Non-solvable groups
Groups whose derived series never reaches the trivial subgroup — equivalently, with no subnormal series of abelian factors. Each is shown with the first step of that series.
| order | group | G′ | G/G′ |
|---|
| 900 | C3×C5×A5 #11744676 | A5 | C3×C5 |
| 960 | A5⋊C16 #11746442 | A5 | C16 |
| 960 | #11746443 | SL(2,𝔽5) | C8 |
| 960 | SL(2,𝔽5)⋊C8 #11746444 | SL(2,𝔽5) | C8 |
| 960 | C16×A5 #11746445 | A5 | C16 |
| 960 | #11746446 | SL(2,𝔽5) | C8 |
| 960 | C8×SL(2,𝔽5) #11746447 | SL(2,𝔽5) | C8 |
| 960 | C8×S5 #11751486 | A5 | C2×C8 |
| 960 | #11751487 | C4×A5 | C22 |
| 960 | #11751488 | C4×A5 | C22 |
| 960 | #11751489 | C4×A5 | C22 |
| 960 | #11751490 | SL(2,𝔽5) | C2×C4 |
| 960 | #11751491 | C2×A5 | C2×C4 |
| 960 | #11751492 | SL(2,𝔽5) | C2×C4 |
| 960 | #11751493 | #6732 | C22 |
| 960 | #11751494 | #6732 | C22 |
| 960 | #11751495 | #6732 | C22 |
| 960 | #11751496 | C2×A5 | C2×C4 |
| 960 | C2×A5⋊C8 #11751497 | A5 | C2×C8 |
| 960 | C2×GL(2,𝔽5) #11751498 | SL(2,𝔽5) | C2×C4 |
| 960 | #11751499 | SL(2,𝔽5) | C2×C4 |
| 960 | C4×#6728 #11751500 | SL(2,𝔽5) | C2×C4 |
| 960 | C4×#6729 #11751501 | SL(2,𝔽5) | C2×C4 |
| 960 | C4⋊(A5⋊C4) #11751502 | C2×A5 | C2×C4 |
| 960 | C4⋊#6728 #11751503 | C2×SL(2,𝔽5) | C22 |
| 960 | C4⋊#6729 #11751504 | C2×SL(2,𝔽5) | C22 |
| 960 | #11751505 | C2×SL(2,𝔽5) | C22 |
| 960 | C4×A5⋊C4 #11751506 | A5 | C42 |
| 960 | (C2×S5)⋊C4 #11751507 | C2×A5 | C2×C4 |
| 960 | (A5⋊C4)⋊C4 #11751508 | C2×A5 | C2×C4 |
| 960 | #11751509 | SL(2,𝔽5) | C2×C4 |
| 960 | #11751510 | SL(2,𝔽5) | C2×C4 |
| 960 | #11751511 | C2×SL(2,𝔽5) | C22 |
| 960 | #11751512 | C2×SL(2,𝔽5) | C22 |
| 960 | #11751513 | C2×SL(2,𝔽5) | C22 |
| 960 | #11751514 | C2×SL(2,𝔽5) | C22 |
| 960 | #11751515 | SL(2,𝔽5) | C2×C4 |
| 960 | #11751516 | SL(2,𝔽5) | C2×C4 |
| 960 | #11751517 | C2×SL(2,𝔽5) | C22 |
| 960 | #11751518 | C4×A5 | C22 |
| 960 | #11751519 | C4×A5 | C22 |
| 960 | #11751520 | #6732 | C22 |
| 960 | #11751521 | #6732 | C22 |
| 960 | #11751522 | C4×A5 | C22 |
| 960 | #11751523 | C4×A5 | C22 |
| 960 | #11751524 | #6732 | C22 |
| 960 | #11751525 | #6732 | C22 |
| 960 | C22⋊(A5⋊C4) #11751526 | C2×A5 | C2×C4 |
| 960 | C22⋊#6728 #11751527 | C2×SL(2,𝔽5) | C22 |
| 960 | C22⋊#6729 #11751528 | C2×SL(2,𝔽5) | C22 |
| 960 | C2×#91143 #11751529 | SL(2,𝔽5) | C2×C4 |
| 960 | #11751530 | SL(2,𝔽5) | C2×C4 |
| 960 | C42×A5 #11751531 | A5 | C42 |
| 960 | C4×#6732 #11751532 | SL(2,𝔽5) | C2×C4 |
| 960 | C22⋊C4×A5 #11751533 | C2×A5 | C2×C4 |
| 960 | #11751534 | SL(2,𝔽5) | C2×C4 |
| 960 | C22⋊#6732 #11751535 | C2×SL(2,𝔽5) | C22 |
| 960 | C4⋊C4×A5 #11751536 | C2×A5 | C2×C4 |
| 960 | C4⋊#6732 #11751537 | C2×SL(2,𝔽5) | C22 |
| 960 | #11751538 | C2×SL(2,𝔽5) | C22 |
| 960 | #11751539 | SL(2,𝔽5) | C2×C4 |
| 960 | C2×C8×A5 #11751540 | A5 | C2×C8 |
| 960 | C2×#91145 #11751541 | SL(2,𝔽5) | C2×C4 |
| 960 | M16×A5 #11751542 | C2×A5 | C2×C4 |
| 960 | #11751543 | SL(2,𝔽5) | C2×C4 |
| 960 | D8×A5 #11751544 | C4×A5 | C22 |
| 960 | #11751545 | #6732 | C22 |
| 960 | SD16×A5 #11751546 | C4×A5 | C22 |
| 960 | #11751547 | #6732 | C22 |
| 960 | Q16×A5 #11751548 | C4×A5 | C22 |
| 960 | #11751549 | #6732 | C22 |
| 960 | C2×C4×SL(2,𝔽5) #11751550 | SL(2,𝔽5) | C2×C4 |
| 960 | D4×SL(2,𝔽5) #11751551 | C2×SL(2,𝔽5) | C22 |
| 960 | Q8×SL(2,𝔽5) #11751552 | C2×SL(2,𝔽5) | C22 |
| 960 | C2×C4×S5 #11756668 | A5 | C22×C4 |
| 960 | #11756669 | C2×A5 | C23 |
| 960 | C2×C4⋊S5 #11756670 | C2×A5 | C23 |
| 960 | C2×A5⋊Q8 #11756671 | C2×A5 | C23 |
| 960 | C2×#91870 #11756672 | SL(2,𝔽5) | C23 |
| 960 | C2×#91871 #11756673 | SL(2,𝔽5) | C23 |
| 960 | C2×#91872 #11756674 | SL(2,𝔽5) | C23 |
| 960 | #11756675 | SL(2,𝔽5) | C23 |
| 960 | D4×S5 #11756676 | C2×A5 | C23 |
| 960 | #11756677 | SL(2,𝔽5) | C23 |
| 960 | #11756678 | SL(2,𝔽5) | C23 |
| 960 | #11756679 | C2×A5 | C23 |
| 960 | Q8×S5 #11756680 | C2×A5 | C23 |
| 960 | #11756681 | C2×A5 | C23 |
| 960 | #11756682 | SL(2,𝔽5) | C23 |
| 960 | #11756683 | SL(2,𝔽5) | C23 |
| 960 | C22×#6728 #11756684 | SL(2,𝔽5) | C23 |
| 960 | C22×#6729 #11756685 | SL(2,𝔽5) | C23 |
| 960 | C22×A5⋊C4 #11756686 | A5 | C22×C4 |
| 960 | C2×C22⋊S5 #11756687 | C2×A5 | C23 |
| 960 | C2×#91877 #11756688 | SL(2,𝔽5) | C23 |
| 960 | C22×C4×A5 #11756689 | A5 | C22×C4 |
| 960 | C22×#6732 #11756690 | SL(2,𝔽5) | C23 |
| 960 | C2×D4×A5 #11756691 | C2×A5 | C23 |
| 960 | C2×#91881 #11756692 | SL(2,𝔽5) | C23 |
| 960 | C2×Q8×A5 #11756693 | C2×A5 | C23 |
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