Abelian groups

A group is abelian or commutative if gh=hg for all g and h, in other words if all elements commute. Such a group is a direct product of cyclic groups (structure theorem)

G = Cn1×···×Cnk,
in a unique way if we require n1|n2|×···|nk. We say that G is of type [n1,n2,...,nk]. A group Cp×Cp×···×Cp for a prime number p is elementary abelian - these are the additive groups of finite fields. Abelian groups are soluble, nilpotent and monomial. Classes extending abelian groups are metabelian groups (commutator is abelian) and A-groups (abelian Sylows). See also non-abelian groups.

Groups of order 1

dρLabelID
C1Trivial group11+C11,1

Groups of order 2

dρLabelID
C2Cyclic group21+C22,1

Groups of order 3

dρLabelID
C3Cyclic group; = A3 = triangle rotations31C33,1

Groups of order 4

dρLabelID
C4Cyclic group; = square rotations41C44,1
C22Klein 4-group V4 = elementary abelian group of type [2,2]; = rectangle symmetries4C2^24,2

Groups of order 5

dρLabelID
C5Cyclic group; = pentagon rotations51C55,1

Groups of order 6

dρLabelID
C6Cyclic group; = hexagon rotations61C66,2

Groups of order 7

dρLabelID
C7Cyclic group71C77,1

Groups of order 8

dρLabelID
C8Cyclic group81C88,1
C23Elementary abelian group of type [2,2,2]8C2^38,5
C2×C4Abelian group of type [2,4]8C2xC48,2

Groups of order 9

dρLabelID
C9Cyclic group91C99,1
C32Elementary abelian group of type [3,3]9C3^29,2

Groups of order 10

dρLabelID
C10Cyclic group101C1010,2

Groups of order 11

dρLabelID
C11Cyclic group111C1111,1

Groups of order 12

dρLabelID
C12Cyclic group121C1212,2
C2×C6Abelian group of type [2,6]12C2xC612,5

Groups of order 13

dρLabelID
C13Cyclic group131C1313,1

Groups of order 14

dρLabelID
C14Cyclic group141C1414,2

Groups of order 15

dρLabelID
C15Cyclic group151C1515,1

Groups of order 16

dρLabelID
C16Cyclic group161C1616,1
C42Abelian group of type [4,4]16C4^216,2
C24Elementary abelian group of type [2,2,2,2]16C2^416,14
C2×C8Abelian group of type [2,8]16C2xC816,5
C22×C4Abelian group of type [2,2,4]16C2^2xC416,10

Groups of order 17

dρLabelID
C17Cyclic group171C1717,1

Groups of order 18

dρLabelID
C18Cyclic group181C1818,2
C3×C6Abelian group of type [3,6]18C3xC618,5

Groups of order 19

dρLabelID
C19Cyclic group191C1919,1

Groups of order 20

dρLabelID
C20Cyclic group201C2020,2
C2×C10Abelian group of type [2,10]20C2xC1020,5

Groups of order 21

dρLabelID
C21Cyclic group211C2121,2

Groups of order 22

dρLabelID
C22Cyclic group221C2222,2

Groups of order 23

dρLabelID
C23Cyclic group231C2323,1

Groups of order 24

dρLabelID
C24Cyclic group241C2424,2
C2×C12Abelian group of type [2,12]24C2xC1224,9
C22×C6Abelian group of type [2,2,6]24C2^2xC624,15

Groups of order 25

dρLabelID
C25Cyclic group251C2525,1
C52Elementary abelian group of type [5,5]25C5^225,2

Groups of order 26

dρLabelID
C26Cyclic group261C2626,2

Groups of order 27

dρLabelID
C27Cyclic group271C2727,1
C33Elementary abelian group of type [3,3,3]27C3^327,5
C3×C9Abelian group of type [3,9]27C3xC927,2

Groups of order 28

dρLabelID
C28Cyclic group281C2828,2
C2×C14Abelian group of type [2,14]28C2xC1428,4

Groups of order 29

dρLabelID
C29Cyclic group291C2929,1

Groups of order 30

dρLabelID
C30Cyclic group301C3030,4

Groups of order 31

dρLabelID
C31Cyclic group311C3131,1

Groups of order 32

dρLabelID
C32Cyclic group321C3232,1
C25Elementary abelian group of type [2,2,2,2,2]32C2^532,51
C4×C8Abelian group of type [4,8]32C4xC832,3
C2×C16Abelian group of type [2,16]32C2xC1632,16
C2×C42Abelian group of type [2,4,4]32C2xC4^232,21
C22×C8Abelian group of type [2,2,8]32C2^2xC832,36
C23×C4Abelian group of type [2,2,2,4]32C2^3xC432,45

Groups of order 33

dρLabelID
C33Cyclic group331C3333,1

Groups of order 34

dρLabelID
C34Cyclic group341C3434,2

Groups of order 35

dρLabelID
C35Cyclic group351C3535,1

Groups of order 36

dρLabelID
C36Cyclic group361C3636,2
C62Abelian group of type [6,6]36C6^236,14
C2×C18Abelian group of type [2,18]36C2xC1836,5
C3×C12Abelian group of type [3,12]36C3xC1236,8

Groups of order 37

dρLabelID
C37Cyclic group371C3737,1

Groups of order 38

dρLabelID
C38Cyclic group381C3838,2

Groups of order 39

dρLabelID
C39Cyclic group391C3939,2

Groups of order 40

dρLabelID
C40Cyclic group401C4040,2
C2×C20Abelian group of type [2,20]40C2xC2040,9
C22×C10Abelian group of type [2,2,10]40C2^2xC1040,14

Groups of order 41

dρLabelID
C41Cyclic group411C4141,1

Groups of order 42

dρLabelID
C42Cyclic group421C4242,6

Groups of order 43

dρLabelID
C43Cyclic group431C4343,1

Groups of order 44

dρLabelID
C44Cyclic group441C4444,2
C2×C22Abelian group of type [2,22]44C2xC2244,4

Groups of order 45

dρLabelID
C45Cyclic group451C4545,1
C3×C15Abelian group of type [3,15]45C3xC1545,2

Groups of order 46

dρLabelID
C46Cyclic group461C4646,2

Groups of order 47

dρLabelID
C47Cyclic group471C4747,1

Groups of order 48

dρLabelID
C48Cyclic group481C4848,2
C4×C12Abelian group of type [4,12]48C4xC1248,20
C2×C24Abelian group of type [2,24]48C2xC2448,23
C23×C6Abelian group of type [2,2,2,6]48C2^3xC648,52
C22×C12Abelian group of type [2,2,12]48C2^2xC1248,44

Groups of order 49

dρLabelID
C49Cyclic group491C4949,1
C72Elementary abelian group of type [7,7]49C7^249,2

Groups of order 50

dρLabelID
C50Cyclic group501C5050,2
C5×C10Abelian group of type [5,10]50C5xC1050,5

Groups of order 51

dρLabelID
C51Cyclic group511C5151,1

Groups of order 52

dρLabelID
C52Cyclic group521C5252,2
C2×C26Abelian group of type [2,26]52C2xC2652,5

Groups of order 53

dρLabelID
C53Cyclic group531C5353,1

Groups of order 54

dρLabelID
C54Cyclic group541C5454,2
C3×C18Abelian group of type [3,18]54C3xC1854,9
C32×C6Abelian group of type [3,3,6]54C3^2xC654,15

Groups of order 55

dρLabelID
C55Cyclic group551C5555,2

Groups of order 56

dρLabelID
C56Cyclic group561C5656,2
C2×C28Abelian group of type [2,28]56C2xC2856,8
C22×C14Abelian group of type [2,2,14]56C2^2xC1456,13

Groups of order 57

dρLabelID
C57Cyclic group571C5757,2

Groups of order 58

dρLabelID
C58Cyclic group581C5858,2

Groups of order 59

dρLabelID
C59Cyclic group591C5959,1

Groups of order 60

dρLabelID
C60Cyclic group601C6060,4
C2×C30Abelian group of type [2,30]60C2xC3060,13

Groups of order 61

dρLabelID
C61Cyclic group611C6161,1

Groups of order 62

dρLabelID
C62Cyclic group621C6262,2

Groups of order 63

dρLabelID
C63Cyclic group631C6363,2
C3×C21Abelian group of type [3,21]63C3xC2163,4

Groups of order 64

dρLabelID
C64Cyclic group641C6464,1
C82Abelian group of type [8,8]64C8^264,2
C43Abelian group of type [4,4,4]64C4^364,55
C26Elementary abelian group of type [2,2,2,2,2,2]64C2^664,267
C4×C16Abelian group of type [4,16]64C4xC1664,26
C2×C32Abelian group of type [2,32]64C2xC3264,50
C23×C8Abelian group of type [2,2,2,8]64C2^3xC864,246
C24×C4Abelian group of type [2,2,2,2,4]64C2^4xC464,260
C22×C16Abelian group of type [2,2,16]64C2^2xC1664,183
C22×C42Abelian group of type [2,2,4,4]64C2^2xC4^264,192
C2×C4×C8Abelian group of type [2,4,8]64C2xC4xC864,83

Groups of order 65

dρLabelID
C65Cyclic group651C6565,1

Groups of order 66

dρLabelID
C66Cyclic group661C6666,4

Groups of order 67

dρLabelID
C67Cyclic group671C6767,1

Groups of order 68

dρLabelID
C68Cyclic group681C6868,2
C2×C34Abelian group of type [2,34]68C2xC3468,5

Groups of order 69

dρLabelID
C69Cyclic group691C6969,1

Groups of order 70

dρLabelID
C70Cyclic group701C7070,4

Groups of order 71

dρLabelID
C71Cyclic group711C7171,1

Groups of order 72

dρLabelID
C72Cyclic group721C7272,2
C2×C36Abelian group of type [2,36]72C2xC3672,9
C3×C24Abelian group of type [3,24]72C3xC2472,14
C6×C12Abelian group of type [6,12]72C6xC1272,36
C2×C62Abelian group of type [2,6,6]72C2xC6^272,50
C22×C18Abelian group of type [2,2,18]72C2^2xC1872,18

Groups of order 73

dρLabelID
C73Cyclic group731C7373,1

Groups of order 74

dρLabelID
C74Cyclic group741C7474,2

Groups of order 75

dρLabelID
C75Cyclic group751C7575,1
C5×C15Abelian group of type [5,15]75C5xC1575,3

Groups of order 76

dρLabelID
C76Cyclic group761C7676,2
C2×C38Abelian group of type [2,38]76C2xC3876,4

Groups of order 77

dρLabelID
C77Cyclic group771C7777,1

Groups of order 78

dρLabelID
C78Cyclic group781C7878,6

Groups of order 79

dρLabelID
C79Cyclic group791C7979,1

Groups of order 80

dρLabelID
C80Cyclic group801C8080,2
C4×C20Abelian group of type [4,20]80C4xC2080,20
C2×C40Abelian group of type [2,40]80C2xC4080,23
C22×C20Abelian group of type [2,2,20]80C2^2xC2080,45
C23×C10Abelian group of type [2,2,2,10]80C2^3xC1080,52

Groups of order 81

dρLabelID
C81Cyclic group811C8181,1
C92Abelian group of type [9,9]81C9^281,2
C34Elementary abelian group of type [3,3,3,3]81C3^481,15
C3×C27Abelian group of type [3,27]81C3xC2781,5
C32×C9Abelian group of type [3,3,9]81C3^2xC981,11

Groups of order 82

dρLabelID
C82Cyclic group821C8282,2

Groups of order 83

dρLabelID
C83Cyclic group831C8383,1

Groups of order 84

dρLabelID
C84Cyclic group841C8484,6
C2×C42Abelian group of type [2,42]84C2xC4284,15

Groups of order 85

dρLabelID
C85Cyclic group851C8585,1

Groups of order 86

dρLabelID
C86Cyclic group861C8686,2

Groups of order 87

dρLabelID
C87Cyclic group871C8787,1

Groups of order 88

dρLabelID
C88Cyclic group881C8888,2
C2×C44Abelian group of type [2,44]88C2xC4488,8
C22×C22Abelian group of type [2,2,22]88C2^2xC2288,12

Groups of order 89

dρLabelID
C89Cyclic group891C8989,1

Groups of order 90

dρLabelID
C90Cyclic group901C9090,4
C3×C30Abelian group of type [3,30]90C3xC3090,10

Groups of order 91

dρLabelID
C91Cyclic group911C9191,1

Groups of order 92

dρLabelID
C92Cyclic group921C9292,2
C2×C46Abelian group of type [2,46]92C2xC4692,4

Groups of order 93

dρLabelID
C93Cyclic group931C9393,2

Groups of order 94

dρLabelID
C94Cyclic group941C9494,2

Groups of order 95

dρLabelID
C95Cyclic group951C9595,1

Groups of order 96

dρLabelID
C96Cyclic group961C9696,2
C4×C24Abelian group of type [4,24]96C4xC2496,46
C2×C48Abelian group of type [2,48]96C2xC4896,59
C24×C6Abelian group of type [2,2,2,2,6]96C2^4xC696,231
C22×C24Abelian group of type [2,2,24]96C2^2xC2496,176
C23×C12Abelian group of type [2,2,2,12]96C2^3xC1296,220
C2×C4×C12Abelian group of type [2,4,12]96C2xC4xC1296,161

Groups of order 97

dρLabelID
C97Cyclic group971C9797,1

Groups of order 98

dρLabelID
C98Cyclic group981C9898,2
C7×C14Abelian group of type [7,14]98C7xC1498,5

Groups of order 99

dρLabelID
C99Cyclic group991C9999,1
C3×C33Abelian group of type [3,33]99C3xC3399,2

Groups of order 100

dρLabelID
C100Cyclic group1001C100100,2
C102Abelian group of type [10,10]100C10^2100,16
C2×C50Abelian group of type [2,50]100C2xC50100,5
C5×C20Abelian group of type [5,20]100C5xC20100,8

Groups of order 101

dρLabelID
C101Cyclic group1011C101101,1

Groups of order 102

dρLabelID
C102Cyclic group1021C102102,4

Groups of order 103

dρLabelID
C103Cyclic group1031C103103,1

Groups of order 104

dρLabelID
C104Cyclic group1041C104104,2
C2×C52Abelian group of type [2,52]104C2xC52104,9
C22×C26Abelian group of type [2,2,26]104C2^2xC26104,14

Groups of order 105

dρLabelID
C105Cyclic group1051C105105,2

Groups of order 106

dρLabelID
C106Cyclic group1061C106106,2

Groups of order 107

dρLabelID
C107Cyclic group1071C107107,1

Groups of order 108

dρLabelID
C108Cyclic group1081C108108,2
C2×C54Abelian group of type [2,54]108C2xC54108,5
C3×C36Abelian group of type [3,36]108C3xC36108,12
C6×C18Abelian group of type [6,18]108C6xC18108,29
C3×C62Abelian group of type [3,6,6]108C3xC6^2108,45
C32×C12Abelian group of type [3,3,12]108C3^2xC12108,35

Groups of order 109

dρLabelID
C109Cyclic group1091C109109,1

Groups of order 110

dρLabelID
C110Cyclic group1101C110110,6

Groups of order 111

dρLabelID
C111Cyclic group1111C111111,2

Groups of order 112

dρLabelID
C112Cyclic group1121C112112,2
C4×C28Abelian group of type [4,28]112C4xC28112,19
C2×C56Abelian group of type [2,56]112C2xC56112,22
C22×C28Abelian group of type [2,2,28]112C2^2xC28112,37
C23×C14Abelian group of type [2,2,2,14]112C2^3xC14112,43

Groups of order 113

dρLabelID
C113Cyclic group1131C113113,1

Groups of order 114

dρLabelID
C114Cyclic group1141C114114,6

Groups of order 115

dρLabelID
C115Cyclic group1151C115115,1

Groups of order 116

dρLabelID
C116Cyclic group1161C116116,2
C2×C58Abelian group of type [2,58]116C2xC58116,5

Groups of order 117

dρLabelID
C117Cyclic group1171C117117,2
C3×C39Abelian group of type [3,39]117C3xC39117,4

Groups of order 118

dρLabelID
C118Cyclic group1181C118118,2

Groups of order 119

dρLabelID
C119Cyclic group1191C119119,1

Groups of order 120

dρLabelID
C120Cyclic group1201C120120,4
C2×C60Abelian group of type [2,60]120C2xC60120,31
C22×C30Abelian group of type [2,2,30]120C2^2xC30120,47

Groups of order 121

dρLabelID
C121Cyclic group1211C121121,1
C112Elementary abelian group of type [11,11]121C11^2121,2

Groups of order 122

dρLabelID
C122Cyclic group1221C122122,2

Groups of order 123

dρLabelID
C123Cyclic group1231C123123,1

Groups of order 124

dρLabelID
C124Cyclic group1241C124124,2
C2×C62Abelian group of type [2,62]124C2xC62124,4

Groups of order 125

dρLabelID
C125Cyclic group1251C125125,1
C53Elementary abelian group of type [5,5,5]125C5^3125,5
C5×C25Abelian group of type [5,25]125C5xC25125,2

Groups of order 126

dρLabelID
C126Cyclic group1261C126126,6
C3×C42Abelian group of type [3,42]126C3xC42126,16

Groups of order 127

dρLabelID
C127Cyclic group1271C127127,1

Groups of order 128

dρLabelID
C128Cyclic group1281C128128,1
C27Elementary abelian group of type [2,2,2,2,2,2,2]128C2^7128,2328
C8×C16Abelian group of type [8,16]128C8xC16128,42
C4×C32Abelian group of type [4,32]128C4xC32128,128
C2×C64Abelian group of type [2,64]128C2xC64128,159
C2×C82Abelian group of type [2,8,8]128C2xC8^2128,179
C42×C8Abelian group of type [4,4,8]128C4^2xC8128,456
C2×C43Abelian group of type [2,4,4,4]128C2xC4^3128,997
C24×C8Abelian group of type [2,2,2,2,8]128C2^4xC8128,2301
C25×C4Abelian group of type [2,2,2,2,2,4]128C2^5xC4128,2319
C22×C32Abelian group of type [2,2,32]128C2^2xC32128,988
C23×C16Abelian group of type [2,2,2,16]128C2^3xC16128,2136
C23×C42Abelian group of type [2,2,2,4,4]128C2^3xC4^2128,2150
C2×C4×C16Abelian group of type [2,4,16]128C2xC4xC16128,837
C22×C4×C8Abelian group of type [2,2,4,8]128C2^2xC4xC8128,1601

Groups of order 129

dρLabelID
C129Cyclic group1291C129129,2

Groups of order 130

dρLabelID
C130Cyclic group1301C130130,4

Groups of order 131

dρLabelID
C131Cyclic group1311C131131,1

Groups of order 132

dρLabelID
C132Cyclic group1321C132132,4
C2×C66Abelian group of type [2,66]132C2xC66132,10

Groups of order 133

dρLabelID
C133Cyclic group1331C133133,1

Groups of order 134

dρLabelID
C134Cyclic group1341C134134,2

Groups of order 135

dρLabelID
C135Cyclic group1351C135135,1
C3×C45Abelian group of type [3,45]135C3xC45135,2
C32×C15Abelian group of type [3,3,15]135C3^2xC15135,5

Groups of order 136

dρLabelID
C136Cyclic group1361C136136,2
C2×C68Abelian group of type [2,68]136C2xC68136,9
C22×C34Abelian group of type [2,2,34]136C2^2xC34136,15

Groups of order 137

dρLabelID
C137Cyclic group1371C137137,1

Groups of order 138

dρLabelID
C138Cyclic group1381C138138,4

Groups of order 139

dρLabelID
C139Cyclic group1391C139139,1

Groups of order 140

dρLabelID
C140Cyclic group1401C140140,4
C2×C70Abelian group of type [2,70]140C2xC70140,11

Groups of order 141

dρLabelID
C141Cyclic group1411C141141,1

Groups of order 142

dρLabelID
C142Cyclic group1421C142142,2

Groups of order 143

dρLabelID
C143Cyclic group1431C143143,1

Groups of order 144

dρLabelID
C144Cyclic group1441C144144,2
C122Abelian group of type [12,12]144C12^2144,101
C4×C36Abelian group of type [4,36]144C4xC36144,20
C2×C72Abelian group of type [2,72]144C2xC72144,23
C3×C48Abelian group of type [3,48]144C3xC48144,30
C6×C24Abelian group of type [6,24]144C6xC24144,104
C22×C36Abelian group of type [2,2,36]144C2^2xC36144,47
C23×C18Abelian group of type [2,2,2,18]144C2^3xC18144,113
C22×C62Abelian group of type [2,2,6,6]144C2^2xC6^2144,197
C2×C6×C12Abelian group of type [2,6,12]144C2xC6xC12144,178

Groups of order 145

dρLabelID
C145Cyclic group1451C145145,1

Groups of order 146

dρLabelID
C146Cyclic group1461C146146,2

Groups of order 147

dρLabelID
C147Cyclic group1471C147147,2
C7×C21Abelian group of type [7,21]147C7xC21147,6

Groups of order 148

dρLabelID
C148Cyclic group1481C148148,2
C2×C74Abelian group of type [2,74]148C2xC74148,5

Groups of order 149

dρLabelID
C149Cyclic group1491C149149,1

Groups of order 150

dρLabelID
C150Cyclic group1501C150150,4
C5×C30Abelian group of type [5,30]150C5xC30150,13

Groups of order 151

dρLabelID
C151Cyclic group1511C151151,1

Groups of order 152

dρLabelID
C152Cyclic group1521C152152,2
C2×C76Abelian group of type [2,76]152C2xC76152,8
C22×C38Abelian group of type [2,2,38]152C2^2xC38152,12

Groups of order 153

dρLabelID
C153Cyclic group1531C153153,1
C3×C51Abelian group of type [3,51]153C3xC51153,2

Groups of order 154

dρLabelID
C154Cyclic group1541C154154,4

Groups of order 155

dρLabelID
C155Cyclic group1551C155155,2

Groups of order 156

dρLabelID
C156Cyclic group1561C156156,6
C2×C78Abelian group of type [2,78]156C2xC78156,18

Groups of order 157

dρLabelID
C157Cyclic group1571C157157,1

Groups of order 158

dρLabelID
C158Cyclic group1581C158158,2

Groups of order 159

dρLabelID
C159Cyclic group1591C159159,1

Groups of order 160

dρLabelID
C160Cyclic group1601C160160,2
C4×C40Abelian group of type [4,40]160C4xC40160,46
C2×C80Abelian group of type [2,80]160C2xC80160,59
C22×C40Abelian group of type [2,2,40]160C2^2xC40160,190
C23×C20Abelian group of type [2,2,2,20]160C2^3xC20160,228
C24×C10Abelian group of type [2,2,2,2,10]160C2^4xC10160,238
C2×C4×C20Abelian group of type [2,4,20]160C2xC4xC20160,175

Groups of order 161

dρLabelID
C161Cyclic group1611C161161,1

Groups of order 162

dρLabelID
C162Cyclic group1621C162162,2
C9×C18Abelian group of type [9,18]162C9xC18162,23
C3×C54Abelian group of type [3,54]162C3xC54162,26
C33×C6Abelian group of type [3,3,3,6]162C3^3xC6162,55
C32×C18Abelian group of type [3,3,18]162C3^2xC18162,47

Groups of order 163

dρLabelID
C163Cyclic group1631C163163,1

Groups of order 164

dρLabelID
C164Cyclic group1641C164164,2
C2×C82Abelian group of type [2,82]164C2xC82164,5

Groups of order 165

dρLabelID
C165Cyclic group1651C165165,2

Groups of order 166

dρLabelID
C166Cyclic group1661C166166,2

Groups of order 167

dρLabelID
C167Cyclic group1671C167167,1

Groups of order 168

dρLabelID
C168Cyclic group1681C168168,6
C2×C84Abelian group of type [2,84]168C2xC84168,39
C22×C42Abelian group of type [2,2,42]168C2^2xC42168,57

Groups of order 169

dρLabelID
C169Cyclic group1691C169169,1
C132Elementary abelian group of type [13,13]169C13^2169,2

Groups of order 170

dρLabelID
C170Cyclic group1701C170170,4

Groups of order 171

dρLabelID
C171Cyclic group1711C171171,2
C3×C57Abelian group of type [3,57]171C3xC57171,5

Groups of order 172

dρLabelID
C172Cyclic group1721C172172,2
C2×C86Abelian group of type [2,86]172C2xC86172,4

Groups of order 173

dρLabelID
C173Cyclic group1731C173173,1

Groups of order 174

dρLabelID
C174Cyclic group1741C174174,4

Groups of order 175

dρLabelID
C175Cyclic group1751C175175,1
C5×C35Abelian group of type [5,35]175C5xC35175,2

Groups of order 176

dρLabelID
C176Cyclic group1761C176176,2
C4×C44Abelian group of type [4,44]176C4xC44176,19
C2×C88Abelian group of type [2,88]176C2xC88176,22
C22×C44Abelian group of type [2,2,44]176C2^2xC44176,37
C23×C22Abelian group of type [2,2,2,22]176C2^3xC22176,42

Groups of order 177

dρLabelID
C177Cyclic group1771C177177,1

Groups of order 178

dρLabelID
C178Cyclic group1781C178178,2

Groups of order 179

dρLabelID
C179Cyclic group1791C179179,1

Groups of order 180

dρLabelID
C180Cyclic group1801C180180,4
C2×C90Abelian group of type [2,90]180C2xC90180,12
C3×C60Abelian group of type [3,60]180C3xC60180,18
C6×C30Abelian group of type [6,30]180C6xC30180,37

Groups of order 181

dρLabelID
C181Cyclic group1811C181181,1

Groups of order 182

dρLabelID
C182Cyclic group1821C182182,4

Groups of order 183

dρLabelID
C183Cyclic group1831C183183,2

Groups of order 184

dρLabelID
C184Cyclic group1841C184184,2
C2×C92Abelian group of type [2,92]184C2xC92184,8
C22×C46Abelian group of type [2,2,46]184C2^2xC46184,12

Groups of order 185

dρLabelID
C185Cyclic group1851C185185,1

Groups of order 186

dρLabelID
C186Cyclic group1861C186186,6

Groups of order 187

dρLabelID
C187Cyclic group1871C187187,1

Groups of order 188

dρLabelID
C188Cyclic group1881C188188,2
C2×C94Abelian group of type [2,94]188C2xC94188,4

Groups of order 189

dρLabelID
C189Cyclic group1891C189189,2
C3×C63Abelian group of type [3,63]189C3xC63189,9
C32×C21Abelian group of type [3,3,21]189C3^2xC21189,13

Groups of order 190

dρLabelID
C190Cyclic group1901C190190,4

Groups of order 191

dρLabelID
C191Cyclic group1911C191191,1

Groups of order 192

dρLabelID
C192Cyclic group1921C192192,2
C8×C24Abelian group of type [8,24]192C8xC24192,127
C4×C48Abelian group of type [4,48]192C4xC48192,151
C2×C96Abelian group of type [2,96]192C2xC96192,175
C25×C6Abelian group of type [2,2,2,2,2,6]192C2^5xC6192,1543
C42×C12Abelian group of type [4,4,12]192C4^2xC12192,807
C22×C48Abelian group of type [2,2,48]192C2^2xC48192,935
C23×C24Abelian group of type [2,2,2,24]192C2^3xC24192,1454
C24×C12Abelian group of type [2,2,2,2,12]192C2^4xC12192,1530
C2×C4×C24Abelian group of type [2,4,24]192C2xC4xC24192,835
C22×C4×C12Abelian group of type [2,2,4,12]192C2^2xC4xC12192,1400

Groups of order 193

dρLabelID
C193Cyclic group1931C193193,1

Groups of order 194

dρLabelID
C194Cyclic group1941C194194,2

Groups of order 195

dρLabelID
C195Cyclic group1951C195195,2

Groups of order 196

dρLabelID
C196Cyclic group1961C196196,2
C142Abelian group of type [14,14]196C14^2196,12
C2×C98Abelian group of type [2,98]196C2xC98196,4
C7×C28Abelian group of type [7,28]196C7xC28196,7

Groups of order 197

dρLabelID
C197Cyclic group1971C197197,1

Groups of order 198

dρLabelID
C198Cyclic group1981C198198,4
C3×C66Abelian group of type [3,66]198C3xC66198,10

Groups of order 199

dρLabelID
C199Cyclic group1991C199199,1

Groups of order 200

dρLabelID
C200Cyclic group2001C200200,2
C5×C40Abelian group of type [5,40]200C5xC40200,17
C2×C100Abelian group of type [2,100]200C2xC100200,9
C10×C20Abelian group of type [10,20]200C10xC20200,37
C22×C50Abelian group of type [2,2,50]200C2^2xC50200,14
C2×C102Abelian group of type [2,10,10]200C2xC10^2200,52

Groups of order 201

dρLabelID
C201Cyclic group2011C201201,2

Groups of order 202

dρLabelID
C202Cyclic group2021C202202,2

Groups of order 203

dρLabelID
C203Cyclic group2031C203203,2

Groups of order 204

dρLabelID
C204Cyclic group2041C204204,4
C2×C102Abelian group of type [2,102]204C2xC102204,12

Groups of order 205

dρLabelID
C205Cyclic group2051C205205,2

Groups of order 206

dρLabelID
C206Cyclic group2061C206206,2

Groups of order 207

dρLabelID
C207Cyclic group2071C207207,1
C3×C69Abelian group of type [3,69]207C3xC69207,2

Groups of order 208

dρLabelID
C208Cyclic group2081C208208,2
C4×C52Abelian group of type [4,52]208C4xC52208,20
C2×C104Abelian group of type [2,104]208C2xC104208,23
C22×C52Abelian group of type [2,2,52]208C2^2xC52208,45
C23×C26Abelian group of type [2,2,2,26]208C2^3xC26208,51

Groups of order 209

dρLabelID
C209Cyclic group2091C209209,1

Groups of order 210

dρLabelID
C210Cyclic group2101C210210,12

Groups of order 211

dρLabelID
C211Cyclic group2111C211211,1

Groups of order 212

dρLabelID
C212Cyclic group2121C212212,2
C2×C106Abelian group of type [2,106]212C2xC106212,5

Groups of order 213

dρLabelID
C213Cyclic group2131C213213,1

Groups of order 214

dρLabelID
C214Cyclic group2141C214214,2

Groups of order 215

dρLabelID
C215Cyclic group2151C215215,1

Groups of order 216

dρLabelID
C216Cyclic group2161C216216,2
C63Abelian group of type [6,6,6]216C6^3216,177
C3×C72Abelian group of type [3,72]216C3xC72216,18
C6×C36Abelian group of type [6,36]216C6xC36216,73
C2×C108Abelian group of type [2,108]216C2xC108216,9
C22×C54Abelian group of type [2,2,54]216C2^2xC54216,24
C32×C24Abelian group of type [3,3,24]216C3^2xC24216,85
C2×C6×C18Abelian group of type [2,6,18]216C2xC6xC18216,114
C3×C6×C12Abelian group of type [3,6,12]216C3xC6xC12216,150

Groups of order 217

dρLabelID
C217Cyclic group2171C217217,1

Groups of order 218

dρLabelID
C218Cyclic group2181C218218,2

Groups of order 219

dρLabelID
C219Cyclic group2191C219219,2

Groups of order 220

dρLabelID
C220Cyclic group2201C220220,6
C2×C110Abelian group of type [2,110]220C2xC110220,15

Groups of order 221

dρLabelID
C221Cyclic group2211C221221,1

Groups of order 222

dρLabelID
C222Cyclic group2221C222222,6

Groups of order 223

dρLabelID
C223Cyclic group2231C223223,1

Groups of order 224

dρLabelID
C224Cyclic group2241C224224,2
C4×C56Abelian group of type [4,56]224C4xC56224,45
C2×C112Abelian group of type [2,112]224C2xC112224,58
C22×C56Abelian group of type [2,2,56]224C2^2xC56224,164
C23×C28Abelian group of type [2,2,2,28]224C2^3xC28224,189
C24×C14Abelian group of type [2,2,2,2,14]224C2^4xC14224,197
C2×C4×C28Abelian group of type [2,4,28]224C2xC4xC28224,149

Groups of order 225

dρLabelID
C225Cyclic group2251C225225,1
C152Abelian group of type [15,15]225C15^2225,6
C3×C75Abelian group of type [3,75]225C3xC75225,2
C5×C45Abelian group of type [5,45]225C5xC45225,4

Groups of order 226

dρLabelID
C226Cyclic group2261C226226,2

Groups of order 227

dρLabelID
C227Cyclic group2271C227227,1

Groups of order 228

dρLabelID
C228Cyclic group2281C228228,6
C2×C114Abelian group of type [2,114]228C2xC114228,15

Groups of order 229

dρLabelID
C229Cyclic group2291C229229,1

Groups of order 230

dρLabelID
C230Cyclic group2301C230230,4

Groups of order 231

dρLabelID
C231Cyclic group2311C231231,2

Groups of order 232

dρLabelID
C232Cyclic group2321C232232,2
C2×C116Abelian group of type [2,116]232C2xC116232,9
C22×C58Abelian group of type [2,2,58]232C2^2xC58232,14

Groups of order 233

dρLabelID
C233Cyclic group2331C233233,1

Groups of order 234

dρLabelID
C234Cyclic group2341C234234,6
C3×C78Abelian group of type [3,78]234C3xC78234,16

Groups of order 235

dρLabelID
C235Cyclic group2351C235235,1

Groups of order 236

dρLabelID
C236Cyclic group2361C236236,2
C2×C118Abelian group of type [2,118]236C2xC118236,4

Groups of order 237

dρLabelID
C237Cyclic group2371C237237,2

Groups of order 238

dρLabelID
C238Cyclic group2381C238238,4

Groups of order 239

dρLabelID
C239Cyclic group2391C239239,1

Groups of order 240

dρLabelID
C240Cyclic group2401C240240,4
C4×C60Abelian group of type [4,60]240C4xC60240,81
C2×C120Abelian group of type [2,120]240C2xC120240,84
C22×C60Abelian group of type [2,2,60]240C2^2xC60240,185
C23×C30Abelian group of type [2,2,2,30]240C2^3xC30240,208

Groups of order 241

dρLabelID
C241Cyclic group2411C241241,1

Groups of order 242

dρLabelID
C242Cyclic group2421C242242,2
C11×C22Abelian group of type [11,22]242C11xC22242,5

Groups of order 243

dρLabelID
C243Cyclic group2431C243243,1
C35Elementary abelian group of type [3,3,3,3,3]243C3^5243,67
C9×C27Abelian group of type [9,27]243C9xC27243,10
C3×C81Abelian group of type [3,81]243C3xC81243,23
C3×C92Abelian group of type [3,9,9]243C3xC9^2243,31
C33×C9Abelian group of type [3,3,3,9]243C3^3xC9243,61
C32×C27Abelian group of type [3,3,27]243C3^2xC27243,48

Groups of order 244

dρLabelID
C244Cyclic group2441C244244,2
C2×C122Abelian group of type [2,122]244C2xC122244,5

Groups of order 245

dρLabelID
C245Cyclic group2451C245245,1
C7×C35Abelian group of type [7,35]245C7xC35245,2

Groups of order 246

dρLabelID
C246Cyclic group2461C246246,4

Groups of order 247

dρLabelID
C247Cyclic group2471C247247,1

Groups of order 248

dρLabelID
C248Cyclic group2481C248248,2
C2×C124Abelian group of type [2,124]248C2xC124248,8
C22×C62Abelian group of type [2,2,62]248C2^2xC62248,12

Groups of order 249

dρLabelID
C249Cyclic group2491C249249,1

Groups of order 250

dρLabelID
C250Cyclic group2501C250250,2
C5×C50Abelian group of type [5,50]250C5xC50250,9
C52×C10Abelian group of type [5,5,10]250C5^2xC10250,15

Groups of order 251

dρLabelID
C251Cyclic group2511C251251,1

Groups of order 252

dρLabelID
C252Cyclic group2521C252252,6
C3×C84Abelian group of type [3,84]252C3xC84252,25
C6×C42Abelian group of type [6,42]252C6xC42252,46
C2×C126Abelian group of type [2,126]252C2xC126252,15

Groups of order 253

dρLabelID
C253Cyclic group2531C253253,2

Groups of order 254

dρLabelID
C254Cyclic group2541C254254,2

Groups of order 255

dρLabelID
C255Cyclic group2551C255255,1

Groups of order 257

dρLabelID
C257Cyclic group2571C257257,1

Groups of order 258

dρLabelID
C258Cyclic group2581C258258,6

Groups of order 259

dρLabelID
C259Cyclic group2591C259259,1

Groups of order 260

dρLabelID
C260Cyclic group2601C260260,4
C2×C130Abelian group of type [2,130]260C2xC130260,15

Groups of order 261

dρLabelID
C261Cyclic group2611C261261,1
C3×C87Abelian group of type [3,87]261C3xC87261,2

Groups of order 262

dρLabelID
C262Cyclic group2621C262262,2

Groups of order 263

dρLabelID
C263Cyclic group2631C263263,1

Groups of order 264

dρLabelID
C264Cyclic group2641C264264,4
C2×C132Abelian group of type [2,132]264C2xC132264,28
C22×C66Abelian group of type [2,2,66]264C2^2xC66264,39

Groups of order 265

dρLabelID
C265Cyclic group2651C265265,1

Groups of order 266

dρLabelID
C266Cyclic group2661C266266,4

Groups of order 267

dρLabelID
C267Cyclic group2671C267267,1

Groups of order 268

dρLabelID
C268Cyclic group2681C268268,2
C2×C134Abelian group of type [2,134]268C2xC134268,4

Groups of order 269

dρLabelID
C269Cyclic group2691C269269,1

Groups of order 270

dρLabelID
C270Cyclic group2701C270270,4
C3×C90Abelian group of type [3,90]270C3xC90270,20
C32×C30Abelian group of type [3,3,30]270C3^2xC30270,30

Groups of order 271

dρLabelID
C271Cyclic group2711C271271,1

Groups of order 272

dρLabelID
C272Cyclic group2721C272272,2
C4×C68Abelian group of type [4,68]272C4xC68272,20
C2×C136Abelian group of type [2,136]272C2xC136272,23
C22×C68Abelian group of type [2,2,68]272C2^2xC68272,46
C23×C34Abelian group of type [2,2,2,34]272C2^3xC34272,54

Groups of order 273

dρLabelID
C273Cyclic group2731C273273,5

Groups of order 274

dρLabelID
C274Cyclic group2741C274274,2

Groups of order 275

dρLabelID
C275Cyclic group2751C275275,2
C5×C55Abelian group of type [5,55]275C5xC55275,4

Groups of order 276

dρLabelID
C276Cyclic group2761C276276,4
C2×C138Abelian group of type [2,138]276C2xC138276,10

Groups of order 277

dρLabelID
C277Cyclic group2771C277277,1

Groups of order 278

dρLabelID
C278Cyclic group2781C278278,2

Groups of order 279

dρLabelID
C279Cyclic group2791C279279,2
C3×C93Abelian group of type [3,93]279C3xC93279,4

Groups of order 280

dρLabelID
C280Cyclic group2801C280280,4
C2×C140Abelian group of type [2,140]280C2xC140280,29
C22×C70Abelian group of type [2,2,70]280C2^2xC70280,40

Groups of order 281

dρLabelID
C281Cyclic group2811C281281,1

Groups of order 282

dρLabelID
C282Cyclic group2821C282282,4

Groups of order 283

dρLabelID
C283Cyclic group2831C283283,1

Groups of order 284

dρLabelID
C284Cyclic group2841C284284,2
C2×C142Abelian group of type [2,142]284C2xC142284,4

Groups of order 285

dρLabelID
C285Cyclic group2851C285285,2

Groups of order 286

dρLabelID
C286Cyclic group2861C286286,4

Groups of order 287

dρLabelID
C287Cyclic group2871C287287,1

Groups of order 288

dρLabelID
C288Cyclic group2881C288288,2
C4×C72Abelian group of type [4,72]288C4xC72288,46
C3×C96Abelian group of type [3,96]288C3xC96288,66
C6×C48Abelian group of type [6,48]288C6xC48288,327
C2×C144Abelian group of type [2,144]288C2xC144288,59
C12×C24Abelian group of type [12,24]288C12xC24288,314
C22×C72Abelian group of type [2,2,72]288C2^2xC72288,179
C23×C36Abelian group of type [2,2,2,36]288C2^3xC36288,367
C2×C122Abelian group of type [2,12,12]288C2xC12^2288,811
C24×C18Abelian group of type [2,2,2,2,18]288C2^4xC18288,840
C23×C62Abelian group of type [2,2,2,6,6]288C2^3xC6^2288,1045
C2×C4×C36Abelian group of type [2,4,36]288C2xC4xC36288,164
C2×C6×C24Abelian group of type [2,6,24]288C2xC6xC24288,826
C22×C6×C12Abelian group of type [2,2,6,12]288C2^2xC6xC12288,1018

Groups of order 289

dρLabelID
C289Cyclic group2891C289289,1
C172Elementary abelian group of type [17,17]289C17^2289,2

Groups of order 290

dρLabelID
C290Cyclic group2901C290290,4

Groups of order 291

dρLabelID
C291Cyclic group2911C291291,2

Groups of order 292

dρLabelID
C292Cyclic group2921C292292,2
C2×C146Abelian group of type [2,146]292C2xC146292,5

Groups of order 293

dρLabelID
C293Cyclic group2931C293293,1

Groups of order 294

dρLabelID
C294Cyclic group2941C294294,6
C7×C42Abelian group of type [7,42]294C7xC42294,23

Groups of order 295

dρLabelID
C295Cyclic group2951C295295,1

Groups of order 296

dρLabelID
C296Cyclic group2961C296296,2
C2×C148Abelian group of type [2,148]296C2xC148296,9
C22×C74Abelian group of type [2,2,74]296C2^2xC74296,14

Groups of order 297

dρLabelID
C297Cyclic group2971C297297,1
C3×C99Abelian group of type [3,99]297C3xC99297,2
C32×C33Abelian group of type [3,3,33]297C3^2xC33297,5

Groups of order 298

dρLabelID
C298Cyclic group2981C298298,2

Groups of order 299

dρLabelID
C299Cyclic group2991C299299,1

Groups of order 300

dρLabelID
C300Cyclic group3001C300300,4
C5×C60Abelian group of type [5,60]300C5xC60300,21
C2×C150Abelian group of type [2,150]300C2xC150300,12
C10×C30Abelian group of type [10,30]300C10xC30300,49

Groups of order 301

dρLabelID
C301Cyclic group3011C301301,2

Groups of order 302

dρLabelID
C302Cyclic group3021C302302,2

Groups of order 303

dρLabelID
C303Cyclic group3031C303303,1

Groups of order 304

dρLabelID
C304Cyclic group3041C304304,2
C4×C76Abelian group of type [4,76]304C4xC76304,19
C2×C152Abelian group of type [2,152]304C2xC152304,22
C22×C76Abelian group of type [2,2,76]304C2^2xC76304,37
C23×C38Abelian group of type [2,2,2,38]304C2^3xC38304,42

Groups of order 305

dρLabelID
C305Cyclic group3051C305305,2

Groups of order 306

dρLabelID
C306Cyclic group3061C306306,4
C3×C102Abelian group of type [3,102]306C3xC102306,10

Groups of order 307

dρLabelID
C307Cyclic group3071C307307,1

Groups of order 308

dρLabelID
C308Cyclic group3081C308308,4
C2×C154Abelian group of type [2,154]308C2xC154308,9

Groups of order 309

dρLabelID
C309Cyclic group3091C309309,2

Groups of order 310

dρLabelID
C310Cyclic group3101C310310,6

Groups of order 311

dρLabelID
C311Cyclic group3111C311311,1

Groups of order 312

dρLabelID
C312Cyclic group3121C312312,6
C2×C156Abelian group of type [2,156]312C2xC156312,42
C22×C78Abelian group of type [2,2,78]312C2^2xC78312,61

Groups of order 313

dρLabelID
C313Cyclic group3131C313313,1

Groups of order 314

dρLabelID
C314Cyclic group3141C314314,2

Groups of order 315

dρLabelID
C315Cyclic group3151C315315,2
C3×C105Abelian group of type [3,105]315C3xC105315,4

Groups of order 316

dρLabelID
C316Cyclic group3161C316316,2
C2×C158Abelian group of type [2,158]316C2xC158316,4

Groups of order 317

dρLabelID
C317Cyclic group3171C317317,1

Groups of order 318

dρLabelID
C318Cyclic group3181C318318,4

Groups of order 319

dρLabelID
C319Cyclic group3191C319319,1

Groups of order 320

dρLabelID
C320Cyclic group3201C320320,2
C8×C40Abelian group of type [8,40]320C8xC40320,126
C4×C80Abelian group of type [4,80]320C4xC80320,150
C2×C160Abelian group of type [2,160]320C2xC160320,174
C42×C20Abelian group of type [4,4,20]320C4^2xC20320,875
C22×C80Abelian group of type [2,2,80]320C2^2xC80320,1003
C23×C40Abelian group of type [2,2,2,40]320C2^3xC40320,1567
C24×C20Abelian group of type [2,2,2,2,20]320C2^4xC20320,1628
C25×C10Abelian group of type [2,2,2,2,2,10]320C2^5xC10320,1640
C2×C4×C40Abelian group of type [2,4,40]320C2xC4xC40320,903
C22×C4×C20Abelian group of type [2,2,4,20]320C2^2xC4xC20320,1513

Groups of order 321

dρLabelID
C321Cyclic group3211C321321,1

Groups of order 322

dρLabelID
C322Cyclic group3221C322322,4

Groups of order 323

dρLabelID
C323Cyclic group3231C323323,1

Groups of order 324

dρLabelID
C324Cyclic group3241C324324,2
C182Abelian group of type [18,18]324C18^2324,81
C9×C36Abelian group of type [9,36]324C9xC36324,26
C6×C54Abelian group of type [6,54]324C6xC54324,84
C2×C162Abelian group of type [2,162]324C2xC162324,5
C3×C108Abelian group of type [3,108]324C3xC108324,29
C32×C36Abelian group of type [3,3,36]324C3^2xC36324,105
C33×C12Abelian group of type [3,3,3,12]324C3^3xC12324,159
C32×C62Abelian group of type [3,3,6,6]324C3^2xC6^2324,176
C3×C6×C18Abelian group of type [3,6,18]324C3xC6xC18324,151

Groups of order 325

dρLabelID
C325Cyclic group3251C325325,1
C5×C65Abelian group of type [5,65]325C5xC65325,2

Groups of order 326

dρLabelID
C326Cyclic group3261C326326,2

Groups of order 327

dρLabelID
C327Cyclic group3271C327327,2

Groups of order 328

dρLabelID
C328Cyclic group3281C328328,2
C2×C164Abelian group of type [2,164]328C2xC164328,9
C22×C82Abelian group of type [2,2,82]328C2^2xC82328,15

Groups of order 329

dρLabelID
C329Cyclic group3291C329329,1

Groups of order 330

dρLabelID
C330Cyclic group3301C330330,12

Groups of order 331

dρLabelID
C331Cyclic group3311C331331,1

Groups of order 332

dρLabelID
C332Cyclic group3321C332332,2
C2×C166Abelian group of type [2,166]332C2xC166332,4

Groups of order 333

dρLabelID
C333Cyclic group3331C333333,2
C3×C111Abelian group of type [3,111]333C3xC111333,5

Groups of order 334

dρLabelID
C334Cyclic group3341C334334,2

Groups of order 335

dρLabelID
C335Cyclic group3351C335335,1

Groups of order 336

dρLabelID
C336Cyclic group3361C336336,6
C4×C84Abelian group of type [4,84]336C4xC84336,106
C2×C168Abelian group of type [2,168]336C2xC168336,109
C22×C84Abelian group of type [2,2,84]336C2^2xC84336,204
C23×C42Abelian group of type [2,2,2,42]336C2^3xC42336,228

Groups of order 337

dρLabelID
C337Cyclic group3371C337337,1

Groups of order 338

dρLabelID
C338Cyclic group3381C338338,2
C13×C26Abelian group of type [13,26]338C13xC26338,5

Groups of order 339

dρLabelID
C339Cyclic group3391C339339,1

Groups of order 340

dρLabelID
C340Cyclic group3401C340340,4
C2×C170Abelian group of type [2,170]340C2xC170340,15

Groups of order 341

dρLabelID
C341Cyclic group3411C341341,1

Groups of order 342

dρLabelID
C342Cyclic group3421C342342,6
C3×C114Abelian group of type [3,114]342C3xC114342,18

Groups of order 343

dρLabelID
C343Cyclic group3431C343343,1
C73Elementary abelian group of type [7,7,7]343C7^3343,5
C7×C49Abelian group of type [7,49]343C7xC49343,2

Groups of order 344

dρLabelID
C344Cyclic group3441C344344,2
C2×C172Abelian group of type [2,172]344C2xC172344,8
C22×C86Abelian group of type [2,2,86]344C2^2xC86344,12

Groups of order 345

dρLabelID
C345Cyclic group3451C345345,1

Groups of order 346

dρLabelID
C346Cyclic group3461C346346,2

Groups of order 347

dρLabelID
C347Cyclic group3471C347347,1

Groups of order 348

dρLabelID
C348Cyclic group3481C348348,4
C2×C174Abelian group of type [2,174]348C2xC174348,12

Groups of order 349

dρLabelID
C349Cyclic group3491C349349,1

Groups of order 350

dρLabelID
C350Cyclic group3501C350350,4
C5×C70Abelian group of type [5,70]350C5xC70350,10

Groups of order 351

dρLabelID
C351Cyclic group3511C351351,2
C3×C117Abelian group of type [3,117]351C3xC117351,9
C32×C39Abelian group of type [3,3,39]351C3^2xC39351,14

Groups of order 352

dρLabelID
C352Cyclic group3521C352352,2
C4×C88Abelian group of type [4,88]352C4xC88352,45
C2×C176Abelian group of type [2,176]352C2xC176352,58
C22×C88Abelian group of type [2,2,88]352C2^2xC88352,164
C23×C44Abelian group of type [2,2,2,44]352C2^3xC44352,188
C24×C22Abelian group of type [2,2,2,2,22]352C2^4xC22352,195
C2×C4×C44Abelian group of type [2,4,44]352C2xC4xC44352,149

Groups of order 353

dρLabelID
C353Cyclic group3531C353353,1

Groups of order 354

dρLabelID
C354Cyclic group3541C354354,4

Groups of order 355

dρLabelID
C355Cyclic group3551C355355,2

Groups of order 356

dρLabelID
C356Cyclic group3561C356356,2
C2×C178Abelian group of type [2,178]356C2xC178356,5

Groups of order 357

dρLabelID
C357Cyclic group3571C357357,2

Groups of order 358

dρLabelID
C358Cyclic group3581C358358,2

Groups of order 359

dρLabelID
C359Cyclic group3591C359359,1

Groups of order 360

dρLabelID
C360Cyclic group3601C360360,4
C6×C60Abelian group of type [6,60]360C6xC60360,115
C2×C180Abelian group of type [2,180]360C2xC180360,30
C3×C120Abelian group of type [3,120]360C3xC120360,38
C22×C90Abelian group of type [2,2,90]360C2^2xC90360,50
C2×C6×C30Abelian group of type [2,6,30]360C2xC6xC30360,162

Groups of order 361

dρLabelID
C361Cyclic group3611C361361,1
C192Elementary abelian group of type [19,19]361C19^2361,2

Groups of order 362

dρLabelID
C362Cyclic group3621C362362,2

Groups of order 363

dρLabelID
C363Cyclic group3631C363363,1
C11×C33Abelian group of type [11,33]363C11xC33363,3

Groups of order 364

dρLabelID
C364Cyclic group3641C364364,4
C2×C182Abelian group of type [2,182]364C2xC182364,11

Groups of order 365

dρLabelID
C365Cyclic group3651C365365,1

Groups of order 366

dρLabelID
C366Cyclic group3661C366366,6

Groups of order 367

dρLabelID
C367Cyclic group3671C367367,1

Groups of order 368

dρLabelID
C368Cyclic group3681C368368,2
C4×C92Abelian group of type [4,92]368C4xC92368,19
C2×C184Abelian group of type [2,184]368C2xC184368,22
C22×C92Abelian group of type [2,2,92]368C2^2xC92368,37
C23×C46Abelian group of type [2,2,2,46]368C2^3xC46368,42

Groups of order 369

dρLabelID
C369Cyclic group3691C369369,1
C3×C123Abelian group of type [3,123]369C3xC123369,2

Groups of order 370

dρLabelID
C370Cyclic group3701C370370,4

Groups of order 371

dρLabelID
C371Cyclic group3711C371371,1

Groups of order 372

dρLabelID
C372Cyclic group3721C372372,6
C2×C186Abelian group of type [2,186]372C2xC186372,15

Groups of order 373

dρLabelID
C373Cyclic group3731C373373,1

Groups of order 374

dρLabelID
C374Cyclic group3741C374374,4

Groups of order 375

dρLabelID
C375Cyclic group3751C375375,1
C5×C75Abelian group of type [5,75]375C5xC75375,3
C52×C15Abelian group of type [5,5,15]375C5^2xC15375,7

Groups of order 376

dρLabelID
C376Cyclic group3761C376376,2
C2×C188Abelian group of type [2,188]376C2xC188376,8
C22×C94Abelian group of type [2,2,94]376C2^2xC94376,12

Groups of order 377

dρLabelID
C377Cyclic group3771C377377,1

Groups of order 378

dρLabelID
C378Cyclic group3781C378378,6
C3×C126Abelian group of type [3,126]378C3xC126378,44
C32×C42Abelian group of type [3,3,42]378C3^2xC42378,60

Groups of order 379

dρLabelID
C379Cyclic group3791C379379,1

Groups of order 380

dρLabelID
C380Cyclic group3801C380380,4
C2×C190Abelian group of type [2,190]380C2xC190380,11

Groups of order 381

dρLabelID
C381Cyclic group3811C381381,2

Groups of order 382

dρLabelID
C382Cyclic group3821C382382,2

Groups of order 383

dρLabelID
C383Cyclic group3831C383383,1

Groups of order 385

dρLabelID
C385Cyclic group3851C385385,2

Groups of order 386

dρLabelID
C386Cyclic group3861C386386,2

Groups of order 387

dρLabelID
C387Cyclic group3871C387387,2
C3×C129Abelian group of type [3,129]387C3xC129387,4

Groups of order 388

dρLabelID
C388Cyclic group3881C388388,2
C2×C194Abelian group of type [2,194]388C2xC194388,5

Groups of order 389

dρLabelID
C389Cyclic group3891C389389,1

Groups of order 390

dρLabelID
C390Cyclic group3901C390390,12

Groups of order 391

dρLabelID
C391Cyclic group3911C391391,1

Groups of order 392

dρLabelID
C392Cyclic group3921C392392,2
C7×C56Abelian group of type [7,56]392C7xC56392,16
C2×C196Abelian group of type [2,196]392C2xC196392,8
C14×C28Abelian group of type [14,28]392C14xC28392,33
C22×C98Abelian group of type [2,2,98]392C2^2xC98392,13
C2×C142Abelian group of type [2,14,14]392C2xC14^2392,44

Groups of order 393

dρLabelID
C393Cyclic group3931C393393,1

Groups of order 394

dρLabelID
C394Cyclic group3941C394394,2

Groups of order 395

dρLabelID
C395Cyclic group3951C395395,1

Groups of order 396

dρLabelID
C396Cyclic group3961C396396,4
C6×C66Abelian group of type [6,66]396C6xC66396,30
C2×C198Abelian group of type [2,198]396C2xC198396,10
C3×C132Abelian group of type [3,132]396C3xC132396,16

Groups of order 397

dρLabelID
C397Cyclic group3971C397397,1

Groups of order 398

dρLabelID
C398Cyclic group3981C398398,2

Groups of order 399

dρLabelID
C399Cyclic group3991C399399,5

Groups of order 400

dρLabelID
C400Cyclic group4001C400400,2
C202Abelian group of type [20,20]400C20^2400,108
C5×C80Abelian group of type [5,80]400C5xC80400,51
C4×C100Abelian group of type [4,100]400C4xC100400,20
C2×C200Abelian group of type [2,200]400C2xC200400,23
C10×C40Abelian group of type [10,40]400C10xC40400,111
C23×C50Abelian group of type [2,2,2,50]400C2^3xC50400,55
C22×C100Abelian group of type [2,2,100]400C2^2xC100400,45
C22×C102Abelian group of type [2,2,10,10]400C2^2xC10^2400,221
C2×C10×C20Abelian group of type [2,10,20]400C2xC10xC20400,201

Groups of order 401

dρLabelID
C401Cyclic group4011C401401,1

Groups of order 402

dρLabelID
C402Cyclic group4021C402402,6

Groups of order 403

dρLabelID
C403Cyclic group4031C403403,1

Groups of order 404

dρLabelID
C404Cyclic group4041C404404,2
C2×C202Abelian group of type [2,202]404C2xC202404,5

Groups of order 405

dρLabelID
C405Cyclic group4051C405405,1
C9×C45Abelian group of type [9,45]405C9xC45405,2
C3×C135Abelian group of type [3,135]405C3xC135405,5
C32×C45Abelian group of type [3,3,45]405C3^2xC45405,11
C33×C15Abelian group of type [3,3,3,15]405C3^3xC15405,16

Groups of order 406

dρLabelID
C406Cyclic group4061C406406,6

Groups of order 407

dρLabelID
C407Cyclic group4071C407407,1

Groups of order 408

dρLabelID
C408Cyclic group4081C408408,4
C2×C204Abelian group of type [2,204]408C2xC204408,30
C22×C102Abelian group of type [2,2,102]408C2^2xC102408,46

Groups of order 409

dρLabelID
C409Cyclic group4091C409409,1

Groups of order 410

dρLabelID
C410Cyclic group4101C410410,6

Groups of order 411

dρLabelID
C411Cyclic group4111C411411,1

Groups of order 412

dρLabelID
C412Cyclic group4121C412412,2
C2×C206Abelian group of type [2,206]412C2xC206412,4

Groups of order 413

dρLabelID
C413Cyclic group4131C413413,1

Groups of order 414

dρLabelID
C414Cyclic group4141C414414,4
C3×C138Abelian group of type [3,138]414C3xC138414,10

Groups of order 415

dρLabelID
C415Cyclic group4151C415415,1

Groups of order 416

dρLabelID
C416Cyclic group4161C416416,2
C4×C104Abelian group of type [4,104]416C4xC104416,46
C2×C208Abelian group of type [2,208]416C2xC208416,59
C23×C52Abelian group of type [2,2,2,52]416C2^3xC52416,227
C24×C26Abelian group of type [2,2,2,2,26]416C2^4xC26416,235
C22×C104Abelian group of type [2,2,104]416C2^2xC104416,190
C2×C4×C52Abelian group of type [2,4,52]416C2xC4xC52416,175

Groups of order 417

dρLabelID
C417Cyclic group4171C417417,2

Groups of order 418

dρLabelID
C418Cyclic group4181C418418,4

Groups of order 419

dρLabelID
C419Cyclic group4191C419419,1

Groups of order 420

dρLabelID
C420Cyclic group4201C420420,12
C2×C210Abelian group of type [2,210]420C2xC210420,41

Groups of order 421

dρLabelID
C421Cyclic group4211C421421,1

Groups of order 422

dρLabelID
C422Cyclic group4221C422422,2

Groups of order 423

dρLabelID
C423Cyclic group4231C423423,1
C3×C141Abelian group of type [3,141]423C3xC141423,2

Groups of order 424

dρLabelID
C424Cyclic group4241C424424,2
C2×C212Abelian group of type [2,212]424C2xC212424,9
C22×C106Abelian group of type [2,2,106]424C2^2xC106424,14

Groups of order 425

dρLabelID
C425Cyclic group4251C425425,1
C5×C85Abelian group of type [5,85]425C5xC85425,2

Groups of order 426

dρLabelID
C426Cyclic group4261C426426,4

Groups of order 427

dρLabelID
C427Cyclic group4271C427427,1

Groups of order 428

dρLabelID
C428Cyclic group4281C428428,2
C2×C214Abelian group of type [2,214]428C2xC214428,4

Groups of order 429

dρLabelID
C429Cyclic group4291C429429,2

Groups of order 430

dρLabelID
C430Cyclic group4301C430430,4

Groups of order 431

dρLabelID
C431Cyclic group4311C431431,1

Groups of order 432

dρLabelID
C432Cyclic group4321C432432,2
C6×C72Abelian group of type [6,72]432C6xC72432,209
C4×C108Abelian group of type [4,108]432C4xC108432,20
C2×C216Abelian group of type [2,216]432C2xC216432,23
C3×C144Abelian group of type [3,144]432C3xC144432,34
C12×C36Abelian group of type [12,36]432C12xC36432,200
C2×C63Abelian group of type [2,6,6,6]432C2xC6^3432,775
C23×C54Abelian group of type [2,2,2,54]432C2^3xC54432,228
C32×C48Abelian group of type [3,3,48]432C3^2xC48432,232
C3×C122Abelian group of type [3,12,12]432C3xC12^2432,512
C62×C12Abelian group of type [6,6,12]432C6^2xC12432,730
C22×C108Abelian group of type [2,2,108]432C2^2xC108432,53
C2×C6×C36Abelian group of type [2,6,36]432C2xC6xC36432,400
C3×C6×C24Abelian group of type [3,6,24]432C3xC6xC24432,515
C22×C6×C18Abelian group of type [2,2,6,18]432C2^2xC6xC18432,562

Groups of order 433

dρLabelID
C433Cyclic group4331C433433,1

Groups of order 434

dρLabelID
C434Cyclic group4341C434434,4

Groups of order 435

dρLabelID
C435Cyclic group4351C435435,1

Groups of order 436

dρLabelID
C436Cyclic group4361C436436,2
C2×C218Abelian group of type [2,218]436C2xC218436,5

Groups of order 437

dρLabelID
C437Cyclic group4371C437437,1

Groups of order 438

dρLabelID
C438Cyclic group4381C438438,6

Groups of order 439

dρLabelID
C439Cyclic group4391C439439,1

Groups of order 440

dρLabelID
C440Cyclic group4401C440440,6
C2×C220Abelian group of type [2,220]440C2xC220440,39
C22×C110Abelian group of type [2,2,110]440C2^2xC110440,51

Groups of order 441

dρLabelID
C441Cyclic group4411C441441,2
C212Abelian group of type [21,21]441C21^2441,13
C7×C63Abelian group of type [7,63]441C7xC63441,8
C3×C147Abelian group of type [3,147]441C3xC147441,4

Groups of order 442

dρLabelID
C442Cyclic group4421C442442,4

Groups of order 443

dρLabelID
C443Cyclic group4431C443443,1

Groups of order 444

dρLabelID
C444Cyclic group4441C444444,6
C2×C222Abelian group of type [2,222]444C2xC222444,18

Groups of order 445

dρLabelID
C445Cyclic group4451C445445,1

Groups of order 446

dρLabelID
C446Cyclic group4461C446446,2

Groups of order 447

dρLabelID
C447Cyclic group4471C447447,1

Groups of order 448

dρLabelID
C448Cyclic group4481C448448,2
C8×C56Abelian group of type [8,56]448C8xC56448,125
C4×C112Abelian group of type [4,112]448C4xC112448,149
C2×C224Abelian group of type [2,224]448C2xC224448,173
C42×C28Abelian group of type [4,4,28]448C4^2xC28448,782
C23×C56Abelian group of type [2,2,2,56]448C2^3xC56448,1348
C24×C28Abelian group of type [2,2,2,2,28]448C2^4xC28448,1385
C25×C14Abelian group of type [2,2,2,2,2,14]448C2^5xC14448,1396
C22×C112Abelian group of type [2,2,112]448C2^2xC112448,910
C2×C4×C56Abelian group of type [2,4,56]448C2xC4xC56448,810
C22×C4×C28Abelian group of type [2,2,4,28]448C2^2xC4xC28448,1294

Groups of order 449

dρLabelID
C449Cyclic group4491C449449,1

Groups of order 450

dρLabelID
C450Cyclic group4501C450450,4
C5×C90Abelian group of type [5,90]450C5xC90450,19
C3×C150Abelian group of type [3,150]450C3xC150450,10
C15×C30Abelian group of type [15,30]450C15xC30450,34

Groups of order 451

dρLabelID
C451Cyclic group4511C451451,1

Groups of order 452

dρLabelID
C452Cyclic group4521C452452,2
C2×C226Abelian group of type [2,226]452C2xC226452,5

Groups of order 453

dρLabelID
C453Cyclic group4531C453453,2

Groups of order 454

dρLabelID
C454Cyclic group4541C454454,2

Groups of order 455

dρLabelID
C455Cyclic group4551C455455,1

Groups of order 456

dρLabelID
C456Cyclic group4561C456456,6
C2×C228Abelian group of type [2,228]456C2xC228456,39
C22×C114Abelian group of type [2,2,114]456C2^2xC114456,54

Groups of order 457

dρLabelID
C457Cyclic group4571C457457,1

Groups of order 458

dρLabelID
C458Cyclic group4581C458458,2

Groups of order 459

dρLabelID
C459Cyclic group4591C459459,1
C3×C153Abelian group of type [3,153]459C3xC153459,2
C32×C51Abelian group of type [3,3,51]459C3^2xC51459,5

Groups of order 460

dρLabelID
C460Cyclic group4601C460460,4
C2×C230Abelian group of type [2,230]460C2xC230460,11

Groups of order 461

dρLabelID
C461Cyclic group4611C461461,1

Groups of order 462

dρLabelID
C462Cyclic group4621C462462,12

Groups of order 463

dρLabelID
C463Cyclic group4631C463463,1

Groups of order 464

dρLabelID
C464Cyclic group4641C464464,2
C4×C116Abelian group of type [4,116]464C4xC116464,20
C2×C232Abelian group of type [2,232]464C2xC232464,23
C23×C58Abelian group of type [2,2,2,58]464C2^3xC58464,51
C22×C116Abelian group of type [2,2,116]464C2^2xC116464,45

Groups of order 465

dρLabelID
C465Cyclic group4651C465465,4

Groups of order 466

dρLabelID
C466Cyclic group4661C466466,2

Groups of order 467

dρLabelID
C467Cyclic group4671C467467,1

Groups of order 468

dρLabelID
C468Cyclic group4681C468468,6
C6×C78Abelian group of type [6,78]468C6xC78468,55
C2×C234Abelian group of type [2,234]468C2xC234468,18
C3×C156Abelian group of type [3,156]468C3xC156468,28

Groups of order 469

dρLabelID
C469Cyclic group4691C469469,1

Groups of order 470

dρLabelID
C470Cyclic group4701C470470,4

Groups of order 471

dρLabelID
C471Cyclic group4711C471471,2

Groups of order 472

dρLabelID
C472Cyclic group4721C472472,2
C2×C236Abelian group of type [2,236]472C2xC236472,8
C22×C118Abelian group of type [2,2,118]472C2^2xC118472,12

Groups of order 473

dρLabelID
C473Cyclic group4731C473473,1

Groups of order 474

dρLabelID
C474Cyclic group4741C474474,6

Groups of order 475

dρLabelID
C475Cyclic group4751C475475,1
C5×C95Abelian group of type [5,95]475C5xC95475,2

Groups of order 476

dρLabelID
C476Cyclic group4761C476476,4
C2×C238Abelian group of type [2,238]476C2xC238476,11

Groups of order 477

dρLabelID
C477Cyclic group4771C477477,1
C3×C159Abelian group of type [3,159]477C3xC159477,2

Groups of order 478

dρLabelID
C478Cyclic group4781C478478,2

Groups of order 479

dρLabelID
C479Cyclic group4791C479479,1

Groups of order 480

dρLabelID
C480Cyclic group4801C480480,4
C4×C120Abelian group of type [4,120]480C4xC120480,199
C2×C240Abelian group of type [2,240]480C2xC240480,212
C23×C60Abelian group of type [2,2,2,60]480C2^3xC60480,1180
C24×C30Abelian group of type [2,2,2,2,30]480C2^4xC30480,1213
C22×C120Abelian group of type [2,2,120]480C2^2xC120480,934
C2×C4×C60Abelian group of type [2,4,60]480C2xC4xC60480,919

Groups of order 481

dρLabelID
C481Cyclic group4811C481481,1

Groups of order 482

dρLabelID
C482Cyclic group4821C482482,2

Groups of order 483

dρLabelID
C483Cyclic group4831C483483,2

Groups of order 484

dρLabelID
C484Cyclic group4841C484484,2
C222Abelian group of type [22,22]484C22^2484,12
C2×C242Abelian group of type [2,242]484C2xC242484,4
C11×C44Abelian group of type [11,44]484C11xC44484,7

Groups of order 485

dρLabelID
C485Cyclic group4851C485485,1

Groups of order 486

dρLabelID
C486Cyclic group4861C486486,2
C9×C54Abelian group of type [9,54]486C9xC54486,70
C3×C162Abelian group of type [3,162]486C3xC162486,83
C34×C6Abelian group of type [3,3,3,3,6]486C3^4xC6486,261
C32×C54Abelian group of type [3,3,54]486C3^2xC54486,207
C33×C18Abelian group of type [3,3,3,18]486C3^3xC18486,250
C3×C9×C18Abelian group of type [3,9,18]486C3xC9xC18486,190

Groups of order 487

dρLabelID
C487Cyclic group4871C487487,1

Groups of order 488

dρLabelID
C488Cyclic group4881C488488,2
C2×C244Abelian group of type [2,244]488C2xC244488,9
C22×C122Abelian group of type [2,2,122]488C2^2xC122488,14

Groups of order 489

dρLabelID
C489Cyclic group4891C489489,2

Groups of order 490

dρLabelID
C490Cyclic group4901C490490,4
C7×C70Abelian group of type [7,70]490C7xC70490,10

Groups of order 491

dρLabelID
C491Cyclic group4911C491491,1

Groups of order 492

dρLabelID
C492Cyclic group4921C492492,4
C2×C246Abelian group of type [2,246]492C2xC246492,12

Groups of order 493

dρLabelID
C493Cyclic group4931C493493,1

Groups of order 494

dρLabelID
C494Cyclic group4941C494494,4

Groups of order 495

dρLabelID
C495Cyclic group4951C495495,2
C3×C165Abelian group of type [3,165]495C3xC165495,4

Groups of order 496

dρLabelID
C496Cyclic group4961C496496,2
C4×C124Abelian group of type [4,124]496C4xC124496,19
C2×C248Abelian group of type [2,248]496C2xC248496,22
C23×C62Abelian group of type [2,2,2,62]496C2^3xC62496,42
C22×C124Abelian group of type [2,2,124]496C2^2xC124496,37

Groups of order 497

dρLabelID
C497Cyclic group4971C497497,2

Groups of order 498

dρLabelID
C498Cyclic group4981C498498,4

Groups of order 499

dρLabelID
C499Cyclic group4991C499499,1

Groups of order 500

dρLabelID
C500Cyclic group5001C500500,2
C2×C250Abelian group of type [2,250]500C2xC250500,5
C5×C100Abelian group of type [5,100]500C5xC100500,12
C10×C50Abelian group of type [10,50]500C10xC50500,34
C52×C20Abelian group of type [5,5,20]500C5^2xC20500,40
C5×C102Abelian group of type [5,10,10]500C5xC10^2500,56
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