Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1156 conjugacy classes of subgroups.
The subgroup lattice has 966 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23777561 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #23772796 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#19098754 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23772760 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23765414 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #23765409 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #23765397 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #23765392 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #23765067 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#19098354 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C79×#2121 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14579206 | C22 | 1 | 1 | yes | characteristic |
| 13 | #19099363 | — | 2 | 1 | no | — |
| 14 | #19099316 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #19099308 | — | 2 | 1 | no | — |
| 16 | #19099302 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #19099297 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #19099260 | — | 2 | 1 | no | — |
| 19 | #19099250 | — | 2 | 1 | no | — |
| 20 | #19099244 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #19099239 | — | 2 | 1 | no | — |
| 22 | #19099211 | — | 2 | 1 | no | — |
| 23 | #19099207 | — | 2 | 1 | no | — |
| 24 | #19099180 | — | 2 | 1 | no | — |
| 25 | #19099163 | — | 2 | 1 | no | — |
| 26 | #19099156 | — | 2 | 1 | no | — |
| 27 | #19099148 | — | 2 | 1 | no | — |
| 28 | #19099148 | — | 2 | 1 | no | — |
| 29 | #19099130 | C22 | 1 | 1 | yes | characteristic |
| 30 | #19099122 | — | 2 | 1 | no | — |
| 31 | #19099069 | — | 2 | 1 | no | — |
| 32 | C2×#14579145 | — | 2 | 1 | no | — |
| 33 | C2×#14579142 | C22 | 1 | 1 | yes | characteristic |
| 34 | #19098754 | — | 2 | 1 | no | — |
| 35 | #19098754 | — | 2 | 1 | no | — |
| 36 | #19098754 | C22 | 1 | 2 | yes | — |
| 37 | #19098754 | C22 | 1 | 2 | yes | — |
| 38 | #19098752 | — | 2 | 1 | no | — |
| 39 | #19098752 | C22 | 1 | 2 | yes | — |
| 40 | #19098749 | — | 2 | 1 | no | — |
| 41 | #19098749 | C22 | 1 | 2 | yes | — |
| 42 | #19098743 | — | 2 | 1 | no | — |
| 43 | #19098743 | C22 | 1 | 2 | yes | — |
| 44 | #19098733 | — | 2 | 1 | no | — |
| 45 | #19098733 | C22 | 1 | 2 | yes | — |
| 46 | #19098579 | — | 2 | 1 | no | — |
| 47 | C2×#14579076 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#14579075 | — | 2 | 1 | no | — |
| 49 | C2×#14579075 | — | 2 | 1 | no | — |
| 50 | #19098357 | C22 | 1 | 2 | yes | complemented |
| 51 | #19098355 | C22 | 1 | 2 | yes | complemented |
| 52 | #19098354 | C22 | 1 | 2 | yes | complemented |
| 53 | #19098354 | C22 | 1 | 2 | yes | complemented |
| 54 | #534×C79 | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×#100×C79 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#99×C79 | C22 | 1 | 1 | yes | characteristic |
| 57 | #352×C79 | C22 | 1 | 2 | yes | complemented |
| 58 | AΣL(1,𝔽16)×C79 | C22 | 1 | 2 | yes | complemented |
| 59 | #14579206 | — | 2 | 1 | no | — |
| 60 | #14579206 | — | 2 | 1 | no | — |
| 61 | #14579206 | — | 2 | 1 | no | — |
| 62 | #14579206 | — | 4 | 2 | no | — |
| 63 | #14579206 | C23 | 1 | 2 | yes | — |
| 64 | C2×#11929624 | — | 2 | 1 | no | — |
| 65 | C2×#11929624 | D4 | 1 | 1 | yes | characteristic, complemented |
| 66 | C2×#11929623 | — | 2 | 1 | no | — |
| 67 | C2×#11929623 | — | 4 | 1 | no | — |
| 68 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 69 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 70 | C2×D4×D79 | — | 4 | 1 | no | — |
| 71 | C23×Dic79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 72 | #14579194 | — | 2 | 2 | no | — |
| 73 | #14579194 | — | 4 | 1 | no | — |
| 74 | #14579189 | — | 2 | 2 | no | — |
| 75 | #14579189 | — | 4 | 1 | no | — |
| 76 | #14579183 | — | 4 | 2 | no | — |
| 77 | #14579160 | — | 2 | 1 | no | — |
| 78 | #14579157 | D4 | 1 | 1 | yes | characteristic, complemented |
| 79 | #14579157 | C23 | 1 | 1 | yes | characteristic |
| 80 | #14579154 | — | 2 | 1 | no | — |
| 81 | #14579154 | — | 2 | 1 | no | — |
| 82 | #14579154 | — | 2 | 1 | no | — |
| 83 | #14579154 | — | 2 | 1 | no | — |
| 84 | #14579154 | — | 2 | 1 | no | — |
| 85 | #14579154 | — | 2 | 1 | no | — |
| 86 | #14579152 | — | 2 | 1 | no | — |
| 87 | #14579151 | — | 2 | 1 | no | — |
| 88 | #14579151 | — | 2 | 1 | no | — |
| 89 | #14579148 | — | 2 | 1 | no | — |
| 90 | #14579148 | — | 2 | 1 | no | — |
| 91 | #14579148 | D4 | 1 | 1 | yes | characteristic, complemented |
| 92 | #14579148 | C23 | 1 | 1 | yes | characteristic |
| 93 | #14579147 | — | 2 | 1 | no | — |
| 94 | #14579147 | — | 2 | 1 | no | — |
| 95 | #14579146 | — | 2 | 1 | no | — |
| 96 | #14579145 | — | 2 | 1 | no | — |
| 97 | #14579145 | — | 2 | 2 | no | — |
| 98 | #14579145 | — | 2 | 2 | no | — |
| 99 | #14579145 | — | 4 | 2 | no | — |
| 100 | #14579144 | — | 2 | 1 | no | — |
| 101 | #14579144 | — | 2 | 2 | no | — |
| 102 | #14579143 | — | 2 | 1 | no | — |
| 103 | #14579143 | — | 2 | 1 | no | — |
| 104 | #14579143 | — | 2 | 1 | no | — |
| 105 | #14579142 | — | 2 | 1 | no | — |
| 106 | #14579142 | — | 2 | 1 | no | — |
| 107 | #14579142 | — | 2 | 1 | no | — |
| 108 | #14579142 | — | 2 | 1 | no | — |
| 109 | #14579142 | — | 2 | 1 | no | — |
| 110 | #14579142 | — | 4 | 1 | no | — |
| 111 | #14579142 | D4 | 1 | 1 | yes | characteristic, complemented |
| 112 | #14579142 | D4 | 1 | 1 | yes | characteristic, complemented |
| 113 | #14579142 | C23 | 1 | 1 | yes | characteristic |
| 114 | #14579142 | C23 | 1 | 1 | yes | characteristic |
| 115 | #14579140 | — | 2 | 1 | no | — |
| 116 | #14579140 | — | 2 | 1 | no | — |
| 117 | #14579139 | — | 2 | 1 | no | — |
| 118 | #14579138 | — | 2 | 1 | no | — |
| 119 | #14579138 | — | 2 | 1 | no | — |
| 120 | #14579138 | — | 2 | 1 | no | — |
| 121 | #14579138 | — | 2 | 1 | no | — |
| 122 | #14579138 | — | 2 | 1 | no | — |
| 123 | #14579134 | — | 2 | 1 | no | — |
| 124 | #14579133 | — | 2 | 1 | no | — |
| 125 | #14579133 | — | 2 | 1 | no | — |
| 126 | #14579133 | — | 2 | 1 | no | — |
| 127 | #14579133 | — | 2 | 1 | no | — |
| 128 | #14579133 | — | 2 | 1 | no | — |
| 129 | #14579133 | — | 4 | 2 | no | — |
| 130 | #14579132 | — | 2 | 1 | no | — |
| 131 | #14579132 | — | 2 | 1 | no | — |
| 132 | #14579132 | — | 2 | 1 | no | — |
| 133 | #14579132 | — | 2 | 1 | no | — |
| 134 | #14579130 | — | 2 | 1 | no | — |
| 135 | #14579130 | — | 2 | 1 | no | — |
| 136 | #14579130 | — | 2 | 1 | no | — |
| 137 | #14579130 | — | 2 | 2 | no | — |
| 138 | #14579129 | — | 4 | 1 | no | — |
| 139 | #14579126 | — | 2 | 1 | no | — |
| 140 | D4×Dic79 | — | 2 | 1 | no | — |
| 141 | D4×Dic79 | — | 2 | 1 | no | — |
| 142 | D4×Dic79 | — | 2 | 1 | no | — |
| 143 | C4×C22⋊D79 | — | 2 | 1 | no | — |
| 144 | C4×C22⋊D79 | — | 2 | 1 | no | — |
| 145 | (C22⋊D79)⋊C4 | — | 2 | 1 | no | — |
| 146 | (C22⋊D79)⋊C4 | — | 2 | 1 | no | — |
| 147 | (C22⋊D79)⋊C4 | — | 2 | 1 | no | — |
| 148 | (C22⋊D79)⋊C4 | — | 2 | 1 | no | — |
| 149 | #14579120 | — | 2 | 1 | no | — |
| 150 | #14579120 | D4 | 1 | 1 | yes | characteristic, complemented |
| 151 | #14579117 | — | 2 | 1 | no | — |
| 152 | #14579117 | — | 2 | 1 | no | — |
| 153 | C2×C4⋊Dic79 | — | 4 | 1 | no | — |
| 154 | C2×Dic79⋊C4 | — | 2 | 1 | no | — |
| 155 | C4⋊C4×D79 | — | 2 | 1 | no | — |
| 156 | C2×C22⋊Dic79 | — | 2 | 1 | no | — |
| 157 | C2×C22⋊Dic79 | — | 2 | 1 | no | — |
| 158 | C2×C22⋊Dic79 | — | 2 | 1 | no | — |
| 159 | C2×C22⋊Dic79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 160 | C2×(C2×D79)⋊C4 | — | 4 | 1 | no | — |
| 161 | #14579087 | — | 2 | 2 | no | — |
| 162 | #14579087 | — | 2 | 2 | no | — |
| 163 | #14579076 | — | 2 | 1 | no | — |
| 164 | #14579076 | C23 | 1 | 2 | yes | — |
| 165 | #14579075 | — | 2 | 2 | no | — |
| 166 | #14579075 | — | 2 | 2 | no | — |
| 167 | #14579075 | — | 2 | 2 | no | — |
| 168 | #14579075 | — | 2 | 2 | no | — |
| 169 | C22×D4×C79 | D4 | 1 | 1 | yes | characteristic |
| 170 | C22×D4×C79 | C23 | 1 | 1 | yes | characteristic |
| 171 | C2×M16×C79 | — | 2 | 1 | no | — |
| 172 | #123×C79 | — | 2 | 1 | no | — |
| 173 | #123×C79 | D4 | 1 | 1 | yes | characteristic |
| 174 | #123×C79 | C23 | 1 | 1 | yes | characteristic |
| 175 | #121×C79 | — | 2 | 1 | no | — |
| 176 | #121×C79 | — | 2 | 1 | no | — |
| 177 | #120×C79 | — | 2 | 1 | no | — |
| 178 | #120×C79 | D4 | 1 | 1 | yes | characteristic |
| 179 | #120×C79 | C23 | 1 | 1 | yes | characteristic |
| 180 | C2×C22⋊C4×C79 | — | 2 | 1 | no | — |
| 181 | C2×C22⋊C4×C79 | D4 | 1 | 1 | yes | characteristic |
| 182 | #100×C79 | — | 2 | 1 | no | — |
| 183 | #100×C79 | C23 | 1 | 2 | yes | — |
| 184 | #99×C79 | — | 2 | 1 | no | — |
| 185 | #99×C79 | C23 | 1 | 2 | yes | — |
| 186 | C23×D79 | — | 2 | 1 | no | — |
| 187 | C23×D79 | — | 2 | 1 | no | — |
| 188 | #11929624 | — | 2 | 2 | no | — |
| 189 | #11929624 | — | 2 | 2 | no | — |
| 190 | #11929624 | — | 4 | 1 | no | — |
| 191 | #11929624 | — | 4 | 1 | no | — |
| 192 | #11929624 | — | 4 | 1 | no | — |
| 193 | #11929624 | — | 4 | 1 | no | — |
| 194 | #11929623 | — | 4 | 2 | no | — |
| 195 | #11929623 | — | 4 | 2 | no | — |
| 196 | #11929623 | — | 4 | 2 | no | — |
| 197 | #11929623 | — | 4 | 2 | no | — |
| 198 | #11929623 | — | 8 | 1 | no | — |
| 199 | #11929623 | — | 8 | 1 | no | — |
| 200 | C2×Dic158 | — | 2 | 1 | no | — |
| 201 | C2×Dic158 | — | 2 | 1 | no | — |
| 202 | C2×Dic158 | — | 2 | 1 | no | — |
| 203 | C2×Dic158 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C2×D316 | — | 2 | 1 | no | — |
| 205 | C2×D316 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 207 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 208 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 209 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 210 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 211 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 212 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 213 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 214 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 215 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 216 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 217 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 218 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 219 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 220 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 221 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 222 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 223 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 224 | C2×C22⋊D79 | — | 4 | 2 | no | — |
| 225 | D4×D79 | — | 4 | 2 | no | — |
| 226 | D4×D79 | — | 4 | 2 | no | — |
| 227 | D4×D79 | — | 4 | 2 | no | — |
| 228 | D4×D79 | — | 4 | 2 | no | — |
| 229 | C22×Dic79 | — | 2 | 1 | no | — |
| 230 | C22×Dic79 | — | 2 | 1 | no | — |
| 231 | C22×Dic79 | — | 2 | 1 | no | — |
| 232 | C22×Dic79 | — | 2 | 1 | no | — |
| 233 | C22×Dic79 | — | 2 | 1 | no | — |
| 234 | C22×Dic79 | — | 2 | 1 | no | — |
| 235 | C22×Dic79 | — | 2 | 1 | no | — |
| 236 | C22×Dic79 | — | 4 | 1 | no | — |
| 237 | C22×Dic79 | — | 4 | 1 | no | — |
| 238 | C22×Dic79 | — | 4 | 1 | no | — |
| 239 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C2×C4×D79 | — | 2 | 1 | no | — |
| 242 | C2×C4×D79 | — | 2 | 1 | no | — |
| 243 | C2×C4×D79 | — | 2 | 1 | no | — |
| 244 | C2×C4×D79 | — | 4 | 1 | no | — |
| 245 | Dic316 | — | 4 | 2 | no | — |
| 246 | #11929613 | — | 4 | 2 | no | — |
| 247 | #11929613 | — | 4 | 2 | no | — |
| 248 | D632 | — | 4 | 2 | no | — |
| 249 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 250 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 251 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 252 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 253 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 254 | C4⋊Dic79 | — | 4 | 2 | no | — |
| 255 | C4⋊Dic79 | — | 4 | 2 | no | — |
| 256 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 257 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 258 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 259 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 260 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 261 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 262 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 263 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 264 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 265 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 266 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 267 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 268 | Dic79⋊C4 | — | 4 | 2 | no | — |
| 269 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 270 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 271 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 272 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 273 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 274 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 275 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 276 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 277 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 278 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 279 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 280 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 281 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 282 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 283 | C22⋊Dic79 | — | 2 | 2 | no | — |
| 284 | C22⋊Dic79 | — | 4 | 1 | no | — |
| 285 | C22⋊Dic79 | — | 4 | 2 | no | — |
| 286 | C22⋊Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | C22⋊Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 288 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 289 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 290 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 291 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 292 | (C2×D79)⋊C4 | — | 4 | 2 | no | — |
| 293 | (C2×D79)⋊C4 | — | 4 | 2 | no | — |
| 294 | (C2×D79)⋊C4 | — | 4 | 2 | no | — |
| 295 | C4×Dic79 | — | 2 | 1 | no | — |
| 296 | C4×Dic79 | — | 2 | 1 | no | — |
| 297 | C4×Dic79 | — | 2 | 1 | no | — |
| 298 | C4×Dic79 | — | 2 | 1 | no | — |
| 299 | C4×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 300 | C4×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 301 | C24×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 302 | C24×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 303 | C24×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 304 | C2×D4×C79 | — | 2 | 1 | no | — |
| 305 | C2×D4×C79 | — | 2 | 1 | no | — |
| 306 | C2×D4×C79 | — | 2 | 1 | no | — |
| 307 | C2×D4×C79 | — | 2 | 1 | no | — |
| 308 | C2×D4×C79 | — | 4 | 1 | no | — |
| 309 | C2×D4×C79 | — | 4 | 1 | no | — |
| 310 | C2×D4×C79 | — | 4 | 1 | no | — |
| 311 | C2×D4×C79 | — | 4 | 1 | no | — |
| 312 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 313 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 314 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 315 | C2×D4×C79 | C24 | 1 | 1 | yes | characteristic |
| 316 | C22×C4×C79 | — | 2 | 1 | no | — |
| 317 | C22×C4×C79 | — | 4 | 1 | no | — |
| 318 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 319 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 320 | M16×C79 | — | 2 | 2 | no | — |
| 321 | M16×C79 | — | 4 | 1 | no | — |
| 322 | C2×C8×C79 | — | 4 | 1 | no | — |
| 323 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 324 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 325 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 326 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 327 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 328 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 329 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 330 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 331 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 332 | C22⋊C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 333 | C22⋊C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 334 | C23×C79 | — | 2 | 1 | no | — |
| 335 | C23×C79 | — | 2 | 1 | no | — |
| 336 | C23×C79 | — | 2 | 1 | no | — |
| 337 | C23×C79 | — | 2 | 1 | no | — |
| 338 | C23×C79 | — | 2 | 1 | no | — |
| 339 | C23×C79 | — | 4 | 1 | no | — |
| 340 | C23×C79 | — | 8 | 1 | no | — |
| 341 | C23×C79 | — | 8 | 1 | no | — |
| 342 | C23×C79 | — | 8 | 1 | no | — |
| 343 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 344 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 345 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 346 | C23×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 347 | C23×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 348 | C22×D79 | — | 2 | 1 | no | — |
| 349 | C22×D79 | — | 2 | 2 | no | — |
| 350 | C22×D79 | — | 2 | 2 | no | — |
| 351 | C22×D79 | — | 4 | 1 | no | — |
| 352 | C22×D79 | — | 4 | 1 | no | — |
| 353 | C22×D79 | — | 4 | 1 | no | — |
| 354 | C22×D79 | — | 8 | 2 | no | — |
| 355 | C22×D79 | — | 16 | 1 | no | — |
| 356 | D4×C79 | — | 4 | 1 | no | — |
| 357 | D4×C79 | — | 4 | 1 | no | — |
| 358 | D4×C79 | — | 4 | 1 | no | — |
| 359 | D4×C79 | — | 4 | 1 | no | — |
| 360 | D4×C79 | — | 4 | 1 | no | — |
| 361 | D4×C79 | — | 4 | 1 | no | — |
| 362 | D4×C79 | — | 8 | 1 | no | — |
| 363 | D4×C79 | — | 8 | 1 | no | — |
| 364 | D4×C79 | — | 8 | 1 | no | — |
| 365 | C2×C4×C79 | — | 2 | 1 | no | — |
| 366 | C2×C4×C79 | — | 2 | 1 | no | — |
| 367 | C2×C4×C79 | — | 2 | 1 | no | — |
| 368 | C2×C4×C79 | — | 2 | 1 | no | — |
| 369 | C2×C4×C79 | — | 2 | 1 | no | — |
| 370 | C2×C4×C79 | — | 4 | 1 | no | — |
| 371 | C2×C4×C79 | — | 4 | 2 | no | — |
| 372 | C2×C4×C79 | — | 8 | 1 | no | — |
| 373 | C2×C4×C79 | — | 8 | 2 | no | — |
| 374 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 375 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 376 | C22⋊D79 | — | 4 | 2 | no | — |
| 377 | C22⋊D79 | — | 4 | 2 | no | — |
| 378 | C22⋊D79 | — | 4 | 2 | no | — |
| 379 | C22⋊D79 | — | 4 | 2 | no | — |
| 380 | C22⋊D79 | — | 4 | 2 | no | — |
| 381 | C22⋊D79 | — | 4 | 2 | no | — |
| 382 | C22⋊D79 | — | 4 | 1 | no | — |
| 383 | C22⋊D79 | — | 4 | 1 | no | — |
| 384 | C22⋊D79 | — | 8 | 1 | no | — |
| 385 | C22⋊D79 | — | 8 | 1 | no | — |
| 386 | C22⋊D79 | — | 8 | 1 | no | — |
| 387 | C22⋊D79 | — | 8 | 1 | no | — |
| 388 | C22⋊D79 | — | 8 | 1 | no | — |
| 389 | C22⋊D79 | — | 8 | 1 | no | — |
| 390 | C22⋊D79 | — | 16 | 2 | no | — |
| 391 | C2×Dic79 | — | 2 | 2 | no | — |
| 392 | C2×Dic79 | — | 2 | 2 | no | — |
| 393 | C2×Dic79 | — | 2 | 1 | no | — |
| 394 | C2×Dic79 | — | 2 | 1 | no | — |
| 395 | C2×Dic79 | — | 2 | 1 | no | — |
| 396 | C2×Dic79 | — | 2 | 1 | no | — |
| 397 | C2×Dic79 | — | 2 | 1 | no | — |
| 398 | C2×Dic79 | — | 2 | 1 | no | — |
| 399 | C2×Dic79 | — | 2 | 1 | no | — |
| 400 | C2×Dic79 | — | 4 | 1 | no | — |
| 401 | C2×Dic79 | — | 4 | 1 | no | — |
| 402 | C2×Dic79 | — | 4 | 1 | no | — |
| 403 | C2×Dic79 | — | 4 | 1 | no | — |
| 404 | C2×Dic79 | — | 4 | 1 | no | — |
| 405 | C2×Dic79 | — | 4 | 1 | no | — |
| 406 | C2×Dic79 | — | 4 | 1 | no | — |
| 407 | C2×Dic79 | — | 4 | 2 | no | — |
| 408 | C2×Dic79 | — | 8 | 1 | no | — |
| 409 | C2×Dic79 | — | 8 | 1 | no | — |
| 410 | C2×Dic79 | — | 8 | 1 | no | — |
| 411 | C2×Dic79 | — | 8 | 1 | no | — |
| 412 | C2×Dic79 | — | 16 | 1 | no | — |
| 413 | D316 | — | 2 | 2 | no | — |
| 414 | D316 | — | 4 | 1 | no | — |
| 415 | D316 | — | 4 | 1 | no | — |
| 416 | C4×D79 | — | 4 | 2 | no | — |
| 417 | C4×D79 | — | 4 | 2 | no | — |
| 418 | C4×D79 | — | 8 | 1 | no | — |
| 419 | C4×D79 | — | 8 | 1 | no | — |
| 420 | C4×D79 | — | 8 | 1 | no | — |
| 421 | Dic158 | — | 2 | 2 | no | — |
| 422 | Dic158 | — | 4 | 1 | no | — |
| 423 | Dic158 | — | 4 | 1 | no | — |
| 424 | Dic158 | — | 8 | 1 | no | — |
| 425 | Dic158 | — | 8 | 1 | no | — |
| 426 | C8×C79 | — | 4 | 2 | no | — |
| 427 | C22×C79 | — | 2 | 1 | no | — |
| 428 | C22×C79 | — | 2 | 1 | no | — |
| 429 | C22×C79 | — | 2 | 1 | no | — |
| 430 | C22×C79 | — | 2 | 1 | no | — |
| 431 | C22×C79 | — | 4 | 1 | no | — |
| 432 | C22×C79 | — | 4 | 1 | no | — |
| 433 | C22×C79 | — | 4 | 1 | no | — |
| 434 | C22×C79 | — | 4 | 1 | no | — |
| 435 | C22×C79 | — | 4 | 1 | no | — |
| 436 | C22×C79 | — | 4 | 2 | no | — |
| 437 | C22×C79 | — | 4 | 1 | no | — |
| 438 | C22×C79 | — | 4 | 1 | no | — |
| 439 | C22×C79 | — | 4 | 1 | no | — |
| 440 | C22×C79 | — | 8 | 1 | no | — |
| 441 | C22×C79 | — | 8 | 1 | no | — |
| 442 | C22×C79 | — | 8 | 1 | no | — |
| 443 | C22×C79 | — | 8 | 2 | no | — |
| 444 | C22×C79 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 445 | C22×C79 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 446 | C22×C79 | C2×#120 | 1 | 1 | yes | characteristic |
| 447 | C2×D79 | — | 4 | 1 | no | — |
| 448 | C2×D79 | — | 4 | 1 | no | — |
| 449 | C2×D79 | — | 4 | 2 | no | — |
| 450 | C2×D79 | — | 4 | 1 | no | — |
| 451 | C2×D79 | — | 8 | 2 | no | — |
| 452 | C2×D79 | — | 8 | 2 | no | — |
| 453 | C2×D79 | — | 8 | 2 | no | — |
| 454 | C2×D79 | — | 16 | 1 | no | — |
| 455 | C2×D79 | — | 16 | 1 | no | — |
| 456 | C4×C79 | — | 2 | 1 | no | — |
| 457 | C4×C79 | — | 2 | 1 | no | — |
| 458 | C4×C79 | — | 4 | 1 | no | — |
| 459 | C4×C79 | — | 4 | 1 | no | — |
| 460 | C4×C79 | — | 4 | 1 | no | — |
| 461 | C4×C79 | — | 8 | 2 | no | — |
| 462 | Dic79 | — | 4 | 1 | no | — |
| 463 | Dic79 | — | 4 | 1 | no | — |
| 464 | Dic79 | — | 4 | 1 | no | — |
| 465 | Dic79 | — | 4 | 1 | no | — |
| 466 | Dic79 | — | 4 | 2 | no | — |
| 467 | Dic79 | — | 4 | 1 | no | — |
| 468 | Dic79 | — | 4 | 1 | no | — |
| 469 | Dic79 | — | 4 | 1 | no | — |
| 470 | Dic79 | — | 8 | 2 | no | — |
| 471 | #33552 | — | 79 | 1 | no | maximal, Sylow |
| 472 | C2×C79 | — | 2 | 1 | no | — |
| 473 | C2×C79 | — | 2 | 1 | no | — |
| 474 | C2×C79 | — | 2 | 1 | no | — |
| 475 | C2×C79 | — | 4 | 1 | no | — |
| 476 | C2×C79 | — | 4 | 1 | no | — |
| 477 | C2×C79 | — | 4 | 1 | no | — |
| 478 | C2×C79 | — | 4 | 1 | no | — |
| 479 | C2×C79 | — | 8 | 1 | no | — |
| 480 | C2×C79 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 481 | D79 | — | 8 | 1 | no | — |
| 482 | D79 | — | 8 | 2 | no | — |
| 483 | #3533 | — | 79 | 1 | no | — |
| 484 | #3026 | — | 79 | 1 | no | — |
| 485 | C2×#458 | — | 79 | 1 | no | — |
| 486 | #3019 | — | 79 | 1 | no | — |
| 487 | #2201 | — | 79 | 2 | no | — |
| 488 | #2200 | — | 79 | 2 | no | — |
| 489 | #2198 | — | 79 | 2 | no | — |
| 490 | #2197 | — | 79 | 2 | no | — |
| 491 | #2127 | — | 79 | 1 | no | — |
| 492 | #2121 | D79 | 1 | 1 | yes | characteristic, complemented |
| 493 | C2×#352 | — | 79 | 1 | no | — |
| 494 | C79 | #33552 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 495 | C2×H(5,𝔽2) | — | 79 | 1 | no | — |
| 496 | #575 | — | 158 | 1 | no | — |
| 497 | #563 | — | 79 | 1 | no | — |
| 498 | #562 | — | 158 | 1 | no | — |
| 499 | #560 | — | 79 | 1 | no | — |
| 500 | #559 | — | 79 | 1 | no | — |
| 501 | #553 | — | 158 | 1 | no | — |
| 502 | #552 | — | 158 | 1 | no | — |
| 503 | #551 | — | 79 | 1 | no | — |
| 504 | #551 | — | 158 | 1 | no | — |
| 505 | #547 | — | 158 | 1 | no | — |
| 506 | #546 | — | 158 | 1 | no | — |
| 507 | #542 | — | 158 | 1 | no | — |
| 508 | #540 | — | 158 | 1 | no | — |
| 509 | #539 | — | 158 | 1 | no | — |
| 510 | #538 | — | 158 | 1 | no | — |
| 511 | #538 | — | 158 | 1 | no | — |
| 512 | #535 | — | 79 | 1 | no | — |
| 513 | #534 | — | 158 | 1 | no | — |
| 514 | #534 | C2×D79 | 1 | 1 | yes | characteristic |
| 515 | #525 | — | 158 | 1 | no | — |
| 516 | C2×#123 | — | 79 | 1 | no | — |
| 517 | C2×#123 | — | 158 | 1 | no | — |
| 518 | #458 | — | 79 | 2 | no | — |
| 519 | #458 | — | 79 | 2 | no | — |
| 520 | #458 | — | 79 | 2 | no | — |
| 521 | #458 | — | 158 | 1 | no | — |
| 522 | #458 | — | 158 | 1 | no | — |
| 523 | #458 | — | 158 | 1 | no | — |
| 524 | B(4,𝔽2) | — | 79 | 2 | no | — |
| 525 | B(4,𝔽2) | — | 158 | 1 | no | — |
| 526 | #455 | — | 79 | 2 | no | — |
| 527 | #455 | — | 158 | 1 | no | — |
| 528 | #453 | — | 79 | 2 | no | — |
| 529 | #453 | — | 158 | 1 | no | — |
| 530 | #421 | — | 158 | 1 | no | — |
| 531 | C2×#100 | C2×D79 | 1 | 1 | yes | characteristic |
| 532 | C2×#99 | — | 79 | 1 | no | — |
| 533 | C2×#99 | — | 158 | 1 | no | — |
| 534 | C2×#99 | — | 158 | 1 | no | — |
| 535 | C2×#99 | C2×D79 | 1 | 1 | yes | characteristic |
| 536 | #354 | — | 79 | 2 | no | — |
| 537 | #353 | — | 79 | 2 | no | — |
| 538 | #352 | — | 79 | 2 | no | — |
| 539 | #352 | — | 79 | 2 | no | — |
| 540 | #352 | C2×D79 | 1 | 2 | yes | complemented |
| 541 | AΣL(1,𝔽16) | C2×D79 | 1 | 2 | yes | complemented |
| 542 | H(5,𝔽2) | — | 316 | 2 | no | — |
| 543 | H(5,𝔽2) | — | 79 | 2 | no | — |
| 544 | H(5,𝔽2) | — | 158 | 1 | no | — |
| 545 | H(5,𝔽2) | — | 158 | 1 | no | — |
| 546 | H(5,𝔽2) | — | 158 | 1 | no | — |
| 547 | C2×#41 | — | 316 | 1 | no | — |
| 548 | C2×#41 | — | 79 | 1 | no | — |
| 549 | C2×#41 | — | 158 | 1 | no | — |
| 550 | C2×#41 | — | 158 | 1 | no | — |
| 551 | C22×D4 | — | 316 | 1 | no | — |
| 552 | C22×D4 | — | 158 | 1 | no | — |
| 553 | C22×D4 | — | 158 | 1 | no | — |
| 554 | C22×D4 | D316 | 1 | 1 | yes | characteristic |
| 555 | C22×D4 | C22×D79 | 1 | 1 | yes | characteristic |
| 556 | C23×C4 | — | 79 | 1 | no | — |
| 557 | #137 | — | 316 | 1 | no | — |
| 558 | #137 | — | 158 | 2 | no | — |
| 559 | AGL(1,ℤ/8) | — | 316 | 1 | no | — |
| 560 | AGL(1,ℤ/8) | — | 158 | 2 | no | — |
| 561 | #135 | — | 316 | 2 | no | — |
| 562 | C2×M16 | — | 2 | 1 | no | — |
| 563 | C4⋊Q8 | — | 158 | 1 | no | — |
| 564 | #127 | — | 79 | 1 | no | — |
| 565 | #127 | — | 79 | 1 | no | — |
| 566 | #126 | — | 158 | 1 | no | — |
| 567 | #126 | — | 158 | 1 | no | — |
| 568 | #126 | — | 158 | 1 | no | — |
| 569 | #126 | — | 158 | 1 | no | — |
| 570 | #126 | — | 158 | 1 | no | — |
| 571 | #126 | — | 158 | 1 | no | — |
| 572 | #125 | — | 158 | 1 | no | — |
| 573 | #125 | — | 158 | 1 | no | — |
| 574 | #125 | — | 158 | 1 | no | — |
| 575 | #124 | — | 79 | 1 | no | — |
| 576 | #124 | — | 79 | 1 | no | — |
| 577 | #124 | — | 158 | 1 | no | — |
| 578 | #124 | — | 158 | 1 | no | — |
| 579 | #124 | — | 158 | 1 | no | — |
| 580 | #124 | — | 158 | 1 | no | — |
| 581 | #123 | — | 2 | 1 | no | — |
| 582 | #123 | — | 316 | 2 | no | — |
| 583 | #123 | — | 316 | 1 | no | — |
| 584 | #123 | — | 79 | 1 | no | — |
| 585 | #123 | — | 79 | 1 | no | — |
| 586 | #123 | — | 79 | 1 | no | — |
| 587 | #123 | — | 79 | 1 | no | — |
| 588 | #123 | — | 158 | 2 | no | — |
| 589 | #123 | — | 158 | 2 | no | — |
| 590 | #123 | — | 158 | 1 | no | — |
| 591 | #123 | — | 158 | 1 | no | — |
| 592 | #123 | — | 158 | 1 | no | — |
| 593 | #123 | — | 158 | 2 | no | — |
| 594 | #123 | — | 158 | 1 | no | — |
| 595 | #123 | — | 158 | 1 | no | — |
| 596 | #123 | — | 158 | 1 | no | — |
| 597 | #123 | — | 158 | 1 | no | — |
| 598 | #123 | — | 158 | 1 | no | — |
| 599 | #123 | — | 158 | 1 | no | — |
| 600 | #123 | — | 158 | 1 | no | — |
| 601 | #123 | — | 158 | 1 | no | — |
| 602 | #123 | D316 | 1 | 1 | yes | characteristic |
| 603 | #123 | C22×D79 | 1 | 1 | yes | characteristic |
| 604 | C22⋊Q8 | — | 158 | 1 | no | — |
| 605 | C22⋊Q8 | — | 158 | 1 | no | — |
| 606 | C22⋊Q8 | — | 158 | 1 | no | — |
| 607 | C22⋊Q8 | — | 158 | 1 | no | — |
| 608 | C22⋊Q8 | — | 158 | 1 | no | — |
| 609 | C22⋊Q8 | — | 158 | 1 | no | — |
| 610 | C22⋊Q8 | — | 158 | 1 | no | — |
| 611 | C22⋊Q8 | — | 158 | 1 | no | — |
| 612 | #121 | — | 2 | 1 | no | — |
| 613 | #121 | — | 2 | 1 | no | — |
| 614 | #121 | — | 316 | 2 | no | — |
| 615 | #121 | — | 158 | 1 | no | — |
| 616 | #121 | — | 158 | 1 | no | — |
| 617 | #121 | — | 158 | 1 | no | — |
| 618 | #121 | — | 158 | 1 | no | — |
| 619 | #121 | — | 158 | 1 | no | — |
| 620 | #121 | — | 158 | 1 | no | — |
| 621 | #121 | — | 158 | 1 | no | — |
| 622 | #121 | — | 158 | 1 | no | — |
| 623 | #121 | — | 158 | 1 | no | — |
| 624 | #121 | — | 158 | 1 | no | — |
| 625 | #120 | — | 2 | 1 | no | — |
| 626 | #120 | — | 316 | 1 | no | — |
| 627 | #120 | — | 158 | 2 | no | — |
| 628 | #120 | — | 158 | 1 | no | — |
| 629 | #120 | — | 158 | 1 | no | — |
| 630 | #120 | — | 158 | 1 | no | — |
| 631 | #120 | D316 | 1 | 1 | yes | characteristic |
| 632 | #120 | C22×D79 | 1 | 1 | yes | characteristic |
| 633 | C4×Q8 | — | 158 | 1 | no | — |
| 634 | C4×D4 | — | 158 | 1 | no | — |
| 635 | C4×D4 | — | 158 | 1 | no | — |
| 636 | C4×D4 | — | 158 | 1 | no | — |
| 637 | C4×D4 | — | 158 | 1 | no | — |
| 638 | C4×D4 | — | 158 | 1 | no | — |
| 639 | C4×D4 | — | 158 | 1 | no | — |
| 640 | C4×D4 | — | 158 | 1 | no | — |
| 641 | C4×D4 | — | 158 | 1 | no | — |
| 642 | C4×D4 | — | 158 | 1 | no | — |
| 643 | #117 | — | 79 | 1 | no | — |
| 644 | #117 | — | 158 | 1 | no | — |
| 645 | #117 | — | 158 | 1 | no | — |
| 646 | #117 | — | 158 | 1 | no | — |
| 647 | C2×C4⋊C4 | — | 316 | 1 | no | — |
| 648 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 649 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 650 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 651 | C2×C22⋊C4 | — | 316 | 1 | no | — |
| 652 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 653 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 654 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 655 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 656 | C2×C22⋊C4 | D316 | 1 | 1 | yes | characteristic |
| 657 | #104 | — | 158 | 2 | no | — |
| 658 | #104 | — | 158 | 2 | no | — |
| 659 | #100 | — | 2 | 1 | no | — |
| 660 | #100 | C22×D79 | 1 | 2 | yes | — |
| 661 | #99 | — | 2 | 1 | no | — |
| 662 | #99 | — | 79 | 2 | no | — |
| 663 | #99 | — | 158 | 2 | no | — |
| 664 | #99 | — | 158 | 2 | no | — |
| 665 | #99 | — | 158 | 1 | no | — |
| 666 | #99 | — | 158 | 2 | no | — |
| 667 | #99 | — | 158 | 2 | no | — |
| 668 | #99 | C22×D79 | 1 | 2 | yes | — |
| 669 | C24 | — | 158 | 1 | no | — |
| 670 | C24 | — | 158 | 1 | no | — |
| 671 | C24 | D4×D79 | 1 | 1 | yes | characteristic |
| 672 | C24 | C2×D316 | 1 | 1 | yes | characteristic |
| 673 | C24 | C2×D316 | 1 | 1 | yes | characteristic |
| 674 | #41 | — | 316 | 1 | no | — |
| 675 | #41 | — | 316 | 1 | no | — |
| 676 | #41 | — | 316 | 1 | no | — |
| 677 | #41 | — | 316 | 2 | no | — |
| 678 | #41 | — | 316 | 2 | no | — |
| 679 | #41 | — | 316 | 2 | no | — |
| 680 | #41 | — | 316 | 1 | no | — |
| 681 | #41 | — | 316 | 2 | no | — |
| 682 | #41 | — | 632 | 1 | no | — |
| 683 | #41 | — | 632 | 1 | no | — |
| 684 | #41 | — | 158 | 2 | no | — |
| 685 | #41 | — | 158 | 2 | no | — |
| 686 | C2×Q8 | — | 79 | 1 | no | — |
| 687 | C2×Q8 | — | 158 | 1 | no | — |
| 688 | C2×Q8 | — | 158 | 1 | no | — |
| 689 | C2×Q8 | — | 158 | 1 | no | — |
| 690 | C2×D4 | — | 2 | 1 | no | — |
| 691 | C2×D4 | — | 2 | 1 | no | — |
| 692 | C2×D4 | — | 2 | 1 | no | — |
| 693 | C2×D4 | — | 2 | 1 | no | — |
| 694 | C2×D4 | — | 4 | 1 | no | — |
| 695 | C2×D4 | — | 4 | 1 | no | — |
| 696 | C2×D4 | — | 4 | 1 | no | — |
| 697 | C2×D4 | — | 4 | 1 | no | — |
| 698 | C2×D4 | — | 316 | 2 | no | — |
| 699 | C2×D4 | — | 316 | 2 | no | — |
| 700 | C2×D4 | — | 316 | 2 | no | — |
| 701 | C2×D4 | — | 316 | 2 | no | — |
| 702 | C2×D4 | — | 316 | 1 | no | — |
| 703 | C2×D4 | — | 316 | 1 | no | — |
| 704 | C2×D4 | — | 316 | 1 | no | — |
| 705 | C2×D4 | — | 316 | 1 | no | — |
| 706 | C2×D4 | — | 316 | 1 | no | — |
| 707 | C2×D4 | — | 316 | 1 | no | — |
| 708 | C2×D4 | — | 316 | 1 | no | — |
| 709 | C2×D4 | — | 316 | 2 | no | — |
| 710 | C2×D4 | — | 79 | 1 | no | — |
| 711 | C2×D4 | — | 158 | 1 | no | — |
| 712 | C2×D4 | — | 158 | 2 | no | — |
| 713 | C2×D4 | — | 158 | 2 | no | — |
| 714 | C2×D4 | — | 158 | 1 | no | — |
| 715 | C2×D4 | — | 158 | 2 | no | — |
| 716 | C2×D4 | — | 158 | 2 | no | — |
| 717 | C2×D4 | — | 158 | 1 | no | — |
| 718 | C2×D4 | — | 158 | 1 | no | — |
| 719 | C2×D4 | — | 158 | 1 | no | — |
| 720 | C2×D4 | — | 158 | 1 | no | — |
| 721 | C2×D4 | — | 158 | 1 | no | — |
| 722 | C2×D4 | — | 158 | 1 | no | — |
| 723 | C2×D4 | D4×D79 | 1 | 1 | yes | characteristic |
| 724 | C2×D4 | D4×D79 | 1 | 1 | yes | characteristic |
| 725 | C2×D4 | C2×D316 | 1 | 1 | yes | characteristic |
| 726 | C2×D4 | C23×D79 | 1 | 1 | yes | characteristic |
| 727 | C22×C4 | — | 2 | 1 | no | — |
| 728 | C22×C4 | — | 4 | 1 | no | — |
| 729 | C22×C4 | — | 316 | 1 | no | — |
| 730 | C22×C4 | — | 316 | 1 | no | — |
| 731 | C22×C4 | — | 316 | 1 | no | — |
| 732 | C22×C4 | — | 316 | 1 | no | — |
| 733 | C22×C4 | — | 79 | 1 | no | — |
| 734 | C22×C4 | — | 79 | 1 | no | — |
| 735 | C22×C4 | — | 158 | 1 | no | — |
| 736 | C22×C4 | — | 158 | 1 | no | — |
| 737 | C22×C4 | — | 158 | 1 | no | — |
| 738 | C22×C4 | — | 158 | 1 | no | — |
| 739 | C22×C4 | — | 158 | 1 | no | — |
| 740 | C22×C4 | — | 158 | 1 | no | — |
| 741 | C22×C4 | — | 158 | 1 | no | — |
| 742 | C22×C4 | — | 158 | 1 | no | — |
| 743 | C22×C4 | — | 158 | 1 | no | — |
| 744 | C22×C4 | — | 158 | 1 | no | — |
| 745 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 746 | C22×C4 | C2×D316 | 1 | 1 | yes | characteristic |
| 747 | Q16 | — | 316 | 2 | no | — |
| 748 | SD16 | — | 316 | 2 | no | — |
| 749 | SD16 | — | 316 | 2 | no | — |
| 750 | D8 | — | 316 | 2 | no | — |
| 751 | M16 | — | 2 | 2 | no | — |
| 752 | M16 | — | 4 | 1 | no | — |
| 753 | C2×C8 | — | 4 | 1 | no | — |
| 754 | C4⋊C4 | — | 2 | 1 | no | — |
| 755 | C4⋊C4 | — | 2 | 1 | no | — |
| 756 | C4⋊C4 | — | 316 | 2 | no | — |
| 757 | C4⋊C4 | — | 316 | 2 | no | — |
| 758 | C4⋊C4 | — | 316 | 2 | no | — |
| 759 | C4⋊C4 | — | 158 | 1 | no | — |
| 760 | C4⋊C4 | — | 158 | 1 | no | — |
| 761 | C4⋊C4 | — | 158 | 1 | no | — |
| 762 | C4⋊C4 | — | 158 | 1 | no | — |
| 763 | C4⋊C4 | — | 158 | 1 | no | — |
| 764 | C4⋊C4 | — | 158 | 1 | no | — |
| 765 | C4⋊C4 | — | 158 | 1 | no | — |
| 766 | C4⋊C4 | — | 158 | 1 | no | — |
| 767 | C4⋊C4 | — | 158 | 1 | no | — |
| 768 | C4⋊C4 | — | 158 | 1 | no | — |
| 769 | C4⋊C4 | — | 158 | 1 | no | — |
| 770 | C4⋊C4 | — | 158 | 1 | no | — |
| 771 | C4⋊C4 | — | 158 | 1 | no | — |
| 772 | C4⋊C4 | — | 158 | 1 | no | — |
| 773 | C4⋊C4 | — | 158 | 1 | no | — |
| 774 | C4⋊C4 | — | 158 | 1 | no | — |
| 775 | C4⋊C4 | — | 158 | 1 | no | — |
| 776 | C22⋊C4 | — | 2 | 1 | no | — |
| 777 | C22⋊C4 | — | 2 | 1 | no | — |
| 778 | C22⋊C4 | — | 2 | 1 | no | — |
| 779 | C22⋊C4 | — | 2 | 1 | no | — |
| 780 | C22⋊C4 | — | 2 | 1 | no | — |
| 781 | C22⋊C4 | — | 2 | 2 | no | — |
| 782 | C22⋊C4 | — | 4 | 1 | no | — |
| 783 | C22⋊C4 | — | 316 | 2 | no | — |
| 784 | C22⋊C4 | — | 316 | 2 | no | — |
| 785 | C22⋊C4 | — | 316 | 2 | no | — |
| 786 | C22⋊C4 | — | 316 | 1 | no | — |
| 787 | C22⋊C4 | — | 316 | 2 | no | — |
| 788 | C22⋊C4 | — | 79 | 1 | no | — |
| 789 | C22⋊C4 | — | 79 | 1 | no | — |
| 790 | C22⋊C4 | — | 158 | 1 | no | — |
| 791 | C22⋊C4 | — | 158 | 1 | no | — |
| 792 | C22⋊C4 | — | 158 | 1 | no | — |
| 793 | C22⋊C4 | — | 158 | 1 | no | — |
| 794 | C22⋊C4 | — | 158 | 2 | no | — |
| 795 | C22⋊C4 | — | 158 | 1 | no | — |
| 796 | C22⋊C4 | — | 158 | 1 | no | — |
| 797 | C22⋊C4 | — | 158 | 1 | no | — |
| 798 | C22⋊C4 | — | 158 | 1 | no | — |
| 799 | C22⋊C4 | — | 158 | 1 | no | — |
| 800 | C22⋊C4 | — | 158 | 1 | no | — |
| 801 | C22⋊C4 | — | 158 | 1 | no | — |
| 802 | C22⋊C4 | — | 158 | 1 | no | — |
| 803 | C22⋊C4 | — | 158 | 1 | no | — |
| 804 | C22⋊C4 | — | 158 | 1 | no | — |
| 805 | C22⋊C4 | — | 158 | 1 | no | — |
| 806 | C22⋊C4 | — | 158 | 1 | no | — |
| 807 | C22⋊C4 | — | 158 | 1 | no | — |
| 808 | C22⋊C4 | — | 158 | 1 | no | — |
| 809 | C22⋊C4 | C2×D316 | 1 | 1 | yes | characteristic |
| 810 | C22⋊C4 | C2×D316 | 1 | 1 | yes | characteristic |
| 811 | C42 | — | 79 | 1 | no | — |
| 812 | C42 | — | 79 | 1 | no | — |
| 813 | C42 | — | 158 | 1 | no | — |
| 814 | C42 | — | 158 | 1 | no | — |
| 815 | C42 | — | 158 | 1 | no | — |
| 816 | C42 | — | 158 | 1 | no | — |
| 817 | C23 | — | 2 | 1 | no | — |
| 818 | C23 | — | 2 | 1 | no | — |
| 819 | C23 | — | 2 | 1 | no | — |
| 820 | C23 | — | 2 | 1 | no | — |
| 821 | C23 | — | 2 | 1 | no | — |
| 822 | C23 | — | 4 | 1 | no | — |
| 823 | C23 | — | 8 | 1 | no | — |
| 824 | C23 | — | 8 | 1 | no | — |
| 825 | C23 | — | 8 | 1 | no | — |
| 826 | C23 | — | 316 | 1 | no | — |
| 827 | C23 | — | 316 | 1 | no | — |
| 828 | C23 | — | 316 | 1 | no | — |
| 829 | C23 | — | 632 | 2 | no | — |
| 830 | C23 | — | 158 | 2 | no | — |
| 831 | C23 | — | 158 | 2 | no | — |
| 832 | C23 | — | 158 | 1 | no | — |
| 833 | C23 | — | 1264 | 1 | no | — |
| 834 | C23 | #14579131 | 1 | 1 | yes | characteristic |
| 835 | C23 | #14579131 | 1 | 1 | yes | characteristic |
| 836 | C23 | #14579131 | 1 | 1 | yes | characteristic |
| 837 | C23 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 838 | C23 | C22×D316 | 1 | 1 | yes | characteristic |
| 839 | Q8 | — | 316 | 1 | no | — |
| 840 | Q8 | — | 316 | 1 | no | — |
| 841 | Q8 | — | 632 | 1 | no | — |
| 842 | Q8 | — | 632 | 1 | no | — |
| 843 | Q8 | — | 158 | 2 | no | — |
| 844 | D4 | — | 4 | 1 | no | — |
| 845 | D4 | — | 4 | 1 | no | — |
| 846 | D4 | — | 4 | 1 | no | — |
| 847 | D4 | — | 4 | 1 | no | — |
| 848 | D4 | — | 4 | 1 | no | — |
| 849 | D4 | — | 4 | 1 | no | — |
| 850 | D4 | — | 8 | 1 | no | — |
| 851 | D4 | — | 8 | 1 | no | — |
| 852 | D4 | — | 8 | 1 | no | — |
| 853 | D4 | — | 316 | 1 | no | — |
| 854 | D4 | — | 316 | 1 | no | — |
| 855 | D4 | — | 316 | 2 | no | — |
| 856 | D4 | — | 316 | 2 | no | — |
| 857 | D4 | — | 316 | 2 | no | — |
| 858 | D4 | — | 316 | 2 | no | — |
| 859 | D4 | — | 316 | 2 | no | — |
| 860 | D4 | — | 316 | 1 | no | — |
| 861 | D4 | — | 316 | 1 | no | — |
| 862 | D4 | — | 316 | 2 | no | — |
| 863 | D4 | — | 632 | 1 | no | — |
| 864 | D4 | — | 632 | 1 | no | — |
| 865 | D4 | — | 632 | 1 | no | — |
| 866 | D4 | — | 632 | 1 | no | — |
| 867 | D4 | — | 632 | 1 | no | — |
| 868 | D4 | — | 632 | 1 | no | — |
| 869 | D4 | — | 158 | 2 | no | — |
| 870 | D4 | — | 1264 | 2 | no | — |
| 871 | C2×C4 | — | 2 | 1 | no | — |
| 872 | C2×C4 | — | 2 | 1 | no | — |
| 873 | C2×C4 | — | 2 | 1 | no | — |
| 874 | C2×C4 | — | 2 | 1 | no | — |
| 875 | C2×C4 | — | 2 | 1 | no | — |
| 876 | C2×C4 | — | 4 | 1 | no | — |
| 877 | C2×C4 | — | 4 | 2 | no | — |
| 878 | C2×C4 | — | 8 | 1 | no | — |
| 879 | C2×C4 | — | 8 | 2 | no | — |
| 880 | C2×C4 | — | 316 | 2 | no | — |
| 881 | C2×C4 | — | 316 | 2 | no | — |
| 882 | C2×C4 | — | 316 | 1 | no | — |
| 883 | C2×C4 | — | 316 | 1 | no | — |
| 884 | C2×C4 | — | 316 | 1 | no | — |
| 885 | C2×C4 | — | 316 | 1 | no | — |
| 886 | C2×C4 | — | 316 | 1 | no | — |
| 887 | C2×C4 | — | 316 | 1 | no | — |
| 888 | C2×C4 | — | 316 | 1 | no | — |
| 889 | C2×C4 | — | 316 | 2 | no | — |
| 890 | C2×C4 | — | 632 | 1 | no | — |
| 891 | C2×C4 | — | 632 | 1 | no | — |
| 892 | C2×C4 | — | 632 | 1 | no | — |
| 893 | C2×C4 | — | 632 | 1 | no | — |
| 894 | C2×C4 | — | 632 | 1 | no | — |
| 895 | C2×C4 | — | 632 | 1 | no | — |
| 896 | C2×C4 | — | 632 | 1 | no | — |
| 897 | C2×C4 | — | 158 | 2 | no | — |
| 898 | C2×C4 | — | 158 | 2 | no | — |
| 899 | C2×C4 | — | 158 | 1 | no | — |
| 900 | C2×C4 | — | 158 | 1 | no | — |
| 901 | C2×C4 | — | 158 | 1 | no | — |
| 902 | C2×C4 | — | 158 | 1 | no | — |
| 903 | C2×C4 | — | 158 | 1 | no | — |
| 904 | C2×C4 | — | 158 | 1 | no | — |
| 905 | C2×C4 | — | 158 | 1 | no | — |
| 906 | C2×C4 | — | 1264 | 1 | no | — |
| 907 | C2×C4 | #14579131 | 1 | 1 | yes | characteristic |
| 908 | C2×C4 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 909 | C8 | — | 4 | 2 | no | — |
| 910 | C22 | — | 2 | 1 | no | — |
| 911 | C22 | — | 2 | 1 | no | — |
| 912 | C22 | — | 2 | 1 | no | — |
| 913 | C22 | — | 2 | 1 | no | — |
| 914 | C22 | — | 4 | 1 | no | — |
| 915 | C22 | — | 4 | 1 | no | — |
| 916 | C22 | — | 4 | 1 | no | — |
| 917 | C22 | — | 4 | 1 | no | — |
| 918 | C22 | — | 4 | 1 | no | — |
| 919 | C22 | — | 4 | 2 | no | — |
| 920 | C22 | — | 4 | 1 | no | — |
| 921 | C22 | — | 4 | 1 | no | — |
| 922 | C22 | — | 4 | 1 | no | — |
| 923 | C22 | — | 8 | 1 | no | — |
| 924 | C22 | — | 8 | 1 | no | — |
| 925 | C22 | — | 8 | 1 | no | — |
| 926 | C22 | — | 8 | 2 | no | — |
| 927 | C22 | — | 316 | 1 | no | — |
| 928 | C22 | — | 316 | 1 | no | — |
| 929 | C22 | — | 316 | 2 | no | — |
| 930 | C22 | — | 316 | 1 | no | — |
| 931 | C22 | — | 632 | 2 | no | — |
| 932 | C22 | — | 632 | 2 | no | — |
| 933 | C22 | — | 632 | 2 | no | — |
| 934 | C22 | — | 1264 | 1 | no | — |
| 935 | C22 | — | 1264 | 1 | no | — |
| 936 | C22 | #19098751 | 1 | 1 | yes | characteristic |
| 937 | C22 | #19098751 | 1 | 1 | yes | characteristic |
| 938 | C22 | C2×#14579131 | 1 | 1 | yes | characteristic |
| 939 | C4 | — | 2 | 1 | no | — |
| 940 | C4 | — | 2 | 1 | no | — |
| 941 | C4 | — | 4 | 1 | no | — |
| 942 | C4 | — | 4 | 1 | no | — |
| 943 | C4 | — | 4 | 1 | no | — |
| 944 | C4 | — | 8 | 2 | no | — |
| 945 | C4 | — | 316 | 1 | no | — |
| 946 | C4 | — | 316 | 1 | no | — |
| 947 | C4 | — | 316 | 1 | no | — |
| 948 | C4 | — | 316 | 1 | no | — |
| 949 | C4 | — | 316 | 2 | no | — |
| 950 | C4 | — | 316 | 1 | no | — |
| 951 | C4 | — | 316 | 1 | no | — |
| 952 | C4 | — | 316 | 1 | no | — |
| 953 | C4 | — | 632 | 2 | no | — |
| 954 | C2 | — | 2 | 1 | no | — |
| 955 | C2 | — | 2 | 1 | no | — |
| 956 | C2 | — | 2 | 1 | no | — |
| 957 | C2 | — | 4 | 1 | no | — |
| 958 | C2 | — | 4 | 1 | no | — |
| 959 | C2 | — | 4 | 1 | no | — |
| 960 | C2 | — | 4 | 1 | no | — |
| 961 | C2 | — | 8 | 1 | no | — |
| 962 | C2 | — | 632 | 1 | no | — |
| 963 | C2 | — | 632 | 2 | no | — |
| 964 | C2 | C2×#19098751 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23777561 | C2 | semidirect |
| 2. #23772796 | C2 | semidirect |
| 3. C2×#19098754 | C2 | semidirect |
| 4. #23772760 | C2 | semidirect |
| 5. #23765414 | C2 | semidirect |
| 6. #23765409 | C2 | semidirect |
| 7. #23765397 | C2 | semidirect |
| 8. #23765392 | C2 | semidirect |
| 9. #23765067 | C2 | semidirect |
| 10. C2×#19098354 | C2 | semidirect |
| 11. C79×#2121 | C2 | semidirect |
| 14. #19099316 | C22 | semidirect |
| 16. #19099302 | C22 | semidirect |
| 17. #19099297 | C22 | semidirect |
| 20. #19099244 | C22 | semidirect |
| 50. #19098357 | C22 | semidirect |
| 51. #19098355 | C22 | semidirect |
| 52. #19098354 | C22 | semidirect |
| 53. #19098354 | C22 | semidirect |
| 57. #352×C79 | C22 | semidirect |
| 58. AΣL(1,𝔽16)×C79 | C22 | semidirect |
| 65. C2×#11929624 | D4 | semidirect |
| 71. C23×Dic79 | D4 | semidirect |
| 78. #14579157 | D4 | semidirect |
| 91. #14579148 | D4 | semidirect |
| 111. #14579142 | D4 | semidirect |
| 112. #14579142 | D4 | semidirect |
| 150. #14579120 | D4 | semidirect |
| 159. C2×C22⋊Dic79 | D4 | semidirect |
| 492. #2121 | D79 | semidirect |
| 494. C79 | #33552 | semidirect |
| 540. #352 | C2×D79 | semidirect |
| 541. AΣL(1,𝔽16) | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777561 | 2 |
| #23772796 | 2 |
| C2×#19098754 | 2 |
| #23772760 | 2 |
| #23765414 | 2 |
| #23765409 | 2 |
| #23765397 | 2 |
| #23765392 | 2 |
| #23765067 | 2 |
| C2×#19098354 | 2 |
| C79×#2121 | 2 |
| #33552 | 79 |