Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1312 conjugacy classes of subgroups.
The subgroup lattice has 542 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#66100 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10610837 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10610521 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×#65006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#1971 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10602862 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10601385 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10601079 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10600632 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10600486 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10600485 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#4147 | C22 | 1 | 2 | yes | — |
| 13 | C22×C5×Q16 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#4088 | C22 | 1 | 2 | yes | — |
| 15 | #66100 | — | 2 | 4 | no | — |
| 16 | #66100 | C4 | 1 | 8 | yes | complemented |
| 17 | C2×#4065 | — | 2 | 1 | no | — |
| 18 | C2×#4064 | — | 2 | 2 | no | — |
| 19 | C2×D5×Q16 | — | 2 | 1 | no | — |
| 20 | C2×#4050 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#4047 | C22 | 1 | 2 | yes | — |
| 22 | C2×#4047 | C22 | 1 | 1 | yes | characteristic |
| 23 | #65838 | C22 | 1 | 2 | yes | — |
| 24 | C2×C5×#106 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C5×#103 | C22 | 1 | 2 | yes | — |
| 26 | C2×C5×#97 | C22 | 1 | 1 | yes | characteristic |
| 27 | C5×#391 | C22 | 1 | 2 | yes | — |
| 28 | C2×#3968 | C22 | 1 | 2 | yes | — |
| 29 | #65514 | C22 | 1 | 2 | yes | — |
| 30 | #65402 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#3951 | C22 | 1 | 1 | yes | characteristic |
| 32 | #65390 | C22 | 1 | 1 | yes | characteristic |
| 33 | #65255 | C22 | 1 | 2 | yes | — |
| 34 | #65255 | C22 | 1 | 2 | yes | — |
| 35 | C2×#3937 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#3937 | C22 | 1 | 2 | yes | — |
| 37 | #65158 | — | 2 | 1 | no | — |
| 38 | #65142 | — | 2 | 1 | no | — |
| 39 | #65141 | — | 2 | 2 | no | — |
| 40 | #65093 | — | 2 | 2 | no | — |
| 41 | #65092 | — | 2 | 2 | no | — |
| 42 | #65091 | — | 2 | 2 | no | — |
| 43 | D5×#103 | — | 2 | 2 | no | — |
| 44 | #65006 | — | 2 | 4 | no | — |
| 45 | #64772 | C22 | 1 | 1 | yes | characteristic |
| 46 | #64750 | C22 | 1 | 2 | yes | — |
| 47 | #64743 | C22 | 1 | 1 | yes | characteristic |
| 48 | #22465 | — | 5 | 1 | no | maximal, Sylow |
| 49 | C22×C5×Q8 | C23 | 1 | 2 | yes | — |
| 50 | #4147 | — | 2 | 4 | no | — |
| 51 | #4147 | — | 2 | 4 | no | — |
| 52 | #4147 | — | 4 | 2 | no | — |
| 53 | #4147 | C2×C4 | 1 | 8 | yes | complemented |
| 54 | C2×#713 | — | 2 | 2 | no | — |
| 55 | C2×#713 | — | 2 | 2 | no | — |
| 56 | C2×Q8×D5 | — | 2 | 2 | no | — |
| 57 | C2×Q8×D5 | — | 2 | 2 | no | — |
| 58 | C2×#709 | — | 4 | 2 | no | — |
| 59 | C2×#709 | C23 | 1 | 2 | yes | — |
| 60 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C5×Q16 | — | 2 | 1 | no | — |
| 62 | C2×C5×Q16 | — | 2 | 1 | no | — |
| 63 | C2×C5×Q16 | — | 2 | 2 | no | — |
| 64 | C2×C5×Q16 | C2×C4 | 1 | 4 | yes | complemented |
| 65 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 66 | C22×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 68 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×#689 | — | 2 | 2 | no | — |
| 70 | #4088 | — | 2 | 4 | no | — |
| 71 | #4088 | C2×C4 | 1 | 8 | yes | complemented |
| 72 | C2×#688 | — | 2 | 2 | no | — |
| 73 | C4×C22⋊D5 | — | 4 | 2 | no | — |
| 74 | #4072 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×#681 | C23 | 1 | 2 | yes | — |
| 77 | C2×#681 | C23 | 1 | 1 | yes | characteristic |
| 78 | #4065 | — | 2 | 8 | no | — |
| 79 | #4064 | — | 2 | 16 | no | — |
| 80 | D5×Q16 | — | 2 | 8 | no | — |
| 81 | C2×Dic20 | D4 | 1 | 1 | yes | characteristic |
| 82 | #4050 | C2×C4 | 1 | 4 | yes | — |
| 83 | #4050 | D4 | 1 | 4 | yes | — |
| 84 | C2×D40 | D4 | 1 | 1 | yes | characteristic |
| 85 | C2×#677 | D4 | 1 | 2 | yes | — |
| 86 | #4047 | — | 2 | 2 | no | — |
| 87 | #4047 | — | 2 | 4 | no | — |
| 88 | #4047 | — | 4 | 2 | no | — |
| 89 | #4047 | C2×C4 | 1 | 4 | yes | complemented |
| 90 | C2×#676 | — | 2 | 1 | no | — |
| 91 | C2×#676 | — | 2 | 2 | no | — |
| 92 | C2×C8×D5 | — | 2 | 1 | no | — |
| 93 | C2×C8×D5 | — | 2 | 2 | no | — |
| 94 | #4039 | — | 2 | 2 | no | — |
| 95 | #4038 | — | 2 | 2 | no | — |
| 96 | D5×C4⋊C4 | — | 2 | 2 | no | — |
| 97 | #4033 | — | 2 | 2 | no | — |
| 98 | C5×#106 | — | 2 | 1 | no | — |
| 99 | C5×#106 | — | 2 | 1 | no | — |
| 100 | C5×#103 | — | 2 | 2 | no | — |
| 101 | C5×#103 | — | 2 | 2 | no | — |
| 102 | C5×#97 | — | 2 | 2 | no | — |
| 103 | C5×#95 | — | 4 | 2 | no | — |
| 104 | #3968 | — | 4 | 2 | no | — |
| 105 | #3967 | — | 2 | 2 | no | — |
| 106 | #3967 | — | 2 | 2 | no | — |
| 107 | #3953 | D4 | 1 | 2 | yes | — |
| 108 | #3951 | — | 2 | 2 | no | — |
| 109 | #3948 | D4 | 1 | 2 | yes | — |
| 110 | #3947 | — | 2 | 1 | no | — |
| 111 | C8×Dic5 | — | 2 | 1 | no | — |
| 112 | #3942 | — | 2 | 2 | no | — |
| 113 | #3942 | — | 2 | 2 | no | — |
| 114 | #3941 | — | 2 | 2 | no | — |
| 115 | #3941 | — | 2 | 2 | no | — |
| 116 | #3937 | — | 2 | 4 | no | — |
| 117 | #3937 | — | 2 | 2 | no | — |
| 118 | C2×#578 | — | 5 | 1 | no | — |
| 119 | C2×#444 | — | 5 | 1 | no | — |
| 120 | #2952 | — | 5 | 1 | no | — |
| 121 | #2898 | — | 5 | 2 | no | — |
| 122 | #1979 | — | 5 | 1 | no | — |
| 123 | #1971 | D5 | 1 | 1 | yes | characteristic, complemented |
| 124 | #1908 | — | 5 | 2 | no | — |
| 125 | #1882 | — | 5 | 2 | no | — |
| 126 | #1815 | — | 5 | 1 | no | — |
| 127 | #1793 | — | 5 | 2 | no | — |
| 128 | #1765 | — | 5 | 1 | no | — |
| 129 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 130 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 131 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 132 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 133 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 134 | C2×C5×Q8 | C22×C4 | 1 | 4 | yes | — |
| 135 | C22×C4×C5 | — | 2 | 2 | no | — |
| 136 | C22×C4×C5 | — | 2 | 1 | no | — |
| 137 | C22×C4×C5 | — | 2 | 2 | no | — |
| 138 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 139 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 140 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 141 | #713 | — | 2 | 8 | no | — |
| 142 | #713 | — | 2 | 8 | no | — |
| 143 | #713 | — | 4 | 4 | no | — |
| 144 | #713 | — | 4 | 4 | no | — |
| 145 | Q8×D5 | — | 2 | 8 | no | — |
| 146 | Q8×D5 | — | 2 | 8 | no | — |
| 147 | Q8×D5 | — | 4 | 4 | no | — |
| 148 | Q8×D5 | — | 4 | 4 | no | — |
| 149 | #709 | — | 2 | 1 | no | — |
| 150 | #709 | — | 2 | 2 | no | — |
| 151 | #709 | — | 2 | 1 | no | — |
| 152 | #709 | — | 2 | 2 | no | — |
| 153 | #709 | — | 4 | 8 | no | — |
| 154 | #709 | — | 4 | 8 | no | — |
| 155 | #709 | C22×C4 | 1 | 4 | yes | — |
| 156 | #709 | C22×C4 | 1 | 2 | yes | — |
| 157 | #709 | C2×D4 | 1 | 4 | yes | — |
| 158 | #709 | #41 | 1 | 2 | yes | — |
| 159 | C2×D20 | — | 4 | 2 | no | — |
| 160 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 161 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×D5 | — | 2 | 1 | no | — |
| 163 | C2×C4×D5 | — | 2 | 2 | no | — |
| 164 | C2×C4×D5 | — | 4 | 2 | no | — |
| 165 | C2×C4×D5 | — | 4 | 2 | no | — |
| 166 | C2×C4×D5 | — | 4 | 2 | no | — |
| 167 | C2×Dic10 | — | 4 | 2 | no | — |
| 168 | C2×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 169 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C5×Q16 | — | 2 | 4 | no | — |
| 171 | C5×Q16 | — | 2 | 4 | no | — |
| 172 | C2×C5×C8 | — | 2 | 1 | no | — |
| 173 | C2×C5×C8 | — | 2 | 1 | no | — |
| 174 | C2×C5×C8 | C22×C4 | 1 | 2 | yes | — |
| 175 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 176 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 179 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 180 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 181 | C42×C5 | — | 2 | 1 | no | — |
| 182 | C42×C5 | — | 2 | 1 | no | — |
| 183 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 184 | #689 | — | 2 | 8 | no | — |
| 185 | #688 | — | 2 | 8 | no | — |
| 186 | #685 | — | 4 | 2 | no | — |
| 187 | C4⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 188 | #683 | — | 4 | 2 | no | — |
| 189 | C4×Dic5 | — | 2 | 1 | no | — |
| 190 | C4×Dic5 | — | 4 | 2 | no | — |
| 191 | #681 | — | 2 | 1 | no | — |
| 192 | #681 | — | 2 | 2 | no | — |
| 193 | #681 | — | 2 | 1 | no | — |
| 194 | #681 | — | 2 | 1 | no | — |
| 195 | #681 | — | 2 | 2 | no | — |
| 196 | #681 | C22×C4 | 1 | 2 | yes | — |
| 197 | C2×#168 | — | 2 | 1 | no | — |
| 198 | C2×#168 | — | 2 | 1 | no | — |
| 199 | C2×#168 | — | 2 | 2 | no | — |
| 200 | Dic20 | C22⋊C4 | 1 | 4 | yes | — |
| 201 | D40 | C22⋊C4 | 1 | 4 | yes | — |
| 202 | #677 | C22⋊C4 | 1 | 8 | yes | — |
| 203 | #676 | — | 2 | 4 | no | — |
| 204 | #676 | — | 4 | 4 | no | — |
| 205 | C8×D5 | — | 2 | 4 | no | — |
| 206 | C8×D5 | — | 4 | 4 | no | — |
| 207 | C2×2−1+4 | — | 5 | 2 | no | — |
| 208 | #578 | — | 5 | 8 | no | — |
| 209 | #578 | — | 10 | 4 | no | — |
| 210 | C2×#137 | — | 5 | 2 | no | — |
| 211 | C2×#137 | — | 10 | 2 | no | — |
| 212 | C2×#135 | — | 5 | 1 | no | — |
| 213 | C2×#135 | — | 10 | 1 | no | — |
| 214 | C22×Q16 | — | 10 | 1 | no | — |
| 215 | C22×Q16 | C2×D5 | 1 | 1 | yes | characteristic |
| 216 | C2×#131 | — | 5 | 1 | no | — |
| 217 | C2×#131 | — | 5 | 2 | no | — |
| 218 | #520 | — | 5 | 2 | no | — |
| 219 | #444 | — | 10 | 4 | no | — |
| 220 | #442 | — | 10 | 1 | no | — |
| 221 | #441 | — | 10 | 1 | no | — |
| 222 | C4×SD16 | — | 10 | 2 | no | — |
| 223 | C2×#108 | — | 5 | 1 | no | — |
| 224 | C2×#106 | C2×D5 | 1 | 1 | yes | characteristic |
| 225 | C2×#104 | — | 5 | 1 | no | — |
| 226 | C2×#104 | — | 5 | 2 | no | — |
| 227 | #419 | — | 5 | 2 | no | — |
| 228 | #419 | — | 10 | 2 | no | — |
| 229 | #417 | — | 5 | 2 | no | — |
| 230 | #417 | — | 5 | 2 | no | — |
| 231 | #417 | — | 10 | 2 | no | — |
| 232 | #416 | — | 5 | 1 | no | — |
| 233 | #416 | — | 10 | 2 | no | — |
| 234 | C2×#103 | — | 10 | 2 | no | — |
| 235 | C2×#103 | C2×D5 | 1 | 2 | yes | — |
| 236 | C2×#101 | — | 5 | 2 | no | — |
| 237 | #405 | — | 5 | 1 | no | — |
| 238 | C2×#97 | C2×D5 | 1 | 1 | yes | characteristic |
| 239 | #391 | C2×D5 | 1 | 2 | yes | — |
| 240 | #343 | — | 5 | 2 | no | — |
| 241 | #341 | — | 5 | 1 | no | — |
| 242 | #339 | — | 5 | 1 | no | — |
| 243 | C23×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 244 | C22×D5 | — | 2 | 2 | no | — |
| 245 | C22×D5 | — | 2 | 1 | no | — |
| 246 | C5×Q8 | — | 2 | 4 | no | — |
| 247 | C5×Q8 | — | 2 | 4 | no | — |
| 248 | C5×Q8 | — | 4 | 2 | no | — |
| 249 | C5×Q8 | — | 4 | 2 | no | — |
| 250 | C2×C4×C5 | — | 2 | 4 | no | — |
| 251 | C2×C4×C5 | — | 4 | 2 | no | — |
| 252 | C2×C4×C5 | — | 4 | 2 | no | — |
| 253 | C2×C4×C5 | — | 4 | 2 | no | — |
| 254 | C2×C4×C5 | — | 4 | 2 | no | — |
| 255 | C2×C4×C5 | — | 4 | 1 | no | — |
| 256 | C2×C4×C5 | — | 8 | 2 | no | — |
| 257 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 262 | C2×C4×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 263 | C22⋊D5 | — | 2 | 2 | no | — |
| 264 | C22⋊D5 | — | 2 | 4 | no | — |
| 265 | C22⋊D5 | — | 2 | 2 | no | — |
| 266 | C22⋊D5 | — | 2 | 4 | no | — |
| 267 | C2×Dic5 | — | 2 | 2 | no | — |
| 268 | C2×Dic5 | — | 2 | 1 | no | — |
| 269 | C2×Dic5 | — | 2 | 2 | no | — |
| 270 | D20 | — | 2 | 1 | no | — |
| 271 | D20 | — | 2 | 2 | no | — |
| 272 | D20 | — | 4 | 8 | no | — |
| 273 | D20 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 274 | D20 | C4×D4 | 1 | 2 | yes | — |
| 275 | C4×D5 | — | 2 | 2 | no | — |
| 276 | C4×D5 | — | 2 | 4 | no | — |
| 277 | C4×D5 | — | 2 | 4 | no | — |
| 278 | C4×D5 | — | 2 | 2 | no | — |
| 279 | C4×D5 | — | 4 | 8 | no | — |
| 280 | C4×D5 | — | 4 | 8 | no | — |
| 281 | C4×D5 | — | 16 | 2 | no | — |
| 282 | Dic10 | — | 2 | 1 | no | — |
| 283 | Dic10 | — | 2 | 2 | no | — |
| 284 | Dic10 | — | 4 | 8 | no | — |
| 285 | Dic10 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 286 | Dic10 | C4×D4 | 1 | 2 | yes | — |
| 287 | C5×C8 | — | 2 | 2 | no | — |
| 288 | C5×C8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 289 | C5×C8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 290 | #168 | — | 2 | 2 | no | — |
| 291 | #168 | — | 4 | 2 | no | — |
| 292 | #168 | — | 4 | 1 | no | — |
| 293 | 2−1+4 | — | 5 | 8 | no | — |
| 294 | 2−1+4 | — | 10 | 4 | no | — |
| 295 | 2−1+4 | — | 10 | 4 | no | — |
| 296 | 2−1+4 | — | 20 | 2 | no | — |
| 297 | C2×#41 | — | 5 | 2 | no | — |
| 298 | C2×#41 | — | 5 | 1 | no | — |
| 299 | C2×#41 | — | 10 | 2 | no | — |
| 300 | C2×#41 | — | 10 | 2 | no | — |
| 301 | C2×#41 | — | 20 | 2 | no | — |
| 302 | C22×Q8 | — | 10 | 2 | no | — |
| 303 | C22×Q8 | — | 10 | 2 | no | — |
| 304 | C22×Q8 | C22×D5 | 1 | 2 | yes | — |
| 305 | #137 | — | 5 | 8 | no | — |
| 306 | #137 | — | 10 | 16 | no | — |
| 307 | #137 | — | 10 | 4 | no | — |
| 308 | #135 | — | 5 | 4 | no | — |
| 309 | #135 | — | 5 | 4 | no | — |
| 310 | #135 | — | 10 | 8 | no | — |
| 311 | C2×Q16 | — | 2 | 1 | no | — |
| 312 | C2×Q16 | — | 2 | 1 | no | — |
| 313 | C2×Q16 | — | 2 | 2 | no | — |
| 314 | C2×Q16 | — | 5 | 1 | no | — |
| 315 | C2×Q16 | — | 10 | 8 | no | — |
| 316 | C2×Q16 | — | 10 | 2 | no | — |
| 317 | C2×Q16 | C4×D5 | 1 | 4 | yes | complemented |
| 318 | C2×SD16 | — | 5 | 2 | no | — |
| 319 | C2×SD16 | — | 10 | 2 | no | — |
| 320 | C2×D8 | — | 5 | 1 | no | — |
| 321 | #131 | — | 5 | 4 | no | — |
| 322 | #131 | — | 10 | 4 | no | — |
| 323 | #131 | — | 10 | 2 | no | — |
| 324 | #131 | — | 20 | 2 | no | — |
| 325 | C2×M16 | — | 5 | 1 | no | — |
| 326 | C2×M16 | — | 5 | 2 | no | — |
| 327 | C2×M16 | — | 5 | 1 | no | — |
| 328 | C2×M16 | — | 10 | 1 | no | — |
| 329 | C2×M16 | — | 10 | 2 | no | — |
| 330 | C22×C8 | — | 10 | 1 | no | — |
| 331 | C22×C8 | — | 10 | 2 | no | — |
| 332 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 333 | C22×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 334 | C4×Q8 | — | 10 | 2 | no | — |
| 335 | C4×D4 | — | 10 | 2 | no | — |
| 336 | C4×D4 | — | 20 | 2 | no | — |
| 337 | #117 | — | 5 | 1 | no | — |
| 338 | #117 | — | 10 | 2 | no | — |
| 339 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 340 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 341 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 342 | #108 | — | 10 | 2 | no | — |
| 343 | #106 | — | 2 | 1 | no | — |
| 344 | #106 | — | 2 | 1 | no | — |
| 345 | #104 | — | 10 | 2 | no | — |
| 346 | #104 | — | 10 | 4 | no | — |
| 347 | #103 | — | 2 | 2 | no | — |
| 348 | #103 | — | 2 | 2 | no | — |
| 349 | #103 | — | 5 | 2 | no | — |
| 350 | #103 | — | 10 | 2 | no | — |
| 351 | #103 | — | 10 | 2 | no | — |
| 352 | #103 | — | 10 | 2 | no | — |
| 353 | #103 | — | 10 | 2 | no | — |
| 354 | #102 | — | 5 | 2 | no | — |
| 355 | #102 | — | 10 | 2 | no | — |
| 356 | #102 | — | 10 | 2 | no | — |
| 357 | #101 | — | 20 | 2 | no | — |
| 358 | #97 | — | 2 | 2 | no | — |
| 359 | #97 | — | 10 | 1 | no | — |
| 360 | C4×C8 | — | 10 | 1 | no | — |
| 361 | #95 | — | 4 | 2 | no | — |
| 362 | C22×C5 | — | 2 | 2 | no | — |
| 363 | C22×C5 | #518 | 1 | 1 | yes | characteristic |
| 364 | C22×C5 | D42 | 1 | 1 | yes | characteristic |
| 365 | C22×C5 | #546 | 1 | 1 | yes | characteristic |
| 366 | C2×D5 | — | 2 | 2 | no | — |
| 367 | C2×D5 | — | 2 | 4 | no | — |
| 368 | C2×D5 | — | 4 | 2 | no | — |
| 369 | C2×D5 | — | 4 | 2 | no | — |
| 370 | C2×D5 | — | 4 | 2 | no | — |
| 371 | C4×C5 | — | 4 | 4 | no | — |
| 372 | C4×C5 | — | 8 | 1 | no | — |
| 373 | C4×C5 | — | 8 | 2 | no | — |
| 374 | C4×C5 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 375 | C4×C5 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 376 | C4×C5 | D42 | 1 | 1 | yes | characteristic |
| 377 | C4×C5 | #546 | 1 | 1 | yes | characteristic |
| 378 | Dic5 | — | 2 | 2 | no | — |
| 379 | Dic5 | — | 2 | 4 | no | — |
| 380 | Dic5 | — | 4 | 2 | no | — |
| 381 | #41 | — | 5 | 2 | no | — |
| 382 | #41 | — | 5 | 4 | no | — |
| 383 | #41 | — | 5 | 4 | no | — |
| 384 | #41 | — | 5 | 2 | no | — |
| 385 | #41 | — | 10 | 1 | no | — |
| 386 | #41 | — | 10 | 2 | no | — |
| 387 | #41 | — | 10 | 2 | no | — |
| 388 | #41 | — | 10 | 1 | no | — |
| 389 | #41 | — | 10 | 8 | no | — |
| 390 | #41 | — | 10 | 8 | no | — |
| 391 | #41 | — | 20 | 8 | no | — |
| 392 | #41 | — | 20 | 8 | no | — |
| 393 | #41 | — | 20 | 4 | no | — |
| 394 | #41 | — | 20 | 4 | no | — |
| 395 | C2×Q8 | — | 2 | 2 | no | — |
| 396 | C2×Q8 | — | 2 | 2 | no | — |
| 397 | C2×Q8 | — | 2 | 2 | no | — |
| 398 | C2×Q8 | — | 2 | 2 | no | — |
| 399 | C2×Q8 | — | 2 | 2 | no | — |
| 400 | C2×Q8 | — | 5 | 1 | no | — |
| 401 | C2×Q8 | — | 5 | 2 | no | — |
| 402 | C2×Q8 | — | 10 | 8 | no | — |
| 403 | C2×Q8 | — | 10 | 8 | no | — |
| 404 | C2×Q8 | — | 20 | 2 | no | — |
| 405 | C2×Q8 | — | 20 | 4 | no | — |
| 406 | C2×Q8 | — | 20 | 4 | no | — |
| 407 | C2×Q8 | C2×C4×D5 | 1 | 4 | yes | — |
| 408 | C2×D4 | — | 5 | 1 | no | — |
| 409 | C2×D4 | — | 5 | 2 | no | — |
| 410 | C2×D4 | — | 10 | 2 | no | — |
| 411 | C2×D4 | — | 10 | 1 | no | — |
| 412 | C2×D4 | — | 20 | 2 | no | — |
| 413 | C22×C4 | — | 2 | 2 | no | — |
| 414 | C22×C4 | — | 2 | 1 | no | — |
| 415 | C22×C4 | — | 2 | 2 | no | — |
| 416 | C22×C4 | — | 10 | 2 | no | — |
| 417 | C22×C4 | — | 10 | 1 | no | — |
| 418 | C22×C4 | — | 20 | 2 | no | — |
| 419 | C22×C4 | — | 20 | 2 | no | — |
| 420 | C22×C4 | — | 20 | 2 | no | — |
| 421 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 422 | Q16 | — | 2 | 4 | no | — |
| 423 | Q16 | — | 2 | 4 | no | — |
| 424 | Q16 | — | 5 | 4 | no | — |
| 425 | Q16 | — | 10 | 8 | no | — |
| 426 | SD16 | — | 5 | 8 | no | — |
| 427 | SD16 | — | 10 | 8 | no | — |
| 428 | D8 | — | 5 | 4 | no | — |
| 429 | M16 | — | 5 | 2 | no | — |
| 430 | M16 | — | 10 | 1 | no | — |
| 431 | M16 | — | 10 | 4 | no | — |
| 432 | M16 | — | 10 | 2 | no | — |
| 433 | M16 | — | 10 | 1 | no | — |
| 434 | M16 | — | 10 | 1 | no | — |
| 435 | M16 | — | 10 | 2 | no | — |
| 436 | M16 | — | 20 | 4 | no | — |
| 437 | C2×C8 | — | 2 | 1 | no | — |
| 438 | C2×C8 | — | 2 | 1 | no | — |
| 439 | C2×C8 | — | 10 | 1 | no | — |
| 440 | C2×C8 | — | 10 | 4 | no | — |
| 441 | C2×C8 | — | 10 | 1 | no | — |
| 442 | C2×C8 | — | 10 | 2 | no | — |
| 443 | C2×C8 | — | 20 | 4 | no | — |
| 444 | C2×C8 | C2×C4×D5 | 1 | 2 | yes | — |
| 445 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 446 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 447 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 448 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 449 | C4⋊C4 | — | 2 | 2 | no | — |
| 450 | C4⋊C4 | — | 2 | 2 | no | — |
| 451 | C4⋊C4 | — | 5 | 2 | no | — |
| 452 | C4⋊C4 | — | 20 | 2 | no | — |
| 453 | C22⋊C4 | — | 10 | 1 | no | — |
| 454 | C22⋊C4 | — | 20 | 2 | no | — |
| 455 | C42 | — | 2 | 1 | no | — |
| 456 | C42 | — | 2 | 1 | no | — |
| 457 | C42 | — | 10 | 1 | no | — |
| 458 | C42 | — | 20 | 2 | no | — |
| 459 | C2×C5 | — | 2 | 1 | no | — |
| 460 | C2×C5 | — | 2 | 1 | no | — |
| 461 | C2×C5 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 462 | C2×C5 | #3289 | 1 | 2 | yes | — |
| 463 | D5 | — | 4 | 2 | no | — |
| 464 | D5 | — | 4 | 4 | no | — |
| 465 | C23 | — | 10 | 2 | no | — |
| 466 | C23 | — | 10 | 1 | no | — |
| 467 | C23 | #4144 | 1 | 1 | yes | characteristic |
| 468 | Q8 | — | 2 | 4 | no | — |
| 469 | Q8 | — | 2 | 4 | no | — |
| 470 | Q8 | — | 4 | 2 | no | — |
| 471 | Q8 | — | 4 | 2 | no | — |
| 472 | Q8 | — | 5 | 4 | no | — |
| 473 | Q8 | — | 5 | 2 | no | — |
| 474 | Q8 | — | 10 | 1 | no | — |
| 475 | Q8 | — | 10 | 2 | no | — |
| 476 | Q8 | — | 20 | 8 | no | — |
| 477 | D4 | — | 5 | 4 | no | — |
| 478 | D4 | — | 5 | 2 | no | — |
| 479 | D4 | — | 10 | 2 | no | — |
| 480 | D4 | — | 10 | 4 | no | — |
| 481 | D4 | — | 10 | 2 | no | — |
| 482 | D4 | — | 10 | 4 | no | — |
| 483 | D4 | — | 10 | 1 | no | — |
| 484 | D4 | — | 10 | 2 | no | — |
| 485 | D4 | — | 20 | 8 | no | — |
| 486 | C2×C4 | — | 2 | 4 | no | — |
| 487 | C2×C4 | — | 4 | 2 | no | — |
| 488 | C2×C4 | — | 4 | 2 | no | — |
| 489 | C2×C4 | — | 4 | 2 | no | — |
| 490 | C2×C4 | — | 4 | 2 | no | — |
| 491 | C2×C4 | — | 4 | 1 | no | — |
| 492 | C2×C4 | — | 8 | 2 | no | — |
| 493 | C2×C4 | — | 10 | 2 | no | — |
| 494 | C2×C4 | — | 10 | 1 | no | — |
| 495 | C2×C4 | — | 10 | 2 | no | — |
| 496 | C2×C4 | — | 10 | 4 | no | — |
| 497 | C2×C4 | — | 10 | 4 | no | — |
| 498 | C2×C4 | — | 10 | 2 | no | — |
| 499 | C2×C4 | — | 10 | 2 | no | — |
| 500 | C2×C4 | — | 20 | 8 | no | — |
| 501 | C2×C4 | — | 20 | 8 | no | — |
| 502 | C2×C4 | — | 80 | 2 | no | — |
| 503 | C2×C4 | C22×C4×D5 | 1 | 1 | yes | characteristic |
| 504 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 505 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 506 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 507 | C2×C4 | D5×#41 | 1 | 1 | yes | characteristic |
| 508 | C2×C4 | #4149 | 1 | 1 | yes | characteristic |
| 509 | C8 | — | 2 | 2 | no | — |
| 510 | C8 | — | 10 | 2 | no | — |
| 511 | C8 | — | 20 | 2 | no | — |
| 512 | C8 | — | 20 | 1 | no | — |
| 513 | C8 | D5×C22⋊C4 | 1 | 2 | yes | — |
| 514 | C8 | D5×C22⋊C4 | 1 | 2 | yes | — |
| 515 | C5 | #22465 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 516 | C22 | — | 2 | 2 | no | — |
| 517 | C22 | — | 10 | 2 | no | — |
| 518 | C22 | — | 10 | 4 | no | — |
| 519 | C22 | — | 20 | 2 | no | — |
| 520 | C22 | — | 20 | 2 | no | — |
| 521 | C22 | — | 20 | 2 | no | — |
| 522 | C22 | #65879 | 1 | 1 | yes | characteristic |
| 523 | C22 | #65946 | 1 | 1 | yes | characteristic |
| 524 | C22 | #66051 | 1 | 1 | yes | characteristic |
| 525 | C4 | — | 4 | 4 | no | — |
| 526 | C4 | — | 8 | 1 | no | — |
| 527 | C4 | — | 8 | 2 | no | — |
| 528 | C4 | — | 10 | 2 | no | — |
| 529 | C4 | — | 10 | 4 | no | — |
| 530 | C4 | — | 20 | 2 | no | — |
| 531 | C4 | C2×D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 532 | C4 | C4×D4×D5 | 1 | 1 | yes | characteristic |
| 533 | C4 | #65943 | 1 | 1 | yes | characteristic |
| 534 | C4 | #66010 | 1 | 1 | yes | characteristic |
| 535 | C2 | — | 2 | 1 | no | — |
| 536 | C2 | — | 2 | 1 | no | — |
| 537 | C2 | — | 20 | 2 | no | — |
| 538 | C2 | — | 20 | 4 | no | — |
| 539 | C2 | #10608162 | 1 | 1 | yes | characteristic |
| 540 | C2 | #10613616 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10610837 | C2 | semidirect |
| 3. #10610521 | C2 | semidirect |
| 4. C2×#65006 | C2 | semidirect |
| 5. C5×#1971 | C2 | semidirect |
| 6. #10602862 | C2 | semidirect |
| 7. #10601385 | C2 | semidirect |
| 8. #10601079 | C2 | semidirect |
| 9. #10600632 | C2 | semidirect |
| 10. #10600486 | C2 | semidirect |
| 11. #10600485 | C2 | semidirect |
| 16. #66100 | C4 | semidirect |
| 53. #4147 | C2×C4 | semidirect |
| 64. C2×C5×Q16 | C2×C4 | semidirect |
| 71. #4088 | C2×C4 | semidirect |
| 89. #4047 | C2×C4 | semidirect |
| 123. #1971 | D5 | semidirect |
| 317. C2×Q16 | C4×D5 | semidirect |
| 515. C5 | #22465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66100 | 2 |
| #10610837 | 2 |
| #10610521 | 2 |
| C2×#65006 | 2 |
| C5×#1971 | 2 |
| #10602862 | 2 |
| #10601385 | 2 |
| #10601079 | 2 |
| #10600632 | 2 |
| #10600486 | 2 |
| #10600485 | 2 |
| #22465 | 5 |