Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1094 conjugacy classes of subgroups.
The subgroup lattice has 651 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13107056 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13105924 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#11716943 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#65295 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13101308 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13101288 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C5×#64753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#87900 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×C4⋊(C5⋊D5) | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C5×#709 | C22 | 1 | 1 | yes | characteristic |
| 11 | C52×#117 | C22 | 1 | 1 | yes | characteristic |
| 12 | #11717215 | — | 2 | 2 | no | — |
| 13 | #11717202 | — | 2 | 2 | no | — |
| 14 | #11717195 | — | 2 | 1 | no | — |
| 15 | #11717194 | — | 2 | 1 | no | — |
| 16 | C5×#4072 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C5×#681 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C5×#681 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11716951 | — | 2 | 1 | no | — |
| 20 | C2×#87774 | — | 2 | 1 | no | — |
| 21 | #11716949 | — | 2 | 1 | no | — |
| 22 | #11716948 | — | 2 | 1 | no | — |
| 23 | #11716947 | — | 2 | 2 | no | — |
| 24 | #11716943 | — | 2 | 2 | no | — |
| 25 | #11716943 | — | 2 | 1 | no | — |
| 26 | #11716943 | — | 2 | 2 | no | — |
| 27 | C2×#87771 | — | 2 | 1 | no | — |
| 28 | C5×#3938 | — | 2 | 2 | no | — |
| 29 | #11716611 | — | 2 | 2 | no | — |
| 30 | #11716605 | — | 2 | 2 | no | — |
| 31 | #10600843 | — | 5 | 1 | no | maximal |
| 32 | #10599821 | — | 5 | 1 | no | maximal |
| 33 | C23×C5⋊D5 | — | 2 | 1 | no | — |
| 34 | C22×C4×C52 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 36 | #87900 | — | 2 | 1 | no | — |
| 37 | #87900 | — | 2 | 1 | no | — |
| 38 | #87900 | — | 2 | 1 | no | — |
| 39 | #87900 | — | 2 | 1 | no | — |
| 40 | C2×C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 41 | C2×C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 42 | C2×C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 43 | C2×C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 44 | C2×C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 45 | C2×C4⋊(C5⋊D5) | — | 2 | 4 | no | — |
| 46 | C2×C4⋊(C5⋊D5) | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×C4⋊(C5⋊D5) | D4 | 1 | 2 | yes | — |
| 48 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 49 | C2×#6045 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×C5×C22⋊D5 | — | 2 | 1 | no | — |
| 51 | C5×#709 | — | 2 | 1 | no | — |
| 52 | C5×#709 | — | 2 | 1 | no | — |
| 53 | C5×#709 | — | 2 | 1 | no | — |
| 54 | C5×#709 | — | 2 | 1 | no | — |
| 55 | C2×C5×D20 | D4 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×C4×C5×D5 | — | 2 | 1 | no | — |
| 57 | C2×C5×Dic10 | D4 | 1 | 1 | yes | characteristic, complemented |
| 58 | C52×C4⋊C4 | — | 2 | 1 | no | — |
| 59 | C52×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 60 | C42×C52 | — | 2 | 1 | no | — |
| 61 | #87808 | — | 2 | 4 | no | — |
| 62 | C5×C22⋊Dic5 | — | 2 | 1 | no | — |
| 63 | C5×C4⋊Dic5 | — | 2 | 1 | no | — |
| 64 | C4×C5×Dic5 | — | 2 | 1 | no | — |
| 65 | C5×#681 | — | 2 | 1 | no | — |
| 66 | C5×#681 | — | 2 | 1 | no | — |
| 67 | C5×#681 | — | 2 | 1 | no | — |
| 68 | C5×#681 | D4 | 1 | 2 | yes | complemented |
| 69 | C2×C5×#168 | — | 2 | 1 | no | — |
| 70 | C2×C5×#168 | D4 | 1 | 2 | yes | complemented |
| 71 | #87776 | — | 2 | 2 | no | — |
| 72 | #87774 | — | 2 | 4 | no | — |
| 73 | #87774 | — | 2 | 2 | no | — |
| 74 | #87773 | — | 2 | 2 | no | — |
| 75 | #87771 | — | 2 | 4 | no | — |
| 76 | #87771 | — | 2 | 2 | no | — |
| 77 | #66156 | — | 5 | 1 | no | — |
| 78 | C2×#4095 | — | 5 | 1 | no | — |
| 79 | #66082 | — | 5 | 1 | no | — |
| 80 | C2×#4054 | — | 5 | 1 | no | — |
| 81 | #65859 | — | 5 | 1 | no | — |
| 82 | #65859 | — | 5 | 1 | no | — |
| 83 | #65859 | — | 10 | 2 | no | — |
| 84 | C5×#410 | — | 5 | 1 | no | — |
| 85 | #65428 | — | 5 | 1 | no | — |
| 86 | #65420 | — | 5 | 1 | no | — |
| 87 | #65295 | D5 | 1 | 1 | yes | characteristic, complemented |
| 88 | #65294 | — | 5 | 1 | no | — |
| 89 | #65290 | — | 5 | 1 | no | — |
| 90 | C5×#344 | — | 5 | 1 | no | — |
| 91 | #64753 | D5 | 1 | 1 | yes | characteristic, complemented |
| 92 | C23×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C22×C5⋊D5 | — | 2 | 2 | no | — |
| 94 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 95 | C22×C5⋊D5 | — | 4 | 1 | no | — |
| 96 | C22×C5⋊D5 | — | 4 | 1 | no | — |
| 97 | C22×C5⋊D5 | — | 8 | 2 | no | — |
| 98 | C22×C5×D5 | — | 2 | 1 | no | — |
| 99 | C2×C4×C52 | — | 2 | 2 | no | — |
| 100 | C2×C4×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C2×C4×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C4×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×C4×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C52 | #41 | 1 | 1 | yes | characteristic |
| 106 | C22⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 107 | C22⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 108 | C2×#1039 | — | 2 | 1 | no | — |
| 109 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 110 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 111 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 112 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 113 | C4⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 114 | C4⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 115 | C4⋊(C5⋊D5) | — | 8 | 4 | no | — |
| 116 | C4×C5⋊D5 | — | 4 | 1 | no | — |
| 117 | C4×C5⋊D5 | — | 4 | 1 | no | — |
| 118 | #6045 | — | 2 | 1 | no | — |
| 119 | #6045 | — | 2 | 1 | no | — |
| 120 | C5×C22⋊D5 | — | 4 | 1 | no | — |
| 121 | C5×C22⋊D5 | — | 4 | 1 | no | — |
| 122 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 123 | C2×C5×Dic5 | — | 4 | 1 | no | — |
| 124 | C5×D20 | — | 2 | 1 | no | — |
| 125 | C5×D20 | — | 2 | 1 | no | — |
| 126 | C4×C5×D5 | — | 4 | 1 | no | — |
| 127 | C4×C5×D5 | — | 4 | 1 | no | — |
| 128 | C5×Dic10 | — | 2 | 1 | no | — |
| 129 | C5×Dic10 | — | 2 | 1 | no | — |
| 130 | C5×#168 | — | 2 | 2 | no | — |
| 131 | C5×#168 | — | 2 | 2 | no | — |
| 132 | C2×C5×#41 | — | 5 | 1 | no | — |
| 133 | C2×#709 | — | 5 | 1 | no | — |
| 134 | C2×#709 | — | 5 | 1 | no | — |
| 135 | C2×#709 | — | 10 | 2 | no | — |
| 136 | C2×#709 | C2×D5 | 1 | 1 | yes | characteristic |
| 137 | C22×D20 | — | 5 | 1 | no | — |
| 138 | C22×D20 | — | 5 | 1 | no | — |
| 139 | C22×D20 | — | 10 | 2 | no | — |
| 140 | C2×C5×M16 | — | 5 | 1 | no | — |
| 141 | C2×C5×M16 | — | 5 | 1 | no | — |
| 142 | C5×#117 | — | 2 | 2 | no | — |
| 143 | C5×#117 | — | 5 | 1 | no | — |
| 144 | C5×#117 | C2×D5 | 1 | 1 | yes | characteristic |
| 145 | C5×#117 | C2×D5 | 1 | 1 | yes | characteristic |
| 146 | #4097 | — | 10 | 1 | no | — |
| 147 | #4096 | — | 10 | 2 | no | — |
| 148 | #4095 | — | 10 | 2 | no | — |
| 149 | #4095 | — | 10 | 1 | no | — |
| 150 | #4095 | — | 10 | 2 | no | — |
| 151 | #4088 | — | 10 | 1 | no | — |
| 152 | C2×#688 | — | 10 | 1 | no | — |
| 153 | #4078 | — | 10 | 1 | no | — |
| 154 | C2×#686 | — | 10 | 1 | no | — |
| 155 | #4072 | C2×D5 | 1 | 1 | yes | characteristic |
| 156 | C2×#681 | C2×D5 | 1 | 1 | yes | characteristic |
| 157 | C2×#681 | C2×D5 | 1 | 1 | yes | characteristic |
| 158 | #4055 | — | 10 | 1 | no | — |
| 159 | #4055 | — | 10 | 1 | no | — |
| 160 | #4054 | — | 10 | 2 | no | — |
| 161 | #4054 | — | 10 | 2 | no | — |
| 162 | #4054 | — | 10 | 1 | no | — |
| 163 | #4054 | — | 10 | 1 | no | — |
| 164 | #4050 | — | 10 | 2 | no | — |
| 165 | C2×D40 | — | 10 | 1 | no | — |
| 166 | C2×#677 | — | 10 | 1 | no | — |
| 167 | #4041 | — | 10 | 2 | no | — |
| 168 | #4041 | — | 10 | 2 | no | — |
| 169 | #4041 | — | 10 | 8 | no | — |
| 170 | #4028 | — | 10 | 8 | no | — |
| 171 | #4028 | — | 10 | 2 | no | — |
| 172 | #4028 | — | 10 | 2 | no | — |
| 173 | #4021 | — | 10 | 1 | no | — |
| 174 | #4021 | — | 10 | 1 | no | — |
| 175 | #4021 | — | 10 | 4 | no | — |
| 176 | #4020 | — | 10 | 1 | no | — |
| 177 | #4020 | — | 10 | 1 | no | — |
| 178 | #4020 | — | 10 | 4 | no | — |
| 179 | C5×#99 | — | 10 | 2 | no | — |
| 180 | #3957 | — | 10 | 2 | no | — |
| 181 | #3953 | — | 10 | 2 | no | — |
| 182 | #3941 | — | 10 | 2 | no | — |
| 183 | #3938 | — | 2 | 2 | no | — |
| 184 | #3937 | — | 10 | 2 | no | — |
| 185 | #2008 | — | 25 | 1 | no | Sylow |
| 186 | C22×C52 | — | 4 | 1 | no | — |
| 187 | C22×C52 | #120 | 1 | 1 | yes | characteristic |
| 188 | C22×C52 | #121 | 1 | 1 | yes | characteristic |
| 189 | C22×C52 | #127 | 1 | 1 | yes | characteristic |
| 190 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 191 | C2×C5⋊D5 | — | 4 | 4 | no | — |
| 192 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 193 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 194 | C2×C5⋊D5 | — | 8 | 2 | no | — |
| 195 | C2×C5⋊D5 | — | 8 | 2 | no | — |
| 196 | C2×C5×D5 | — | 4 | 1 | no | — |
| 197 | C2×C5×D5 | — | 8 | 1 | no | — |
| 198 | C4×C52 | — | 4 | 2 | no | — |
| 199 | C4×C52 | #120 | 1 | 1 | yes | characteristic |
| 200 | C4×C52 | #120 | 1 | 1 | yes | characteristic |
| 201 | C4×C52 | #121 | 1 | 1 | yes | characteristic |
| 202 | C4×C52 | #121 | 1 | 1 | yes | characteristic |
| 203 | #1039 | — | 4 | 1 | no | — |
| 204 | C5×Dic5 | — | 4 | 1 | no | — |
| 205 | C5×Dic5 | — | 8 | 1 | no | — |
| 206 | C23×D5 | — | 10 | 4 | no | — |
| 207 | C23×D5 | — | 10 | 1 | no | — |
| 208 | C23×D5 | — | 10 | 1 | no | — |
| 209 | C5×#41 | — | 10 | 1 | no | — |
| 210 | C5×#41 | — | 10 | 1 | no | — |
| 211 | C5×#41 | — | 10 | 1 | no | — |
| 212 | C5×#41 | — | 10 | 1 | no | — |
| 213 | C2×C5×Q8 | — | 5 | 1 | no | — |
| 214 | C2×C5×D4 | — | 5 | 1 | no | — |
| 215 | C2×C5×D4 | — | 10 | 1 | no | — |
| 216 | C22×C4×C5 | — | 2 | 2 | no | — |
| 217 | C22×C4×C5 | — | 10 | 1 | no | — |
| 218 | C22×C4×C5 | C22×D5 | 1 | 1 | yes | characteristic |
| 219 | C22×C4×C5 | C22×D5 | 1 | 1 | yes | characteristic |
| 220 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 221 | C2×C22⋊D5 | — | 10 | 4 | no | — |
| 222 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 223 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 224 | #709 | — | 2 | 1 | no | — |
| 225 | #709 | — | 2 | 1 | no | — |
| 226 | #709 | — | 2 | 1 | no | — |
| 227 | #709 | — | 2 | 1 | no | — |
| 228 | #709 | — | 10 | 1 | no | — |
| 229 | #709 | — | 10 | 1 | no | — |
| 230 | #709 | — | 10 | 1 | no | — |
| 231 | #709 | — | 10 | 1 | no | — |
| 232 | #709 | — | 10 | 1 | no | — |
| 233 | #709 | — | 10 | 1 | no | — |
| 234 | #709 | — | 10 | 1 | no | — |
| 235 | #709 | — | 10 | 1 | no | — |
| 236 | #709 | — | 20 | 2 | no | — |
| 237 | #709 | — | 20 | 2 | no | — |
| 238 | #709 | — | 20 | 2 | no | — |
| 239 | #709 | — | 20 | 2 | no | — |
| 240 | C2×D20 | — | 5 | 2 | no | — |
| 241 | C2×D20 | — | 5 | 2 | no | — |
| 242 | C2×D20 | — | 5 | 1 | no | — |
| 243 | C2×D20 | — | 5 | 1 | no | — |
| 244 | C2×D20 | — | 10 | 4 | no | — |
| 245 | C2×D20 | — | 10 | 2 | no | — |
| 246 | C2×D20 | — | 10 | 1 | no | — |
| 247 | C2×D20 | — | 10 | 1 | no | — |
| 248 | C2×D20 | — | 10 | 1 | no | — |
| 249 | C2×D20 | — | 10 | 1 | no | — |
| 250 | C2×D20 | — | 10 | 1 | no | — |
| 251 | C2×D20 | — | 10 | 1 | no | — |
| 252 | C2×D20 | — | 10 | 1 | no | — |
| 253 | C2×D20 | — | 10 | 1 | no | — |
| 254 | C2×D20 | — | 10 | 4 | no | — |
| 255 | C2×D20 | — | 10 | 1 | no | — |
| 256 | C2×D20 | — | 10 | 1 | no | — |
| 257 | C2×D20 | — | 10 | 16 | no | — |
| 258 | C2×D20 | — | 10 | 4 | no | — |
| 259 | C2×D20 | — | 10 | 4 | no | — |
| 260 | C2×D20 | — | 20 | 2 | no | — |
| 261 | C2×D20 | — | 20 | 2 | no | — |
| 262 | C2×D20 | — | 20 | 2 | no | — |
| 263 | C2×D20 | — | 20 | 2 | no | — |
| 264 | C2×D20 | D20 | 1 | 1 | yes | characteristic, complemented |
| 265 | C2×C4×D5 | — | 2 | 1 | no | — |
| 266 | C2×C4×D5 | — | 10 | 4 | no | — |
| 267 | C2×C4×D5 | — | 10 | 1 | no | — |
| 268 | C2×C4×D5 | — | 10 | 1 | no | — |
| 269 | C2×Dic10 | — | 5 | 1 | no | — |
| 270 | C2×Dic10 | — | 5 | 1 | no | — |
| 271 | C2×Dic10 | — | 10 | 2 | no | — |
| 272 | C2×Dic10 | D20 | 1 | 1 | yes | characteristic, complemented |
| 273 | C5×M16 | — | 5 | 2 | no | — |
| 274 | C5×M16 | — | 10 | 1 | no | — |
| 275 | C5×M16 | — | 10 | 1 | no | — |
| 276 | C5×M16 | — | 10 | 1 | no | — |
| 277 | C2×C5×C8 | — | 5 | 2 | no | — |
| 278 | C2×C5×C8 | — | 10 | 1 | no | — |
| 279 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 280 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 281 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 282 | C5×C4⋊C4 | — | 10 | 1 | no | — |
| 283 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 284 | C5×C22⋊C4 | — | 10 | 1 | no | — |
| 285 | C5×C22⋊C4 | D20 | 1 | 2 | yes | — |
| 286 | C5×C22⋊C4 | C22⋊D5 | 1 | 2 | yes | — |
| 287 | C42×C5 | — | 2 | 4 | no | — |
| 288 | C42×C5 | — | 2 | 1 | no | — |
| 289 | C42×C5 | — | 2 | 1 | no | — |
| 290 | C42×C5 | — | 10 | 1 | no | — |
| 291 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 292 | #689 | — | 10 | 2 | no | — |
| 293 | #688 | — | 10 | 2 | no | — |
| 294 | #688 | — | 10 | 4 | no | — |
| 295 | #687 | — | 10 | 2 | no | — |
| 296 | #686 | — | 10 | 2 | no | — |
| 297 | #686 | — | 10 | 4 | no | — |
| 298 | #685 | — | 10 | 16 | no | — |
| 299 | #685 | — | 10 | 4 | no | — |
| 300 | #685 | — | 10 | 4 | no | — |
| 301 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 302 | C4×Dic5 | — | 2 | 1 | no | — |
| 303 | #681 | — | 2 | 1 | no | — |
| 304 | #681 | — | 2 | 1 | no | — |
| 305 | #681 | — | 2 | 1 | no | — |
| 306 | #681 | D20 | 1 | 2 | yes | complemented |
| 307 | C2×#168 | — | 2 | 1 | no | — |
| 308 | C2×#168 | D20 | 1 | 2 | yes | complemented |
| 309 | Dic20 | — | 10 | 2 | no | — |
| 310 | D40 | — | 10 | 4 | no | — |
| 311 | D40 | — | 10 | 2 | no | — |
| 312 | #677 | — | 10 | 4 | no | — |
| 313 | #677 | — | 10 | 2 | no | — |
| 314 | #677 | — | 10 | 2 | no | — |
| 315 | #575 | — | 25 | 1 | no | — |
| 316 | C2×AGL(1,ℤ/8) | — | 25 | 1 | no | — |
| 317 | #535 | — | 25 | 1 | no | — |
| 318 | #421 | — | 25 | 1 | no | — |
| 319 | #418 | — | 25 | 1 | no | — |
| 320 | #410 | — | 5 | 1 | no | — |
| 321 | #344 | — | 5 | 1 | no | — |
| 322 | C2×C52 | — | 2 | 1 | no | — |
| 323 | C2×C52 | — | 2 | 1 | no | — |
| 324 | C2×C52 | — | 2 | 1 | no | — |
| 325 | C2×C52 | #392 | 1 | 1 | yes | characteristic |
| 326 | C5⋊D5 | — | 8 | 1 | no | — |
| 327 | C5⋊D5 | — | 8 | 2 | no | — |
| 328 | C5×D5 | — | 8 | 1 | no | — |
| 329 | C23×C5 | — | 2 | 2 | no | — |
| 330 | C23×C5 | — | 10 | 1 | no | — |
| 331 | C23×C5 | C2×D20 | 1 | 1 | yes | characteristic |
| 332 | C23×C5 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 333 | C22×D5 | — | 2 | 1 | no | — |
| 334 | C22×D5 | — | 10 | 8 | no | — |
| 335 | C22×D5 | — | 10 | 4 | no | — |
| 336 | C22×D5 | — | 10 | 2 | no | — |
| 337 | C22×D5 | — | 10 | 1 | no | — |
| 338 | C22×D5 | — | 10 | 2 | no | — |
| 339 | C22×D5 | — | 10 | 1 | no | — |
| 340 | C22×D5 | — | 20 | 4 | no | — |
| 341 | C22×D5 | — | 20 | 4 | no | — |
| 342 | C22×D5 | — | 20 | 1 | no | — |
| 343 | C22×D5 | — | 20 | 1 | no | — |
| 344 | C22×D5 | — | 20 | 1 | no | — |
| 345 | C22×D5 | — | 20 | 1 | no | — |
| 346 | C22×D5 | — | 40 | 2 | no | — |
| 347 | C22×D5 | — | 40 | 2 | no | — |
| 348 | C22×D5 | — | 40 | 8 | no | — |
| 349 | C5×Q8 | — | 10 | 1 | no | — |
| 350 | C5×Q8 | — | 10 | 1 | no | — |
| 351 | C5×D4 | — | 10 | 1 | no | — |
| 352 | C5×D4 | — | 10 | 1 | no | — |
| 353 | C5×D4 | — | 20 | 1 | no | — |
| 354 | C5×D4 | — | 20 | 1 | no | — |
| 355 | C2×C4×C5 | — | 2 | 8 | no | — |
| 356 | C2×C4×C5 | — | 2 | 2 | no | — |
| 357 | C2×C4×C5 | — | 2 | 2 | no | — |
| 358 | C2×C4×C5 | — | 2 | 2 | no | — |
| 359 | C2×C4×C5 | — | 2 | 2 | no | — |
| 360 | C2×C4×C5 | — | 2 | 2 | no | — |
| 361 | C2×C4×C5 | — | 2 | 2 | no | — |
| 362 | C2×C4×C5 | — | 2 | 2 | no | — |
| 363 | C2×C4×C5 | — | 2 | 2 | no | — |
| 364 | C2×C4×C5 | — | 10 | 1 | no | — |
| 365 | C2×C4×C5 | — | 20 | 1 | no | — |
| 366 | C2×C4×C5 | — | 20 | 1 | no | — |
| 367 | C2×C4×C5 | — | 20 | 1 | no | — |
| 368 | C2×C4×C5 | C2×D20 | 1 | 1 | yes | characteristic |
| 369 | C2×C4×C5 | C2×D20 | 1 | 1 | yes | characteristic |
| 370 | C2×C4×C5 | C2×D20 | 1 | 1 | yes | characteristic |
| 371 | C2×C4×C5 | #709 | 1 | 1 | yes | characteristic |
| 372 | C2×C4×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 373 | C2×C4×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 374 | C2×C4×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 375 | C2×C4×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 376 | C2×C4×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 377 | C2×C4×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 378 | C2×C4×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 379 | C2×C4×C5 | #713 | 1 | 1 | yes | characteristic |
| 380 | C22⋊D5 | — | 4 | 1 | no | — |
| 381 | C22⋊D5 | — | 4 | 1 | no | — |
| 382 | C22⋊D5 | — | 20 | 4 | no | — |
| 383 | C22⋊D5 | — | 20 | 4 | no | — |
| 384 | C22⋊D5 | — | 20 | 1 | no | — |
| 385 | C22⋊D5 | — | 20 | 1 | no | — |
| 386 | C22⋊D5 | — | 20 | 1 | no | — |
| 387 | C22⋊D5 | — | 20 | 1 | no | — |
| 388 | C2×Dic5 | — | 2 | 1 | no | — |
| 389 | C2×Dic5 | — | 4 | 1 | no | — |
| 390 | C2×Dic5 | — | 10 | 4 | no | — |
| 391 | C2×Dic5 | — | 10 | 1 | no | — |
| 392 | C2×Dic5 | — | 10 | 1 | no | — |
| 393 | D20 | — | 2 | 1 | no | — |
| 394 | D20 | — | 2 | 1 | no | — |
| 395 | D20 | — | 10 | 2 | no | — |
| 396 | D20 | — | 10 | 1 | no | — |
| 397 | D20 | — | 10 | 2 | no | — |
| 398 | D20 | — | 10 | 1 | no | — |
| 399 | D20 | — | 10 | 2 | no | — |
| 400 | D20 | — | 10 | 1 | no | — |
| 401 | D20 | — | 10 | 2 | no | — |
| 402 | D20 | — | 10 | 1 | no | — |
| 403 | D20 | — | 20 | 4 | no | — |
| 404 | D20 | — | 20 | 4 | no | — |
| 405 | D20 | — | 20 | 2 | no | — |
| 406 | D20 | — | 20 | 2 | no | — |
| 407 | D20 | — | 20 | 4 | no | — |
| 408 | D20 | — | 20 | 4 | no | — |
| 409 | D20 | — | 20 | 1 | no | — |
| 410 | D20 | — | 20 | 1 | no | — |
| 411 | D20 | — | 20 | 1 | no | — |
| 412 | D20 | — | 20 | 1 | no | — |
| 413 | D20 | — | 40 | 16 | no | — |
| 414 | D20 | — | 40 | 4 | no | — |
| 415 | D20 | — | 40 | 4 | no | — |
| 416 | C4×D5 | — | 4 | 1 | no | — |
| 417 | C4×D5 | — | 4 | 1 | no | — |
| 418 | C4×D5 | — | 20 | 4 | no | — |
| 419 | C4×D5 | — | 20 | 4 | no | — |
| 420 | C4×D5 | — | 20 | 1 | no | — |
| 421 | C4×D5 | — | 20 | 1 | no | — |
| 422 | C4×D5 | — | 20 | 1 | no | — |
| 423 | C4×D5 | — | 20 | 1 | no | — |
| 424 | Dic10 | — | 2 | 1 | no | — |
| 425 | Dic10 | — | 2 | 1 | no | — |
| 426 | Dic10 | — | 10 | 1 | no | — |
| 427 | Dic10 | — | 10 | 1 | no | — |
| 428 | Dic10 | — | 10 | 1 | no | — |
| 429 | Dic10 | — | 10 | 1 | no | — |
| 430 | Dic10 | — | 20 | 2 | no | — |
| 431 | Dic10 | — | 20 | 2 | no | — |
| 432 | C5×C8 | — | 10 | 2 | no | — |
| 433 | C5×C8 | — | 10 | 2 | no | — |
| 434 | #168 | — | 2 | 2 | no | — |
| 435 | #168 | — | 2 | 2 | no | — |
| 436 | C2×#41 | — | 5 | 1 | no | — |
| 437 | C2×#41 | — | 25 | 1 | no | — |
| 438 | C22×D4 | — | 25 | 1 | no | — |
| 439 | #137 | — | 50 | 1 | no | — |
| 440 | #137 | — | 50 | 1 | no | — |
| 441 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 442 | AGL(1,ℤ/8) | — | 50 | 1 | no | — |
| 443 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 444 | AGL(1,ℤ/8) | — | 50 | 1 | no | — |
| 445 | #135 | — | 50 | 2 | no | — |
| 446 | C2×SD16 | — | 50 | 1 | no | — |
| 447 | C2×D8 | — | 50 | 1 | no | — |
| 448 | C2×M16 | — | 5 | 1 | no | — |
| 449 | C2×M16 | — | 5 | 1 | no | — |
| 450 | #127 | — | 50 | 1 | no | — |
| 451 | #124 | — | 50 | 1 | no | — |
| 452 | #121 | — | 50 | 2 | no | — |
| 453 | #120 | — | 50 | 2 | no | — |
| 454 | #117 | — | 5 | 1 | no | — |
| 455 | #117 | D52 | 1 | 1 | yes | characteristic |
| 456 | #104 | — | 50 | 2 | no | — |
| 457 | #102 | — | 50 | 2 | no | — |
| 458 | #99 | — | 10 | 2 | no | — |
| 459 | C52 | #2008 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 460 | C22×C5 | — | 2 | 2 | no | — |
| 461 | C22×C5 | — | 2 | 2 | no | — |
| 462 | C22×C5 | — | 2 | 2 | no | — |
| 463 | C22×C5 | — | 4 | 1 | no | — |
| 464 | C22×C5 | — | 4 | 1 | no | — |
| 465 | C22×C5 | — | 4 | 4 | no | — |
| 466 | C22×C5 | — | 20 | 1 | no | — |
| 467 | C22×C5 | — | 40 | 1 | no | — |
| 468 | C22×C5 | #4020 | 1 | 1 | yes | characteristic |
| 469 | C22×C5 | #4028 | 1 | 1 | yes | characteristic |
| 470 | C22×C5 | #4041 | 1 | 1 | yes | characteristic |
| 471 | C22×C5 | #4076 | 1 | 1 | yes | characteristic |
| 472 | C22×C5 | #4083 | 1 | 1 | yes | characteristic |
| 473 | C22×C5 | #4086 | 1 | 1 | yes | characteristic |
| 474 | C2×D5 | — | 4 | 1 | no | — |
| 475 | C2×D5 | — | 8 | 1 | no | — |
| 476 | C2×D5 | — | 20 | 4 | no | — |
| 477 | C2×D5 | — | 20 | 8 | no | — |
| 478 | C2×D5 | — | 20 | 8 | no | — |
| 479 | C2×D5 | — | 20 | 2 | no | — |
| 480 | C2×D5 | — | 20 | 2 | no | — |
| 481 | C2×D5 | — | 20 | 16 | no | — |
| 482 | C2×D5 | — | 20 | 4 | no | — |
| 483 | C2×D5 | — | 20 | 4 | no | — |
| 484 | C2×D5 | — | 20 | 1 | no | — |
| 485 | C2×D5 | — | 20 | 2 | no | — |
| 486 | C2×D5 | — | 20 | 1 | no | — |
| 487 | C2×D5 | — | 20 | 2 | no | — |
| 488 | C2×D5 | — | 40 | 2 | no | — |
| 489 | C2×D5 | — | 40 | 2 | no | — |
| 490 | C2×D5 | — | 40 | 2 | no | — |
| 491 | C2×D5 | — | 40 | 2 | no | — |
| 492 | C2×D5 | — | 40 | 8 | no | — |
| 493 | C2×D5 | — | 40 | 8 | no | — |
| 494 | C4×C5 | — | 2 | 2 | no | — |
| 495 | C4×C5 | — | 2 | 2 | no | — |
| 496 | C4×C5 | — | 2 | 2 | no | — |
| 497 | C4×C5 | — | 2 | 2 | no | — |
| 498 | C4×C5 | — | 4 | 8 | no | — |
| 499 | C4×C5 | — | 4 | 2 | no | — |
| 500 | C4×C5 | — | 4 | 2 | no | — |
| 501 | C4×C5 | — | 20 | 1 | no | — |
| 502 | C4×C5 | — | 40 | 1 | no | — |
| 503 | C4×C5 | #4028 | 1 | 1 | yes | characteristic |
| 504 | C4×C5 | #4028 | 1 | 1 | yes | characteristic |
| 505 | C4×C5 | #4028 | 1 | 1 | yes | characteristic |
| 506 | C4×C5 | #4028 | 1 | 1 | yes | characteristic |
| 507 | C4×C5 | #4030 | 1 | 1 | yes | characteristic |
| 508 | C4×C5 | #4030 | 1 | 1 | yes | characteristic |
| 509 | C4×C5 | #4041 | 1 | 1 | yes | characteristic |
| 510 | C4×C5 | #4041 | 1 | 1 | yes | characteristic |
| 511 | Dic5 | — | 4 | 1 | no | — |
| 512 | Dic5 | — | 8 | 1 | no | — |
| 513 | Dic5 | — | 20 | 4 | no | — |
| 514 | Dic5 | — | 20 | 1 | no | — |
| 515 | Dic5 | — | 20 | 1 | no | — |
| 516 | C24 | — | 50 | 1 | no | — |
| 517 | #41 | — | 10 | 1 | no | — |
| 518 | #41 | — | 10 | 1 | no | — |
| 519 | #41 | — | 10 | 1 | no | — |
| 520 | #41 | — | 10 | 1 | no | — |
| 521 | #41 | — | 50 | 1 | no | — |
| 522 | #41 | — | 50 | 1 | no | — |
| 523 | #41 | — | 50 | 1 | no | — |
| 524 | #41 | — | 50 | 1 | no | — |
| 525 | C2×Q8 | — | 5 | 1 | no | — |
| 526 | C2×Q8 | — | 25 | 1 | no | — |
| 527 | C2×D4 | — | 5 | 1 | no | — |
| 528 | C2×D4 | — | 10 | 1 | no | — |
| 529 | C2×D4 | — | 25 | 2 | no | — |
| 530 | C2×D4 | — | 25 | 1 | no | — |
| 531 | C2×D4 | — | 50 | 4 | no | — |
| 532 | C2×D4 | — | 50 | 1 | no | — |
| 533 | C2×D4 | — | 50 | 1 | no | — |
| 534 | C2×D4 | — | 50 | 1 | no | — |
| 535 | C2×D4 | — | 50 | 1 | no | — |
| 536 | C2×D4 | — | 50 | 1 | no | — |
| 537 | C2×D4 | — | 50 | 1 | no | — |
| 538 | C22×C4 | — | 10 | 1 | no | — |
| 539 | C22×C4 | — | 50 | 1 | no | — |
| 540 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 541 | Q16 | — | 50 | 2 | no | — |
| 542 | SD16 | — | 50 | 2 | no | — |
| 543 | SD16 | — | 50 | 4 | no | — |
| 544 | SD16 | — | 50 | 2 | no | — |
| 545 | D8 | — | 50 | 4 | no | — |
| 546 | D8 | — | 50 | 2 | no | — |
| 547 | M16 | — | 5 | 2 | no | — |
| 548 | M16 | — | 10 | 1 | no | — |
| 549 | M16 | — | 10 | 1 | no | — |
| 550 | M16 | — | 10 | 1 | no | — |
| 551 | C2×C8 | — | 5 | 2 | no | — |
| 552 | C2×C8 | — | 10 | 1 | no | — |
| 553 | C4⋊C4 | — | 2 | 1 | no | — |
| 554 | C4⋊C4 | — | 10 | 1 | no | — |
| 555 | C22⋊C4 | — | 10 | 1 | no | — |
| 556 | C22⋊C4 | — | 50 | 4 | no | — |
| 557 | C22⋊C4 | #6038 | 1 | 2 | yes | — |
| 558 | C42 | — | 2 | 1 | no | — |
| 559 | C42 | — | 10 | 1 | no | — |
| 560 | C2×C5 | — | 2 | 4 | no | — |
| 561 | C2×C5 | — | 2 | 1 | no | — |
| 562 | C2×C5 | — | 2 | 1 | no | — |
| 563 | C2×C5 | — | 2 | 1 | no | — |
| 564 | C2×C5 | — | 2 | 1 | no | — |
| 565 | C2×C5 | — | 2 | 1 | no | — |
| 566 | C2×C5 | — | 2 | 1 | no | — |
| 567 | C2×C5 | — | 2 | 2 | no | — |
| 568 | C2×C5 | — | 4 | 2 | no | — |
| 569 | C2×C5 | — | 4 | 2 | no | — |
| 570 | C2×C5 | — | 40 | 1 | no | — |
| 571 | C2×C5 | #64960 | 1 | 1 | yes | characteristic |
| 572 | C2×C5 | #65249 | 1 | 1 | yes | characteristic |
| 573 | D5 | — | 8 | 1 | no | — |
| 574 | D5 | — | 40 | 4 | no | — |
| 575 | D5 | — | 40 | 8 | no | — |
| 576 | D5 | — | 40 | 1 | no | — |
| 577 | D5 | — | 40 | 2 | no | — |
| 578 | D5 | — | 40 | 1 | no | — |
| 579 | D5 | — | 40 | 2 | no | — |
| 580 | C23 | — | 10 | 1 | no | — |
| 581 | C23 | — | 50 | 2 | no | — |
| 582 | C23 | — | 50 | 1 | no | — |
| 583 | C23 | — | 100 | 1 | no | — |
| 584 | C23 | — | 100 | 1 | no | — |
| 585 | C23 | — | 200 | 2 | no | — |
| 586 | C23 | C2×#6038 | 1 | 1 | yes | characteristic |
| 587 | Q8 | — | 10 | 1 | no | — |
| 588 | Q8 | — | 10 | 1 | no | — |
| 589 | Q8 | — | 50 | 1 | no | — |
| 590 | Q8 | — | 50 | 1 | no | — |
| 591 | D4 | — | 10 | 1 | no | — |
| 592 | D4 | — | 10 | 1 | no | — |
| 593 | D4 | — | 20 | 1 | no | — |
| 594 | D4 | — | 20 | 1 | no | — |
| 595 | D4 | — | 50 | 2 | no | — |
| 596 | D4 | — | 50 | 1 | no | — |
| 597 | D4 | — | 50 | 2 | no | — |
| 598 | D4 | — | 50 | 1 | no | — |
| 599 | D4 | — | 100 | 1 | no | — |
| 600 | D4 | — | 100 | 1 | no | — |
| 601 | D4 | — | 100 | 1 | no | — |
| 602 | D4 | — | 100 | 1 | no | — |
| 603 | D4 | — | 200 | 4 | no | — |
| 604 | C2×C4 | — | 2 | 2 | no | — |
| 605 | C2×C4 | — | 10 | 1 | no | — |
| 606 | C2×C4 | — | 20 | 1 | no | — |
| 607 | C2×C4 | — | 20 | 1 | no | — |
| 608 | C2×C4 | — | 20 | 1 | no | — |
| 609 | C2×C4 | — | 50 | 1 | no | — |
| 610 | C2×C4 | — | 100 | 1 | no | — |
| 611 | C2×C4 | — | 100 | 1 | no | — |
| 612 | C2×C4 | #87874 | 1 | 1 | yes | characteristic |
| 613 | C2×C4 | D5×D20 | 1 | 1 | yes | characteristic |
| 614 | C2×C4 | D5×D20 | 1 | 1 | yes | characteristic |
| 615 | C2×C4 | D5×D20 | 1 | 1 | yes | characteristic |
| 616 | C2×C4 | #87886 | 1 | 1 | yes | characteristic |
| 617 | C2×C4 | #87886 | 1 | 1 | yes | characteristic |
| 618 | C8 | — | 10 | 2 | no | — |
| 619 | C8 | — | 10 | 2 | no | — |
| 620 | C5 | — | 2 | 2 | no | — |
| 621 | C5 | #10599821 | 1 | 1 | yes | characteristic, complemented |
| 622 | C5 | #10600843 | 1 | 1 | yes | characteristic, complemented |
| 623 | C22 | — | 4 | 1 | no | — |
| 624 | C22 | — | 20 | 1 | no | — |
| 625 | C22 | — | 40 | 1 | no | — |
| 626 | C22 | — | 100 | 2 | no | — |
| 627 | C22 | — | 100 | 4 | no | — |
| 628 | C22 | — | 100 | 1 | no | — |
| 629 | C22 | — | 100 | 2 | no | — |
| 630 | C22 | — | 200 | 2 | no | — |
| 631 | C22 | — | 200 | 2 | no | — |
| 632 | C22 | #11717027 | 1 | 1 | yes | characteristic |
| 633 | C22 | #11717029 | 1 | 1 | yes | characteristic |
| 634 | C22 | #11717099 | 1 | 1 | yes | characteristic |
| 635 | C4 | — | 4 | 2 | no | — |
| 636 | C4 | — | 20 | 1 | no | — |
| 637 | C4 | — | 40 | 1 | no | — |
| 638 | C4 | — | 100 | 1 | no | — |
| 639 | C4 | #11717028 | 1 | 1 | yes | characteristic |
| 640 | C4 | #11717028 | 1 | 1 | yes | characteristic |
| 641 | C4 | #11717041 | 1 | 1 | yes | characteristic |
| 642 | C4 | #11717041 | 1 | 1 | yes | characteristic |
| 643 | C2 | — | 2 | 1 | no | — |
| 644 | C2 | — | 2 | 1 | no | — |
| 645 | C2 | — | 2 | 1 | no | — |
| 646 | C2 | — | 40 | 1 | no | — |
| 647 | C2 | — | 200 | 2 | no | — |
| 648 | C2 | — | 200 | 1 | no | — |
| 649 | C2 | #13101569 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107056 | C2 | semidirect |
| 2. #13105924 | C2 | semidirect |
| 3. C2×#11716943 | C2 | semidirect |
| 4. C5×#65295 | C2 | semidirect |
| 5. #13101308 | C2 | semidirect |
| 6. #13101288 | C2 | semidirect |
| 7. C5×#64753 | C2 | semidirect |
| 55. C2×C5×D20 | D4 | semidirect |
| 57. C2×C5×Dic10 | D4 | semidirect |
| 68. C5×#681 | D4 | semidirect |
| 70. C2×C5×#168 | D4 | semidirect |
| 87. #65295 | D5 | semidirect |
| 91. #64753 | D5 | semidirect |
| 264. C2×D20 | D20 | semidirect |
| 272. C2×Dic10 | D20 | semidirect |
| 306. #681 | D20 | semidirect |
| 308. C2×#168 | D20 | semidirect |
| 459. C52 | #2008 | semidirect |
| 621. C5 | #10599821 | semidirect |
| 622. C5 | #10600843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107056 | 2 |
| #13105924 | 2 |
| C2×#11716943 | 2 |
| C5×#65295 | 2 |
| #13101308 | 2 |
| #13101288 | 2 |
| C5×#64753 | 2 |
| #10600843 | 5 |
| #10599821 | 5 |