Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1782 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 | #10617789 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C5×#2952 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10615647 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615645 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10614290 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10611616 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10611577 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10611421 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10611420 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #10610847 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#65149 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10610624 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #10610605 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #10610284 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #10610276 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×C5×#135 | C22 | 1 | 1 | yes | characteristic |
| 17 | C5×#520 | C22 | 1 | 2 | yes | — |
| 18 | #66167 | C22 | 1 | 2 | yes | — |
| 19 | #66162 | C22 | 1 | 2 | yes | — |
| 20 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 21 | C22×C8×D5 | C22 | 1 | 1 | yes | characteristic |
| 22 | #65918 | C22 | 1 | 4 | yes | — |
| 23 | #65915 | C22 | 1 | 4 | yes | — |
| 24 | #65897 | C22 | 1 | 4 | yes | — |
| 25 | #65894 | — | 2 | 4 | no | — |
| 26 | #65892 | C22 | 1 | 4 | yes | — |
| 27 | #65872 | — | 2 | 4 | no | — |
| 28 | #65867 | — | 2 | 2 | no | — |
| 29 | #65866 | — | 2 | 2 | no | — |
| 30 | #65858 | C22 | 1 | 1 | yes | characteristic |
| 31 | #65853 | C22 | 1 | 2 | yes | — |
| 32 | #65848 | — | 2 | 2 | no | — |
| 33 | #65847 | — | 2 | 2 | no | — |
| 34 | #65838 | C22 | 1 | 2 | yes | — |
| 35 | C2×#4038 | C22 | 1 | 2 | yes | — |
| 36 | C5×#442 | C22 | 1 | 2 | yes | complemented |
| 37 | C5×#441 | C22 | 1 | 2 | yes | complemented |
| 38 | C4×C5×SD16 | C22 | 1 | 4 | yes | complemented |
| 39 | C2×C5×#106 | C22 | 1 | 1 | yes | characteristic |
| 40 | C5×#417 | C22 | 1 | 2 | yes | — |
| 41 | C5×#405 | C22 | 1 | 1 | yes | characteristic |
| 42 | #65522 | C22 | 1 | 2 | yes | — |
| 43 | #65521 | C22 | 1 | 2 | yes | — |
| 44 | #65478 | C22 | 1 | 2 | yes | complemented |
| 45 | #65477 | C22 | 1 | 2 | yes | — |
| 46 | #65460 | C22 | 1 | 2 | yes | — |
| 47 | #65460 | C22 | 1 | 2 | yes | — |
| 48 | #65460 | C22 | 1 | 4 | yes | complemented |
| 49 | #65448 | C22 | 1 | 2 | yes | complemented |
| 50 | #65446 | C22 | 1 | 2 | yes | — |
| 51 | #65418 | C22 | 1 | 1 | yes | characteristic |
| 52 | #65415 | C22 | 1 | 1 | yes | characteristic |
| 53 | #65410 | C22 | 1 | 2 | yes | — |
| 54 | #65395 | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×#3949 | C22 | 1 | 1 | yes | characteristic |
| 56 | #65311 | C22 | 1 | 4 | yes | complemented |
| 57 | #65310 | C22 | 1 | 4 | yes | complemented |
| 58 | #65298 | C22 | 1 | 4 | yes | complemented |
| 59 | #65296 | C22 | 1 | 4 | yes | complemented |
| 60 | #65288 | C22 | 1 | 1 | yes | characteristic |
| 61 | #65253 | C22 | 1 | 2 | yes | — |
| 62 | C2×#3939 | C22 | 1 | 2 | yes | — |
| 63 | #65150 | C22 | 1 | 4 | yes | complemented |
| 64 | #65149 | C22 | 1 | 4 | yes | — |
| 65 | #65149 | C22 | 1 | 4 | yes | — |
| 66 | #65149 | C22 | 1 | 2 | yes | complemented |
| 67 | D5×#106 | C22 | 1 | 2 | yes | complemented |
| 68 | #65104 | C22 | 1 | 4 | yes | — |
| 69 | #65104 | C22 | 1 | 4 | yes | complemented |
| 70 | #65103 | C22 | 1 | 4 | yes | — |
| 71 | #65098 | C22 | 1 | 4 | yes | complemented |
| 72 | #65073 | C22 | 1 | 4 | yes | — |
| 73 | #65068 | C22 | 1 | 4 | yes | — |
| 74 | #65068 | C22 | 1 | 4 | yes | complemented |
| 75 | #65063 | C22 | 1 | 4 | yes | complemented |
| 76 | #64995 | C22 | 1 | 4 | yes | — |
| 77 | #64991 | C22 | 1 | 4 | yes | complemented |
| 78 | C8×D20 | C22 | 1 | 4 | yes | — |
| 79 | #64972 | C22 | 1 | 2 | yes | complemented |
| 80 | #64969 | C22 | 1 | 2 | yes | complemented |
| 81 | #61260 | — | 5 | 1 | no | maximal, Sylow |
| 82 | C2×C5×#41 | C23 | 1 | 2 | yes | — |
| 83 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 84 | C22×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 85 | C5×#135 | — | 2 | 4 | no | — |
| 86 | C2×C5×Q16 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C5×SD16 | C23 | 1 | 2 | yes | — |
| 88 | C2×C5×D8 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 91 | C4×C5×Q8 | C23 | 1 | 4 | yes | — |
| 92 | C4×C5×D4 | — | 2 | 4 | no | — |
| 93 | C4×C5×D4 | C23 | 1 | 4 | yes | — |
| 94 | C5×#117 | — | 2 | 2 | no | — |
| 95 | C5×#117 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×C5×C4⋊C4 | — | 2 | 2 | no | — |
| 97 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 98 | #4092 | C23 | 1 | 4 | yes | — |
| 99 | #4092 | C23 | 1 | 2 | yes | — |
| 100 | #4092 | C23 | 1 | 2 | yes | — |
| 101 | #4085 | — | 2 | 4 | no | — |
| 102 | #4084 | C23 | 1 | 4 | yes | — |
| 103 | #4084 | C23 | 1 | 2 | yes | — |
| 104 | #4084 | C23 | 1 | 2 | yes | — |
| 105 | #4083 | — | 2 | 2 | no | — |
| 106 | #4081 | — | 2 | 2 | no | — |
| 107 | #4076 | — | 2 | 2 | no | — |
| 108 | #4076 | — | 2 | 4 | no | — |
| 109 | #4075 | — | 2 | 4 | no | — |
| 110 | C4×C22⋊D5 | — | 2 | 4 | no | — |
| 111 | C4×C22⋊D5 | — | 2 | 2 | no | — |
| 112 | C4×C22⋊D5 | — | 2 | 2 | no | — |
| 113 | C4×C22⋊D5 | — | 2 | 4 | no | — |
| 114 | C2×#685 | — | 2 | 2 | no | — |
| 115 | #4072 | — | 2 | 4 | no | — |
| 116 | #4072 | C23 | 1 | 2 | yes | — |
| 117 | C2×C4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 118 | #4070 | — | 2 | 2 | no | — |
| 119 | C2×C4×Dic5 | — | 2 | 2 | no | — |
| 120 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 121 | C22×#168 | C23 | 1 | 1 | yes | characteristic |
| 122 | #4047 | — | 2 | 4 | no | — |
| 123 | C2×#676 | C23 | 1 | 2 | yes | — |
| 124 | C2×C8×D5 | — | 2 | 4 | no | — |
| 125 | C2×C8×D5 | C23 | 1 | 2 | yes | — |
| 126 | C2×C8×D5 | C23 | 1 | 2 | yes | — |
| 127 | C2×C8×D5 | C23 | 1 | 2 | yes | — |
| 128 | #4044 | — | 2 | 4 | no | — |
| 129 | #4044 | — | 2 | 4 | no | — |
| 130 | #4043 | D4 | 1 | 2 | yes | — |
| 131 | #4041 | D4 | 1 | 2 | yes | — |
| 132 | #4040 | — | 2 | 4 | no | — |
| 133 | #4039 | — | 2 | 2 | no | — |
| 134 | #4038 | — | 2 | 2 | no | — |
| 135 | #4038 | — | 2 | 2 | no | — |
| 136 | #4038 | C23 | 1 | 4 | yes | — |
| 137 | #4038 | C23 | 1 | 4 | yes | — |
| 138 | #4038 | C23 | 1 | 4 | yes | — |
| 139 | D5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 140 | #4036 | — | 2 | 2 | no | — |
| 141 | #4035 | — | 2 | 4 | no | — |
| 142 | #4034 | — | 2 | 2 | no | — |
| 143 | #4033 | — | 2 | 2 | no | — |
| 144 | #4032 | D4 | 1 | 2 | yes | — |
| 145 | #4031 | — | 2 | 4 | no | — |
| 146 | #4031 | — | 2 | 4 | no | — |
| 147 | #4030 | — | 2 | 4 | no | — |
| 148 | #4028 | D4 | 1 | 2 | yes | — |
| 149 | #4025 | — | 2 | 4 | no | — |
| 150 | #4024 | — | 2 | 4 | no | — |
| 151 | #4022 | — | 2 | 4 | no | — |
| 152 | #4021 | — | 2 | 4 | no | — |
| 153 | C4×D20 | C23 | 1 | 4 | yes | — |
| 154 | #4018 | — | 2 | 4 | no | — |
| 155 | #4016 | C23 | 1 | 4 | yes | — |
| 156 | #4015 | C23 | 1 | 4 | yes | — |
| 157 | C4×Dic10 | — | 2 | 4 | no | — |
| 158 | C5×#106 | C23 | 1 | 2 | yes | — |
| 159 | C5×#106 | C23 | 1 | 2 | yes | — |
| 160 | C5×#103 | C23 | 1 | 4 | yes | — |
| 161 | C5×#102 | C23 | 1 | 4 | yes | — |
| 162 | C5×#97 | C23 | 1 | 2 | yes | — |
| 163 | C4×C5×C8 | C23 | 1 | 2 | yes | — |
| 164 | #3967 | C23 | 1 | 2 | yes | — |
| 165 | #3967 | C23 | 1 | 4 | yes | — |
| 166 | #3967 | C23 | 1 | 2 | yes | — |
| 167 | #3964 | C23 | 1 | 2 | yes | — |
| 168 | #3964 | C23 | 1 | 4 | yes | — |
| 169 | #3964 | C23 | 1 | 2 | yes | — |
| 170 | #3952 | C23 | 1 | 4 | yes | — |
| 171 | #3952 | C23 | 1 | 4 | yes | — |
| 172 | #3950 | C23 | 1 | 4 | yes | — |
| 173 | #3950 | C23 | 1 | 2 | yes | — |
| 174 | #3949 | C23 | 1 | 4 | yes | — |
| 175 | #3949 | C23 | 1 | 2 | yes | — |
| 176 | #3949 | C23 | 1 | 2 | yes | — |
| 177 | #3949 | C23 | 1 | 1 | yes | characteristic |
| 178 | #3949 | C23 | 1 | 1 | yes | characteristic |
| 179 | #3940 | C23 | 1 | 4 | yes | — |
| 180 | #3939 | C23 | 1 | 4 | yes | — |
| 181 | #3939 | C23 | 1 | 4 | yes | — |
| 182 | #3939 | C23 | 1 | 4 | yes | — |
| 183 | C4⋊#168 | C23 | 1 | 4 | yes | — |
| 184 | #3493 | — | 5 | 2 | no | — |
| 185 | #3349 | — | 5 | 4 | no | — |
| 186 | #3347 | — | 5 | 4 | no | — |
| 187 | #3340 | — | 5 | 4 | no | — |
| 188 | #3337 | — | 5 | 4 | no | — |
| 189 | #3163 | — | 5 | 1 | no | — |
| 190 | #3098 | — | 5 | 2 | no | — |
| 191 | #3093 | — | 5 | 2 | no | — |
| 192 | #3083 | — | 5 | 2 | no | — |
| 193 | #3060 | — | 5 | 1 | no | — |
| 194 | #3050 | — | 5 | 1 | no | — |
| 195 | #2952 | D5 | 1 | 1 | yes | characteristic, complemented |
| 196 | #2929 | — | 5 | 1 | no | — |
| 197 | #2912 | — | 5 | 1 | no | — |
| 198 | C2×#427 | — | 5 | 1 | no | — |
| 199 | C23×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C5×#41 | — | 2 | 4 | no | — |
| 201 | C5×#41 | — | 2 | 4 | no | — |
| 202 | C2×C5×Q8 | C24 | 1 | 2 | yes | — |
| 203 | C2×C5×D4 | — | 2 | 2 | no | — |
| 204 | C2×C5×D4 | C24 | 1 | 2 | yes | — |
| 205 | C22×C4×C5 | — | 2 | 2 | no | — |
| 206 | C22×C4×C5 | — | 2 | 2 | no | — |
| 207 | C22×C4×C5 | — | 2 | 4 | no | — |
| 208 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 209 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 210 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 211 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 212 | C2×C22⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 213 | C22×Dic5 | — | 2 | 2 | no | — |
| 214 | C22×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | #709 | — | 2 | 2 | no | — |
| 216 | #709 | — | 2 | 2 | no | — |
| 217 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C2×D20 | C2×D4 | 1 | 4 | yes | — |
| 219 | C2×C4×D5 | — | 2 | 2 | no | — |
| 220 | C2×C4×D5 | — | 2 | 2 | no | — |
| 221 | C2×C4×D5 | — | 2 | 4 | no | — |
| 222 | C2×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 223 | C2×C4×D5 | C24 | 1 | 2 | yes | — |
| 224 | C2×C4×D5 | C24 | 1 | 2 | yes | — |
| 225 | C2×Dic10 | — | 2 | 4 | no | — |
| 226 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C5×Q16 | — | 2 | 2 | no | — |
| 228 | C5×SD16 | — | 2 | 4 | no | — |
| 229 | C5×D8 | — | 2 | 2 | no | — |
| 230 | C5×M16 | — | 2 | 2 | no | — |
| 231 | C2×C5×C8 | #41 | 1 | 4 | yes | — |
| 232 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 233 | C2×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 234 | C2×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 235 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 236 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 237 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 238 | C5×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 239 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 240 | C5×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 241 | C42×C5 | — | 2 | 4 | no | — |
| 242 | C42×C5 | C24 | 1 | 2 | yes | — |
| 243 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 244 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 245 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 246 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 247 | #685 | — | 2 | 4 | no | — |
| 248 | #685 | — | 2 | 2 | no | — |
| 249 | #685 | — | 2 | 4 | no | — |
| 250 | #685 | — | 2 | 4 | no | — |
| 251 | #685 | — | 2 | 2 | no | — |
| 252 | #685 | — | 2 | 4 | no | — |
| 253 | #685 | C2×D4 | 1 | 4 | yes | — |
| 254 | #685 | C2×D4 | 1 | 4 | yes | — |
| 255 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 256 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 257 | C4⋊Dic5 | C2×D4 | 1 | 4 | yes | — |
| 258 | C4⋊Dic5 | C24 | 1 | 2 | yes | — |
| 259 | C4⋊Dic5 | C24 | 1 | 4 | yes | — |
| 260 | C4⋊Dic5 | C24 | 1 | 2 | yes | — |
| 261 | #683 | — | 2 | 4 | no | — |
| 262 | #683 | — | 2 | 4 | no | — |
| 263 | #683 | — | 2 | 2 | no | — |
| 264 | #683 | — | 2 | 4 | no | — |
| 265 | #683 | — | 2 | 2 | no | — |
| 266 | #683 | — | 2 | 4 | no | — |
| 267 | C4×Dic5 | — | 2 | 2 | no | — |
| 268 | C4×Dic5 | — | 2 | 4 | no | — |
| 269 | C4×Dic5 | — | 2 | 4 | no | — |
| 270 | C4×Dic5 | — | 2 | 4 | no | — |
| 271 | #681 | — | 2 | 2 | no | — |
| 272 | C2×#168 | — | 2 | 2 | no | — |
| 273 | C2×#168 | C24 | 1 | 2 | yes | — |
| 274 | C2×#168 | C24 | 1 | 2 | yes | — |
| 275 | #676 | — | 2 | 4 | no | — |
| 276 | C8×D5 | — | 2 | 4 | no | — |
| 277 | C8×D5 | — | 2 | 4 | no | — |
| 278 | C8×D5 | — | 2 | 4 | no | — |
| 279 | C2×#135 | C2×D5 | 1 | 1 | yes | characteristic |
| 280 | C2×#131 | — | 5 | 1 | no | — |
| 281 | C23×C8 | — | 5 | 1 | no | — |
| 282 | #556 | — | 5 | 4 | no | — |
| 283 | #556 | — | 10 | 2 | no | — |
| 284 | #555 | — | 5 | 4 | no | — |
| 285 | #555 | — | 10 | 2 | no | — |
| 286 | #553 | — | 5 | 4 | no | — |
| 287 | #553 | — | 10 | 2 | no | — |
| 288 | #552 | — | 5 | 4 | no | — |
| 289 | #552 | — | 10 | 2 | no | — |
| 290 | #544 | — | 5 | 2 | no | — |
| 291 | #538 | — | 10 | 4 | no | — |
| 292 | #537 | — | 5 | 2 | no | — |
| 293 | #529 | — | 10 | 4 | no | — |
| 294 | #525 | — | 5 | 2 | no | — |
| 295 | #525 | — | 5 | 1 | no | — |
| 296 | #520 | — | 5 | 2 | no | — |
| 297 | #520 | C2×D5 | 1 | 2 | yes | — |
| 298 | C2×#117 | — | 5 | 2 | no | — |
| 299 | #501 | — | 5 | 4 | no | — |
| 300 | #499 | — | 5 | 2 | no | — |
| 301 | #498 | — | 5 | 2 | no | — |
| 302 | #485 | — | 5 | 4 | no | — |
| 303 | #485 | — | 5 | 4 | no | — |
| 304 | #485 | — | 5 | 4 | no | — |
| 305 | #484 | — | 5 | 4 | no | — |
| 306 | #482 | — | 5 | 4 | no | — |
| 307 | #482 | — | 5 | 4 | no | — |
| 308 | #482 | — | 5 | 4 | no | — |
| 309 | #480 | — | 5 | 4 | no | — |
| 310 | #479 | — | 5 | 4 | no | — |
| 311 | #478 | — | 5 | 4 | no | — |
| 312 | #477 | — | 5 | 4 | no | — |
| 313 | #474 | — | 5 | 4 | no | — |
| 314 | #470 | — | 5 | 2 | no | — |
| 315 | #469 | — | 5 | 2 | no | — |
| 316 | #467 | — | 5 | 2 | no | — |
| 317 | #466 | — | 5 | 2 | no | — |
| 318 | #465 | — | 5 | 2 | no | — |
| 319 | #465 | — | 5 | 4 | no | — |
| 320 | #465 | — | 5 | 2 | no | — |
| 321 | #442 | C2×D5 | 1 | 2 | yes | complemented |
| 322 | #441 | C2×D5 | 1 | 2 | yes | complemented |
| 323 | C4×SD16 | C2×D5 | 1 | 4 | yes | complemented |
| 324 | #435 | — | 5 | 4 | no | — |
| 325 | C8×D4 | — | 5 | 4 | no | — |
| 326 | #428 | — | 5 | 2 | no | — |
| 327 | #428 | — | 5 | 2 | no | — |
| 328 | #428 | — | 5 | 4 | no | — |
| 329 | #427 | — | 5 | 1 | no | — |
| 330 | #427 | — | 5 | 4 | no | — |
| 331 | #427 | — | 5 | 2 | no | — |
| 332 | #427 | — | 5 | 4 | no | — |
| 333 | C2×#107 | — | 5 | 2 | no | — |
| 334 | C2×#106 | — | 5 | 1 | no | — |
| 335 | C2×#106 | — | 5 | 2 | no | — |
| 336 | C2×#106 | C2×D5 | 1 | 1 | yes | characteristic |
| 337 | #424 | — | 5 | 1 | no | — |
| 338 | #417 | — | 5 | 2 | no | — |
| 339 | #417 | C2×D5 | 1 | 2 | yes | — |
| 340 | #416 | — | 5 | 2 | no | — |
| 341 | #408 | — | 5 | 1 | no | — |
| 342 | #407 | — | 5 | 1 | no | — |
| 343 | #405 | C2×D5 | 1 | 1 | yes | characteristic |
| 344 | C23×C5 | — | 2 | 2 | no | — |
| 345 | C23×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 346 | C22×D5 | — | 2 | 2 | no | — |
| 347 | C22×D5 | — | 4 | 2 | no | — |
| 348 | C22×D5 | C22×D4 | 1 | 2 | yes | — |
| 349 | C22×D5 | C22×D4 | 1 | 2 | yes | — |
| 350 | C5×Q8 | — | 2 | 2 | no | — |
| 351 | C5×Q8 | — | 2 | 2 | no | — |
| 352 | C5×D4 | — | 2 | 2 | no | — |
| 353 | C5×D4 | — | 2 | 2 | no | — |
| 354 | C5×D4 | — | 4 | 4 | no | — |
| 355 | C2×C4×C5 | — | 2 | 4 | no | — |
| 356 | C2×C4×C5 | — | 2 | 2 | no | — |
| 357 | C2×C4×C5 | — | 4 | 4 | no | — |
| 358 | C2×C4×C5 | — | 8 | 4 | no | — |
| 359 | C2×C4×C5 | — | 8 | 2 | no | — |
| 360 | C2×C4×C5 | C22×D4 | 1 | 4 | yes | — |
| 361 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 362 | C2×C4×C5 | C2×#41 | 1 | 2 | yes | — |
| 363 | C2×C4×C5 | 2−1+4 | 1 | 2 | yes | — |
| 364 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 365 | C22⋊D5 | — | 2 | 4 | no | — |
| 366 | C22⋊D5 | — | 8 | 2 | no | — |
| 367 | C22⋊D5 | — | 8 | 4 | no | — |
| 368 | C22⋊D5 | — | 8 | 2 | no | — |
| 369 | C2×Dic5 | — | 2 | 2 | no | — |
| 370 | C2×Dic5 | — | 2 | 2 | no | — |
| 371 | C2×Dic5 | — | 2 | 4 | no | — |
| 372 | C2×Dic5 | — | 2 | 2 | no | — |
| 373 | C2×Dic5 | — | 8 | 2 | no | — |
| 374 | C2×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 375 | C2×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 376 | D20 | — | 2 | 2 | no | — |
| 377 | D20 | — | 4 | 4 | no | — |
| 378 | C4×D5 | — | 2 | 4 | no | — |
| 379 | C4×D5 | — | 2 | 2 | no | — |
| 380 | C4×D5 | — | 2 | 2 | no | — |
| 381 | C4×D5 | — | 2 | 2 | no | — |
| 382 | C4×D5 | — | 2 | 2 | no | — |
| 383 | C4×D5 | — | 8 | 4 | no | — |
| 384 | Dic10 | — | 2 | 2 | no | — |
| 385 | Dic10 | — | 8 | 4 | no | — |
| 386 | C5×C8 | — | 2 | 2 | no | — |
| 387 | C5×C8 | C2×#41 | 1 | 2 | yes | — |
| 388 | C5×C8 | C2×#41 | 1 | 2 | yes | — |
| 389 | #168 | — | 2 | 2 | no | — |
| 390 | #168 | — | 2 | 2 | no | — |
| 391 | C2×#41 | — | 5 | 1 | no | — |
| 392 | C2×#41 | C22×D5 | 1 | 2 | yes | — |
| 393 | C23×C4 | — | 5 | 1 | no | — |
| 394 | #135 | — | 2 | 4 | no | — |
| 395 | C2×Q16 | C22×D5 | 1 | 1 | yes | characteristic |
| 396 | C2×SD16 | C22×D5 | 1 | 2 | yes | — |
| 397 | C2×D8 | C22×D5 | 1 | 1 | yes | characteristic |
| 398 | #131 | — | 10 | 4 | no | — |
| 399 | C2×M16 | — | 5 | 1 | no | — |
| 400 | C2×M16 | — | 5 | 2 | no | — |
| 401 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 402 | C22×C8 | — | 5 | 1 | no | — |
| 403 | C22×C8 | — | 5 | 2 | no | — |
| 404 | C22×C8 | — | 5 | 2 | no | — |
| 405 | C22×C8 | — | 5 | 2 | no | — |
| 406 | C22×C8 | — | 10 | 4 | no | — |
| 407 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 408 | C4⋊Q8 | — | 5 | 4 | no | — |
| 409 | C4⋊Q8 | — | 10 | 2 | no | — |
| 410 | #126 | — | 10 | 4 | no | — |
| 411 | #126 | — | 10 | 4 | no | — |
| 412 | #126 | — | 10 | 4 | no | — |
| 413 | #126 | — | 10 | 4 | no | — |
| 414 | #125 | — | 5 | 4 | no | — |
| 415 | #125 | — | 10 | 4 | no | — |
| 416 | #125 | — | 10 | 2 | no | — |
| 417 | #124 | — | 10 | 4 | no | — |
| 418 | #124 | — | 10 | 4 | no | — |
| 419 | #124 | — | 10 | 4 | no | — |
| 420 | #123 | — | 5 | 2 | no | — |
| 421 | #123 | — | 10 | 4 | no | — |
| 422 | #123 | — | 10 | 4 | no | — |
| 423 | #123 | — | 10 | 2 | no | — |
| 424 | C22⋊Q8 | — | 5 | 2 | no | — |
| 425 | C22⋊Q8 | — | 5 | 2 | no | — |
| 426 | C22⋊Q8 | — | 5 | 2 | no | — |
| 427 | C22⋊Q8 | — | 5 | 4 | no | — |
| 428 | C22⋊Q8 | — | 10 | 2 | no | — |
| 429 | C22⋊Q8 | — | 10 | 4 | no | — |
| 430 | #121 | — | 5 | 2 | no | — |
| 431 | #121 | — | 5 | 2 | no | — |
| 432 | #121 | — | 5 | 2 | no | — |
| 433 | #121 | — | 5 | 4 | no | — |
| 434 | #121 | — | 10 | 4 | no | — |
| 435 | #121 | — | 10 | 2 | no | — |
| 436 | #121 | — | 10 | 4 | no | — |
| 437 | #121 | — | 10 | 4 | no | — |
| 438 | #120 | — | 5 | 2 | no | — |
| 439 | #120 | — | 10 | 2 | no | — |
| 440 | C4×Q8 | — | 10 | 4 | no | — |
| 441 | C4×Q8 | — | 10 | 2 | no | — |
| 442 | C4×Q8 | C22×D5 | 1 | 4 | yes | — |
| 443 | C4×D4 | — | 2 | 4 | no | — |
| 444 | C4×D4 | — | 5 | 4 | no | — |
| 445 | C4×D4 | — | 10 | 4 | no | — |
| 446 | C4×D4 | — | 10 | 2 | no | — |
| 447 | C4×D4 | — | 10 | 2 | no | — |
| 448 | C4×D4 | — | 10 | 2 | no | — |
| 449 | C4×D4 | — | 10 | 4 | no | — |
| 450 | C4×D4 | C22×D5 | 1 | 4 | yes | — |
| 451 | #117 | — | 2 | 2 | no | — |
| 452 | #117 | — | 5 | 2 | no | — |
| 453 | #117 | — | 5 | 4 | no | — |
| 454 | #117 | — | 5 | 4 | no | — |
| 455 | #117 | — | 5 | 4 | no | — |
| 456 | #117 | — | 10 | 4 | no | — |
| 457 | #117 | — | 10 | 2 | no | — |
| 458 | #117 | — | 10 | 2 | no | — |
| 459 | #117 | — | 10 | 4 | no | — |
| 460 | #117 | C22×D5 | 1 | 1 | yes | characteristic |
| 461 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 462 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 463 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 464 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 465 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 466 | C2×C42 | — | 10 | 2 | no | — |
| 467 | #107 | — | 5 | 2 | no | — |
| 468 | #107 | — | 5 | 4 | no | — |
| 469 | #107 | — | 5 | 4 | no | — |
| 470 | #107 | — | 5 | 4 | no | — |
| 471 | #107 | — | 5 | 4 | no | — |
| 472 | #106 | — | 5 | 1 | no | — |
| 473 | #106 | — | 5 | 2 | no | — |
| 474 | #106 | — | 5 | 2 | no | — |
| 475 | #106 | — | 5 | 1 | no | — |
| 476 | #106 | — | 5 | 4 | no | — |
| 477 | #106 | — | 5 | 4 | no | — |
| 478 | #106 | C22×D5 | 1 | 2 | yes | — |
| 479 | #106 | C22×D5 | 1 | 2 | yes | — |
| 480 | C4⋊C8 | — | 5 | 4 | no | — |
| 481 | #103 | — | 5 | 2 | no | — |
| 482 | #103 | — | 5 | 2 | no | — |
| 483 | #103 | — | 5 | 4 | no | — |
| 484 | #103 | C22×D5 | 1 | 4 | yes | — |
| 485 | #102 | — | 5 | 2 | no | — |
| 486 | #102 | — | 5 | 2 | no | — |
| 487 | #102 | — | 5 | 4 | no | — |
| 488 | #102 | C22×D5 | 1 | 4 | yes | — |
| 489 | C22⋊C8 | — | 5 | 4 | no | — |
| 490 | C22⋊C8 | — | 5 | 4 | no | — |
| 491 | #97 | C22×D5 | 1 | 2 | yes | — |
| 492 | C4×C8 | C22×D5 | 1 | 2 | yes | — |
| 493 | C22×C5 | — | 2 | 2 | no | — |
| 494 | C22×C5 | — | 4 | 2 | no | — |
| 495 | C22×C5 | — | 4 | 2 | no | — |
| 496 | C22×C5 | — | 4 | 2 | no | — |
| 497 | C22×C5 | #547 | 1 | 2 | yes | — |
| 498 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 499 | C2×D5 | — | 2 | 4 | no | — |
| 500 | C2×D5 | — | 2 | 2 | no | — |
| 501 | C2×D5 | — | 2 | 2 | no | — |
| 502 | C2×D5 | — | 2 | 2 | no | — |
| 503 | C2×D5 | — | 2 | 2 | no | — |
| 504 | C2×D5 | — | 4 | 4 | no | — |
| 505 | C4×C5 | — | 2 | 4 | no | — |
| 506 | C4×C5 | — | 4 | 4 | no | — |
| 507 | C4×C5 | — | 4 | 2 | no | — |
| 508 | C4×C5 | #547 | 1 | 2 | yes | — |
| 509 | C4×C5 | C22×#41 | 1 | 1 | yes | characteristic |
| 510 | C4×C5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 511 | Dic5 | — | 2 | 2 | no | — |
| 512 | Dic5 | — | 2 | 2 | no | — |
| 513 | Dic5 | — | 4 | 2 | no | — |
| 514 | Dic5 | — | 4 | 4 | no | — |
| 515 | Dic5 | — | 4 | 2 | no | — |
| 516 | C24 | — | 5 | 1 | no | — |
| 517 | #41 | — | 2 | 4 | no | — |
| 518 | #41 | — | 2 | 4 | no | — |
| 519 | #41 | — | 10 | 2 | no | — |
| 520 | #41 | — | 10 | 2 | no | — |
| 521 | C2×Q8 | — | 5 | 1 | no | — |
| 522 | C2×Q8 | — | 10 | 4 | no | — |
| 523 | C2×Q8 | C23×D5 | 1 | 2 | yes | — |
| 524 | C2×D4 | — | 2 | 2 | no | — |
| 525 | C2×D4 | — | 5 | 2 | no | — |
| 526 | C2×D4 | — | 5 | 1 | no | — |
| 527 | C2×D4 | — | 5 | 4 | no | — |
| 528 | C2×D4 | — | 10 | 2 | no | — |
| 529 | C2×D4 | — | 10 | 2 | no | — |
| 530 | C2×D4 | — | 10 | 4 | no | — |
| 531 | C2×D4 | C23×D5 | 1 | 2 | yes | — |
| 532 | C22×C4 | — | 2 | 2 | no | — |
| 533 | C22×C4 | — | 2 | 2 | no | — |
| 534 | C22×C4 | — | 2 | 4 | no | — |
| 535 | C22×C4 | — | 5 | 1 | no | — |
| 536 | C22×C4 | — | 5 | 2 | no | — |
| 537 | C22×C4 | — | 5 | 2 | no | — |
| 538 | C22×C4 | — | 5 | 2 | no | — |
| 539 | C22×C4 | — | 10 | 4 | no | — |
| 540 | C22×C4 | — | 10 | 2 | no | — |
| 541 | C22×C4 | — | 10 | 2 | no | — |
| 542 | C22×C4 | — | 10 | 2 | no | — |
| 543 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 544 | Q16 | — | 2 | 2 | no | — |
| 545 | SD16 | — | 2 | 4 | no | — |
| 546 | D8 | — | 2 | 2 | no | — |
| 547 | M16 | — | 2 | 2 | no | — |
| 548 | M16 | — | 10 | 2 | no | — |
| 549 | M16 | — | 10 | 4 | no | — |
| 550 | C2×C8 | — | 5 | 2 | no | — |
| 551 | C2×C8 | — | 5 | 2 | no | — |
| 552 | C2×C8 | — | 10 | 2 | no | — |
| 553 | C2×C8 | — | 10 | 4 | no | — |
| 554 | C2×C8 | — | 10 | 4 | no | — |
| 555 | C2×C8 | — | 10 | 4 | no | — |
| 556 | C2×C8 | #709 | 1 | 4 | yes | — |
| 557 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 558 | C2×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 559 | C2×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 560 | C4⋊C4 | — | 2 | 2 | no | — |
| 561 | C4⋊C4 | — | 2 | 4 | no | — |
| 562 | C4⋊C4 | — | 5 | 4 | no | — |
| 563 | C4⋊C4 | — | 5 | 2 | no | — |
| 564 | C4⋊C4 | — | 5 | 4 | no | — |
| 565 | C4⋊C4 | — | 5 | 2 | no | — |
| 566 | C4⋊C4 | — | 10 | 4 | no | — |
| 567 | C4⋊C4 | — | 10 | 2 | no | — |
| 568 | C4⋊C4 | — | 10 | 2 | no | — |
| 569 | C4⋊C4 | — | 10 | 4 | no | — |
| 570 | C4⋊C4 | — | 10 | 2 | no | — |
| 571 | C4⋊C4 | — | 10 | 4 | no | — |
| 572 | C4⋊C4 | — | 10 | 4 | no | — |
| 573 | C4⋊C4 | — | 10 | 4 | no | — |
| 574 | C4⋊C4 | D4×D5 | 1 | 2 | yes | — |
| 575 | C4⋊C4 | C23×D5 | 1 | 4 | yes | — |
| 576 | C22⋊C4 | — | 2 | 4 | no | — |
| 577 | C22⋊C4 | — | 5 | 4 | no | — |
| 578 | C22⋊C4 | — | 5 | 4 | no | — |
| 579 | C22⋊C4 | — | 10 | 4 | no | — |
| 580 | C22⋊C4 | — | 10 | 4 | no | — |
| 581 | C22⋊C4 | — | 10 | 4 | no | — |
| 582 | C22⋊C4 | — | 10 | 4 | no | — |
| 583 | C22⋊C4 | — | 10 | 2 | no | — |
| 584 | C22⋊C4 | — | 10 | 2 | no | — |
| 585 | C22⋊C4 | — | 10 | 2 | no | — |
| 586 | C22⋊C4 | — | 10 | 4 | no | — |
| 587 | C22⋊C4 | — | 10 | 2 | no | — |
| 588 | C22⋊C4 | — | 10 | 2 | no | — |
| 589 | C22⋊C4 | D4×D5 | 1 | 2 | yes | — |
| 590 | C42 | — | 2 | 4 | no | — |
| 591 | C42 | — | 10 | 4 | no | — |
| 592 | C42 | — | 10 | 4 | no | — |
| 593 | C42 | — | 10 | 4 | no | — |
| 594 | C42 | — | 10 | 2 | no | — |
| 595 | C42 | C23×D5 | 1 | 2 | yes | — |
| 596 | C2×C5 | — | 2 | 2 | no | — |
| 597 | C2×C5 | — | 8 | 2 | no | — |
| 598 | C2×C5 | C2×#547 | 1 | 1 | yes | characteristic |
| 599 | C2×C5 | #3584 | 1 | 2 | yes | — |
| 600 | D5 | — | 4 | 2 | no | — |
| 601 | D5 | — | 4 | 2 | no | — |
| 602 | C23 | — | 2 | 2 | no | — |
| 603 | C23 | — | 5 | 2 | no | — |
| 604 | C23 | — | 5 | 2 | no | — |
| 605 | C23 | — | 10 | 2 | no | — |
| 606 | C23 | — | 20 | 2 | no | — |
| 607 | C23 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 608 | Q8 | — | 2 | 2 | no | — |
| 609 | Q8 | — | 2 | 2 | no | — |
| 610 | Q8 | — | 10 | 2 | no | — |
| 611 | Q8 | — | 40 | 4 | no | — |
| 612 | D4 | — | 2 | 2 | no | — |
| 613 | D4 | — | 2 | 2 | no | — |
| 614 | D4 | — | 4 | 4 | no | — |
| 615 | D4 | — | 10 | 4 | no | — |
| 616 | D4 | — | 10 | 2 | no | — |
| 617 | D4 | — | 20 | 4 | no | — |
| 618 | D4 | — | 40 | 2 | no | — |
| 619 | D4 | — | 40 | 4 | no | — |
| 620 | D4 | — | 40 | 2 | no | — |
| 621 | C2×C4 | — | 2 | 2 | no | — |
| 622 | C2×C4 | — | 2 | 4 | no | — |
| 623 | C2×C4 | — | 4 | 4 | no | — |
| 624 | C2×C4 | — | 5 | 2 | no | — |
| 625 | C2×C4 | — | 5 | 2 | no | — |
| 626 | C2×C4 | — | 8 | 4 | no | — |
| 627 | C2×C4 | — | 8 | 2 | no | — |
| 628 | C2×C4 | — | 10 | 2 | no | — |
| 629 | C2×C4 | — | 10 | 4 | no | — |
| 630 | C2×C4 | — | 10 | 2 | no | — |
| 631 | C2×C4 | — | 10 | 2 | no | — |
| 632 | C2×C4 | — | 10 | 2 | no | — |
| 633 | C2×C4 | — | 10 | 2 | no | — |
| 634 | C2×C4 | — | 10 | 2 | no | — |
| 635 | C2×C4 | — | 10 | 4 | no | — |
| 636 | C2×C4 | — | 10 | 2 | no | — |
| 637 | C2×C4 | — | 40 | 4 | no | — |
| 638 | C2×C4 | — | 40 | 2 | no | — |
| 639 | C2×C4 | C2×#709 | 1 | 2 | yes | — |
| 640 | C2×C4 | C2×D4×D5 | 1 | 4 | yes | — |
| 641 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 642 | C2×C4 | #4150 | 1 | 2 | yes | — |
| 643 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 644 | C8 | — | 2 | 2 | no | — |
| 645 | C8 | — | 10 | 2 | no | — |
| 646 | C8 | — | 10 | 2 | no | — |
| 647 | C8 | C2×#709 | 1 | 2 | yes | — |
| 648 | C8 | C2×#709 | 1 | 2 | yes | — |
| 649 | C5 | #61260 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 650 | C22 | — | 2 | 2 | no | — |
| 651 | C22 | — | 4 | 2 | no | — |
| 652 | C22 | — | 4 | 2 | no | — |
| 653 | C22 | — | 4 | 2 | no | — |
| 654 | C22 | — | 10 | 2 | no | — |
| 655 | C22 | — | 10 | 2 | no | — |
| 656 | C22 | — | 10 | 4 | no | — |
| 657 | C22 | — | 10 | 2 | no | — |
| 658 | C22 | — | 10 | 2 | no | — |
| 659 | C22 | — | 20 | 4 | no | — |
| 660 | C22 | #65885 | 1 | 2 | yes | — |
| 661 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 662 | C4 | — | 2 | 4 | no | — |
| 663 | C4 | — | 4 | 2 | no | — |
| 664 | C4 | — | 4 | 4 | no | — |
| 665 | C4 | — | 10 | 2 | no | — |
| 666 | C4 | — | 10 | 2 | no | — |
| 667 | C4 | — | 20 | 2 | no | — |
| 668 | C4 | — | 20 | 4 | no | — |
| 669 | C4 | — | 20 | 2 | no | — |
| 670 | C4 | #65885 | 1 | 2 | yes | — |
| 671 | C4 | C22×#709 | 1 | 1 | yes | characteristic |
| 672 | C4 | C2×#4150 | 1 | 1 | yes | characteristic |
| 673 | C2 | — | 2 | 2 | no | — |
| 674 | C2 | — | 8 | 2 | no | — |
| 675 | C2 | — | 20 | 2 | no | — |
| 676 | C2 | — | 20 | 2 | no | — |
| 677 | C2 | C2×#65885 | 1 | 1 | yes | characteristic |
| 678 | C2 | #10619107 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10617789 | C2 | semidirect |
| 2. C5×#2952 | C2 | semidirect |
| 3. #10615647 | C2 | semidirect |
| 4. #10615645 | C2 | semidirect |
| 5. #10614290 | C2 | semidirect |
| 6. #10611616 | C2 | semidirect |
| 7. #10611577 | C2 | semidirect |
| 8. #10611421 | C2 | semidirect |
| 9. #10611420 | C2 | semidirect |
| 10. #10610847 | C2 | semidirect |
| 11. C2×#65149 | C2 | semidirect |
| 12. #10610624 | C2 | semidirect |
| 13. #10610605 | C2 | semidirect |
| 14. #10610284 | C2 | semidirect |
| 15. #10610276 | C2 | semidirect |
| 36. C5×#442 | C22 | semidirect |
| 37. C5×#441 | C22 | semidirect |
| 38. C4×C5×SD16 | C22 | semidirect |
| 44. #65478 | C22 | semidirect |
| 48. #65460 | C22 | semidirect |
| 49. #65448 | C22 | semidirect |
| 56. #65311 | C22 | semidirect |
| 57. #65310 | C22 | semidirect |
| 58. #65298 | C22 | semidirect |
| 59. #65296 | C22 | semidirect |
| 63. #65150 | C22 | semidirect |
| 66. #65149 | C22 | semidirect |
| 67. D5×#106 | C22 | semidirect |
| 69. #65104 | C22 | semidirect |
| 71. #65098 | C22 | semidirect |
| 74. #65068 | C22 | semidirect |
| 75. #65063 | C22 | semidirect |
| 77. #64991 | C22 | semidirect |
| 79. #64972 | C22 | semidirect |
| 80. #64969 | C22 | semidirect |
| 195. #2952 | D5 | semidirect |
| 321. #442 | C2×D5 | semidirect |
| 322. #441 | C2×D5 | semidirect |
| 323. C4×SD16 | C2×D5 | semidirect |
| 649. C5 | #61260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617789 | 2 |
| C5×#2952 | 2 |
| #10615647 | 2 |
| #10615645 | 2 |
| #10614290 | 2 |
| #10611616 | 2 |
| #10611577 | 2 |
| #10611421 | 2 |
| #10611420 | 2 |
| #10610847 | 2 |
| C2×#65149 | 2 |
| #10610624 | 2 |
| #10610605 | 2 |
| #10610284 | 2 |
| #10610276 | 2 |
| #61260 | 5 |