# 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
׿
×
𝔽