Representing and Counting the Subgroups of the Group <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.524701pt" id="M1" height="16.4738pt" version="1.1" viewBox="-0.0657574 -11.9491 62.6265 16.4738" width="62.6265pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g197-37" d="M677 618V662H100V618H469L50 44V0H668V44H252L677 618ZM617 618L200 44H103L523 618H617Z"/></g><g transform="matrix(.013,0,0,-0.013,13.002,4.308)"><path id="g50-110" d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"/></g><g transform="matrix(.018,0,0,-0.018,27.771,0)"><path id="g117-42" d="M528 54L331 254L528 455L492 493L294 291L96 493L60 455L257 254L60 54L96 16L294 217L492 16L528 54Z"/></g><g transform="matrix(.018,0,0,-0.018,42.266,0)"><use xlink:href="#g197-37"/></g><g transform="matrix(.013,0,0,-0.013,55.267,4.308)"><path id="g50-111" d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"/></g></svg>

Journal of Numbers

fig1

Figure 1

Figure 1: Representing and Counting the Subgroups of the Group <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.524701pt" id="M1" height="16.4738pt" version="1.1" viewBox="-0.0657574 -11.9491 62.6265 16.4738" width="62.6265pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g197-37" d="M677 618V662H100V618H469L50 44V0H668V44H252L677 618ZM617 618L200 44H103L523 618H617Z"/></g><g transform="matrix(.013,0,0,-0.013,13.002,4.308)"><path id="g50-110" d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"/></g><g transform="matrix(.018,0,0,-0.018,27.771,0)"><path id="g117-42" d="M528 54L331 254L528 455L492 493L294 291L96 493L60 455L257 254L60 54L96 16L294 217L492 16L528 54Z"/></g><g transform="matrix(.018,0,0,-0.018,42.266,0)"><use xlink:href="#g197-37"/></g><g transform="matrix(.013,0,0,-0.013,55.267,4.308)"><path id="g50-111" d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"/></g></svg> 