Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1276 conjugacy classes of subgroups.
The subgroup lattice has 812 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23777157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #23774200 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #23774197 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23769287 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23762438 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #23762421 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #23762336 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #23762319 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #23761928 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #23761736 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C79×#1510 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14579206 | — | 2 | 1 | no | — |
| 13 | #19099214 | — | 2 | 1 | no | — |
| 14 | #19099213 | — | 2 | 1 | no | — |
| 15 | #19099203 | — | 2 | 2 | no | — |
| 16 | #19099202 | — | 2 | 2 | no | — |
| 17 | #19099197 | — | 2 | 1 | no | — |
| 18 | D4×C22⋊D79 | — | 2 | 1 | no | — |
| 19 | #19099140 | C22 | 1 | 2 | yes | — |
| 20 | #19099122 | — | 2 | 1 | no | — |
| 21 | #19099121 | C22 | 1 | 2 | yes | — |
| 22 | #19099108 | — | 2 | 1 | no | — |
| 23 | C2×#14579135 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#14579135 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #121×D79 | — | 2 | 1 | no | — |
| 26 | C2×C4×C22⋊D79 | C22 | 1 | 1 | yes | characteristic |
| 27 | #19098882 | — | 2 | 1 | no | — |
| 28 | #19098882 | C22 | 1 | 2 | yes | complemented |
| 29 | #19098881 | — | 2 | 1 | no | — |
| 30 | #19098879 | C22 | 1 | 2 | yes | complemented |
| 31 | #19098816 | — | 2 | 2 | no | — |
| 32 | #19098814 | — | 2 | 2 | no | — |
| 33 | #19098699 | — | 2 | 1 | no | — |
| 34 | #19098699 | C22 | 1 | 2 | yes | complemented |
| 35 | #19098697 | — | 2 | 1 | no | — |
| 36 | #19098696 | C22 | 1 | 2 | yes | complemented |
| 37 | #19098527 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #19098503 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #19098500 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #19098481 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #19098479 | — | 2 | 1 | no | — |
| 42 | #19098473 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #19098472 | — | 2 | 1 | no | — |
| 44 | #19098455 | — | 2 | 1 | no | — |
| 45 | #19098441 | — | 2 | 1 | no | — |
| 46 | #19098296 | C22 | 1 | 2 | yes | complemented |
| 47 | #19098296 | C22 | 1 | 2 | yes | complemented |
| 48 | #19098288 | C22 | 1 | 2 | yes | complemented |
| 49 | #19098286 | C22 | 1 | 2 | yes | complemented |
| 50 | C2×#121×C79 | C22 | 1 | 1 | yes | characteristic |
| 51 | #407×C79 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | #381×C79 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #327×C79 | C22 | 1 | 2 | yes | complemented |
| 54 | #327×C79 | C22 | 1 | 2 | yes | complemented |
| 55 | #14579206 | — | 4 | 4 | no | — |
| 56 | #14579206 | — | 4 | 4 | no | — |
| 57 | C2×#11929624 | — | 2 | 2 | no | — |
| 58 | C2×#11929623 | — | 2 | 2 | no | — |
| 59 | C2×#11929623 | — | 2 | 2 | no | — |
| 60 | C22×D316 | — | 2 | 1 | no | — |
| 61 | C22×D316 | D4 | 1 | 1 | yes | characteristic, complemented |
| 62 | C22×D316 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×C22⋊D79 | — | 2 | 2 | no | — |
| 64 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 65 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 66 | C22×C22⋊D79 | D4 | 1 | 1 | yes | characteristic |
| 67 | C2×D4×D79 | — | 2 | 2 | no | — |
| 68 | C2×D4×D79 | — | 2 | 2 | no | — |
| 69 | C2×D4×D79 | — | 2 | 1 | no | — |
| 70 | C22×C4×D79 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×D632 | — | 2 | 2 | no | — |
| 72 | C2×#11929609 | — | 2 | 2 | no | — |
| 73 | C2×#11929608 | — | 2 | 1 | no | — |
| 74 | #14579160 | — | 2 | 1 | no | — |
| 75 | #14579157 | — | 2 | 1 | no | — |
| 76 | #14579147 | — | 2 | 2 | no | — |
| 77 | #14579146 | — | 2 | 2 | no | — |
| 78 | #14579144 | — | 2 | 2 | no | — |
| 79 | #14579143 | — | 2 | 2 | no | — |
| 80 | #14579142 | — | 2 | 2 | no | — |
| 81 | #14579139 | — | 2 | 2 | no | — |
| 82 | #14579138 | — | 2 | 2 | no | — |
| 83 | #14579136 | — | 2 | 1 | no | — |
| 84 | #14579135 | — | 2 | 1 | no | — |
| 85 | #14579135 | — | 2 | 1 | no | — |
| 86 | #14579135 | — | 2 | 1 | no | — |
| 87 | #14579135 | — | 2 | 1 | no | — |
| 88 | #14579135 | — | 2 | 1 | no | — |
| 89 | #14579135 | — | 2 | 1 | no | — |
| 90 | #14579135 | D4 | 1 | 2 | yes | complemented |
| 91 | #14579135 | C23 | 1 | 2 | yes | — |
| 92 | #14579134 | — | 2 | 2 | no | — |
| 93 | #14579134 | — | 2 | 2 | no | — |
| 94 | #14579133 | — | 2 | 2 | no | — |
| 95 | #14579133 | — | 2 | 2 | no | — |
| 96 | #14579133 | — | 2 | 2 | no | — |
| 97 | #14579132 | — | 2 | 1 | no | — |
| 98 | #14579131 | — | 2 | 2 | no | — |
| 99 | #14579130 | — | 2 | 2 | no | — |
| 100 | #14579129 | — | 2 | 2 | no | — |
| 101 | #14579129 | — | 2 | 2 | no | — |
| 102 | D4×Dic79 | — | 2 | 1 | no | — |
| 103 | #14579123 | — | 2 | 1 | no | — |
| 104 | C4×C22⋊D79 | — | 2 | 1 | no | — |
| 105 | C4×C22⋊D79 | — | 2 | 1 | no | — |
| 106 | C4×C22⋊D79 | — | 2 | 1 | no | — |
| 107 | C4×C22⋊D79 | — | 2 | 1 | no | — |
| 108 | (C22⋊D79)⋊C4 | — | 2 | 2 | no | — |
| 109 | C2×C4⋊Dic79 | — | 2 | 1 | no | — |
| 110 | C2×C4⋊Dic79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 111 | C2×C4⋊Dic79 | C23 | 1 | 1 | yes | characteristic |
| 112 | C2×Dic79⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 113 | C4⋊C4×D79 | — | 2 | 1 | no | — |
| 114 | C2×C22⋊Dic79 | D4 | 1 | 1 | yes | characteristic |
| 115 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 116 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 117 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 118 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 119 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 120 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 121 | C2×(C2×D79)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 122 | C22⋊C4×D79 | — | 2 | 2 | no | — |
| 123 | C2×C4×Dic79 | D4 | 1 | 1 | yes | characteristic |
| 124 | #14579093 | — | 2 | 2 | no | — |
| 125 | #14579092 | — | 2 | 2 | no | — |
| 126 | #14579083 | — | 2 | 2 | no | — |
| 127 | #14579083 | — | 2 | 2 | no | — |
| 128 | #14579082 | — | 2 | 2 | no | — |
| 129 | #14579081 | — | 2 | 2 | no | — |
| 130 | C22⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 131 | C22⋊(C79⋊C8) | C23 | 1 | 2 | yes | — |
| 132 | C79⋊#95 | — | 2 | 1 | no | — |
| 133 | C79⋊#95 | — | 2 | 1 | no | — |
| 134 | C22×D4×C79 | — | 2 | 1 | no | — |
| 135 | C22×D4×C79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 136 | C23×C4×C79 | C23 | 1 | 1 | yes | characteristic |
| 137 | C2×M16×C79 | — | 2 | 1 | no | — |
| 138 | #121×C79 | — | 2 | 1 | no | — |
| 139 | #121×C79 | — | 2 | 1 | no | — |
| 140 | #121×C79 | D4 | 1 | 2 | yes | complemented |
| 141 | #121×C79 | C23 | 1 | 2 | yes | — |
| 142 | C2×C4⋊C4×C79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 143 | C2×C22⋊C4×C79 | — | 2 | 1 | no | — |
| 144 | C2×C22⋊C4×C79 | — | 2 | 1 | no | — |
| 145 | C22⋊C8×C79 | — | 2 | 1 | no | — |
| 146 | C22⋊C8×C79 | C23 | 1 | 2 | yes | — |
| 147 | #95×C79 | — | 2 | 1 | no | — |
| 148 | #95×C79 | C23 | 1 | 1 | yes | characteristic |
| 149 | #95×C79 | C23 | 1 | 1 | yes | characteristic |
| 150 | C23×D79 | — | 2 | 2 | no | — |
| 151 | C23×D79 | — | 2 | 1 | no | — |
| 152 | C23×D79 | — | 2 | 1 | no | — |
| 153 | C23×D79 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | #11929624 | — | 4 | 8 | no | — |
| 155 | #11929623 | — | 4 | 8 | no | — |
| 156 | #11929623 | — | 4 | 4 | no | — |
| 157 | #11929623 | — | 4 | 4 | no | — |
| 158 | C2×Dic158 | — | 2 | 2 | no | — |
| 159 | C2×D316 | — | 2 | 2 | no | — |
| 160 | C2×D316 | — | 2 | 1 | no | — |
| 161 | C2×D316 | — | 2 | 1 | no | — |
| 162 | C2×D316 | — | 2 | 1 | no | — |
| 163 | C2×D316 | — | 4 | 2 | no | — |
| 164 | C2×D316 | — | 8 | 1 | no | — |
| 165 | C2×D316 | — | 8 | 1 | no | — |
| 166 | C2×D316 | — | 8 | 1 | no | — |
| 167 | C2×D316 | — | 8 | 1 | no | — |
| 168 | C2×D316 | C2×D4 | 1 | 2 | yes | — |
| 169 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 170 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 171 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 172 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 173 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 174 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 175 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 176 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 177 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 178 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 179 | C2×C22⋊D79 | — | 4 | 8 | no | — |
| 180 | C2×C22⋊D79 | — | 4 | 2 | no | — |
| 181 | C2×C22⋊D79 | — | 4 | 2 | no | — |
| 182 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 183 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 184 | C2×C22⋊D79 | — | 8 | 1 | no | — |
| 185 | C2×C22⋊D79 | — | 8 | 1 | no | — |
| 186 | D4×D79 | — | 4 | 8 | no | — |
| 187 | D4×D79 | — | 4 | 4 | no | — |
| 188 | D4×D79 | — | 4 | 4 | no | — |
| 189 | D4×D79 | — | 8 | 2 | no | — |
| 190 | C22×Dic79 | — | 2 | 2 | no | — |
| 191 | C22×Dic79 | — | 2 | 1 | no | — |
| 192 | C22×Dic79 | — | 2 | 1 | no | — |
| 193 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C2×C4×D79 | — | 2 | 2 | no | — |
| 197 | C2×C4×D79 | — | 2 | 2 | no | — |
| 198 | C2×C4×D79 | — | 2 | 1 | no | — |
| 199 | C2×C4×D79 | — | 2 | 1 | no | — |
| 200 | C2×C4×D79 | — | 8 | 1 | no | — |
| 201 | D632 | — | 8 | 2 | no | — |
| 202 | #11929609 | — | 8 | 2 | no | — |
| 203 | #11929608 | — | 8 | 1 | no | — |
| 204 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 205 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 206 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 207 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 208 | C4⋊Dic79 | — | 8 | 1 | no | — |
| 209 | C4⋊Dic79 | C2×D4 | 1 | 2 | yes | — |
| 210 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 211 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 212 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 213 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 214 | C22⋊Dic79 | — | 2 | 2 | no | — |
| 215 | C22⋊Dic79 | — | 2 | 2 | no | — |
| 216 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 217 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 218 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 219 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 220 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 221 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 222 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 223 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 224 | (C2×D79)⋊C4 | — | 4 | 2 | no | — |
| 225 | (C2×D79)⋊C4 | — | 4 | 1 | no | — |
| 226 | (C2×D79)⋊C4 | — | 4 | 1 | no | — |
| 227 | (C2×D79)⋊C4 | — | 8 | 1 | no | — |
| 228 | (C2×D79)⋊C4 | — | 8 | 1 | no | — |
| 229 | (C2×D79)⋊C4 | — | 8 | 1 | no | — |
| 230 | C4×Dic79 | — | 2 | 1 | no | — |
| 231 | C4×Dic79 | — | 2 | 1 | no | — |
| 232 | C24×C79 | — | 2 | 1 | no | — |
| 233 | C24×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C2×D4×C79 | — | 2 | 2 | no | — |
| 235 | C2×D4×C79 | — | 2 | 2 | no | — |
| 236 | C2×D4×C79 | — | 2 | 1 | no | — |
| 237 | C2×D4×C79 | — | 4 | 2 | no | — |
| 238 | C2×D4×C79 | — | 4 | 2 | no | — |
| 239 | C2×D4×C79 | — | 8 | 1 | no | — |
| 240 | C2×D4×C79 | C2×D4 | 1 | 2 | yes | — |
| 241 | C22×C4×C79 | — | 2 | 1 | no | — |
| 242 | C22×C4×C79 | — | 2 | 1 | no | — |
| 243 | C22×C4×C79 | — | 2 | 1 | no | — |
| 244 | C22×C4×C79 | — | 8 | 1 | no | — |
| 245 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 247 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C22×C4×C79 | C24 | 1 | 1 | yes | characteristic |
| 251 | M16×C79 | — | 8 | 1 | no | — |
| 252 | C2×C8×C79 | — | 2 | 2 | no | — |
| 253 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 254 | C4⋊C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 255 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 256 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 257 | C22⋊C4×C79 | — | 8 | 1 | no | — |
| 258 | C23×C79 | — | 2 | 1 | no | — |
| 259 | C23×C79 | — | 2 | 1 | no | — |
| 260 | C23×C79 | — | 2 | 2 | no | — |
| 261 | C23×C79 | — | 4 | 1 | no | — |
| 262 | C23×C79 | — | 4 | 1 | no | — |
| 263 | C23×C79 | — | 4 | 2 | no | — |
| 264 | C23×C79 | — | 8 | 1 | no | — |
| 265 | C23×C79 | — | 8 | 1 | no | — |
| 266 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 267 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 268 | C23×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 269 | C22×D79 | — | 2 | 1 | no | — |
| 270 | C22×D79 | — | 2 | 1 | no | — |
| 271 | C22×D79 | — | 2 | 2 | no | — |
| 272 | C22×D79 | — | 4 | 4 | no | — |
| 273 | C22×D79 | — | 4 | 1 | no | — |
| 274 | C22×D79 | — | 4 | 1 | no | — |
| 275 | C22×D79 | — | 4 | 2 | no | — |
| 276 | C22×D79 | — | 4 | 1 | no | — |
| 277 | C22×D79 | — | 4 | 1 | no | — |
| 278 | C22×D79 | — | 4 | 1 | no | — |
| 279 | C22×D79 | — | 4 | 1 | no | — |
| 280 | C22×D79 | — | 4 | 1 | no | — |
| 281 | C22×D79 | — | 4 | 1 | no | — |
| 282 | C22×D79 | — | 4 | 1 | no | — |
| 283 | C22×D79 | — | 8 | 1 | no | — |
| 284 | C22×D79 | — | 8 | 1 | no | — |
| 285 | C22×D79 | — | 8 | 2 | no | — |
| 286 | C22×D79 | — | 8 | 2 | no | — |
| 287 | C22×D79 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 288 | D4×C79 | — | 4 | 2 | no | — |
| 289 | D4×C79 | — | 4 | 2 | no | — |
| 290 | D4×C79 | — | 4 | 4 | no | — |
| 291 | D4×C79 | — | 4 | 2 | no | — |
| 292 | D4×C79 | — | 4 | 2 | no | — |
| 293 | C2×C4×C79 | — | 2 | 2 | no | — |
| 294 | C2×C4×C79 | — | 4 | 1 | no | — |
| 295 | C2×C4×C79 | — | 4 | 1 | no | — |
| 296 | C2×C4×C79 | — | 4 | 1 | no | — |
| 297 | C2×C4×C79 | — | 4 | 1 | no | — |
| 298 | C2×C4×C79 | — | 4 | 1 | no | — |
| 299 | C2×C4×C79 | — | 4 | 1 | no | — |
| 300 | C2×C4×C79 | — | 4 | 2 | no | — |
| 301 | C2×C4×C79 | — | 4 | 1 | no | — |
| 302 | C2×C4×C79 | — | 4 | 1 | no | — |
| 303 | C2×C4×C79 | — | 4 | 1 | no | — |
| 304 | C2×C4×C79 | — | 4 | 1 | no | — |
| 305 | C2×C4×C79 | — | 4 | 1 | no | — |
| 306 | C2×C4×C79 | — | 4 | 1 | no | — |
| 307 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 308 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 309 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 310 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 311 | C22⋊D79 | — | 2 | 4 | no | — |
| 312 | C22⋊D79 | — | 2 | 4 | no | — |
| 313 | C22⋊D79 | — | 4 | 4 | no | — |
| 314 | C22⋊D79 | — | 4 | 4 | no | — |
| 315 | C22⋊D79 | — | 4 | 4 | no | — |
| 316 | C22⋊D79 | — | 4 | 2 | no | — |
| 317 | C22⋊D79 | — | 4 | 2 | no | — |
| 318 | C22⋊D79 | — | 8 | 2 | no | — |
| 319 | C22⋊D79 | — | 8 | 2 | no | — |
| 320 | C22⋊D79 | — | 8 | 2 | no | — |
| 321 | C22⋊D79 | — | 8 | 2 | no | — |
| 322 | C2×Dic79 | — | 2 | 1 | no | — |
| 323 | C2×Dic79 | — | 2 | 1 | no | — |
| 324 | C2×Dic79 | — | 2 | 1 | no | — |
| 325 | C2×Dic79 | — | 2 | 1 | no | — |
| 326 | C2×Dic79 | — | 2 | 2 | no | — |
| 327 | C2×Dic79 | — | 4 | 4 | no | — |
| 328 | C2×Dic79 | — | 4 | 2 | no | — |
| 329 | C2×Dic79 | — | 4 | 1 | no | — |
| 330 | C2×Dic79 | — | 4 | 1 | no | — |
| 331 | C2×Dic79 | — | 4 | 1 | no | — |
| 332 | C2×Dic79 | — | 4 | 1 | no | — |
| 333 | C2×Dic79 | — | 4 | 1 | no | — |
| 334 | C2×Dic79 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 335 | D316 | — | 4 | 2 | no | — |
| 336 | D316 | — | 4 | 2 | no | — |
| 337 | D316 | — | 4 | 2 | no | — |
| 338 | D316 | — | 4 | 2 | no | — |
| 339 | D316 | — | 4 | 4 | no | — |
| 340 | D316 | — | 8 | 4 | no | — |
| 341 | C4×D79 | — | 4 | 4 | no | — |
| 342 | C4×D79 | — | 4 | 2 | no | — |
| 343 | C4×D79 | — | 4 | 4 | no | — |
| 344 | C4×D79 | — | 8 | 1 | no | — |
| 345 | Dic158 | — | 4 | 4 | no | — |
| 346 | C8×C79 | — | 4 | 2 | no | — |
| 347 | C79⋊C8 | — | 4 | 2 | no | — |
| 348 | C22×C79 | — | 2 | 1 | no | — |
| 349 | C22×C79 | — | 2 | 1 | no | — |
| 350 | C22×C79 | — | 2 | 1 | no | — |
| 351 | C22×C79 | — | 2 | 1 | no | — |
| 352 | C22×C79 | — | 2 | 1 | no | — |
| 353 | C22×C79 | — | 2 | 1 | no | — |
| 354 | C22×C79 | — | 2 | 1 | no | — |
| 355 | C22×C79 | — | 2 | 1 | no | — |
| 356 | C22×C79 | — | 4 | 2 | no | — |
| 357 | C22×C79 | — | 4 | 2 | no | — |
| 358 | C22×C79 | — | 4 | 2 | no | — |
| 359 | C22×C79 | — | 8 | 1 | no | — |
| 360 | C22×C79 | — | 8 | 1 | no | — |
| 361 | C22×C79 | — | 16 | 2 | no | — |
| 362 | C22×C79 | C2×#120 | 1 | 1 | yes | characteristic |
| 363 | C22×C79 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 364 | C22×C79 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 365 | C2×D79 | — | 2 | 2 | no | — |
| 366 | C2×D79 | — | 4 | 1 | no | — |
| 367 | C2×D79 | — | 4 | 1 | no | — |
| 368 | C2×D79 | — | 4 | 2 | no | — |
| 369 | C2×D79 | — | 4 | 2 | no | — |
| 370 | C2×D79 | — | 4 | 2 | no | — |
| 371 | C2×D79 | — | 4 | 2 | no | — |
| 372 | C2×D79 | — | 8 | 1 | no | — |
| 373 | C2×D79 | — | 8 | 1 | no | — |
| 374 | C2×D79 | — | 8 | 1 | no | — |
| 375 | C2×D79 | — | 8 | 1 | no | — |
| 376 | C2×D79 | — | 8 | 1 | no | — |
| 377 | C2×D79 | — | 8 | 1 | no | — |
| 378 | C2×D79 | — | 8 | 1 | no | — |
| 379 | C2×D79 | — | 8 | 1 | no | — |
| 380 | C2×D79 | — | 16 | 4 | no | — |
| 381 | C2×D79 | — | 16 | 2 | no | — |
| 382 | C4×C79 | — | 2 | 1 | no | — |
| 383 | C4×C79 | — | 2 | 1 | no | — |
| 384 | C4×C79 | — | 2 | 1 | no | — |
| 385 | C4×C79 | — | 2 | 1 | no | — |
| 386 | C4×C79 | — | 4 | 2 | no | — |
| 387 | C4×C79 | — | 8 | 1 | no | — |
| 388 | C4×C79 | — | 8 | 1 | no | — |
| 389 | Dic79 | — | 2 | 2 | no | — |
| 390 | Dic79 | — | 4 | 2 | no | — |
| 391 | Dic79 | — | 4 | 1 | no | — |
| 392 | Dic79 | — | 4 | 1 | no | — |
| 393 | Dic79 | — | 8 | 1 | no | — |
| 394 | #18350 | — | 79 | 1 | no | maximal, Sylow |
| 395 | C2×C79 | — | 2 | 1 | no | — |
| 396 | C2×C79 | — | 2 | 1 | no | — |
| 397 | C2×C79 | — | 4 | 1 | no | — |
| 398 | C2×C79 | — | 4 | 1 | no | — |
| 399 | C2×C79 | — | 8 | 2 | no | — |
| 400 | C2×C79 | #3003 | 1 | 1 | yes | characteristic |
| 401 | C2×C79 | #3021 | 1 | 1 | yes | characteristic |
| 402 | C2×C79 | #3026 | 1 | 1 | yes | characteristic |
| 403 | D79 | — | 4 | 2 | no | — |
| 404 | D79 | — | 8 | 2 | no | — |
| 405 | D79 | — | 16 | 1 | no | — |
| 406 | #3496 | — | 79 | 1 | no | — |
| 407 | #3192 | — | 79 | 1 | no | — |
| 408 | #3192 | — | 79 | 1 | no | — |
| 409 | #2635 | — | 79 | 1 | no | — |
| 410 | #1616 | — | 79 | 2 | no | — |
| 411 | #1613 | — | 79 | 2 | no | — |
| 412 | #1598 | — | 79 | 2 | no | — |
| 413 | #1595 | — | 79 | 2 | no | — |
| 414 | #1510 | — | 79 | 1 | no | — |
| 415 | #1510 | D79 | 1 | 1 | yes | characteristic, complemented |
| 416 | #1465 | — | 79 | 1 | no | — |
| 417 | C79 | #18350 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 418 | C2×H(5,𝔽2) | — | 158 | 1 | no | — |
| 419 | #547 | — | 158 | 1 | no | — |
| 420 | #547 | — | 158 | 1 | no | — |
| 421 | #546 | — | 158 | 2 | no | — |
| 422 | #546 | — | 158 | 2 | no | — |
| 423 | D42 | — | 158 | 1 | no | — |
| 424 | D42 | — | 158 | 1 | no | — |
| 425 | #537 | — | 79 | 2 | no | — |
| 426 | #534 | — | 79 | 2 | no | — |
| 427 | #534 | — | 158 | 1 | no | — |
| 428 | #532 | — | 158 | 1 | no | — |
| 429 | C2×#121 | — | 79 | 1 | no | — |
| 430 | C2×#121 | — | 79 | 1 | no | — |
| 431 | C2×#121 | — | 158 | 1 | no | — |
| 432 | C2×#121 | C2×D79 | 1 | 1 | yes | characteristic |
| 433 | C2×C4×D4 | — | 79 | 1 | no | — |
| 434 | #481 | — | 79 | 2 | no | — |
| 435 | #481 | — | 79 | 2 | no | — |
| 436 | #481 | — | 158 | 1 | no | — |
| 437 | #481 | — | 158 | 1 | no | — |
| 438 | #469 | — | 158 | 2 | no | — |
| 439 | #469 | — | 158 | 2 | no | — |
| 440 | #447 | — | 79 | 2 | no | — |
| 441 | #447 | — | 79 | 2 | no | — |
| 442 | #447 | — | 158 | 1 | no | — |
| 443 | #447 | — | 158 | 1 | no | — |
| 444 | #407 | — | 79 | 1 | no | — |
| 445 | #407 | C2×D79 | 1 | 1 | yes | characteristic, complemented |
| 446 | #400 | — | 79 | 1 | no | — |
| 447 | #399 | — | 79 | 1 | no | — |
| 448 | #394 | — | 79 | 1 | no | — |
| 449 | #394 | — | 158 | 1 | no | — |
| 450 | #392 | — | 79 | 1 | no | — |
| 451 | #392 | — | 158 | 1 | no | — |
| 452 | #388 | — | 158 | 1 | no | — |
| 453 | #386 | — | 158 | 1 | no | — |
| 454 | #381 | C2×D79 | 1 | 1 | yes | characteristic, complemented |
| 455 | #327 | — | 79 | 2 | no | — |
| 456 | #327 | — | 79 | 2 | no | — |
| 457 | #327 | C2×D79 | 1 | 2 | yes | complemented |
| 458 | #327 | C2×D79 | 1 | 2 | yes | complemented |
| 459 | #324 | — | 79 | 2 | no | — |
| 460 | #323 | — | 79 | 2 | no | — |
| 461 | H(5,𝔽2) | — | 316 | 4 | no | — |
| 462 | H(5,𝔽2) | — | 316 | 4 | no | — |
| 463 | C2×#41 | — | 158 | 2 | no | — |
| 464 | C2×#41 | — | 158 | 2 | no | — |
| 465 | C2×#41 | — | 158 | 2 | no | — |
| 466 | C22×D4 | — | 2 | 1 | no | — |
| 467 | C22×D4 | — | 79 | 1 | no | — |
| 468 | C22×D4 | — | 79 | 1 | no | — |
| 469 | C22×D4 | — | 79 | 1 | no | — |
| 470 | C22×D4 | — | 158 | 1 | no | — |
| 471 | C22×D4 | — | 158 | 2 | no | — |
| 472 | C22×D4 | — | 158 | 2 | no | — |
| 473 | C22×D4 | — | 158 | 1 | no | — |
| 474 | C22×D4 | — | 158 | 2 | no | — |
| 475 | C22×D4 | — | 158 | 1 | no | — |
| 476 | C22×D4 | — | 158 | 1 | no | — |
| 477 | C22×D4 | D316 | 1 | 1 | yes | characteristic, complemented |
| 478 | C23×C4 | — | 79 | 1 | no | — |
| 479 | C23×C4 | C22×D79 | 1 | 1 | yes | characteristic |
| 480 | C2×D8 | — | 158 | 2 | no | — |
| 481 | C2×D8 | — | 158 | 2 | no | — |
| 482 | C2×M16 | — | 2 | 1 | no | — |
| 483 | C2×M16 | — | 158 | 1 | no | — |
| 484 | C4⋊Q8 | — | 158 | 1 | no | — |
| 485 | #127 | — | 158 | 1 | no | — |
| 486 | #124 | — | 158 | 2 | no | — |
| 487 | #123 | — | 158 | 2 | no | — |
| 488 | #123 | — | 158 | 2 | no | — |
| 489 | #123 | — | 158 | 2 | no | — |
| 490 | #123 | — | 158 | 2 | no | — |
| 491 | C22⋊Q8 | — | 158 | 2 | no | — |
| 492 | C22⋊Q8 | — | 158 | 2 | no | — |
| 493 | #121 | — | 2 | 1 | no | — |
| 494 | #121 | — | 2 | 1 | no | — |
| 495 | #121 | — | 79 | 2 | no | — |
| 496 | #121 | — | 79 | 2 | no | — |
| 497 | #121 | — | 158 | 2 | no | — |
| 498 | #121 | — | 158 | 2 | no | — |
| 499 | #121 | — | 158 | 1 | no | — |
| 500 | #121 | — | 158 | 1 | no | — |
| 501 | #121 | — | 158 | 1 | no | — |
| 502 | #121 | — | 158 | 1 | no | — |
| 503 | #121 | — | 158 | 1 | no | — |
| 504 | #121 | — | 158 | 2 | no | — |
| 505 | #121 | — | 158 | 2 | no | — |
| 506 | #121 | — | 158 | 1 | no | — |
| 507 | #121 | — | 158 | 2 | no | — |
| 508 | #121 | — | 158 | 1 | no | — |
| 509 | #121 | — | 158 | 1 | no | — |
| 510 | #121 | D316 | 1 | 2 | yes | complemented |
| 511 | #121 | C22×D79 | 1 | 2 | yes | — |
| 512 | #120 | — | 158 | 2 | no | — |
| 513 | #120 | — | 158 | 2 | no | — |
| 514 | #120 | — | 158 | 2 | no | — |
| 515 | #120 | — | 158 | 2 | no | — |
| 516 | C4×D4 | — | 158 | 2 | no | — |
| 517 | C4×D4 | — | 158 | 1 | no | — |
| 518 | C4×D4 | — | 158 | 1 | no | — |
| 519 | C4×D4 | — | 158 | 1 | no | — |
| 520 | C4×D4 | — | 158 | 1 | no | — |
| 521 | C4×D4 | — | 158 | 1 | no | — |
| 522 | C4×D4 | — | 158 | 1 | no | — |
| 523 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 524 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 525 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 526 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 527 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 528 | C2×C4⋊C4 | D316 | 1 | 1 | yes | characteristic, complemented |
| 529 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 530 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 531 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 532 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 533 | C2×C22⋊C4 | — | 158 | 2 | no | — |
| 534 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 535 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 536 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 537 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 538 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 539 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 540 | C2×C42 | — | 79 | 1 | no | — |
| 541 | #106 | — | 158 | 2 | no | — |
| 542 | #106 | — | 158 | 2 | no | — |
| 543 | #102 | — | 158 | 2 | no | — |
| 544 | #102 | — | 158 | 2 | no | — |
| 545 | #102 | — | 158 | 2 | no | — |
| 546 | #102 | — | 158 | 2 | no | — |
| 547 | C22⋊C8 | — | 2 | 1 | no | — |
| 548 | C22⋊C8 | — | 79 | 2 | no | — |
| 549 | C22⋊C8 | — | 158 | 1 | no | — |
| 550 | C22⋊C8 | C22×D79 | 1 | 2 | yes | — |
| 551 | #95 | — | 2 | 1 | no | — |
| 552 | #95 | — | 158 | 1 | no | — |
| 553 | #95 | — | 158 | 1 | no | — |
| 554 | #95 | C22×D79 | 1 | 1 | yes | characteristic |
| 555 | #95 | C22×D79 | 1 | 1 | yes | characteristic |
| 556 | C24 | — | 2 | 1 | no | — |
| 557 | C24 | — | 79 | 1 | no | — |
| 558 | C24 | — | 158 | 2 | no | — |
| 559 | C24 | — | 158 | 1 | no | — |
| 560 | C24 | — | 158 | 1 | no | — |
| 561 | C24 | D4×D79 | 1 | 1 | yes | characteristic |
| 562 | #41 | — | 316 | 8 | no | — |
| 563 | #41 | — | 316 | 8 | no | — |
| 564 | #41 | — | 316 | 4 | no | — |
| 565 | #41 | — | 316 | 4 | no | — |
| 566 | C2×Q8 | — | 158 | 2 | no | — |
| 567 | C2×D4 | — | 2 | 2 | no | — |
| 568 | C2×D4 | — | 2 | 2 | no | — |
| 569 | C2×D4 | — | 2 | 1 | no | — |
| 570 | C2×D4 | — | 4 | 2 | no | — |
| 571 | C2×D4 | — | 4 | 2 | no | — |
| 572 | C2×D4 | — | 8 | 1 | no | — |
| 573 | C2×D4 | — | 316 | 2 | no | — |
| 574 | C2×D4 | — | 316 | 4 | no | — |
| 575 | C2×D4 | — | 316 | 4 | no | — |
| 576 | C2×D4 | — | 316 | 8 | no | — |
| 577 | C2×D4 | — | 316 | 2 | no | — |
| 578 | C2×D4 | — | 316 | 2 | no | — |
| 579 | C2×D4 | — | 316 | 8 | no | — |
| 580 | C2×D4 | — | 316 | 1 | no | — |
| 581 | C2×D4 | — | 316 | 1 | no | — |
| 582 | C2×D4 | — | 79 | 2 | no | — |
| 583 | C2×D4 | — | 632 | 1 | no | — |
| 584 | C2×D4 | — | 632 | 1 | no | — |
| 585 | C2×D4 | — | 632 | 1 | no | — |
| 586 | C2×D4 | — | 632 | 1 | no | — |
| 587 | C2×D4 | — | 632 | 2 | no | — |
| 588 | C2×D4 | — | 632 | 1 | no | — |
| 589 | C2×D4 | — | 632 | 1 | no | — |
| 590 | C2×D4 | — | 158 | 2 | no | — |
| 591 | C2×D4 | — | 158 | 2 | no | — |
| 592 | C2×D4 | — | 158 | 2 | no | — |
| 593 | C2×D4 | — | 158 | 2 | no | — |
| 594 | C2×D4 | — | 158 | 2 | no | — |
| 595 | C2×D4 | — | 158 | 2 | no | — |
| 596 | C2×D4 | — | 158 | 2 | no | — |
| 597 | C2×D4 | — | 158 | 2 | no | — |
| 598 | C2×D4 | — | 158 | 2 | no | — |
| 599 | C2×D4 | — | 158 | 1 | no | — |
| 600 | C2×D4 | — | 158 | 1 | no | — |
| 601 | C2×D4 | — | 158 | 1 | no | — |
| 602 | C2×D4 | — | 158 | 1 | no | — |
| 603 | C2×D4 | — | 158 | 1 | no | — |
| 604 | C2×D4 | C2×D316 | 1 | 2 | yes | — |
| 605 | C22×C4 | — | 2 | 1 | no | — |
| 606 | C22×C4 | — | 2 | 1 | no | — |
| 607 | C22×C4 | — | 2 | 1 | no | — |
| 608 | C22×C4 | — | 8 | 1 | no | — |
| 609 | C22×C4 | — | 79 | 1 | no | — |
| 610 | C22×C4 | — | 79 | 1 | no | — |
| 611 | C22×C4 | — | 79 | 1 | no | — |
| 612 | C22×C4 | — | 632 | 1 | no | — |
| 613 | C22×C4 | — | 158 | 2 | no | — |
| 614 | C22×C4 | — | 158 | 2 | no | — |
| 615 | C22×C4 | — | 158 | 1 | no | — |
| 616 | C22×C4 | — | 158 | 2 | no | — |
| 617 | C22×C4 | — | 158 | 1 | no | — |
| 618 | C22×C4 | — | 158 | 1 | no | — |
| 619 | C22×C4 | — | 158 | 1 | no | — |
| 620 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 621 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 622 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 623 | C22×C4 | C2×D316 | 1 | 1 | yes | characteristic |
| 624 | C22×C4 | C2×D316 | 1 | 1 | yes | characteristic |
| 625 | C22×C4 | C23×D79 | 1 | 1 | yes | characteristic |
| 626 | D8 | — | 632 | 2 | no | — |
| 627 | D8 | — | 632 | 2 | no | — |
| 628 | M16 | — | 8 | 1 | no | — |
| 629 | M16 | — | 632 | 1 | no | — |
| 630 | C2×C8 | — | 2 | 2 | no | — |
| 631 | C2×C8 | — | 158 | 2 | no | — |
| 632 | C4⋊C4 | — | 2 | 1 | no | — |
| 633 | C4⋊C4 | — | 79 | 2 | no | — |
| 634 | C4⋊C4 | — | 632 | 1 | no | — |
| 635 | C4⋊C4 | — | 158 | 2 | no | — |
| 636 | C4⋊C4 | — | 158 | 2 | no | — |
| 637 | C4⋊C4 | — | 158 | 1 | no | — |
| 638 | C4⋊C4 | — | 158 | 1 | no | — |
| 639 | C4⋊C4 | — | 158 | 1 | no | — |
| 640 | C4⋊C4 | — | 158 | 1 | no | — |
| 641 | C4⋊C4 | — | 158 | 1 | no | — |
| 642 | C4⋊C4 | C2×D316 | 1 | 2 | yes | — |
| 643 | C22⋊C4 | — | 2 | 2 | no | — |
| 644 | C22⋊C4 | — | 2 | 2 | no | — |
| 645 | C22⋊C4 | — | 8 | 1 | no | — |
| 646 | C22⋊C4 | — | 316 | 2 | no | — |
| 647 | C22⋊C4 | — | 316 | 1 | no | — |
| 648 | C22⋊C4 | — | 316 | 1 | no | — |
| 649 | C22⋊C4 | — | 632 | 1 | no | — |
| 650 | C22⋊C4 | — | 632 | 1 | no | — |
| 651 | C22⋊C4 | — | 632 | 1 | no | — |
| 652 | C22⋊C4 | — | 158 | 2 | no | — |
| 653 | C22⋊C4 | — | 158 | 2 | no | — |
| 654 | C22⋊C4 | — | 158 | 2 | no | — |
| 655 | C22⋊C4 | — | 158 | 2 | no | — |
| 656 | C22⋊C4 | — | 158 | 1 | no | — |
| 657 | C22⋊C4 | — | 158 | 1 | no | — |
| 658 | C22⋊C4 | — | 158 | 2 | no | — |
| 659 | C22⋊C4 | — | 158 | 1 | no | — |
| 660 | C22⋊C4 | — | 158 | 1 | no | — |
| 661 | C22⋊C4 | — | 158 | 2 | no | — |
| 662 | C42 | — | 158 | 1 | no | — |
| 663 | C42 | — | 158 | 1 | no | — |
| 664 | C23 | — | 2 | 1 | no | — |
| 665 | C23 | — | 2 | 1 | no | — |
| 666 | C23 | — | 2 | 2 | no | — |
| 667 | C23 | — | 4 | 1 | no | — |
| 668 | C23 | — | 4 | 1 | no | — |
| 669 | C23 | — | 4 | 2 | no | — |
| 670 | C23 | — | 8 | 1 | no | — |
| 671 | C23 | — | 8 | 1 | no | — |
| 672 | C23 | — | 316 | 1 | no | — |
| 673 | C23 | — | 316 | 1 | no | — |
| 674 | C23 | — | 316 | 2 | no | — |
| 675 | C23 | — | 316 | 1 | no | — |
| 676 | C23 | — | 316 | 1 | no | — |
| 677 | C23 | — | 316 | 1 | no | — |
| 678 | C23 | — | 316 | 1 | no | — |
| 679 | C23 | — | 316 | 4 | no | — |
| 680 | C23 | — | 316 | 1 | no | — |
| 681 | C23 | — | 316 | 1 | no | — |
| 682 | C23 | — | 316 | 1 | no | — |
| 683 | C23 | — | 79 | 2 | no | — |
| 684 | C23 | — | 632 | 1 | no | — |
| 685 | C23 | — | 632 | 1 | no | — |
| 686 | C23 | — | 632 | 2 | no | — |
| 687 | C23 | — | 632 | 2 | no | — |
| 688 | C23 | — | 158 | 2 | no | — |
| 689 | C23 | — | 158 | 1 | no | — |
| 690 | C23 | — | 158 | 1 | no | — |
| 691 | C23 | #14579131 | 1 | 1 | yes | characteristic |
| 692 | C23 | #14579131 | 1 | 1 | yes | characteristic |
| 693 | C23 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 694 | Q8 | — | 316 | 4 | no | — |
| 695 | D4 | — | 4 | 2 | no | — |
| 696 | D4 | — | 4 | 2 | no | — |
| 697 | D4 | — | 4 | 4 | no | — |
| 698 | D4 | — | 4 | 2 | no | — |
| 699 | D4 | — | 4 | 2 | no | — |
| 700 | D4 | — | 316 | 2 | no | — |
| 701 | D4 | — | 316 | 2 | no | — |
| 702 | D4 | — | 316 | 2 | no | — |
| 703 | D4 | — | 316 | 2 | no | — |
| 704 | D4 | — | 316 | 4 | no | — |
| 705 | D4 | — | 316 | 4 | no | — |
| 706 | D4 | — | 316 | 4 | no | — |
| 707 | D4 | — | 316 | 2 | no | — |
| 708 | D4 | — | 316 | 2 | no | — |
| 709 | D4 | — | 316 | 4 | no | — |
| 710 | D4 | — | 632 | 4 | no | — |
| 711 | D4 | — | 632 | 2 | no | — |
| 712 | D4 | — | 632 | 2 | no | — |
| 713 | D4 | — | 632 | 2 | no | — |
| 714 | D4 | — | 632 | 2 | no | — |
| 715 | D4 | — | 158 | 4 | no | — |
| 716 | D4 | — | 158 | 4 | no | — |
| 717 | C2×C4 | — | 2 | 2 | no | — |
| 718 | C2×C4 | — | 4 | 1 | no | — |
| 719 | C2×C4 | — | 4 | 1 | no | — |
| 720 | C2×C4 | — | 4 | 1 | no | — |
| 721 | C2×C4 | — | 4 | 1 | no | — |
| 722 | C2×C4 | — | 4 | 1 | no | — |
| 723 | C2×C4 | — | 4 | 1 | no | — |
| 724 | C2×C4 | — | 4 | 2 | no | — |
| 725 | C2×C4 | — | 4 | 1 | no | — |
| 726 | C2×C4 | — | 4 | 1 | no | — |
| 727 | C2×C4 | — | 4 | 1 | no | — |
| 728 | C2×C4 | — | 4 | 1 | no | — |
| 729 | C2×C4 | — | 4 | 1 | no | — |
| 730 | C2×C4 | — | 4 | 1 | no | — |
| 731 | C2×C4 | — | 316 | 2 | no | — |
| 732 | C2×C4 | — | 316 | 4 | no | — |
| 733 | C2×C4 | — | 316 | 4 | no | — |
| 734 | C2×C4 | — | 316 | 2 | no | — |
| 735 | C2×C4 | — | 316 | 4 | no | — |
| 736 | C2×C4 | — | 316 | 1 | no | — |
| 737 | C2×C4 | — | 316 | 1 | no | — |
| 738 | C2×C4 | — | 316 | 1 | no | — |
| 739 | C2×C4 | — | 316 | 1 | no | — |
| 740 | C2×C4 | — | 316 | 1 | no | — |
| 741 | C2×C4 | — | 79 | 2 | no | — |
| 742 | C2×C4 | — | 632 | 1 | no | — |
| 743 | C2×C4 | — | 158 | 1 | no | — |
| 744 | C2×C4 | — | 158 | 1 | no | — |
| 745 | C2×C4 | — | 158 | 2 | no | — |
| 746 | C2×C4 | — | 158 | 1 | no | — |
| 747 | C2×C4 | — | 158 | 1 | no | — |
| 748 | C2×C4 | #14579131 | 1 | 1 | yes | characteristic |
| 749 | C2×C4 | #14579131 | 1 | 1 | yes | characteristic |
| 750 | C2×C4 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 751 | C2×C4 | C22×D316 | 1 | 1 | yes | characteristic |
| 752 | C8 | — | 4 | 2 | no | — |
| 753 | C8 | — | 316 | 2 | no | — |
| 754 | C22 | — | 2 | 1 | no | — |
| 755 | C22 | — | 2 | 1 | no | — |
| 756 | C22 | — | 2 | 1 | no | — |
| 757 | C22 | — | 2 | 1 | no | — |
| 758 | C22 | — | 2 | 1 | no | — |
| 759 | C22 | — | 2 | 1 | no | — |
| 760 | C22 | — | 2 | 1 | no | — |
| 761 | C22 | — | 2 | 1 | no | — |
| 762 | C22 | — | 4 | 2 | no | — |
| 763 | C22 | — | 4 | 2 | no | — |
| 764 | C22 | — | 4 | 2 | no | — |
| 765 | C22 | — | 8 | 1 | no | — |
| 766 | C22 | — | 8 | 1 | no | — |
| 767 | C22 | — | 16 | 2 | no | — |
| 768 | C22 | — | 316 | 2 | no | — |
| 769 | C22 | — | 316 | 1 | no | — |
| 770 | C22 | — | 316 | 1 | no | — |
| 771 | C22 | — | 316 | 2 | no | — |
| 772 | C22 | — | 316 | 2 | no | — |
| 773 | C22 | — | 316 | 2 | no | — |
| 774 | C22 | — | 632 | 1 | no | — |
| 775 | C22 | — | 632 | 1 | no | — |
| 776 | C22 | — | 632 | 1 | no | — |
| 777 | C22 | — | 632 | 1 | no | — |
| 778 | C22 | — | 632 | 1 | no | — |
| 779 | C22 | — | 632 | 1 | no | — |
| 780 | C22 | — | 632 | 1 | no | — |
| 781 | C22 | — | 632 | 1 | no | — |
| 782 | C22 | — | 158 | 2 | no | — |
| 783 | C22 | — | 1264 | 2 | no | — |
| 784 | C22 | — | 1264 | 4 | no | — |
| 785 | C22 | C2×#14579131 | 1 | 1 | yes | characteristic |
| 786 | C22 | AGL(1,ℤ/8)×D79 | 1 | 1 | yes | characteristic |
| 787 | C22 | AGL(1,ℤ/8)×D79 | 1 | 1 | yes | characteristic |
| 788 | C4 | — | 2 | 1 | no | — |
| 789 | C4 | — | 2 | 1 | no | — |
| 790 | C4 | — | 2 | 1 | no | — |
| 791 | C4 | — | 2 | 1 | no | — |
| 792 | C4 | — | 4 | 2 | no | — |
| 793 | C4 | — | 8 | 1 | no | — |
| 794 | C4 | — | 8 | 1 | no | — |
| 795 | C4 | — | 316 | 1 | no | — |
| 796 | C4 | — | 316 | 1 | no | — |
| 797 | C4 | — | 316 | 2 | no | — |
| 798 | C4 | — | 632 | 1 | no | — |
| 799 | C4 | — | 158 | 2 | no | — |
| 800 | C2 | — | 2 | 1 | no | — |
| 801 | C2 | — | 2 | 1 | no | — |
| 802 | C2 | — | 4 | 1 | no | — |
| 803 | C2 | — | 4 | 1 | no | — |
| 804 | C2 | — | 8 | 2 | no | — |
| 805 | C2 | — | 316 | 2 | no | — |
| 806 | C2 | — | 632 | 2 | no | — |
| 807 | C2 | — | 1264 | 1 | no | — |
| 808 | C2 | #23772629 | 1 | 1 | yes | characteristic |
| 809 | C2 | #23772773 | 1 | 1 | yes | characteristic |
| 810 | C2 | #23772799 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23777157 | C2 | semidirect |
| 2. #23774200 | C2 | semidirect |
| 3. #23774197 | C2 | semidirect |
| 4. #23769287 | C2 | semidirect |
| 5. #23762438 | C2 | semidirect |
| 6. #23762421 | C2 | semidirect |
| 7. #23762336 | C2 | semidirect |
| 8. #23762319 | C2 | semidirect |
| 9. #23761928 | C2 | semidirect |
| 10. #23761736 | C2 | semidirect |
| 11. C79×#1510 | C2 | semidirect |
| 24. C2×#14579135 | C22 | semidirect |
| 28. #19098882 | C22 | semidirect |
| 30. #19098879 | C22 | semidirect |
| 34. #19098699 | C22 | semidirect |
| 36. #19098696 | C22 | semidirect |
| 37. #19098527 | C22 | semidirect |
| 38. #19098503 | C22 | semidirect |
| 39. #19098500 | C22 | semidirect |
| 40. #19098481 | C22 | semidirect |
| 42. #19098473 | C22 | semidirect |
| 46. #19098296 | C22 | semidirect |
| 47. #19098296 | C22 | semidirect |
| 48. #19098288 | C22 | semidirect |
| 49. #19098286 | C22 | semidirect |
| 51. #407×C79 | C22 | semidirect |
| 52. #381×C79 | C22 | semidirect |
| 53. #327×C79 | C22 | semidirect |
| 54. #327×C79 | C22 | semidirect |
| 61. C22×D316 | D4 | semidirect |
| 90. #14579135 | D4 | semidirect |
| 110. C2×C4⋊Dic79 | D4 | semidirect |
| 135. C22×D4×C79 | D4 | semidirect |
| 140. #121×C79 | D4 | semidirect |
| 142. C2×C4⋊C4×C79 | D4 | semidirect |
| 415. #1510 | D79 | semidirect |
| 417. C79 | #18350 | semidirect |
| 445. #407 | C2×D79 | semidirect |
| 454. #381 | C2×D79 | semidirect |
| 457. #327 | C2×D79 | semidirect |
| 458. #327 | C2×D79 | semidirect |
| 477. C22×D4 | D316 | semidirect |
| 510. #121 | D316 | semidirect |
| 528. C2×C4⋊C4 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777157 | 2 |
| #23774200 | 2 |
| #23774197 | 2 |
| #23769287 | 2 |
| #23762438 | 2 |
| #23762421 | 2 |
| #23762336 | 2 |
| #23762319 | 2 |
| #23761928 | 2 |
| #23761736 | 2 |
| C79×#1510 | 2 |
| #18350 | 79 |