_9$, $(C_4\times S_3).A_9$, $(C_3\times D_4).A_9$ |
| Order 4147200: $C_2^2.A_6^2.D_4$ x 6, $C_4.A_6^2.D_4$ x 4, $S_6^2.D_4$ x 2, $D_4.A_6^2.C_4$, $D_4.A_6^2.C_2^2$, $D_4.A_6.A_6.C_2^2$ |
| Order 3981312: $C_2^8.C_3^4:Q_8:S_4$, $A_4^2\wr C_2.C_2^2.S_4$, $C_2^8.C_3^4.C_2\wr A_4$ |
| Order 3870720: $(C_2^2\times S_4).A_8.C_2$ x 5, $\GL(2,\mathbb{Z}/4).A_8.C_2$ x 4, $C_2^3:A_4.A_8.C_2$ x 4, $C_2^2:S_4.A_8.C_2$ x 4, $C_4:S_4.A_8.C_2$ x 2, $C_2^2\wr C_2:C_3.A_8.C_2$ x 2, $(D_4\times A_4).A_8.C_2$ x 2, $(C_4\times S_4).A_8.C_2$ x 2, $C_2^3:S_4.A_8$, $C_2^3:A_4:C_2.A_8$, $C_2^2:S_4:C_2.A_8$, $C_2\wr A_4.A_8$, $(D_4\times S_4).A_8$ |
| Order 3810240: $\SL(2,8).A_7.C_3$, $C_7:C_3.A_9$ |
| Order 3628800: $A_4.A_7.S_5$ x 4, $D_5\times S_9$ x 4, $S_6\times S_7$ x 4, $S_{10}$ x 4, $C_2\times A_{10}$ x 3, $C_{10}.A_9.C_2$ x 2, $A_4.A_7.A_5.C_2$ x 2, $S_3\times S_5\times S_7$ x 2, $A_9:F_5$ x 2, $F_5\times A_9$ x 2, $S_4.A_7.A_5$, $D_{10}.A_9$, $(C_3\times A_5).A_8$, $C_2\times A_6\times S_7$, $(C_2\times A_6).S_7$, $C_2\times S_6\times A_7$ |
| Order 3612672: $C_2^6.\GL(3,2)\wr C_2$ |
| Order 3456000: $S_5^3.C_2$ x 2 |
| Order 3386880: $A_8\times \PSL(2,7)$ x 2, $A_8\times F_8:C_3$, $A_7\times C_2^3.\PSL(2,7)$ |
| Order 3265920: $C_3^3.S_4.A_7.C_2$ x 4, $C_3^3:C_2^2.C_6.A_7.C_2$ x 2, $C_3\times S_3\times A_9$ x 2, $C_3^2:S_9$ x 2, $C_3^3:C_2^2.D_6.A_7$, $C_3:S_3\times A_9$, $C_3^2.S_9$, $C_3^2\times S_9$ |
| Order 3110400: $A_4.A_6.A_6.C_2$ x 4, $A_4.A_6^2.C_2$ x 2, $S_4.A_6.A_6$, $S_3\times S_6^2$, $(C_3\times A_6^2).D_4$, $A_6^2.D_{12}$, $S_6^2.S_3$, $S_6^2.C_6$, $(S_3\times A_6^2).C_4$, $A_6^2.(C_2\times D_6)$ |
| Order 2903040: $S_8\times S_3\wr C_2$ x 8, $S_9\times D_4$ x 8, $(C_2\times S_3^2).A_8.C_2$ x 4, $(C_2\times C_3:S_3.C_2).A_8.C_2$ x 2, $C_2^3\times S_9$ x 2, $C_2^3.S_9$ x 2, $A_4^2.A_8$, $(C_2\times S_3\wr C_2).A_8$, $C_2\times C_4\times S_9$, $(C_2\times C_4).S_9$, $C_2\times A_9\times D_4$, $S_4^2\times S_7$, $C_3.(S_4\times S_8)$, $S_8\times C_3:S_4$, $(S_3\times A_4).S_8$, $S_3\times S_8\times A_4$, $S_3\times S_4\times A_8$, $(C_3\times S_4).S_8$, $C_3\times S_4\times S_8$, $(A_4^2\times A_7).D_4$, $A_4^2.(C_4\times S_7)$, $(A_4^2\times A_7).D_4$, $S_7\times \POPlus(4,3)$, $A_4^2.D_4\times A_7$, $S_4^2.S_7$ |
| Order 2764800: $C_2^5.A_6.S_5.C_2$ |
| Order 2721600: $C_3.A_6.A_7$ |
| Order 2654208: $C_2^8.S_3\wr D_4$ |
| Order 2592000: $A_5.A_5.A_6.C_2$ x 5, $A_6.A_5^2.C_2$ x 2, $A_5^3.A_4$, $A_5^3:D_6$ |
| Order 2580480: $C_2\wr C_4.A_8.C_2$ x 4, $C_2\wr C_2^2.A_8.C_2$ x 4, $D_4^2.A_8.C_2$ x 2, $D_4:D_4.A_8.C_2$ x 2, $C_4^2:C_4.A_8.C_2$ x 2, $D_4^2.C_2\times A_8$, $C_2^7.A_8$ |
| Order 2540160: $C_7.A_9.C_2$ x 2, $\SL(2,8).A_7.C_2$, $D_7.A_9$ |
| Order 2419200: $C_2^2.A_7.S_5.C_2$ x 6, $A_5\times S_8$ x 4, $A_5.S_8$ x 4, $S_5\times A_8$ x 4, $C_4.A_7.S_5.C_2$ x 3, $D_4.A_7.S_5$ x 2, $C_3:F_5.A_8.C_2$ x 2, $C_2^2.A_7.A_5.C_2^2$ x 2, $(C_3\times F_5).A_8.C_2$ x 2, $C_2\times A_8\times A_5$ x 2, $S_3.A_8\times F_5$, $S_3.A_8.C_2\times D_5$, $D_4.A_7.A_5.C_2$, $C_4.A_7.A_5.C_2^2$, $(S_3\times D_5).A_8.C_2$, $(F_5\times S_4).A_7.C_2$ |
| Order 2280960: $S_4.M_{12}$ |
| Order 2257920: $F_8.A_8.C_2$ |
| Order 2177280: $S_3\times S_9$ x 15, $D_6.A_9$ x 6, $C_6\times S_9$ x 6, $C_2\times C_3:S_9$ x 6, $A_4\times A_9$ x 3, $C_6.A_9.C_2$ x 2, $(C_2\times C_6).A_9$ x 2, $\AGL(2,3).A_7.C_2$, $C_{12}.A_9$, $C_3:C_4.A_9$, $(S_3\times S_3\wr C_2).A_7.C_2$ |
| Order 2073600: $S_6^2.C_2^2$ x 13, $C_2^2.A_6.A_6.C_2^2$ x 6, $C_2^2.A_6^2.C_2^2$ x 4, $C_2.A_6^2.D_4$ x 4, $C_4.A_6^2.C_2^2$ x 3, $C_4.A_6.A_6.C_2^2$ x 3, $S_6^2.C_4$ x 3, $D_4.A_6.A_6.C_2$ x 2, $C_4.A_6^2.C_4$ x 2, $C_2^2.A_6^2.C_4$ x 2, $A_6:S_6.D_4$ x 2, $A_6^2.(C_2\times D_4)$ x 2, $S_4\times S_5\times S_6$ x 2, $S_3\wr C_2.A_5^2.D_4$, $D_4.A_6^2.C_2$ |
| Order 1990656: $C_2^6.C_3^3.A_4^2.C_2^3$, $A_4^2\wr C_2.C_2^2.A_4$ |
| Order 1: $C_1$ |
