Elements of the group are displayed as permutations of degree 13.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
5P |
| $D_4\times S_4\times A_5$ |
1A |
$1$ |
$1$ |
$D_4\times S_4\times A_5$ |
1A |
1A |
1A |
$()$ |
| $D_4\times S_4\times A_5$ |
2A |
$2$ |
$1$ |
$D_4\times S_4\times A_5$ |
1A |
2A |
2A |
$(1,3)(2,4)$ |
| $D_4\times S_4\times A_5$ |
2B |
$2$ |
$2$ |
$C_2^2\times S_4\times A_5$ |
1A |
2B |
2B |
$(2,4)$ |
| $D_4\times S_4\times A_5$ |
2C |
$2$ |
$2$ |
$C_2^2\times S_4\times A_5$ |
1A |
2C |
2C |
$(1,2)(3,4)$ |
| $D_4\times S_4\times A_5$ |
2D |
$2$ |
$3$ |
$A_5\times D_4^2$ |
1A |
2D |
2D |
$(5,7)(6,8)$ |
| $D_4\times S_4\times A_5$ |
2E |
$2$ |
$3$ |
$A_5\times D_4^2$ |
1A |
2E |
2E |
$(1,3)(2,4)(5,7)(6,8)$ |
| $D_4\times S_4\times A_5$ |
2F |
$2$ |
$6$ |
$C_2^2\times D_4\times A_5$ |
1A |
2F |
2F |
$(7,8)$ |
| $D_4\times S_4\times A_5$ |
2G |
$2$ |
$6$ |
$C_2^2\times D_4\times A_5$ |
1A |
2G |
2G |
$(2,4)(5,6)(7,8)$ |
| $D_4\times S_4\times A_5$ |
2H |
$2$ |
$6$ |
$C_2^2\times D_4\times A_5$ |
1A |
2H |
2H |
$(1,2)(3,4)(5,6)(7,8)$ |
| $D_4\times S_4\times A_5$ |
2I |
$2$ |
$6$ |
$C_2^2\times D_4\times A_5$ |
1A |
2I |
2I |
$(1,3)(2,4)(7,8)$ |
| $D_4\times S_4\times A_5$ |
2J |
$2$ |
$12$ |
$C_2^4\times A_5$ |
1A |
2J |
2J |
$(1,4)(2,3)(7,8)$ |
| $D_4\times S_4\times A_5$ |
2K |
$2$ |
$12$ |
$C_2^4\times A_5$ |
1A |
2K |
2K |
$(1,3)(7,8)$ |
| $D_4\times S_4\times A_5$ |
2L |
$2$ |
$15$ |
$\GL(2,\mathbb{Z}/4):C_2^3$ |
1A |
2L |
2L |
$(1,3)(2,4)(9,12)(10,13)$ |
| $D_4\times S_4\times A_5$ |
2M |
$2$ |
$15$ |
$\GL(2,\mathbb{Z}/4):C_2^3$ |
1A |
2M |
2M |
$(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
2N |
$2$ |
$30$ |
$C_2^4\times S_4$ |
1A |
2N |
2N |
$(1,3)(9,12)(10,13)$ |
| $D_4\times S_4\times A_5$ |
2O |
$2$ |
$30$ |
$C_2^4\times S_4$ |
1A |
2O |
2O |
$(1,4)(2,3)(9,12)(10,13)$ |
| $D_4\times S_4\times A_5$ |
2P |
$2$ |
$45$ |
$C_2^2\times D_4^2$ |
1A |
2P |
2P |
$(5,6)(7,8)(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
2Q |
$2$ |
$45$ |
$C_2^2\times D_4^2$ |
1A |
2Q |
2Q |
$(1,3)(2,4)(5,6)(7,8)(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
2R |
$2$ |
$90$ |
$D_4\times C_2^4$ |
1A |
2R |
2R |
$(7,8)(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
2S |
$2$ |
$90$ |
$D_4\times C_2^4$ |
1A |
2S |
2S |
$(2,4)(5,6)(7,8)(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
2T |
$2$ |
$90$ |
$D_4\times C_2^4$ |
1A |
2T |
2T |
$(1,2)(3,4)(5,6)(7,8)(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
2U |
$2$ |
$90$ |
$D_4\times C_2^4$ |
1A |
2U |
2U |
$(1,3)(2,4)(7,8)(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
2V |
$2$ |
$180$ |
$C_2^6$ |
1A |
2V |
2V |
$(1,4)(2,3)(6,8)(9,12)(10,13)$ |
| $D_4\times S_4\times A_5$ |
2W |
$2$ |
$180$ |
$C_2^6$ |
1A |
2W |
2W |
$(2,4)(7,8)(9,10)(11,13)$ |
| $D_4\times S_4\times A_5$ |
3A |
$3$ |
$8$ |
$D_4\times \GL(2,4)$ |
3A |
1A |
3A |
$(5,8,6)$ |
| $D_4\times S_4\times A_5$ |
3B |
$3$ |
$20$ |
$\GL(2,\mathbb{Z}/4):C_6$ |
3B |
1A |
3B |
$(11,13,12)$ |
| $D_4\times S_4\times A_5$ |
3C |
$3$ |
$160$ |
$D_4\times C_3^2$ |
3C |
1A |
3C |
$(5,7,6)(11,12,13)$ |
| $D_4\times S_4\times A_5$ |
4A |
$4$ |
$2$ |
$C_4\times S_4\times A_5$ |
2A |
4A |
4A |
$(1,4,3,2)$ |
| $D_4\times S_4\times A_5$ |
4B |
$4$ |
$6$ |
$C_4\times D_4\times A_5$ |
2D |
4B |
4B |
$(5,6,7,8)$ |
| $D_4\times S_4\times A_5$ |
4C |
$4$ |
$6$ |
$C_4\times D_4\times A_5$ |
2A |
4C |
4C |
$(1,2,3,4)(5,6)(7,8)$ |
| $D_4\times S_4\times A_5$ |
4D |
$4$ |
$6$ |
$C_4\times D_4\times A_5$ |
2D |
4D |
4D |
$(1,3)(2,4)(5,6,7,8)$ |
| $D_4\times S_4\times A_5$ |
4E |
$4$ |
$12$ |
$C_4\times C_2^2\times A_5$ |
2A |
4E |
4E |
$(1,4,3,2)(5,8)$ |
| $D_4\times S_4\times A_5$ |
4F |
$4$ |
$12$ |
$C_4\times C_2^2\times A_5$ |
2D |
4F |
4F |
$(1,3)(5,7,6,8)$ |
| $D_4\times S_4\times A_5$ |
4G |
$4$ |
$12$ |
$C_4^2\times A_5$ |
2E |
4G |
4G |
$(1,4,3,2)(5,7,8,6)$ |
| $D_4\times S_4\times A_5$ |
4H |
$4$ |
$12$ |
$C_4\times C_2^2\times A_5$ |
2D |
4H |
4H |
$(1,2)(3,4)(5,8,7,6)$ |
| $D_4\times S_4\times A_5$ |
4I |
$4$ |
$30$ |
$C_2^5.D_6$ |
2A |
4I |
4I |
$(1,4,3,2)(9,11)(10,12)$ |
| $D_4\times S_4\times A_5$ |
4J |
$4$ |
$90$ |
$C_4^2:C_2^3$ |
2D |
4J |
4J |
$(5,6,7,8)(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
4K |
$4$ |
$90$ |
$C_4^2:C_2^3$ |
2A |
4K |
4K |
$(1,2,3,4)(5,6)(7,8)(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
4L |
$4$ |
$90$ |
$C_4^2:C_2^3$ |
2D |
4L |
4L |
$(1,3)(2,4)(5,6,7,8)(10,11)(12,13)$ |
| $D_4\times S_4\times A_5$ |
4M |
$4$ |
$180$ |
$C_2^2\times C_4^2$ |
2E |
4M |
4M |
$(1,2,3,4)(5,8,7,6)(9,12)(10,13)$ |
| $D_4\times S_4\times A_5$ |
4N |
$4$ |
$180$ |
$C_2^4\times C_4$ |
2D |
4N |
4N |
$(1,2)(3,4)(5,7,6,8)(9,12)(10,13)$ |
| $D_4\times S_4\times A_5$ |
4O |
$4$ |
$180$ |
$C_2^4\times C_4$ |
2A |
4O |
4O |
$(1,4,3,2)(6,7)(9,11)(10,12)$ |
| $D_4\times S_4\times A_5$ |
4P |
$4$ |
$180$ |
$C_2^4\times C_4$ |
2D |
4P |
4P |
$(2,4)(5,8,6,7)(9,10)(11,13)$ |
| $D_4\times S_4\times A_5$ |
5A1 |
$5$ |
$12$ |
$\GL(2,\mathbb{Z}/4):C_{10}$ |
5A2 |
5A2 |
1A |
$(9,11,13,10,12)$ |
| $D_4\times S_4\times A_5$ |
5A2 |
$5$ |
$12$ |
$\GL(2,\mathbb{Z}/4):C_{10}$ |
5A1 |
5A1 |
1A |
$(9,13,12,11,10)$ |
| $D_4\times S_4\times A_5$ |
6A |
$6$ |
$8$ |
$D_4\times \GL(2,4)$ |
3A |
2A |
6A |
$(1,3)(2,4)(6,8,7)$ |
| $D_4\times S_4\times A_5$ |
6B |
$6$ |
$16$ |
$C_2^2\times \GL(2,4)$ |
3A |
2B |
6B |
$(2,4)(5,8,7)$ |
| $D_4\times S_4\times A_5$ |
6C |
$6$ |
$16$ |
$C_2^2\times \GL(2,4)$ |
3A |
2C |
6C |
$(1,2)(3,4)(5,6,7)$ |
| $D_4\times S_4\times A_5$ |
6D |
$6$ |
$20$ |
$\GL(2,\mathbb{Z}/4):C_6$ |
3B |
2A |
6D |
$(1,3)(2,4)(11,13,12)$ |
| $D_4\times S_4\times A_5$ |
6E |
$6$ |
$40$ |
$C_2\times C_6\times S_4$ |
3B |
2B |
6E |
$(2,4)(11,12,13)$ |
