Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1424 conjugacy classes of subgroups.
The subgroup lattice has 680 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#92098 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#91831 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#91793 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11756269 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C3×C5×#103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751211 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11751067 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11750911 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11750910 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11750909 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11750907 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10610526 | — | 3 | 1 | no | maximal, Hall |
| 13 | C22×C3×C5×Q8 | C22 | 1 | 1 | yes | characteristic |
| 14 | #92098 | — | 2 | 4 | no | — |
| 15 | #92098 | — | 2 | 4 | no | — |
| 16 | C2×#6821 | — | 2 | 1 | no | — |
| 17 | C2×#6821 | C22 | 1 | 2 | yes | — |
| 18 | C2×Q8×D15 | — | 2 | 1 | no | — |
| 19 | C2×Q8×D15 | C22 | 1 | 2 | yes | — |
| 20 | C2×#6817 | — | 2 | 2 | no | — |
| 21 | C2×#6817 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#6817 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#6817 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22×C3×C5×C8 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C3×C5×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#6718 | C22 | 1 | 2 | yes | — |
| 27 | #91831 | — | 2 | 4 | no | — |
| 28 | C2×#6717 | C22 | 1 | 2 | yes | — |
| 29 | #91819 | — | 2 | 2 | no | — |
| 30 | C2×#6710 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×Dic60 | C22 | 1 | 1 | yes | characteristic |
| 32 | #91793 | — | 2 | 4 | no | — |
| 33 | C2×D120 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#6706 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#6706 | C22 | 1 | 1 | yes | characteristic |
| 36 | #91786 | — | 2 | 1 | no | — |
| 37 | #91786 | C22 | 1 | 2 | yes | — |
| 38 | #91784 | — | 2 | 1 | no | — |
| 39 | #91784 | C22 | 1 | 2 | yes | — |
| 40 | C3×C5×#103 | C22 | 1 | 2 | yes | — |
| 41 | C3×C5×#103 | C22 | 1 | 2 | yes | — |
| 42 | #91104 | C22 | 1 | 2 | yes | — |
| 43 | #91104 | C22 | 1 | 2 | yes | — |
| 44 | #91094 | C22 | 1 | 2 | yes | — |
| 45 | #91093 | C22 | 1 | 2 | yes | — |
| 46 | #78795 | — | 5 | 1 | no | maximal, Hall |
| 47 | C2×#4147 | — | 3 | 1 | no | — |
| 48 | C2×#4088 | — | 3 | 1 | no | — |
| 49 | C2×#4050 | — | 3 | 1 | no | — |
| 50 | #65844 | — | 3 | 1 | no | — |
| 51 | C2×C5×#103 | D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | #65399 | — | 3 | 1 | no | — |
| 53 | #65255 | — | 3 | 1 | no | — |
| 54 | #65100 | — | 3 | 2 | no | — |
| 55 | #65099 | — | 3 | 2 | no | — |
| 56 | #65097 | — | 3 | 2 | no | — |
| 57 | #65095 | — | 3 | 2 | no | — |
| 58 | C2×C3×C5×Q8 | — | 2 | 1 | no | — |
| 59 | C2×C3×C5×Q8 | — | 2 | 2 | no | — |
| 60 | C2×C3×C5×Q8 | D4 | 1 | 4 | yes | complemented |
| 61 | C2×C3×C5×Q8 | C23 | 1 | 2 | yes | — |
| 62 | C22×C3×C4×C5 | — | 2 | 1 | no | — |
| 63 | C22×C3×C4×C5 | — | 2 | 1 | no | — |
| 64 | C22×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×#1220 | — | 2 | 1 | no | — |
| 66 | C2×#1220 | — | 2 | 1 | no | — |
| 67 | C2×#1220 | D4 | 1 | 2 | yes | — |
| 68 | #6821 | — | 2 | 8 | no | — |
| 69 | #6821 | — | 2 | 4 | no | — |
| 70 | #6821 | — | 2 | 4 | no | — |
| 71 | Q8×D15 | — | 2 | 8 | no | — |
| 72 | Q8×D15 | — | 2 | 4 | no | — |
| 73 | Q8×D15 | — | 2 | 4 | no | — |
| 74 | #6817 | — | 2 | 16 | no | — |
| 75 | #6817 | — | 2 | 2 | no | — |
| 76 | #6817 | — | 2 | 2 | no | — |
| 77 | #6817 | — | 2 | 2 | no | — |
| 78 | #6817 | — | 2 | 2 | no | — |
| 79 | #6817 | — | 2 | 2 | no | — |
| 80 | #6817 | D4 | 1 | 4 | yes | complemented |
| 81 | C2×D60 | — | 2 | 2 | no | — |
| 82 | C2×D60 | — | 2 | 2 | no | — |
| 83 | C2×D60 | D4 | 1 | 1 | yes | characteristic |
| 84 | C2×D60 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×D60 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×C4×D15 | — | 2 | 2 | no | — |
| 87 | C2×C4×D15 | — | 2 | 1 | no | — |
| 88 | C2×C4×D15 | — | 2 | 2 | no | — |
| 89 | C2×C4×D15 | — | 2 | 1 | no | — |
| 90 | C2×C4×D15 | C23 | 1 | 2 | yes | — |
| 91 | C2×Dic30 | — | 2 | 2 | no | — |
| 92 | C2×Dic30 | D4 | 1 | 1 | yes | characteristic |
| 93 | C2×Dic30 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×Dic30 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C3×C5×C8 | — | 2 | 2 | no | — |
| 96 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 98 | C3×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 99 | C3×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 100 | #6718 | — | 2 | 4 | no | — |
| 101 | #6717 | — | 2 | 4 | no | — |
| 102 | #6714 | — | 2 | 2 | no | — |
| 103 | #6714 | — | 2 | 2 | no | — |
| 104 | C4⋊Dic15 | — | 2 | 2 | no | — |
| 105 | #6710 | — | 2 | 2 | no | — |
| 106 | C2×C3⋊#168 | C23 | 1 | 2 | yes | — |
| 107 | Dic60 | — | 2 | 2 | no | — |
| 108 | D120 | — | 2 | 2 | no | — |
| 109 | #6706 | — | 2 | 2 | no | — |
| 110 | #6706 | — | 2 | 2 | no | — |
| 111 | C2×#1007 | — | 5 | 1 | no | — |
| 112 | C2×#942 | — | 5 | 1 | no | — |
| 113 | C2×#904 | — | 5 | 1 | no | — |
| 114 | #5510 | — | 5 | 1 | no | — |
| 115 | C2×C3×#103 | D5 | 1 | 1 | yes | characteristic, complemented |
| 116 | #5110 | — | 5 | 1 | no | — |
| 117 | #4966 | — | 5 | 1 | no | — |
| 118 | #4810 | — | 5 | 2 | no | — |
| 119 | #4809 | — | 5 | 2 | no | — |
| 120 | #4808 | — | 5 | 2 | no | — |
| 121 | #4806 | — | 5 | 2 | no | — |
| 122 | C22×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 123 | #4147 | — | 6 | 4 | no | — |
| 124 | #4147 | — | 6 | 4 | no | — |
| 125 | C2×#713 | — | 3 | 2 | no | — |
| 126 | C2×#713 | — | 6 | 1 | no | — |
| 127 | C2×Q8×D5 | — | 3 | 2 | no | — |
| 128 | C2×Q8×D5 | — | 6 | 1 | no | — |
| 129 | C2×#709 | — | 3 | 1 | no | — |
| 130 | C2×#709 | — | 3 | 1 | no | — |
| 131 | C2×#709 | — | 3 | 1 | no | — |
| 132 | C2×#709 | — | 6 | 2 | no | — |
| 133 | C22×C5×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 134 | C2×C5×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 135 | C2×#689 | — | 3 | 2 | no | — |
| 136 | #4088 | — | 6 | 4 | no | — |
| 137 | C2×#688 | — | 3 | 2 | no | — |
| 138 | #4076 | — | 6 | 2 | no | — |
| 139 | C2×#681 | — | 3 | 1 | no | — |
| 140 | C2×Dic20 | — | 3 | 1 | no | — |
| 141 | #4050 | — | 6 | 4 | no | — |
| 142 | C2×D40 | — | 3 | 1 | no | — |
| 143 | C2×#677 | — | 3 | 1 | no | — |
| 144 | C2×#677 | — | 3 | 1 | no | — |
| 145 | #4043 | — | 3 | 2 | no | — |
| 146 | #4043 | — | 6 | 1 | no | — |
| 147 | #4041 | — | 3 | 2 | no | — |
| 148 | #4041 | — | 6 | 1 | no | — |
| 149 | C5×#103 | C2×D3 | 1 | 2 | yes | — |
| 150 | C5×#103 | C2×D3 | 1 | 2 | yes | — |
| 151 | #3952 | — | 3 | 2 | no | — |
| 152 | #3952 | — | 3 | 2 | no | — |
| 153 | #3942 | — | 3 | 2 | no | — |
| 154 | #3941 | — | 3 | 2 | no | — |
| 155 | #3013 | — | 15 | 1 | no | Sylow |
| 156 | C23×C3×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C22×D15 | — | 2 | 1 | no | — |
| 158 | C22×D15 | — | 2 | 1 | no | — |
| 159 | C22×D15 | C2×D4 | 1 | 2 | yes | — |
| 160 | C3×C5×Q8 | — | 2 | 4 | no | — |
| 161 | C3×C5×Q8 | — | 2 | 2 | no | — |
| 162 | C3×C5×Q8 | C2×D4 | 1 | 4 | yes | — |
| 163 | C2×C3×C4×C5 | — | 2 | 4 | no | — |
| 164 | C2×C3×C4×C5 | — | 2 | 2 | no | — |
| 165 | C2×C3×C4×C5 | — | 2 | 2 | no | — |
| 166 | C2×C3×C4×C5 | — | 8 | 1 | no | — |
| 167 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×C3×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 169 | C2×C3×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 171 | #1220 | — | 2 | 4 | no | — |
| 172 | #1220 | — | 2 | 4 | no | — |
| 173 | #1220 | — | 4 | 2 | no | — |
| 174 | C2×Dic15 | — | 2 | 1 | no | — |
| 175 | C2×Dic15 | — | 2 | 1 | no | — |
| 176 | C2×Dic15 | C2×D4 | 1 | 2 | yes | — |
| 177 | D60 | — | 2 | 8 | no | — |
| 178 | D60 | — | 2 | 2 | no | — |
| 179 | D60 | — | 2 | 1 | no | — |
| 180 | D60 | — | 2 | 1 | no | — |
| 181 | D60 | — | 2 | 1 | no | — |
| 182 | D60 | — | 8 | 2 | no | — |
| 183 | D60 | C2×D4 | 1 | 2 | yes | — |
| 184 | C4×D15 | — | 2 | 8 | no | — |
| 185 | C4×D15 | — | 2 | 8 | no | — |
| 186 | C4×D15 | — | 2 | 4 | no | — |
| 187 | C4×D15 | — | 2 | 2 | no | — |
| 188 | C4×D15 | — | 2 | 2 | no | — |
| 189 | C4×D15 | — | 4 | 2 | no | — |
| 190 | Dic30 | — | 2 | 8 | no | — |
| 191 | Dic30 | — | 2 | 2 | no | — |
| 192 | Dic30 | — | 2 | 1 | no | — |
| 193 | Dic30 | — | 2 | 1 | no | — |
| 194 | Dic30 | — | 2 | 1 | no | — |
| 195 | Dic30 | C2×D4 | 1 | 2 | yes | — |
| 196 | C3×C5×C8 | — | 2 | 1 | no | — |
| 197 | C3×C5×C8 | — | 2 | 1 | no | — |
| 198 | C3⋊#168 | — | 2 | 2 | no | — |
| 199 | C22×C3×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 200 | #1007 | — | 10 | 4 | no | — |
| 201 | #1007 | — | 10 | 4 | no | — |
| 202 | C2×#239 | — | 5 | 2 | no | — |
| 203 | C2×#239 | — | 10 | 1 | no | — |
| 204 | C2×D3×Q8 | — | 5 | 2 | no | — |
| 205 | C2×D3×Q8 | — | 10 | 1 | no | — |
| 206 | C2×#235 | — | 5 | 1 | no | — |
| 207 | C2×#235 | — | 5 | 1 | no | — |
| 208 | C2×#235 | — | 5 | 1 | no | — |
| 209 | C2×#235 | — | 10 | 2 | no | — |
| 210 | C22×C3×C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 211 | C2×C3×C4⋊C4 | C2×D5 | 1 | 1 | yes | characteristic |
| 212 | C2×#216 | — | 5 | 2 | no | — |
| 213 | #942 | — | 10 | 4 | no | — |
| 214 | C2×#215 | — | 5 | 2 | no | — |
| 215 | #930 | — | 10 | 2 | no | — |
| 216 | C2×#208 | — | 5 | 1 | no | — |
| 217 | C2×Dic12 | — | 5 | 1 | no | — |
| 218 | #904 | — | 10 | 4 | no | — |
| 219 | C2×D24 | — | 5 | 1 | no | — |
| 220 | C2×#204 | — | 5 | 1 | no | — |
| 221 | C2×#204 | — | 5 | 1 | no | — |
| 222 | #897 | — | 5 | 2 | no | — |
| 223 | #897 | — | 10 | 1 | no | — |
| 224 | #895 | — | 5 | 2 | no | — |
| 225 | #895 | — | 10 | 1 | no | — |
| 226 | C3×#103 | C2×D5 | 1 | 2 | yes | — |
| 227 | C3×#103 | C2×D5 | 1 | 2 | yes | — |
| 228 | (C2×D3)⋊C8 | — | 5 | 2 | no | — |
| 229 | (C2×D3)⋊C8 | — | 5 | 2 | no | — |
| 230 | #810 | — | 5 | 2 | no | — |
| 231 | #809 | — | 5 | 2 | no | — |
| 232 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 233 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 234 | C2×C5×Q8 | D12 | 1 | 4 | yes | complemented |
| 235 | C2×C5×Q8 | C22×D3 | 1 | 2 | yes | — |
| 236 | C22×C4×C5 | — | 2 | 1 | no | — |
| 237 | C22×C4×C5 | — | 2 | 1 | no | — |
| 238 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 239 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 240 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 241 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 242 | #713 | — | 6 | 4 | no | — |
| 243 | #713 | — | 6 | 8 | no | — |
| 244 | #713 | — | 6 | 4 | no | — |
| 245 | Q8×D5 | — | 6 | 4 | no | — |
| 246 | Q8×D5 | — | 6 | 8 | no | — |
| 247 | Q8×D5 | — | 6 | 4 | no | — |
| 248 | #709 | — | 3 | 4 | no | — |
| 249 | #709 | — | 6 | 16 | no | — |
| 250 | #709 | — | 6 | 2 | no | — |
| 251 | #709 | — | 6 | 2 | no | — |
| 252 | #709 | — | 6 | 2 | no | — |
| 253 | #709 | — | 6 | 2 | no | — |
| 254 | #709 | — | 6 | 2 | no | — |
| 255 | C2×D20 | — | 3 | 1 | no | — |
| 256 | C2×D20 | — | 3 | 1 | no | — |
| 257 | C2×D20 | — | 3 | 1 | no | — |
| 258 | C2×D20 | — | 6 | 2 | no | — |
| 259 | C2×D20 | — | 6 | 2 | no | — |
| 260 | C2×C4×D5 | — | 3 | 2 | no | — |
| 261 | C2×C4×D5 | — | 6 | 2 | no | — |
| 262 | C2×C4×D5 | — | 6 | 2 | no | — |
| 263 | C2×C4×D5 | — | 6 | 1 | no | — |
| 264 | C2×C4×D5 | — | 6 | 1 | no | — |
| 265 | C2×Dic10 | — | 3 | 1 | no | — |
| 266 | C2×Dic10 | — | 3 | 1 | no | — |
| 267 | C2×Dic10 | — | 3 | 1 | no | — |
| 268 | C2×Dic10 | — | 6 | 2 | no | — |
| 269 | C2×C5×C8 | — | 2 | 2 | no | — |
| 270 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 271 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 272 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 273 | C5×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 274 | #689 | — | 6 | 4 | no | — |
| 275 | #688 | — | 6 | 4 | no | — |
| 276 | #685 | — | 6 | 2 | no | — |
| 277 | #685 | — | 6 | 2 | no | — |
| 278 | C4⋊Dic5 | — | 6 | 2 | no | — |
| 279 | #681 | — | 6 | 2 | no | — |
| 280 | C2×#168 | — | 3 | 2 | no | — |
| 281 | Dic20 | — | 6 | 2 | no | — |
| 282 | D40 | — | 6 | 2 | no | — |
| 283 | #677 | — | 6 | 2 | no | — |
| 284 | #677 | — | 6 | 2 | no | — |
| 285 | C2×2−1+4 | — | 15 | 1 | no | — |
| 286 | C2×#137 | — | 15 | 1 | no | — |
| 287 | C2×#135 | — | 15 | 1 | no | — |
| 288 | #537 | — | 15 | 1 | no | — |
| 289 | #452 | — | 15 | 2 | no | — |
| 290 | #451 | — | 15 | 2 | no | — |
| 291 | #449 | — | 15 | 2 | no | — |
| 292 | #448 | — | 15 | 2 | no | — |
| 293 | #417 | — | 15 | 1 | no | — |
| 294 | C2×#103 | D15 | 1 | 1 | yes | characteristic, complemented |
| 295 | #408 | — | 15 | 1 | no | — |
| 296 | C22×C3×C5 | — | 2 | 1 | no | — |
| 297 | C22×C3×C5 | — | 2 | 1 | no | — |
| 298 | C22×C3×C5 | #120 | 1 | 2 | yes | — |
| 299 | C22×C3×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 300 | C2×D15 | — | 2 | 2 | no | — |
| 301 | C2×D15 | — | 2 | 2 | no | — |
| 302 | C2×D15 | — | 2 | 2 | no | — |
| 303 | C2×D15 | — | 2 | 2 | no | — |
| 304 | C2×D15 | — | 4 | 1 | no | — |
| 305 | C2×D15 | — | 4 | 1 | no | — |
| 306 | C2×D15 | — | 4 | 1 | no | — |
| 307 | C2×D15 | — | 4 | 1 | no | — |
| 308 | C2×D15 | — | 4 | 1 | no | — |
| 309 | C3×C4×C5 | — | 2 | 4 | no | — |
| 310 | C3×C4×C5 | — | 4 | 2 | no | — |
| 311 | C3×C4×C5 | #120 | 1 | 2 | yes | — |
| 312 | C3×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 313 | C3×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 314 | Dic15 | — | 2 | 2 | no | — |
| 315 | Dic15 | — | 2 | 2 | no | — |
| 316 | Dic15 | — | 4 | 1 | no | — |
| 317 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 318 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 319 | C2×C3×Q8 | D20 | 1 | 4 | yes | complemented |
| 320 | C2×C3×Q8 | C22×D5 | 1 | 2 | yes | — |
| 321 | C22×C3×C4 | — | 2 | 1 | no | — |
| 322 | C22×C3×C4 | — | 2 | 1 | no | — |
| 323 | C22×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 324 | C2×#67 | — | 5 | 2 | no | — |
| 325 | C2×#67 | — | 10 | 1 | no | — |
| 326 | C2×#67 | — | 10 | 1 | no | — |
| 327 | #239 | — | 10 | 4 | no | — |
| 328 | #239 | — | 10 | 8 | no | — |
| 329 | #239 | — | 10 | 4 | no | — |
| 330 | D3×Q8 | — | 10 | 4 | no | — |
| 331 | D3×Q8 | — | 10 | 8 | no | — |
| 332 | D3×Q8 | — | 10 | 4 | no | — |
| 333 | #235 | — | 5 | 4 | no | — |
| 334 | #235 | — | 10 | 16 | no | — |
| 335 | #235 | — | 10 | 2 | no | — |
| 336 | #235 | — | 10 | 2 | no | — |
| 337 | #235 | — | 10 | 2 | no | — |
| 338 | #235 | — | 10 | 2 | no | — |
| 339 | #235 | — | 10 | 2 | no | — |
| 340 | C2×D12 | — | 5 | 1 | no | — |
| 341 | C2×D12 | — | 5 | 1 | no | — |
| 342 | C2×D12 | — | 5 | 1 | no | — |
| 343 | C2×D12 | — | 10 | 2 | no | — |
| 344 | C2×D12 | — | 10 | 2 | no | — |
| 345 | C2×C4×D3 | — | 5 | 2 | no | — |
| 346 | C2×C4×D3 | — | 10 | 2 | no | — |
| 347 | C2×C4×D3 | — | 10 | 2 | no | — |
| 348 | C2×C4×D3 | — | 10 | 1 | no | — |
| 349 | C2×C4×D3 | — | 10 | 1 | no | — |
| 350 | C2×Dic6 | — | 5 | 1 | no | — |
| 351 | C2×Dic6 | — | 5 | 1 | no | — |
| 352 | C2×Dic6 | — | 5 | 1 | no | — |
| 353 | C2×Dic6 | — | 10 | 2 | no | — |
| 354 | C2×C3×C8 | — | 2 | 2 | no | — |
| 355 | C2×C3×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 356 | C2×C3×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 357 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 358 | C3×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 359 | #216 | — | 10 | 4 | no | — |
| 360 | #215 | — | 10 | 4 | no | — |
| 361 | (C2×D3)⋊C4 | — | 10 | 2 | no | — |
| 362 | (C2×D3)⋊C4 | — | 10 | 2 | no | — |
| 363 | C4⋊Dic3 | — | 10 | 2 | no | — |
| 364 | #208 | — | 10 | 2 | no | — |
| 365 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 366 | Dic12 | — | 10 | 2 | no | — |
| 367 | D24 | — | 10 | 2 | no | — |
| 368 | #204 | — | 10 | 2 | no | — |
| 369 | #204 | — | 10 | 2 | no | — |
| 370 | C23×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 371 | C22×D5 | — | 3 | 2 | no | — |
| 372 | C22×D5 | — | 6 | 1 | no | — |
| 373 | C22×D5 | — | 6 | 1 | no | — |
| 374 | C5×Q8 | — | 2 | 4 | no | — |
| 375 | C5×Q8 | — | 2 | 2 | no | — |
| 376 | C5×Q8 | C2×D12 | 1 | 4 | yes | — |
| 377 | C2×C4×C5 | — | 2 | 4 | no | — |
| 378 | C2×C4×C5 | — | 2 | 2 | no | — |
| 379 | C2×C4×C5 | — | 2 | 2 | no | — |
| 380 | C2×C4×C5 | — | 8 | 1 | no | — |
| 381 | C2×C4×C5 | C2×D12 | 1 | 2 | yes | — |
| 382 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 383 | C2×C4×C5 | D3×D4 | 1 | 2 | yes | — |
| 384 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 385 | C22⋊D5 | — | 6 | 4 | no | — |
| 386 | C22⋊D5 | — | 6 | 4 | no | — |
| 387 | C22⋊D5 | — | 12 | 2 | no | — |
| 388 | C2×Dic5 | — | 3 | 2 | no | — |
| 389 | C2×Dic5 | — | 6 | 1 | no | — |
| 390 | C2×Dic5 | — | 6 | 1 | no | — |
| 391 | D20 | — | 3 | 2 | no | — |
| 392 | D20 | — | 6 | 8 | no | — |
| 393 | D20 | — | 6 | 2 | no | — |
| 394 | D20 | — | 6 | 1 | no | — |
| 395 | D20 | — | 6 | 1 | no | — |
| 396 | D20 | — | 6 | 1 | no | — |
| 397 | D20 | — | 24 | 2 | no | — |
| 398 | C4×D5 | — | 6 | 8 | no | — |
| 399 | C4×D5 | — | 6 | 8 | no | — |
| 400 | C4×D5 | — | 6 | 4 | no | — |
| 401 | C4×D5 | — | 6 | 2 | no | — |
| 402 | C4×D5 | — | 6 | 2 | no | — |
| 403 | C4×D5 | — | 12 | 2 | no | — |
| 404 | Dic10 | — | 3 | 2 | no | — |
| 405 | Dic10 | — | 6 | 8 | no | — |
| 406 | Dic10 | — | 6 | 2 | no | — |
| 407 | Dic10 | — | 6 | 1 | no | — |
| 408 | Dic10 | — | 6 | 1 | no | — |
| 409 | Dic10 | — | 6 | 1 | no | — |
| 410 | C5×C8 | — | 2 | 1 | no | — |
| 411 | C5×C8 | — | 2 | 1 | no | — |
| 412 | #168 | — | 6 | 2 | no | — |
| 413 | 2−1+4 | — | 30 | 4 | no | — |
| 414 | 2−1+4 | — | 30 | 4 | no | — |
| 415 | C2×#41 | — | 15 | 1 | no | — |
| 416 | C2×#41 | — | 15 | 2 | no | — |
| 417 | C2×#41 | — | 15 | 1 | no | — |
| 418 | C2×#41 | — | 15 | 1 | no | — |
| 419 | C2×#41 | — | 30 | 2 | no | — |
| 420 | C2×#41 | — | 30 | 1 | no | — |
| 421 | C22×Q8 | — | 15 | 2 | no | — |
| 422 | C22×Q8 | — | 30 | 1 | no | — |
| 423 | C22×Q8 | C2×D15 | 1 | 1 | yes | characteristic |
| 424 | #137 | — | 30 | 4 | no | — |
| 425 | #135 | — | 30 | 4 | no | — |
| 426 | C2×Q16 | — | 15 | 2 | no | — |
| 427 | C2×Q16 | — | 15 | 1 | no | — |
| 428 | C2×SD16 | — | 15 | 2 | no | — |
| 429 | C2×SD16 | — | 15 | 1 | no | — |
| 430 | C2×SD16 | — | 15 | 1 | no | — |
| 431 | C2×D8 | — | 15 | 1 | no | — |
| 432 | C2×M16 | — | 15 | 1 | no | — |
| 433 | C22×C8 | C2×D15 | 1 | 1 | yes | characteristic |
| 434 | C22⋊Q8 | — | 15 | 2 | no | — |
| 435 | C22⋊Q8 | — | 30 | 1 | no | — |
| 436 | #121 | — | 15 | 2 | no | — |
| 437 | #121 | — | 30 | 1 | no | — |
| 438 | #121 | — | 30 | 2 | no | — |
| 439 | C2×C4⋊C4 | C2×D15 | 1 | 1 | yes | characteristic |
| 440 | #103 | — | 15 | 2 | no | — |
| 441 | #103 | C2×D15 | 1 | 2 | yes | — |
| 442 | #103 | C2×D15 | 1 | 2 | yes | — |
| 443 | #102 | — | 15 | 2 | no | — |
| 444 | C22⋊C8 | — | 15 | 2 | no | — |
| 445 | C22⋊C8 | — | 15 | 2 | no | — |
| 446 | C2×C3×C5 | — | 2 | 2 | no | — |
| 447 | C2×C3×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 448 | C2×C3×C5 | #577 | 1 | 1 | yes | characteristic |
| 449 | C2×C3×C5 | #578 | 1 | 1 | yes | characteristic |
| 450 | D15 | — | 4 | 2 | no | — |
| 451 | D15 | — | 4 | 2 | no | — |
| 452 | D15 | — | 8 | 1 | no | — |
| 453 | C23×C3 | D4×D5 | 1 | 1 | yes | characteristic |
| 454 | C22×D3 | — | 5 | 2 | no | — |
| 455 | C22×D3 | — | 10 | 1 | no | — |
| 456 | C22×D3 | — | 10 | 1 | no | — |
| 457 | C3×Q8 | — | 2 | 2 | no | — |
| 458 | C3×Q8 | — | 2 | 4 | no | — |
| 459 | C3×Q8 | C2×D20 | 1 | 4 | yes | — |
| 460 | C2×C3×C4 | — | 2 | 2 | no | — |
| 461 | C2×C3×C4 | — | 2 | 4 | no | — |
| 462 | C2×C3×C4 | — | 2 | 2 | no | — |
| 463 | C2×C3×C4 | — | 8 | 1 | no | — |
| 464 | C2×C3×C4 | C2×D20 | 1 | 2 | yes | — |
| 465 | C2×C3×C4 | D4×D5 | 1 | 2 | yes | — |
| 466 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 467 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 468 | #67 | — | 10 | 4 | no | — |
| 469 | #67 | — | 10 | 4 | no | — |
| 470 | #67 | — | 20 | 2 | no | — |
| 471 | C2×Dic3 | — | 5 | 2 | no | — |
| 472 | C2×Dic3 | — | 10 | 1 | no | — |
| 473 | C2×Dic3 | — | 10 | 1 | no | — |
| 474 | D12 | — | 5 | 2 | no | — |
| 475 | D12 | — | 10 | 8 | no | — |
| 476 | D12 | — | 10 | 1 | no | — |
| 477 | D12 | — | 10 | 1 | no | — |
| 478 | D12 | — | 10 | 1 | no | — |
| 479 | D12 | — | 10 | 2 | no | — |
| 480 | D12 | — | 40 | 2 | no | — |
| 481 | C4×D3 | — | 10 | 8 | no | — |
| 482 | C4×D3 | — | 10 | 8 | no | — |
| 483 | C4×D3 | — | 10 | 2 | no | — |
| 484 | C4×D3 | — | 10 | 2 | no | — |
| 485 | C4×D3 | — | 10 | 4 | no | — |
| 486 | C4×D3 | — | 20 | 2 | no | — |
| 487 | Dic6 | — | 5 | 2 | no | — |
| 488 | Dic6 | — | 10 | 8 | no | — |
| 489 | Dic6 | — | 10 | 1 | no | — |
| 490 | Dic6 | — | 10 | 2 | no | — |
| 491 | Dic6 | — | 10 | 1 | no | — |
| 492 | Dic6 | — | 10 | 1 | no | — |
| 493 | C3×C8 | — | 2 | 1 | no | — |
| 494 | C3×C8 | — | 2 | 1 | no | — |
| 495 | C3⋊C8 | — | 10 | 2 | no | — |
| 496 | C22×C5 | — | 2 | 1 | no | — |
| 497 | C22×C5 | — | 2 | 1 | no | — |
| 498 | C22×C5 | #882 | 1 | 2 | yes | — |
| 499 | C22×C5 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 500 | C2×D5 | — | 6 | 2 | no | — |
| 501 | C2×D5 | — | 6 | 2 | no | — |
| 502 | C2×D5 | — | 6 | 2 | no | — |
| 503 | C2×D5 | — | 6 | 2 | no | — |
| 504 | C2×D5 | — | 12 | 1 | no | — |
| 505 | C2×D5 | — | 12 | 1 | no | — |
| 506 | C2×D5 | — | 12 | 1 | no | — |
| 507 | C2×D5 | — | 12 | 1 | no | — |
| 508 | C2×D5 | — | 12 | 1 | no | — |
| 509 | C4×C5 | — | 2 | 4 | no | — |
| 510 | C4×C5 | — | 4 | 2 | no | — |
| 511 | C4×C5 | #882 | 1 | 2 | yes | — |
| 512 | C4×C5 | C22×D12 | 1 | 1 | yes | characteristic |
| 513 | C4×C5 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 514 | Dic5 | — | 6 | 2 | no | — |
| 515 | Dic5 | — | 6 | 2 | no | — |
| 516 | Dic5 | — | 12 | 1 | no | — |
| 517 | #41 | — | 15 | 4 | no | — |
| 518 | #41 | — | 30 | 16 | no | — |
| 519 | #41 | — | 30 | 4 | no | — |
| 520 | #41 | — | 30 | 8 | no | — |
| 521 | #41 | — | 30 | 4 | no | — |
| 522 | #41 | — | 30 | 2 | no | — |
| 523 | #41 | — | 30 | 2 | no | — |
| 524 | #41 | — | 30 | 2 | no | — |
| 525 | #41 | — | 30 | 2 | no | — |
| 526 | #41 | — | 30 | 2 | no | — |
| 527 | C2×Q8 | — | 2 | 1 | no | — |
| 528 | C2×Q8 | — | 2 | 2 | no | — |
| 529 | C2×Q8 | — | 15 | 1 | no | — |
| 530 | C2×Q8 | — | 15 | 1 | no | — |
| 531 | C2×Q8 | — | 15 | 1 | no | — |
| 532 | C2×Q8 | — | 30 | 2 | no | — |
| 533 | C2×Q8 | — | 30 | 4 | no | — |
| 534 | C2×Q8 | — | 30 | 8 | no | — |
| 535 | C2×Q8 | — | 30 | 4 | no | — |
| 536 | C2×Q8 | D60 | 1 | 4 | yes | complemented |
| 537 | C2×Q8 | C22×D15 | 1 | 2 | yes | — |
| 538 | C2×D4 | — | 15 | 2 | no | — |
| 539 | C2×D4 | — | 15 | 1 | no | — |
| 540 | C2×D4 | — | 15 | 1 | no | — |
| 541 | C2×D4 | — | 15 | 1 | no | — |
| 542 | C2×D4 | — | 30 | 2 | no | — |
| 543 | C2×D4 | — | 30 | 2 | no | — |
| 544 | C2×D4 | — | 30 | 1 | no | — |
| 545 | C2×D4 | — | 30 | 1 | no | — |
| 546 | C22×C4 | — | 2 | 1 | no | — |
| 547 | C22×C4 | — | 2 | 1 | no | — |
| 548 | C22×C4 | — | 15 | 2 | no | — |
| 549 | C22×C4 | — | 30 | 2 | no | — |
| 550 | C22×C4 | — | 30 | 2 | no | — |
| 551 | C22×C4 | — | 30 | 1 | no | — |
| 552 | C22×C4 | — | 30 | 1 | no | — |
| 553 | C22×C4 | C22×D15 | 1 | 1 | yes | characteristic |
| 554 | Q16 | — | 30 | 2 | no | — |
| 555 | Q16 | — | 30 | 4 | no | — |
| 556 | SD16 | — | 30 | 2 | no | — |
| 557 | SD16 | — | 30 | 2 | no | — |
| 558 | SD16 | — | 30 | 4 | no | — |
| 559 | D8 | — | 30 | 2 | no | — |
| 560 | M16 | — | 30 | 2 | no | — |
| 561 | C2×C8 | — | 2 | 2 | no | — |
| 562 | C2×C8 | — | 15 | 2 | no | — |
| 563 | C2×C8 | C22×D15 | 1 | 1 | yes | characteristic |
| 564 | C2×C8 | C22×D15 | 1 | 1 | yes | characteristic |
| 565 | C4⋊C4 | — | 2 | 1 | no | — |
| 566 | C4⋊C4 | — | 30 | 2 | no | — |
| 567 | C4⋊C4 | C22×D15 | 1 | 2 | yes | — |
| 568 | C22⋊C4 | — | 30 | 2 | no | — |
| 569 | C22⋊C4 | — | 30 | 2 | no | — |
| 570 | C3×C5 | #3013 | 1 | 1 | yes | characteristic, complemented, Hall |
| 571 | C22×C3 | — | 2 | 1 | no | — |
| 572 | C22×C3 | — | 2 | 1 | no | — |
| 573 | C22×C3 | #4028 | 1 | 2 | yes | — |
| 574 | C22×C3 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 575 | C2×D3 | — | 10 | 2 | no | — |
| 576 | C2×D3 | — | 10 | 2 | no | — |
| 577 | C2×D3 | — | 10 | 2 | no | — |
| 578 | C2×D3 | — | 10 | 2 | no | — |
| 579 | C2×D3 | — | 20 | 1 | no | — |
| 580 | C2×D3 | — | 20 | 1 | no | — |
| 581 | C2×D3 | — | 20 | 1 | no | — |
| 582 | C2×D3 | — | 20 | 1 | no | — |
| 583 | C2×D3 | — | 20 | 1 | no | — |
| 584 | C3×C4 | — | 2 | 4 | no | — |
| 585 | C3×C4 | — | 4 | 2 | no | — |
| 586 | C3×C4 | #4028 | 1 | 2 | yes | — |
| 587 | C3×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 588 | C3×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 589 | Dic3 | — | 10 | 2 | no | — |
| 590 | Dic3 | — | 10 | 2 | no | — |
| 591 | Dic3 | — | 20 | 1 | no | — |
| 592 | C2×C5 | — | 2 | 2 | no | — |
| 593 | C2×C5 | C2×#882 | 1 | 1 | yes | characteristic |
| 594 | C2×C5 | #5762 | 1 | 1 | yes | characteristic |
| 595 | C2×C5 | #5766 | 1 | 1 | yes | characteristic |
| 596 | D5 | — | 12 | 2 | no | — |
| 597 | D5 | — | 12 | 2 | no | — |
| 598 | D5 | — | 24 | 1 | no | — |
| 599 | C23 | — | 15 | 2 | no | — |
| 600 | C23 | — | 30 | 1 | no | — |
| 601 | C23 | — | 30 | 1 | no | — |
| 602 | C23 | D4×D15 | 1 | 1 | yes | characteristic |
| 603 | Q8 | — | 2 | 4 | no | — |
| 604 | Q8 | — | 2 | 2 | no | — |
| 605 | Q8 | — | 15 | 2 | no | — |
| 606 | Q8 | — | 30 | 8 | no | — |
| 607 | Q8 | — | 30 | 2 | no | — |
| 608 | Q8 | — | 30 | 1 | no | — |
| 609 | Q8 | — | 30 | 1 | no | — |
| 610 | Q8 | — | 30 | 1 | no | — |
| 611 | Q8 | C2×D60 | 1 | 4 | yes | — |
| 612 | D4 | — | 15 | 2 | no | — |
| 613 | D4 | — | 30 | 8 | no | — |
| 614 | D4 | — | 30 | 4 | no | — |
| 615 | D4 | — | 30 | 4 | no | — |
| 616 | D4 | — | 30 | 2 | no | — |
| 617 | D4 | — | 30 | 1 | no | — |
| 618 | D4 | — | 30 | 1 | no | — |
| 619 | D4 | — | 30 | 1 | no | — |
| 620 | D4 | — | 60 | 2 | no | — |
| 621 | D4 | — | 120 | 2 | no | — |
| 622 | C2×C4 | — | 2 | 4 | no | — |
| 623 | C2×C4 | — | 2 | 2 | no | — |
| 624 | C2×C4 | — | 2 | 2 | no | — |
| 625 | C2×C4 | — | 8 | 1 | no | — |
| 626 | C2×C4 | — | 15 | 2 | no | — |
| 627 | C2×C4 | — | 30 | 8 | no | — |
| 628 | C2×C4 | — | 30 | 8 | no | — |
| 629 | C2×C4 | — | 30 | 1 | no | — |
| 630 | C2×C4 | — | 30 | 4 | no | — |
| 631 | C2×C4 | — | 30 | 2 | no | — |
| 632 | C2×C4 | — | 30 | 2 | no | — |
| 633 | C2×C4 | — | 30 | 1 | no | — |
| 634 | C2×C4 | — | 60 | 2 | no | — |
| 635 | C2×C4 | C2×D60 | 1 | 2 | yes | — |
| 636 | C2×C4 | D4×D15 | 1 | 1 | yes | characteristic |
| 637 | C2×C4 | D4×D15 | 1 | 2 | yes | — |
| 638 | C2×C4 | C23×D15 | 1 | 1 | yes | characteristic |
| 639 | C8 | — | 2 | 1 | no | — |
| 640 | C8 | — | 2 | 1 | no | — |
| 641 | C8 | — | 30 | 2 | no | — |
| 642 | C2×C3 | — | 2 | 2 | no | — |
| 643 | C2×C3 | C2×#4028 | 1 | 1 | yes | characteristic |
| 644 | C2×C3 | #66096 | 1 | 1 | yes | characteristic |
| 645 | C2×C3 | #66100 | 1 | 1 | yes | characteristic |
| 646 | D3 | — | 20 | 2 | no | — |
| 647 | D3 | — | 20 | 2 | no | — |
| 648 | D3 | — | 40 | 1 | no | — |
| 649 | C5 | #78795 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 650 | C22 | — | 2 | 1 | no | — |
| 651 | C22 | — | 2 | 1 | no | — |
| 652 | C22 | — | 30 | 2 | no | — |
| 653 | C22 | — | 30 | 2 | no | — |
| 654 | C22 | — | 30 | 2 | no | — |
| 655 | C22 | — | 30 | 2 | no | — |
| 656 | C22 | — | 60 | 1 | no | — |
| 657 | C22 | — | 60 | 1 | no | — |
| 658 | C22 | — | 60 | 1 | no | — |
| 659 | C22 | — | 60 | 1 | no | — |
| 660 | C22 | — | 60 | 1 | no | — |
| 661 | C22 | #91771 | 1 | 2 | yes | — |
| 662 | C22 | C2×D4×D15 | 1 | 1 | yes | characteristic |
| 663 | C4 | — | 2 | 4 | no | — |
| 664 | C4 | — | 4 | 2 | no | — |
| 665 | C4 | — | 30 | 2 | no | — |
| 666 | C4 | — | 30 | 2 | no | — |
| 667 | C4 | — | 60 | 1 | no | — |
| 668 | C4 | #91771 | 1 | 2 | yes | — |
| 669 | C4 | C22×D60 | 1 | 1 | yes | characteristic |
| 670 | C4 | C2×D4×D15 | 1 | 1 | yes | characteristic |
| 671 | C3 | #10610526 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 672 | C2 | — | 2 | 2 | no | — |
| 673 | C2 | — | 60 | 2 | no | — |
| 674 | C2 | — | 60 | 2 | no | — |
| 675 | C2 | — | 120 | 1 | no | — |
| 676 | C2 | C2×#91771 | 1 | 1 | yes | characteristic |
| 677 | C2 | #11756521 | 1 | 1 | yes | characteristic |
| 678 | C2 | #11756525 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#92098 | C2 | semidirect |
| 2. C2×#91831 | C2 | semidirect |
| 3. C2×#91793 | C2 | semidirect |
| 4. #11756269 | C2 | semidirect |
| 5. C2×C3×C5×#103 | C2 | semidirect |
| 6. #11751211 | C2 | semidirect |
| 7. #11751067 | C2 | semidirect |
| 8. #11750911 | C2 | semidirect |
| 9. #11750910 | C2 | semidirect |
| 10. #11750909 | C2 | semidirect |
| 11. #11750907 | C2 | semidirect |
| 51. C2×C5×#103 | D3 | semidirect |
| 60. C2×C3×C5×Q8 | D4 | semidirect |
| 80. #6817 | D4 | semidirect |
| 115. C2×C3×#103 | D5 | semidirect |
| 234. C2×C5×Q8 | D12 | semidirect |
| 294. C2×#103 | D15 | semidirect |
| 319. C2×C3×Q8 | D20 | semidirect |
| 536. C2×Q8 | D60 | semidirect |
| 570. C3×C5 | #3013 | semidirect |
| 649. C5 | #78795 | semidirect |
| 671. C3 | #10610526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92098 | 2 |
| C2×#91831 | 2 |
| C2×#91793 | 2 |
| #11756269 | 2 |
| C2×C3×C5×#103 | 2 |
| #11751211 | 2 |
| #11751067 | 2 |
| #11750911 | 2 |
| #11750910 | 2 |
| #11750909 | 2 |
| #11750907 | 2 |
| #10610526 | 3 |
| #78795 | 5 |