Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
908 conjugacy classes of subgroups.
The subgroup lattice has 756 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10618133 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10615022 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10611083 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10610793 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#1557 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10601593 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10601294 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10599254 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10599253 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10599250 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10599249 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10599200 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #10599199 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10599196 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #10599195 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C5×#532 | C22 | 1 | 1 | yes | characteristic |
| 17 | #66165 | — | 2 | 1 | no | — |
| 18 | #66158 | — | 2 | 1 | no | — |
| 19 | #66061 | C22 | 1 | 1 | yes | characteristic |
| 20 | #66055 | C22 | 1 | 1 | yes | characteristic |
| 21 | #66052 | C22 | 1 | 1 | yes | characteristic |
| 22 | #66047 | C22 | 1 | 1 | yes | characteristic |
| 23 | #66016 | — | 2 | 1 | no | — |
| 24 | #66009 | — | 2 | 1 | no | — |
| 25 | #65955 | — | 2 | 2 | no | — |
| 26 | #65953 | — | 2 | 1 | no | — |
| 27 | #65937 | — | 2 | 1 | no | — |
| 28 | #65898 | — | 2 | 2 | no | — |
| 29 | #65893 | — | 2 | 1 | no | — |
| 30 | #65873 | — | 2 | 1 | no | — |
| 31 | #65813 | C22 | 1 | 1 | yes | characteristic |
| 32 | #65811 | C22 | 1 | 1 | yes | characteristic |
| 33 | #65804 | C22 | 1 | 1 | yes | characteristic |
| 34 | C5×#432 | C22 | 1 | 1 | yes | characteristic |
| 35 | C5×#423 | C22 | 1 | 1 | yes | characteristic |
| 36 | #65424 | — | 2 | 1 | no | — |
| 37 | #65423 | — | 2 | 1 | no | — |
| 38 | #65377 | C22 | 1 | 1 | yes | characteristic |
| 39 | #65367 | C22 | 1 | 1 | yes | characteristic |
| 40 | #65362 | C22 | 1 | 1 | yes | characteristic |
| 41 | #65359 | C22 | 1 | 1 | yes | characteristic |
| 42 | #65327 | — | 2 | 2 | no | — |
| 43 | C4×#686 | — | 2 | 2 | no | — |
| 44 | C2×C4×#168 | C22 | 1 | 1 | yes | characteristic |
| 45 | #65140 | C22 | 1 | 1 | yes | characteristic |
| 46 | #65138 | C22 | 1 | 1 | yes | characteristic |
| 47 | #65138 | C22 | 1 | 1 | yes | characteristic |
| 48 | #65137 | C22 | 1 | 1 | yes | characteristic |
| 49 | #65137 | C22 | 1 | 1 | yes | characteristic |
| 50 | #65137 | C22 | 1 | 1 | yes | characteristic |
| 51 | #65136 | — | 2 | 1 | no | — |
| 52 | #65135 | C22 | 1 | 1 | yes | characteristic |
| 53 | #65133 | — | 2 | 1 | no | — |
| 54 | #65132 | C22 | 1 | 1 | yes | characteristic |
| 55 | #65022 | — | 2 | 1 | no | — |
| 56 | #65022 | — | 2 | 1 | no | — |
| 57 | #65004 | — | 2 | 1 | no | — |
| 58 | #65003 | — | 2 | 1 | no | — |
| 59 | C5×#332 | C22 | 1 | 1 | yes | characteristic |
| 60 | C5×#332 | C22 | 1 | 1 | yes | characteristic |
| 61 | C5×#331 | C22 | 1 | 1 | yes | characteristic |
| 62 | C5×#331 | C22 | 1 | 1 | yes | characteristic |
| 63 | #64704 | C22 | 1 | 1 | yes | characteristic |
| 64 | #64704 | C22 | 1 | 1 | yes | characteristic |
| 65 | #64704 | C22 | 1 | 1 | yes | characteristic |
| 66 | #64704 | C22 | 1 | 1 | yes | characteristic |
| 67 | #64704 | C22 | 1 | 1 | yes | characteristic |
| 68 | #64704 | C22 | 1 | 1 | yes | characteristic |
| 69 | #64703 | C22 | 1 | 1 | yes | characteristic |
| 70 | #64703 | C22 | 1 | 1 | yes | characteristic |
| 71 | #18708 | — | 5 | 1 | no | maximal, Sylow |
| 72 | C2×C5×#41 | — | 2 | 1 | no | — |
| 73 | C2×Q8×D5 | — | 2 | 1 | no | — |
| 74 | C2×#711 | — | 2 | 1 | no | — |
| 75 | C2×#709 | — | 2 | 1 | no | — |
| 76 | C2×C5×M16 | — | 2 | 1 | no | — |
| 77 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C5×#127 | C23 | 1 | 1 | yes | characteristic |
| 79 | C5×#124 | — | 2 | 1 | no | — |
| 80 | C5×#121 | — | 2 | 1 | no | — |
| 81 | C5×#121 | D4 | 1 | 2 | yes | — |
| 82 | C4×C5×D4 | — | 2 | 1 | no | — |
| 83 | C4×C5×D4 | D4 | 1 | 2 | yes | — |
| 84 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 85 | #4092 | — | 2 | 1 | no | — |
| 86 | Q8×Dic5 | — | 2 | 1 | no | — |
| 87 | #4090 | — | 2 | 1 | no | — |
| 88 | #4086 | — | 2 | 1 | no | — |
| 89 | #4085 | — | 2 | 2 | no | — |
| 90 | #4085 | — | 2 | 2 | no | — |
| 91 | #4084 | — | 2 | 2 | no | — |
| 92 | #4084 | — | 2 | 1 | no | — |
| 93 | #4082 | — | 2 | 2 | no | — |
| 94 | #4082 | — | 2 | 1 | no | — |
| 95 | #4082 | — | 2 | 1 | no | — |
| 96 | #4081 | — | 2 | 2 | no | — |
| 97 | #4081 | — | 2 | 2 | no | — |
| 98 | D4×Dic5 | — | 2 | 1 | no | — |
| 99 | D4×Dic5 | — | 2 | 1 | no | — |
| 100 | D4×Dic5 | — | 2 | 1 | no | — |
| 101 | C2×#686 | — | 2 | 2 | no | — |
| 102 | #4076 | — | 2 | 1 | no | — |
| 103 | #4076 | — | 2 | 1 | no | — |
| 104 | #4076 | D4 | 1 | 1 | yes | characteristic |
| 105 | #4075 | — | 2 | 2 | no | — |
| 106 | #4075 | — | 2 | 1 | no | — |
| 107 | C4×C22⋊D5 | — | 2 | 2 | no | — |
| 108 | C4×C22⋊D5 | — | 2 | 1 | no | — |
| 109 | #4072 | — | 2 | 1 | no | — |
| 110 | #4070 | — | 2 | 2 | no | — |
| 111 | #4070 | — | 2 | 1 | no | — |
| 112 | #4070 | D4 | 1 | 1 | yes | characteristic |
| 113 | #4070 | D4 | 1 | 1 | yes | characteristic |
| 114 | #4070 | D4 | 1 | 1 | yes | characteristic |
| 115 | C2×#683 | — | 2 | 2 | no | — |
| 116 | C22×#168 | — | 2 | 1 | no | — |
| 117 | C2×Dic20 | — | 2 | 1 | no | — |
| 118 | C2×Dic20 | — | 2 | 1 | no | — |
| 119 | C2×D40 | — | 2 | 1 | no | — |
| 120 | C2×#677 | — | 2 | 1 | no | — |
| 121 | C2×#677 | — | 2 | 1 | no | — |
| 122 | C2×#677 | — | 2 | 1 | no | — |
| 123 | #4042 | — | 2 | 2 | no | — |
| 124 | #4039 | — | 2 | 1 | no | — |
| 125 | #4036 | — | 2 | 1 | no | — |
| 126 | #4035 | — | 2 | 2 | no | — |
| 127 | #4034 | — | 2 | 1 | no | — |
| 128 | #4033 | — | 2 | 1 | no | — |
| 129 | #4032 | — | 2 | 2 | no | — |
| 130 | #4031 | — | 2 | 2 | no | — |
| 131 | #4029 | — | 2 | 2 | no | — |
| 132 | #4029 | — | 2 | 2 | no | — |
| 133 | #4025 | — | 2 | 2 | no | — |
| 134 | #4024 | — | 2 | 2 | no | — |
| 135 | #4024 | — | 2 | 2 | no | — |
| 136 | #4024 | — | 2 | 2 | no | — |
| 137 | #4022 | — | 2 | 1 | no | — |
| 138 | #4021 | — | 2 | 1 | no | — |
| 139 | #4021 | D4 | 1 | 1 | yes | characteristic |
| 140 | #4020 | C23 | 1 | 1 | yes | characteristic |
| 141 | C4×D20 | — | 2 | 1 | no | — |
| 142 | C4×D20 | — | 2 | 1 | no | — |
| 143 | C4×D20 | C23 | 1 | 1 | yes | characteristic |
| 144 | #4018 | — | 2 | 1 | no | — |
| 145 | #4016 | — | 2 | 1 | no | — |
| 146 | #4016 | D4 | 1 | 1 | yes | characteristic |
| 147 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 148 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 149 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 150 | C4×Dic10 | — | 2 | 1 | no | — |
| 151 | C4×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 152 | C4×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 153 | C4×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 154 | C5×C4⋊C8 | — | 2 | 1 | no | — |
| 155 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 156 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 157 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 158 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 159 | C5×C22⋊C8 | — | 2 | 1 | no | — |
| 160 | C5×#97 | — | 2 | 1 | no | — |
| 161 | #3964 | — | 2 | 2 | no | — |
| 162 | #3953 | — | 2 | 1 | no | — |
| 163 | #3953 | — | 2 | 1 | no | — |
| 164 | #3953 | — | 2 | 1 | no | — |
| 165 | #3953 | — | 2 | 1 | no | — |
| 166 | #3953 | — | 2 | 1 | no | — |
| 167 | #3950 | — | 2 | 1 | no | — |
| 168 | #3949 | — | 2 | 1 | no | — |
| 169 | #3948 | — | 2 | 1 | no | — |
| 170 | #3948 | — | 2 | 1 | no | — |
| 171 | #3948 | — | 2 | 1 | no | — |
| 172 | #3941 | — | 2 | 2 | no | — |
| 173 | #3939 | — | 2 | 2 | no | — |
| 174 | C4×#168 | — | 2 | 1 | no | — |
| 175 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 176 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 177 | #3554 | — | 5 | 1 | no | — |
| 178 | #3251 | — | 5 | 1 | no | — |
| 179 | #3216 | — | 5 | 1 | no | — |
| 180 | #3169 | — | 5 | 1 | no | — |
| 181 | #1649 | — | 5 | 1 | no | — |
| 182 | #1648 | — | 5 | 1 | no | — |
| 183 | #1641 | — | 5 | 1 | no | — |
| 184 | #1640 | — | 5 | 1 | no | — |
| 185 | #1627 | — | 5 | 1 | no | — |
| 186 | #1626 | — | 5 | 1 | no | — |
| 187 | #1621 | — | 5 | 1 | no | — |
| 188 | #1620 | — | 5 | 1 | no | — |
| 189 | #1557 | D5 | 1 | 1 | yes | characteristic, complemented |
| 190 | #1494 | — | 5 | 1 | no | — |
| 191 | #1493 | — | 5 | 1 | no | — |
| 192 | C5×#41 | — | 8 | 1 | no | — |
| 193 | C5×#41 | — | 8 | 1 | no | — |
| 194 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 195 | C2×C5×D4 | — | 2 | 2 | no | — |
| 196 | C2×C5×D4 | — | 2 | 1 | no | — |
| 197 | C2×C5×D4 | — | 2 | 1 | no | — |
| 198 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 199 | C22×C4×C5 | — | 2 | 2 | no | — |
| 200 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 204 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 205 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 206 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 207 | C22×Dic5 | — | 2 | 2 | no | — |
| 208 | C22×Dic5 | — | 2 | 2 | no | — |
| 209 | Q8×D5 | — | 8 | 1 | no | — |
| 210 | Q8×D5 | — | 8 | 1 | no | — |
| 211 | #711 | — | 8 | 1 | no | — |
| 212 | #711 | — | 8 | 1 | no | — |
| 213 | #709 | — | 8 | 1 | no | — |
| 214 | #709 | — | 8 | 1 | no | — |
| 215 | C2×D20 | — | 2 | 1 | no | — |
| 216 | C2×D20 | — | 2 | 1 | no | — |
| 217 | C2×D20 | — | 2 | 1 | no | — |
| 218 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×D5 | — | 2 | 1 | no | — |
| 220 | C2×C4×D5 | — | 2 | 2 | no | — |
| 221 | C2×C4×D5 | — | 4 | 1 | no | — |
| 222 | C2×Dic10 | — | 2 | 1 | no | — |
| 223 | C2×Dic10 | — | 2 | 2 | no | — |
| 224 | C2×Dic10 | — | 2 | 1 | no | — |
| 225 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C5×M16 | — | 8 | 1 | no | — |
| 229 | C2×C5×C8 | — | 2 | 1 | no | — |
| 230 | C2×C5×C8 | — | 2 | 1 | no | — |
| 231 | C2×C5×C8 | — | 2 | 1 | no | — |
| 232 | C2×C5×C8 | — | 2 | 1 | no | — |
| 233 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 234 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 235 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 236 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 237 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 241 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 242 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 243 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 244 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 245 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 246 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 247 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 248 | #686 | — | 4 | 4 | no | — |
| 249 | #685 | — | 2 | 2 | no | — |
| 250 | #685 | — | 2 | 1 | no | — |
| 251 | #685 | — | 2 | 1 | no | — |
| 252 | #685 | — | 2 | 1 | no | — |
| 253 | #685 | — | 2 | 1 | no | — |
| 254 | #685 | — | 4 | 1 | no | — |
| 255 | #685 | — | 4 | 1 | no | — |
| 256 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 257 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 258 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 259 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 260 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 261 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 262 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 264 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | #683 | — | 2 | 2 | no | — |
| 267 | #683 | — | 2 | 2 | no | — |
| 268 | #683 | — | 2 | 2 | no | — |
| 269 | #683 | — | 2 | 1 | no | — |
| 270 | #683 | — | 2 | 1 | no | — |
| 271 | #683 | — | 2 | 1 | no | — |
| 272 | #683 | — | 2 | 1 | no | — |
| 273 | #683 | — | 2 | 1 | no | — |
| 274 | #683 | — | 2 | 1 | no | — |
| 275 | #683 | — | 2 | 1 | no | — |
| 276 | #683 | — | 2 | 1 | no | — |
| 277 | C4×Dic5 | — | 2 | 2 | no | — |
| 278 | C4×Dic5 | — | 2 | 1 | no | — |
| 279 | C4×Dic5 | — | 2 | 1 | no | — |
| 280 | C4×Dic5 | — | 2 | 1 | no | — |
| 281 | C2×#168 | — | 2 | 1 | no | — |
| 282 | C2×#168 | — | 2 | 1 | no | — |
| 283 | C2×#168 | — | 4 | 2 | no | — |
| 284 | Dic20 | — | 8 | 1 | no | — |
| 285 | Dic20 | — | 8 | 1 | no | — |
| 286 | D40 | — | 8 | 1 | no | — |
| 287 | #677 | — | 8 | 1 | no | — |
| 288 | #677 | — | 8 | 1 | no | — |
| 289 | #677 | — | 8 | 1 | no | — |
| 290 | #562 | — | 10 | 2 | no | — |
| 291 | #559 | — | 5 | 1 | no | — |
| 292 | #559 | — | 10 | 1 | no | — |
| 293 | #557 | — | 5 | 1 | no | — |
| 294 | #554 | — | 10 | 1 | no | — |
| 295 | #550 | — | 5 | 1 | no | — |
| 296 | D4×Q8 | — | 5 | 1 | no | — |
| 297 | #548 | — | 10 | 1 | no | — |
| 298 | #547 | — | 10 | 1 | no | — |
| 299 | #542 | — | 10 | 1 | no | — |
| 300 | #542 | — | 10 | 1 | no | — |
| 301 | #540 | — | 10 | 1 | no | — |
| 302 | #539 | — | 10 | 2 | no | — |
| 303 | #536 | — | 10 | 1 | no | — |
| 304 | #533 | — | 5 | 1 | no | — |
| 305 | #532 | — | 5 | 1 | no | — |
| 306 | #532 | C2×D5 | 1 | 1 | yes | characteristic |
| 307 | #529 | — | 5 | 1 | no | — |
| 308 | #500 | — | 5 | 1 | no | — |
| 309 | #497 | — | 10 | 1 | no | — |
| 310 | #493 | — | 5 | 1 | no | — |
| 311 | #489 | — | 10 | 1 | no | — |
| 312 | #486 | — | 5 | 1 | no | — |
| 313 | #486 | — | 5 | 1 | no | — |
| 314 | #478 | — | 10 | 1 | no | — |
| 315 | #475 | — | 5 | 1 | no | — |
| 316 | #474 | — | 5 | 1 | no | — |
| 317 | #469 | — | 10 | 1 | no | — |
| 318 | #468 | — | 10 | 1 | no | — |
| 319 | #466 | — | 10 | 2 | no | — |
| 320 | #463 | — | 10 | 1 | no | — |
| 321 | #462 | — | 5 | 1 | no | — |
| 322 | #462 | — | 5 | 1 | no | — |
| 323 | #460 | — | 5 | 1 | no | — |
| 324 | #460 | — | 5 | 1 | no | — |
| 325 | #460 | — | 5 | 1 | no | — |
| 326 | #459 | — | 5 | 1 | no | — |
| 327 | #452 | — | 10 | 1 | no | — |
| 328 | #452 | — | 10 | 1 | no | — |
| 329 | C4×D8 | — | 10 | 2 | no | — |
| 330 | #432 | C2×D5 | 1 | 1 | yes | characteristic |
| 331 | #423 | C2×D5 | 1 | 1 | yes | characteristic |
| 332 | C2×C4×C8 | — | 5 | 1 | no | — |
| 333 | #332 | C2×D5 | 1 | 1 | yes | characteristic |
| 334 | #332 | C2×D5 | 1 | 1 | yes | characteristic |
| 335 | #331 | C2×D5 | 1 | 1 | yes | characteristic |
| 336 | #331 | C2×D5 | 1 | 1 | yes | characteristic |
| 337 | Q8⋊C8 | — | 5 | 1 | no | — |
| 338 | Q8⋊C8 | — | 5 | 1 | no | — |
| 339 | Q8⋊C8 | — | 5 | 1 | no | — |
| 340 | Q8⋊C8 | — | 5 | 1 | no | — |
| 341 | Q8⋊C8 | — | 5 | 1 | no | — |
| 342 | Q8⋊C8 | — | 5 | 1 | no | — |
| 343 | D4⋊C8 | — | 5 | 1 | no | — |
| 344 | D4⋊C8 | — | 5 | 1 | no | — |
| 345 | C23×C5 | — | 2 | 2 | no | — |
| 346 | C23×C5 | #120 | 1 | 1 | yes | characteristic |
| 347 | C22×D5 | — | 2 | 1 | no | — |
| 348 | C22×D5 | — | 4 | 1 | no | — |
| 349 | C5×Q8 | — | 4 | 1 | no | — |
| 350 | C5×Q8 | — | 4 | 1 | no | — |
| 351 | C5×D4 | — | 4 | 2 | no | — |
| 352 | C5×D4 | — | 4 | 1 | no | — |
| 353 | C5×D4 | — | 4 | 1 | no | — |
| 354 | C5×D4 | — | 4 | 1 | no | — |
| 355 | C5×D4 | — | 4 | 1 | no | — |
| 356 | C5×D4 | — | 8 | 2 | no | — |
| 357 | C2×C4×C5 | — | 2 | 1 | no | — |
| 358 | C2×C4×C5 | — | 2 | 1 | no | — |
| 359 | C2×C4×C5 | — | 2 | 1 | no | — |
| 360 | C2×C4×C5 | — | 2 | 1 | no | — |
| 361 | C2×C4×C5 | — | 2 | 2 | no | — |
| 362 | C2×C4×C5 | — | 4 | 1 | no | — |
| 363 | C2×C4×C5 | — | 8 | 2 | no | — |
| 364 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 365 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 366 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 367 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 368 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 369 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 370 | C22⋊D5 | — | 8 | 1 | no | — |
| 371 | C22⋊D5 | — | 8 | 2 | no | — |
| 372 | C22⋊D5 | — | 8 | 2 | no | — |
| 373 | C22⋊D5 | — | 8 | 2 | no | — |
| 374 | C2×Dic5 | — | 2 | 1 | no | — |
| 375 | C2×Dic5 | — | 2 | 1 | no | — |
| 376 | C2×Dic5 | — | 2 | 1 | no | — |
| 377 | C2×Dic5 | — | 2 | 1 | no | — |
| 378 | C2×Dic5 | — | 2 | 1 | no | — |
| 379 | C2×Dic5 | — | 2 | 1 | no | — |
| 380 | C2×Dic5 | — | 2 | 1 | no | — |
| 381 | C2×Dic5 | — | 4 | 1 | no | — |
| 382 | C2×Dic5 | — | 8 | 2 | no | — |
| 383 | C2×Dic5 | — | 8 | 2 | no | — |
| 384 | D20 | — | 2 | 1 | no | — |
| 385 | D20 | — | 2 | 1 | no | — |
| 386 | D20 | — | 4 | 2 | no | — |
| 387 | D20 | — | 4 | 1 | no | — |
| 388 | D20 | — | 4 | 1 | no | — |
| 389 | D20 | — | 4 | 1 | no | — |
| 390 | D20 | — | 4 | 1 | no | — |
| 391 | C4×D5 | — | 4 | 1 | no | — |
| 392 | C4×D5 | — | 4 | 1 | no | — |
| 393 | C4×D5 | — | 8 | 2 | no | — |
| 394 | C4×D5 | — | 8 | 2 | no | — |
| 395 | Dic10 | — | 2 | 1 | no | — |
| 396 | Dic10 | — | 2 | 1 | no | — |
| 397 | Dic10 | — | 2 | 1 | no | — |
| 398 | Dic10 | — | 2 | 1 | no | — |
| 399 | Dic10 | — | 2 | 1 | no | — |
| 400 | Dic10 | — | 2 | 1 | no | — |
| 401 | Dic10 | — | 4 | 1 | no | — |
| 402 | Dic10 | — | 4 | 1 | no | — |
| 403 | Dic10 | — | 8 | 1 | no | — |
| 404 | Dic10 | — | 8 | 2 | no | — |
| 405 | C5×C8 | — | 4 | 1 | no | — |
| 406 | C5×C8 | — | 4 | 1 | no | — |
| 407 | C5×C8 | — | 4 | 1 | no | — |
| 408 | C5×C8 | — | 4 | 1 | no | — |
| 409 | #168 | — | 2 | 2 | no | — |
| 410 | #168 | — | 4 | 1 | no | — |
| 411 | C2×#41 | — | 2 | 1 | no | — |
| 412 | C2×#41 | — | 10 | 1 | no | — |
| 413 | C2×#41 | — | 10 | 1 | no | — |
| 414 | C22×Q8 | — | 10 | 1 | no | — |
| 415 | C2×Q16 | — | 10 | 1 | no | — |
| 416 | C2×Q16 | — | 10 | 1 | no | — |
| 417 | C2×SD16 | — | 10 | 1 | no | — |
| 418 | C2×SD16 | — | 10 | 1 | no | — |
| 419 | C2×SD16 | — | 10 | 1 | no | — |
| 420 | C2×D8 | — | 10 | 1 | no | — |
| 421 | C2×D8 | — | 10 | 2 | no | — |
| 422 | C2×M16 | — | 2 | 1 | no | — |
| 423 | C22×C8 | — | 10 | 1 | no | — |
| 424 | C4⋊Q8 | — | 5 | 1 | no | — |
| 425 | C4⋊Q8 | — | 5 | 1 | no | — |
| 426 | C4⋊Q8 | — | 5 | 1 | no | — |
| 427 | C4⋊Q8 | — | 10 | 1 | no | — |
| 428 | C4⋊Q8 | — | 10 | 1 | no | — |
| 429 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 430 | #127 | — | 5 | 1 | no | — |
| 431 | #127 | — | 10 | 1 | no | — |
| 432 | #127 | C22×D5 | 1 | 1 | yes | characteristic |
| 433 | #126 | — | 10 | 2 | no | — |
| 434 | #126 | — | 10 | 1 | no | — |
| 435 | #125 | — | 5 | 1 | no | — |
| 436 | #125 | — | 10 | 1 | no | — |
| 437 | #125 | — | 10 | 2 | no | — |
| 438 | #125 | — | 10 | 1 | no | — |
| 439 | #124 | — | 2 | 1 | no | — |
| 440 | #124 | — | 5 | 1 | no | — |
| 441 | #124 | — | 10 | 2 | no | — |
| 442 | #124 | — | 10 | 1 | no | — |
| 443 | #124 | — | 10 | 1 | no | — |
| 444 | #124 | — | 10 | 2 | no | — |
| 445 | #124 | — | 10 | 1 | no | — |
| 446 | #123 | — | 10 | 2 | no | — |
| 447 | #123 | — | 10 | 2 | no | — |
| 448 | #123 | — | 10 | 2 | no | — |
| 449 | #123 | — | 10 | 2 | no | — |
| 450 | #123 | — | 10 | 2 | no | — |
| 451 | #123 | — | 10 | 2 | no | — |
| 452 | #123 | — | 10 | 1 | no | — |
| 453 | C22⋊Q8 | — | 5 | 1 | no | — |
| 454 | C22⋊Q8 | — | 5 | 1 | no | — |
| 455 | C22⋊Q8 | — | 5 | 1 | no | — |
| 456 | C22⋊Q8 | — | 10 | 2 | no | — |
| 457 | C22⋊Q8 | — | 10 | 2 | no | — |
| 458 | C22⋊Q8 | — | 10 | 2 | no | — |
| 459 | C22⋊Q8 | — | 10 | 1 | no | — |
| 460 | C22⋊Q8 | — | 10 | 2 | no | — |
| 461 | C22⋊Q8 | — | 10 | 1 | no | — |
| 462 | C22⋊Q8 | — | 10 | 2 | no | — |
| 463 | #121 | — | 2 | 1 | no | — |
| 464 | #121 | — | 5 | 1 | no | — |
| 465 | #121 | — | 10 | 1 | no | — |
| 466 | #121 | — | 10 | 2 | no | — |
| 467 | #121 | — | 10 | 2 | no | — |
| 468 | #121 | — | 10 | 2 | no | — |
| 469 | #121 | — | 10 | 1 | no | — |
| 470 | #121 | — | 10 | 1 | no | — |
| 471 | #121 | D20 | 1 | 2 | yes | — |
| 472 | C4×Q8 | — | 5 | 1 | no | — |
| 473 | C4×Q8 | — | 5 | 1 | no | — |
| 474 | C4×Q8 | — | 5 | 1 | no | — |
| 475 | C4×Q8 | — | 10 | 1 | no | — |
| 476 | C4×Q8 | — | 10 | 1 | no | — |
| 477 | C4×Q8 | — | 10 | 1 | no | — |
| 478 | C4×D4 | — | 2 | 1 | no | — |
| 479 | C4×D4 | — | 5 | 1 | no | — |
| 480 | C4×D4 | — | 10 | 1 | no | — |
| 481 | C4×D4 | — | 10 | 1 | no | — |
| 482 | C4×D4 | — | 10 | 1 | no | — |
| 483 | C4×D4 | — | 10 | 1 | no | — |
| 484 | C4×D4 | — | 10 | 2 | no | — |
| 485 | C4×D4 | — | 10 | 1 | no | — |
| 486 | C4×D4 | — | 10 | 1 | no | — |
| 487 | C4×D4 | — | 10 | 1 | no | — |
| 488 | C4×D4 | D20 | 1 | 2 | yes | — |
| 489 | #117 | — | 10 | 1 | no | — |
| 490 | #117 | — | 10 | 1 | no | — |
| 491 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 492 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 493 | #107 | — | 10 | 1 | no | — |
| 494 | #107 | — | 10 | 2 | no | — |
| 495 | #106 | — | 10 | 1 | no | — |
| 496 | C4⋊C8 | — | 2 | 1 | no | — |
| 497 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 498 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 499 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 500 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 501 | #103 | — | 10 | 1 | no | — |
| 502 | #103 | — | 10 | 1 | no | — |
| 503 | #103 | — | 10 | 1 | no | — |
| 504 | #102 | — | 10 | 1 | no | — |
| 505 | #102 | — | 10 | 1 | no | — |
| 506 | #102 | — | 10 | 1 | no | — |
| 507 | #102 | — | 10 | 1 | no | — |
| 508 | #102 | — | 10 | 1 | no | — |
| 509 | #102 | — | 10 | 2 | no | — |
| 510 | #102 | — | 10 | 2 | no | — |
| 511 | C22⋊C8 | — | 2 | 1 | no | — |
| 512 | #97 | — | 2 | 1 | no | — |
| 513 | C4×C8 | — | 5 | 1 | no | — |
| 514 | C4×C8 | — | 5 | 1 | no | — |
| 515 | C4×C8 | — | 10 | 1 | no | — |
| 516 | C22×C5 | — | 2 | 1 | no | — |
| 517 | C22×C5 | — | 2 | 1 | no | — |
| 518 | C22×C5 | — | 2 | 1 | no | — |
| 519 | C22×C5 | — | 4 | 2 | no | — |
| 520 | C22×C5 | — | 4 | 2 | no | — |
| 521 | C22×C5 | — | 4 | 2 | no | — |
| 522 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 523 | C2×D5 | — | 4 | 1 | no | — |
| 524 | C2×D5 | — | 4 | 1 | no | — |
| 525 | C2×D5 | — | 4 | 1 | no | — |
| 526 | C2×D5 | — | 8 | 1 | no | — |
| 527 | C2×D5 | — | 8 | 1 | no | — |
| 528 | C2×D5 | — | 8 | 1 | no | — |
| 529 | C4×C5 | — | 2 | 1 | no | — |
| 530 | C4×C5 | — | 2 | 1 | no | — |
| 531 | C4×C5 | — | 2 | 1 | no | — |
| 532 | C4×C5 | — | 2 | 1 | no | — |
| 533 | C4×C5 | — | 4 | 2 | no | — |
| 534 | C4×C5 | #576 | 1 | 1 | yes | characteristic |
| 535 | C4×C5 | #576 | 1 | 1 | yes | characteristic |
| 536 | C4×C5 | #577 | 1 | 1 | yes | characteristic |
| 537 | C4×C5 | #578 | 1 | 1 | yes | characteristic |
| 538 | Dic5 | — | 4 | 1 | no | — |
| 539 | Dic5 | — | 4 | 1 | no | — |
| 540 | Dic5 | — | 4 | 1 | no | — |
| 541 | Dic5 | — | 4 | 1 | no | — |
| 542 | Dic5 | — | 4 | 1 | no | — |
| 543 | Dic5 | — | 4 | 1 | no | — |
| 544 | Dic5 | — | 4 | 1 | no | — |
| 545 | Dic5 | — | 8 | 1 | no | — |
| 546 | #41 | — | 8 | 1 | no | — |
| 547 | #41 | — | 8 | 1 | no | — |
| 548 | #41 | — | 40 | 1 | no | — |
| 549 | #41 | — | 40 | 1 | no | — |
| 550 | #41 | — | 40 | 1 | no | — |
| 551 | #41 | — | 40 | 1 | no | — |
| 552 | C2×Q8 | — | 2 | 1 | no | — |
| 553 | C2×Q8 | — | 5 | 1 | no | — |
| 554 | C2×Q8 | — | 5 | 1 | no | — |
| 555 | C2×Q8 | — | 5 | 1 | no | — |
| 556 | C2×Q8 | — | 10 | 2 | no | — |
| 557 | C2×Q8 | — | 10 | 1 | no | — |
| 558 | C2×Q8 | — | 10 | 1 | no | — |
| 559 | C2×Q8 | — | 40 | 1 | no | — |
| 560 | C2×Q8 | — | 40 | 1 | no | — |
| 561 | C2×D4 | — | 2 | 2 | no | — |
| 562 | C2×D4 | — | 2 | 1 | no | — |
| 563 | C2×D4 | — | 2 | 1 | no | — |
| 564 | C2×D4 | — | 5 | 1 | no | — |
| 565 | C2×D4 | — | 10 | 2 | no | — |
| 566 | C2×D4 | — | 10 | 2 | no | — |
| 567 | C2×D4 | — | 10 | 1 | no | — |
| 568 | C2×D4 | — | 10 | 1 | no | — |
| 569 | C2×D4 | — | 10 | 1 | no | — |
| 570 | C2×D4 | — | 10 | 1 | no | — |
| 571 | C2×D4 | — | 20 | 1 | no | — |
| 572 | C2×D4 | C2×D20 | 1 | 2 | yes | — |
| 573 | C22×C4 | — | 2 | 2 | no | — |
| 574 | C22×C4 | — | 10 | 2 | no | — |
| 575 | C22×C4 | — | 10 | 2 | no | — |
| 576 | C22×C4 | — | 10 | 2 | no | — |
| 577 | C22×C4 | — | 10 | 1 | no | — |
| 578 | C22×C4 | — | 20 | 1 | no | — |
| 579 | C22×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 580 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 581 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 582 | Q16 | — | 40 | 1 | no | — |
| 583 | Q16 | — | 40 | 1 | no | — |
| 584 | SD16 | — | 40 | 1 | no | — |
| 585 | SD16 | — | 40 | 1 | no | — |
| 586 | SD16 | — | 40 | 1 | no | — |
| 587 | D8 | — | 20 | 4 | no | — |
| 588 | D8 | — | 40 | 1 | no | — |
| 589 | M16 | — | 8 | 1 | no | — |
| 590 | C2×C8 | — | 2 | 1 | no | — |
| 591 | C2×C8 | — | 2 | 1 | no | — |
| 592 | C2×C8 | — | 2 | 1 | no | — |
| 593 | C2×C8 | — | 2 | 1 | no | — |
| 594 | C2×C8 | — | 10 | 1 | no | — |
| 595 | C2×C8 | — | 10 | 1 | no | — |
| 596 | C2×C8 | — | 20 | 2 | no | — |
| 597 | C4⋊C4 | — | 2 | 1 | no | — |
| 598 | C4⋊C4 | — | 5 | 1 | no | — |
| 599 | C4⋊C4 | — | 5 | 1 | no | — |
| 600 | C4⋊C4 | — | 5 | 1 | no | — |
| 601 | C4⋊C4 | — | 5 | 1 | no | — |
| 602 | C4⋊C4 | — | 10 | 2 | no | — |
| 603 | C4⋊C4 | — | 10 | 2 | no | — |
| 604 | C4⋊C4 | — | 10 | 2 | no | — |
| 605 | C4⋊C4 | — | 10 | 2 | no | — |
| 606 | C4⋊C4 | — | 10 | 1 | no | — |
| 607 | C4⋊C4 | — | 10 | 1 | no | — |
| 608 | C4⋊C4 | — | 10 | 1 | no | — |
| 609 | C4⋊C4 | — | 10 | 1 | no | — |
| 610 | C4⋊C4 | — | 10 | 1 | no | — |
| 611 | C4⋊C4 | — | 10 | 1 | no | — |
| 612 | C4⋊C4 | — | 10 | 1 | no | — |
| 613 | C4⋊C4 | — | 10 | 1 | no | — |
| 614 | C4⋊C4 | — | 10 | 1 | no | — |
| 615 | C4⋊C4 | — | 10 | 1 | no | — |
| 616 | C4⋊C4 | — | 10 | 1 | no | — |
| 617 | C4⋊C4 | — | 10 | 1 | no | — |
| 618 | C4⋊C4 | — | 10 | 1 | no | — |
| 619 | C4⋊C4 | C2×D20 | 1 | 2 | yes | — |
| 620 | C22⋊C4 | — | 2 | 2 | no | — |
| 621 | C22⋊C4 | — | 2 | 2 | no | — |
| 622 | C22⋊C4 | — | 10 | 2 | no | — |
| 623 | C22⋊C4 | — | 10 | 2 | no | — |
| 624 | C22⋊C4 | — | 10 | 2 | no | — |
| 625 | C22⋊C4 | — | 10 | 2 | no | — |
| 626 | C22⋊C4 | — | 10 | 2 | no | — |
| 627 | C22⋊C4 | — | 10 | 1 | no | — |
| 628 | C22⋊C4 | — | 10 | 1 | no | — |
| 629 | C22⋊C4 | — | 10 | 1 | no | — |
| 630 | C22⋊C4 | — | 10 | 1 | no | — |
| 631 | C22⋊C4 | — | 10 | 1 | no | — |
| 632 | C22⋊C4 | — | 10 | 1 | no | — |
| 633 | C22⋊C4 | — | 10 | 1 | no | — |
| 634 | C22⋊C4 | — | 20 | 1 | no | — |
| 635 | C22⋊C4 | — | 20 | 1 | no | — |
| 636 | C42 | — | 10 | 2 | no | — |
| 637 | C42 | — | 10 | 1 | no | — |
| 638 | C42 | — | 10 | 1 | no | — |
| 639 | C42 | — | 10 | 1 | no | — |
| 640 | C42 | C2×D20 | 1 | 1 | yes | characteristic |
| 641 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 642 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 643 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 644 | C2×C5 | — | 4 | 1 | no | — |
| 645 | C2×C5 | — | 8 | 2 | no | — |
| 646 | C2×C5 | #3008 | 1 | 1 | yes | characteristic |
| 647 | C2×C5 | #3013 | 1 | 1 | yes | characteristic |
| 648 | C2×C5 | #3018 | 1 | 1 | yes | characteristic |
| 649 | D5 | — | 8 | 1 | no | — |
| 650 | D5 | — | 16 | 1 | no | — |
| 651 | C23 | — | 2 | 2 | no | — |
| 652 | C23 | — | 10 | 1 | no | — |
| 653 | C23 | — | 20 | 1 | no | — |
| 654 | C23 | #4028 | 1 | 1 | yes | characteristic |
| 655 | Q8 | — | 4 | 1 | no | — |
| 656 | Q8 | — | 4 | 1 | no | — |
| 657 | Q8 | — | 10 | 1 | no | — |
| 658 | Q8 | — | 10 | 1 | no | — |
| 659 | Q8 | — | 10 | 1 | no | — |
| 660 | Q8 | — | 10 | 1 | no | — |
| 661 | Q8 | — | 10 | 1 | no | — |
| 662 | Q8 | — | 10 | 1 | no | — |
| 663 | Q8 | — | 20 | 1 | no | — |
| 664 | Q8 | — | 20 | 1 | no | — |
| 665 | Q8 | — | 40 | 1 | no | — |
| 666 | Q8 | — | 40 | 2 | no | — |
| 667 | D4 | — | 4 | 2 | no | — |
| 668 | D4 | — | 4 | 1 | no | — |
| 669 | D4 | — | 4 | 1 | no | — |
| 670 | D4 | — | 4 | 1 | no | — |
| 671 | D4 | — | 4 | 1 | no | — |
| 672 | D4 | — | 8 | 2 | no | — |
| 673 | D4 | — | 10 | 1 | no | — |
| 674 | D4 | — | 10 | 1 | no | — |
| 675 | D4 | — | 20 | 2 | no | — |
| 676 | D4 | — | 20 | 1 | no | — |
| 677 | D4 | — | 20 | 1 | no | — |
| 678 | D4 | — | 20 | 1 | no | — |
| 679 | D4 | — | 20 | 1 | no | — |
| 680 | D4 | — | 40 | 1 | no | — |
| 681 | D4 | — | 40 | 2 | no | — |
| 682 | D4 | — | 40 | 2 | no | — |
| 683 | D4 | — | 40 | 2 | no | — |
| 684 | C2×C4 | — | 2 | 1 | no | — |
| 685 | C2×C4 | — | 2 | 1 | no | — |
| 686 | C2×C4 | — | 2 | 1 | no | — |
| 687 | C2×C4 | — | 2 | 1 | no | — |
| 688 | C2×C4 | — | 2 | 2 | no | — |
| 689 | C2×C4 | — | 4 | 1 | no | — |
| 690 | C2×C4 | — | 8 | 2 | no | — |
| 691 | C2×C4 | — | 10 | 1 | no | — |
| 692 | C2×C4 | — | 10 | 1 | no | — |
| 693 | C2×C4 | — | 10 | 1 | no | — |
| 694 | C2×C4 | — | 10 | 1 | no | — |
| 695 | C2×C4 | — | 10 | 1 | no | — |
| 696 | C2×C4 | — | 10 | 1 | no | — |
| 697 | C2×C4 | — | 10 | 1 | no | — |
| 698 | C2×C4 | — | 20 | 1 | no | — |
| 699 | C2×C4 | — | 20 | 1 | no | — |
| 700 | C2×C4 | — | 20 | 1 | no | — |
| 701 | C2×C4 | — | 40 | 2 | no | — |
| 702 | C2×C4 | — | 40 | 2 | no | — |
| 703 | C2×C4 | — | 40 | 2 | no | — |
| 704 | C2×C4 | — | 40 | 2 | no | — |
| 705 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 706 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 707 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 708 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 709 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 710 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 711 | C8 | — | 4 | 1 | no | — |
| 712 | C8 | — | 4 | 1 | no | — |
| 713 | C8 | — | 4 | 1 | no | — |
| 714 | C8 | — | 4 | 1 | no | — |
| 715 | C8 | — | 10 | 2 | no | — |
| 716 | C8 | — | 20 | 1 | no | — |
| 717 | C5 | #18708 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 718 | C22 | — | 2 | 1 | no | — |
| 719 | C22 | — | 2 | 1 | no | — |
| 720 | C22 | — | 2 | 1 | no | — |
| 721 | C22 | — | 4 | 2 | no | — |
| 722 | C22 | — | 4 | 2 | no | — |
| 723 | C22 | — | 4 | 2 | no | — |
| 724 | C22 | — | 20 | 1 | no | — |
| 725 | C22 | — | 20 | 1 | no | — |
| 726 | C22 | — | 20 | 1 | no | — |
| 727 | C22 | — | 40 | 1 | no | — |
| 728 | C22 | — | 40 | 1 | no | — |
| 729 | C22 | — | 40 | 1 | no | — |
| 730 | C22 | C2×#4028 | 1 | 1 | yes | characteristic |
| 731 | C4 | — | 2 | 1 | no | — |
| 732 | C4 | — | 2 | 1 | no | — |
| 733 | C4 | — | 2 | 1 | no | — |
| 734 | C4 | — | 2 | 1 | no | — |
| 735 | C4 | — | 4 | 2 | no | — |
| 736 | C4 | — | 20 | 1 | no | — |
| 737 | C4 | — | 20 | 1 | no | — |
| 738 | C4 | — | 20 | 1 | no | — |
| 739 | C4 | — | 20 | 1 | no | — |
| 740 | C4 | — | 20 | 1 | no | — |
| 741 | C4 | — | 20 | 1 | no | — |
| 742 | C4 | — | 20 | 1 | no | — |
| 743 | C4 | — | 40 | 1 | no | — |
| 744 | C4 | #66108 | 1 | 1 | yes | characteristic |
| 745 | C4 | #66108 | 1 | 1 | yes | characteristic |
| 746 | C4 | #66109 | 1 | 1 | yes | characteristic |
| 747 | C4 | #66113 | 1 | 1 | yes | characteristic |
| 748 | C2 | — | 4 | 1 | no | — |
| 749 | C2 | — | 8 | 2 | no | — |
| 750 | C2 | — | 40 | 1 | no | — |
| 751 | C2 | — | 80 | 1 | no | — |
| 752 | C2 | #10610447 | 1 | 1 | yes | characteristic |
| 753 | C2 | #10610618 | 1 | 1 | yes | characteristic |
| 754 | C2 | #10610659 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#4028 |
| commutator, cosocle | C42×C5 | C24 |
| Frattini | C42 | C23×D5 |
| Fitting | C5×#1557 | C2 |
| socle | C22×C5 | C2×#120 |
| hypercenter | #1557 | D5 |
| hypocenter | C5 | #18708 |
| LCS | G ▷ C42×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #1557 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10618133 | C2 | semidirect |
| 2. #10615022 | C2 | semidirect |
| 3. #10611083 | C2 | semidirect |
| 4. #10610793 | C2 | semidirect |
| 5. C5×#1557 | C2 | semidirect |
| 6. #10601593 | C2 | semidirect |
| 7. #10601294 | C2 | semidirect |
| 8. #10599254 | C2 | semidirect |
| 9. #10599253 | C2 | semidirect |
| 10. #10599250 | C2 | semidirect |
| 11. #10599249 | C2 | semidirect |
| 12. #10599200 | C2 | semidirect |
| 13. #10599199 | C2 | semidirect |
| 14. #10599196 | C2 | semidirect |
| 15. #10599195 | C2 | semidirect |
| 189. #1557 | D5 | semidirect |
| 717. C5 | #18708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618133 | 2 |
| #10615022 | 2 |
| #10611083 | 2 |
| #10610793 | 2 |
| C5×#1557 | 2 |
| #10601593 | 2 |
| #10601294 | 2 |
| #10599254 | 2 |
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| #10599250 | 2 |
| #10599249 | 2 |
| #10599200 | 2 |
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| #10599196 | 2 |
| #10599195 | 2 |
| #18708 | 5 |