Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1194 conjugacy classes of subgroups.
The subgroup lattice has 876 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23777584 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#19098702 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #23769119 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23762379 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #23762367 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #23762362 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #23762350 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #23761956 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #23761930 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #23761749 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C79×#3004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#11929611 | — | 2 | 1 | no | — |
| 13 | #19099309 | — | 2 | 1 | no | — |
| 14 | #19099301 | — | 2 | 1 | no | — |
| 15 | #19099262 | — | 2 | 1 | no | — |
| 16 | #19099237 | — | 2 | 1 | no | — |
| 17 | #19099208 | — | 2 | 1 | no | — |
| 18 | #19099201 | — | 2 | 1 | no | — |
| 19 | #19099200 | — | 2 | 1 | no | — |
| 20 | #19099195 | — | 2 | 1 | no | — |
| 21 | #19099164 | — | 2 | 1 | no | — |
| 22 | #19099162 | C22 | 1 | 1 | yes | characteristic |
| 23 | #19099157 | — | 2 | 1 | no | — |
| 24 | #19099153 | C22 | 1 | 1 | yes | characteristic |
| 25 | #19099146 | — | 2 | 1 | no | — |
| 26 | #19099140 | C22 | 1 | 1 | yes | characteristic |
| 27 | #19099124 | — | 2 | 1 | no | — |
| 28 | #19099121 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#14579144 | — | 2 | 1 | no | — |
| 30 | C2×#14579144 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#14579135 | C22 | 1 | 1 | yes | characteristic |
| 32 | #19098702 | — | 2 | 1 | no | — |
| 33 | #19098702 | — | 2 | 1 | no | — |
| 34 | #19098702 | C22 | 1 | 2 | yes | — |
| 35 | #19098702 | C22 | 1 | 2 | yes | complemented |
| 36 | C2×#14579085 | — | 2 | 1 | no | — |
| 37 | C2×C22⋊(C79⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #19098482 | — | 2 | 1 | no | — |
| 39 | #19098482 | C22 | 1 | 2 | yes | complemented |
| 40 | #19098474 | — | 2 | 1 | no | — |
| 41 | #19098474 | C22 | 1 | 2 | yes | complemented |
| 42 | #19098426 | — | 2 | 1 | no | — |
| 43 | #19098426 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #19098300 | C22 | 1 | 2 | yes | complemented |
| 45 | #19098298 | C22 | 1 | 2 | yes | — |
| 46 | #19098298 | C22 | 1 | 2 | yes | complemented |
| 47 | #19098297 | C22 | 1 | 2 | yes | complemented |
| 48 | #19098288 | C22 | 1 | 2 | yes | complemented |
| 49 | #19098286 | C22 | 1 | 2 | yes | complemented |
| 50 | C23×Q8×C79 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C2×#137×C79 | — | 2 | 1 | no | — |
| 52 | #525×C79 | C22 | 1 | 1 | yes | characteristic |
| 53 | #451×C79 | — | 2 | 1 | no | — |
| 54 | #451×C79 | C22 | 1 | 2 | yes | complemented |
| 55 | #448×C79 | — | 2 | 1 | no | — |
| 56 | #448×C79 | C22 | 1 | 2 | yes | complemented |
| 57 | #419×C79 | — | 2 | 1 | no | — |
| 58 | #407×C79 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C2×#11929623 | — | 2 | 1 | no | — |
| 60 | C22×D316 | D4 | 1 | 1 | yes | characteristic |
| 61 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 62 | C22×C22⋊D79 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×D4×D79 | — | 2 | 1 | no | — |
| 64 | C2×D4×D79 | — | 2 | 1 | no | — |
| 65 | C2×#11929611 | — | 2 | 2 | no | — |
| 66 | C2×#11929611 | — | 2 | 2 | no | — |
| 67 | C2×#11929611 | — | 4 | 4 | no | — |
| 68 | C22×C79⋊C8 | — | 2 | 1 | no | — |
| 69 | #14579157 | — | 2 | 1 | no | — |
| 70 | #14579156 | — | 2 | 1 | no | — |
| 71 | #14579156 | — | 2 | 1 | no | — |
| 72 | #14579155 | — | 2 | 1 | no | — |
| 73 | #14579154 | — | 2 | 1 | no | — |
| 74 | #14579152 | — | 2 | 1 | no | — |
| 75 | #14579151 | — | 2 | 1 | no | — |
| 76 | #14579150 | — | 2 | 1 | no | — |
| 77 | #14579149 | — | 2 | 1 | no | — |
| 78 | #14579147 | — | 2 | 1 | no | — |
| 79 | #14579146 | — | 2 | 1 | no | — |
| 80 | #14579146 | — | 2 | 1 | no | — |
| 81 | #14579146 | — | 2 | 1 | no | — |
| 82 | #14579146 | — | 2 | 1 | no | — |
| 83 | #14579145 | — | 2 | 1 | no | — |
| 84 | #14579145 | — | 2 | 1 | no | — |
| 85 | #14579144 | — | 2 | 1 | no | — |
| 86 | #14579144 | — | 2 | 1 | no | — |
| 87 | #14579144 | — | 2 | 1 | no | — |
| 88 | #14579144 | — | 2 | 1 | no | — |
| 89 | #14579144 | — | 2 | 1 | no | — |
| 90 | #14579144 | — | 4 | 4 | no | — |
| 91 | #14579143 | — | 2 | 1 | no | — |
| 92 | #14579143 | — | 2 | 1 | no | — |
| 93 | #14579141 | — | 2 | 1 | no | — |
| 94 | #14579139 | — | 2 | 1 | no | — |
| 95 | #14579138 | — | 2 | 1 | no | — |
| 96 | #14579138 | — | 2 | 1 | no | — |
| 97 | #14579137 | — | 2 | 1 | no | — |
| 98 | #14579136 | — | 2 | 1 | no | — |
| 99 | #14579136 | — | 2 | 1 | no | — |
| 100 | #14579135 | — | 2 | 1 | no | — |
| 101 | #14579135 | — | 2 | 1 | no | — |
| 102 | #14579135 | — | 2 | 1 | no | — |
| 103 | #14579135 | D4 | 1 | 1 | yes | characteristic |
| 104 | #14579135 | D4 | 1 | 1 | yes | characteristic |
| 105 | #14579135 | C23 | 1 | 1 | yes | characteristic |
| 106 | #14579135 | C23 | 1 | 1 | yes | characteristic |
| 107 | #14579134 | — | 2 | 1 | no | — |
| 108 | #14579134 | — | 2 | 1 | no | — |
| 109 | #14579134 | — | 2 | 1 | no | — |
| 110 | #14579134 | — | 2 | 1 | no | — |
| 111 | #14579133 | — | 2 | 1 | no | — |
| 112 | #14579133 | — | 2 | 1 | no | — |
| 113 | #14579133 | — | 2 | 1 | no | — |
| 114 | #14579133 | — | 2 | 1 | no | — |
| 115 | #14579133 | — | 2 | 1 | no | — |
| 116 | #14579132 | — | 2 | 1 | no | — |
| 117 | #14579131 | — | 2 | 1 | no | — |
| 118 | #14579131 | — | 2 | 1 | no | — |
| 119 | #14579131 | — | 2 | 1 | no | — |
| 120 | #14579131 | — | 2 | 1 | no | — |
| 121 | #14579129 | — | 2 | 1 | no | — |
| 122 | #14579129 | — | 2 | 1 | no | — |
| 123 | #14579129 | — | 2 | 1 | no | — |
| 124 | C4×D316 | — | 2 | 1 | no | — |
| 125 | D4×Dic79 | — | 2 | 1 | no | — |
| 126 | C4×C22⋊D79 | — | 2 | 1 | no | — |
| 127 | (C22⋊D79)⋊C4 | — | 2 | 1 | no | — |
| 128 | (C22⋊D79)⋊C4 | — | 2 | 1 | no | — |
| 129 | (C22⋊D79)⋊C4 | — | 2 | 1 | no | — |
| 130 | #14579118 | — | 2 | 1 | no | — |
| 131 | C2×C4⋊Dic79 | D4 | 1 | 1 | yes | characteristic |
| 132 | C2×Dic79⋊C4 | — | 2 | 2 | no | — |
| 133 | C2×Dic79⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 134 | C2×Dic79⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 135 | C2×C22⋊Dic79 | — | 2 | 1 | no | — |
| 136 | C2×C22⋊Dic79 | D4 | 1 | 1 | yes | characteristic |
| 137 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 138 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 139 | C2×(C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 140 | C2×(C2×D79)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 141 | C2×(C2×D79)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 142 | C22⋊C4×D79 | — | 2 | 1 | no | — |
| 143 | #14579085 | — | 2 | 2 | no | — |
| 144 | #14579085 | — | 2 | 2 | no | — |
| 145 | C22⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 146 | C22⋊(C79⋊C8) | C23 | 1 | 2 | yes | — |
| 147 | C79⋊#95 | — | 2 | 1 | no | — |
| 148 | C79⋊#95 | — | 2 | 2 | no | — |
| 149 | C79⋊#95 | — | 2 | 2 | no | — |
| 150 | C79⋊#95 | C23 | 1 | 2 | yes | — |
| 151 | C2×#41×C79 | D4 | 1 | 1 | yes | characteristic |
| 152 | C22×Q8×C79 | — | 2 | 1 | no | — |
| 153 | C22×Q8×C79 | — | 2 | 1 | no | — |
| 154 | C22×Q8×C79 | — | 2 | 1 | no | — |
| 155 | C22×Q8×C79 | — | 2 | 1 | no | — |
| 156 | C22×Q8×C79 | — | 2 | 1 | no | — |
| 157 | C22×Q8×C79 | — | 4 | 4 | no | — |
| 158 | C22×Q8×C79 | C23 | 1 | 2 | yes | — |
| 159 | C23×C4×C79 | — | 2 | 1 | no | — |
| 160 | C23×C4×C79 | C23 | 1 | 1 | yes | characteristic |
| 161 | #137×C79 | — | 4 | 4 | no | — |
| 162 | C2×Q16×C79 | — | 2 | 2 | no | — |
| 163 | C2×SD16×C79 | — | 2 | 2 | no | — |
| 164 | C2×M16×C79 | — | 2 | 1 | no | — |
| 165 | #123×C79 | — | 2 | 1 | no | — |
| 166 | C22⋊Q8×C79 | D4 | 1 | 1 | yes | characteristic |
| 167 | C22⋊Q8×C79 | C23 | 1 | 1 | yes | characteristic |
| 168 | #121×C79 | D4 | 1 | 1 | yes | characteristic |
| 169 | #121×C79 | C23 | 1 | 1 | yes | characteristic |
| 170 | #120×C79 | — | 2 | 1 | no | — |
| 171 | C4×D4×C79 | — | 2 | 1 | no | — |
| 172 | C4×D4×C79 | — | 2 | 1 | no | — |
| 173 | #117×C79 | D4 | 1 | 1 | yes | characteristic |
| 174 | #103×C79 | — | 2 | 2 | no | — |
| 175 | #103×C79 | — | 2 | 2 | no | — |
| 176 | C22⋊C8×C79 | — | 2 | 1 | no | — |
| 177 | C22⋊C8×C79 | C23 | 1 | 2 | yes | — |
| 178 | C23×D79 | — | 2 | 1 | no | — |
| 179 | C23×D79 | — | 2 | 1 | no | — |
| 180 | C23×D79 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | #11929623 | — | 8 | 2 | no | — |
| 182 | C2×Dic158 | — | 2 | 1 | no | — |
| 183 | C2×D316 | — | 2 | 1 | no | — |
| 184 | C2×D316 | — | 2 | 1 | no | — |
| 185 | C2×D316 | — | 2 | 1 | no | — |
| 186 | C2×D316 | — | 2 | 1 | no | — |
| 187 | C2×D316 | — | 4 | 2 | no | — |
| 188 | C2×D316 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×D316 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 191 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 192 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 193 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 194 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 195 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 196 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 197 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 198 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 199 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 200 | C2×C22⋊D79 | — | 4 | 2 | no | — |
| 201 | C2×C22⋊D79 | — | 8 | 2 | no | — |
| 202 | D4×D79 | — | 8 | 2 | no | — |
| 203 | D4×D79 | — | 8 | 2 | no | — |
| 204 | C22×Dic79 | — | 2 | 1 | no | — |
| 205 | C22×Dic79 | — | 2 | 1 | no | — |
| 206 | C22×Dic79 | — | 2 | 2 | no | — |
| 207 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×D79 | — | 2 | 1 | no | — |
| 211 | C2×C4×D79 | — | 2 | 1 | no | — |
| 212 | C2×C4×D79 | — | 2 | 1 | no | — |
| 213 | C2×C4×D79 | — | 2 | 1 | no | — |
| 214 | #11929611 | — | 4 | 4 | no | — |
| 215 | #11929611 | — | 4 | 4 | no | — |
| 216 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 217 | C2×C79⋊C8 | — | 4 | 2 | no | — |
| 218 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 219 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 220 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 221 | C4⋊Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C4⋊Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 224 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 225 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 226 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 227 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 228 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 229 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 230 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 231 | Dic79⋊C4 | — | 4 | 4 | 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 | 2 | no | — |
| 237 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 238 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 239 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 240 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 241 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 242 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 243 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 244 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 245 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 246 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 247 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 248 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 249 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 250 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 251 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 252 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 253 | (C2×D79)⋊C4 | — | 4 | 4 | no | — |
| 254 | C4×Dic79 | — | 2 | 1 | no | — |
| 255 | C4×Dic79 | — | 2 | 1 | no | — |
| 256 | C24×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 257 | #41×C79 | — | 4 | 2 | no | — |
| 258 | C2×Q8×C79 | — | 2 | 4 | no | — |
| 259 | C2×Q8×C79 | — | 2 | 4 | no | — |
| 260 | C2×Q8×C79 | — | 2 | 2 | no | — |
| 261 | C2×Q8×C79 | — | 2 | 2 | no | — |
| 262 | C2×Q8×C79 | — | 4 | 4 | no | — |
| 263 | C2×Q8×C79 | — | 4 | 2 | no | — |
| 264 | C2×Q8×C79 | — | 4 | 2 | no | — |
| 265 | C2×Q8×C79 | — | 4 | 4 | no | — |
| 266 | C2×Q8×C79 | — | 4 | 4 | no | — |
| 267 | C2×Q8×C79 | — | 4 | 4 | no | — |
| 268 | C2×Q8×C79 | — | 4 | 1 | no | — |
| 269 | C2×Q8×C79 | — | 4 | 1 | no | — |
| 270 | C2×Q8×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 271 | C2×D4×C79 | — | 2 | 1 | no | — |
| 272 | C2×D4×C79 | — | 2 | 1 | no | — |
| 273 | C2×D4×C79 | — | 2 | 1 | no | — |
| 274 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 275 | C22×C4×C79 | — | 2 | 4 | no | — |
| 276 | C22×C4×C79 | — | 2 | 2 | no | — |
| 277 | C22×C4×C79 | — | 2 | 1 | no | — |
| 278 | C22×C4×C79 | — | 4 | 2 | no | — |
| 279 | C22×C4×C79 | — | 4 | 2 | no | — |
| 280 | C22×C4×C79 | — | 4 | 1 | no | — |
| 281 | C22×C4×C79 | — | 4 | 1 | no | — |
| 282 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 283 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 284 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 285 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 286 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | C22×C4×C79 | C24 | 1 | 1 | yes | characteristic |
| 288 | Q16×C79 | — | 4 | 4 | no | — |
| 289 | SD16×C79 | — | 4 | 4 | no | — |
| 290 | M16×C79 | — | 4 | 2 | no | — |
| 291 | C2×C8×C79 | — | 2 | 2 | no | — |
| 292 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 293 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 294 | C4⋊C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 295 | C4⋊C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 296 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 297 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 298 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 299 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 300 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 301 | C42×C79 | — | 2 | 1 | no | — |
| 302 | C23×C79 | — | 2 | 2 | no | — |
| 303 | C23×C79 | — | 2 | 2 | no | — |
| 304 | C23×C79 | — | 2 | 1 | no | — |
| 305 | C23×C79 | — | 4 | 1 | no | — |
| 306 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 307 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 308 | C23×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 309 | C22×D79 | — | 2 | 1 | no | — |
| 310 | C22×D79 | — | 2 | 1 | no | — |
| 311 | C22×D79 | — | 2 | 1 | no | — |
| 312 | C22×D79 | — | 2 | 2 | no | — |
| 313 | C22×D79 | — | 4 | 2 | no | — |
| 314 | C22×D79 | — | 4 | 1 | no | — |
| 315 | C22×D79 | — | 4 | 1 | no | — |
| 316 | C22×D79 | — | 8 | 1 | no | — |
| 317 | C22×D79 | — | 8 | 1 | no | — |
| 318 | C22×D79 | — | 8 | 1 | no | — |
| 319 | C22×D79 | — | 8 | 1 | no | — |
| 320 | C22×D79 | — | 8 | 1 | no | — |
| 321 | Q8×C79 | — | 2 | 4 | no | — |
| 322 | Q8×C79 | — | 2 | 4 | no | — |
| 323 | Q8×C79 | — | 4 | 1 | no | — |
| 324 | Q8×C79 | — | 4 | 4 | no | — |
| 325 | Q8×C79 | — | 4 | 4 | no | — |
| 326 | Q8×C79 | — | 4 | 2 | no | — |
| 327 | Q8×C79 | — | 4 | 2 | no | — |
| 328 | D4×C79 | — | 4 | 1 | no | — |
| 329 | D4×C79 | — | 4 | 2 | no | — |
| 330 | D4×C79 | — | 4 | 2 | no | — |
| 331 | D4×C79 | — | 8 | 1 | no | — |
| 332 | C2×C4×C79 | — | 2 | 2 | no | — |
| 333 | C2×C4×C79 | — | 2 | 2 | no | — |
| 334 | C2×C4×C79 | — | 2 | 4 | no | — |
| 335 | C2×C4×C79 | — | 2 | 1 | no | — |
| 336 | C2×C4×C79 | — | 2 | 1 | no | — |
| 337 | C2×C4×C79 | — | 2 | 1 | no | — |
| 338 | C2×C4×C79 | — | 4 | 1 | no | — |
| 339 | C2×C4×C79 | — | 4 | 1 | no | — |
| 340 | C2×C4×C79 | — | 4 | 1 | no | — |
| 341 | C2×C4×C79 | — | 4 | 1 | no | — |
| 342 | C2×C4×C79 | — | 4 | 2 | no | — |
| 343 | C2×C4×C79 | — | 4 | 4 | no | — |
| 344 | C2×C4×C79 | — | 4 | 2 | no | — |
| 345 | C2×C4×C79 | — | 4 | 4 | no | — |
| 346 | C2×C4×C79 | — | 8 | 1 | no | — |
| 347 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 348 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 349 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 350 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 351 | C22⋊D79 | — | 4 | 2 | no | — |
| 352 | C22⋊D79 | — | 4 | 2 | no | — |
| 353 | C22⋊D79 | — | 4 | 2 | no | — |
| 354 | C22⋊D79 | — | 8 | 1 | no | — |
| 355 | C22⋊D79 | — | 8 | 1 | no | — |
| 356 | C22⋊D79 | — | 8 | 1 | no | — |
| 357 | C22⋊D79 | — | 8 | 1 | no | — |
| 358 | C22⋊D79 | — | 8 | 1 | no | — |
| 359 | C22⋊D79 | — | 8 | 1 | no | — |
| 360 | C22⋊D79 | — | 8 | 1 | no | — |
| 361 | C2×Dic79 | — | 2 | 1 | no | — |
| 362 | C2×Dic79 | — | 2 | 1 | no | — |
| 363 | C2×Dic79 | — | 2 | 1 | no | — |
| 364 | C2×Dic79 | — | 2 | 1 | no | — |
| 365 | C2×Dic79 | — | 2 | 1 | no | — |
| 366 | C2×Dic79 | — | 2 | 2 | no | — |
| 367 | C2×Dic79 | — | 4 | 1 | no | — |
| 368 | C2×Dic79 | — | 4 | 1 | no | — |
| 369 | C2×Dic79 | — | 4 | 2 | no | — |
| 370 | C2×Dic79 | — | 4 | 2 | no | — |
| 371 | C2×Dic79 | — | 4 | 2 | no | — |
| 372 | C2×Dic79 | — | 8 | 1 | no | — |
| 373 | C2×Dic79 | — | 8 | 1 | no | — |
| 374 | D316 | — | 4 | 1 | no | — |
| 375 | D316 | — | 4 | 1 | no | — |
| 376 | D316 | — | 8 | 1 | no | — |
| 377 | D316 | — | 8 | 1 | no | — |
| 378 | D316 | — | 8 | 1 | no | — |
| 379 | D316 | — | 8 | 1 | no | — |
| 380 | C4×D79 | — | 8 | 1 | no | — |
| 381 | C4×D79 | — | 8 | 1 | no | — |
| 382 | C4×D79 | — | 8 | 1 | no | — |
| 383 | C4×D79 | — | 8 | 1 | no | — |
| 384 | Dic158 | — | 8 | 1 | no | — |
| 385 | C8×C79 | — | 4 | 2 | no | — |
| 386 | C79⋊C8 | — | 4 | 2 | no | — |
| 387 | C22×C79 | — | 2 | 1 | no | — |
| 388 | C22×C79 | — | 2 | 1 | no | — |
| 389 | C22×C79 | — | 2 | 1 | no | — |
| 390 | C22×C79 | — | 2 | 1 | no | — |
| 391 | C22×C79 | — | 2 | 1 | no | — |
| 392 | C22×C79 | — | 2 | 1 | no | — |
| 393 | C22×C79 | — | 2 | 1 | no | — |
| 394 | C22×C79 | — | 4 | 4 | no | — |
| 395 | C22×C79 | — | 4 | 1 | no | — |
| 396 | C22×C79 | — | 4 | 1 | no | — |
| 397 | C22×C79 | — | 4 | 1 | no | — |
| 398 | C22×C79 | B(4,𝔽2) | 1 | 2 | yes | — |
| 399 | C22×C79 | C2×#120 | 1 | 1 | yes | characteristic |
| 400 | C22×C79 | #577 | 1 | 2 | yes | — |
| 401 | C2×D79 | — | 4 | 1 | no | — |
| 402 | C2×D79 | — | 4 | 1 | no | — |
| 403 | C2×D79 | — | 4 | 1 | no | — |
| 404 | C2×D79 | — | 4 | 1 | no | — |
| 405 | C2×D79 | — | 4 | 1 | no | — |
| 406 | C2×D79 | — | 4 | 1 | no | — |
| 407 | C2×D79 | — | 4 | 1 | no | — |
| 408 | C2×D79 | — | 4 | 1 | no | — |
| 409 | C2×D79 | — | 4 | 1 | no | — |
| 410 | C2×D79 | — | 8 | 2 | no | — |
| 411 | C2×D79 | — | 16 | 2 | no | — |
| 412 | C2×D79 | — | 16 | 2 | no | — |
| 413 | C4×C79 | — | 2 | 1 | no | — |
| 414 | C4×C79 | — | 2 | 1 | no | — |
| 415 | C4×C79 | — | 2 | 1 | no | — |
| 416 | C4×C79 | — | 2 | 1 | no | — |
| 417 | C4×C79 | — | 4 | 1 | no | — |
| 418 | C4×C79 | — | 4 | 1 | no | — |
| 419 | C4×C79 | — | 4 | 4 | no | — |
| 420 | C4×C79 | — | 4 | 1 | no | — |
| 421 | Dic79 | — | 4 | 1 | no | — |
| 422 | Dic79 | — | 4 | 1 | no | — |
| 423 | Dic79 | — | 4 | 1 | no | — |
| 424 | Dic79 | — | 4 | 1 | no | — |
| 425 | Dic79 | — | 4 | 1 | no | — |
| 426 | Dic79 | — | 8 | 2 | no | — |
| 427 | #18225 | — | 79 | 1 | no | maximal, Sylow |
| 428 | C2×C79 | — | 2 | 2 | no | — |
| 429 | C2×C79 | — | 2 | 2 | no | — |
| 430 | C2×C79 | — | 4 | 1 | no | — |
| 431 | C2×C79 | — | 8 | 1 | no | — |
| 432 | C2×C79 | #3009 | 1 | 1 | yes | characteristic |
| 433 | C2×C79 | #3022 | 1 | 1 | yes | characteristic |
| 434 | C2×C79 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 435 | D79 | — | 8 | 1 | no | — |
| 436 | D79 | — | 8 | 1 | no | — |
| 437 | D79 | — | 8 | 1 | no | — |
| 438 | #3534 | — | 79 | 1 | no | — |
| 439 | #3004 | D79 | 1 | 1 | yes | characteristic, complemented |
| 440 | C2×#448 | — | 79 | 1 | no | — |
| 441 | #2614 | — | 79 | 1 | no | — |
| 442 | #1606 | — | 79 | 2 | no | — |
| 443 | #1604 | — | 79 | 2 | no | — |
| 444 | #1603 | — | 79 | 2 | no | — |
| 445 | #1601 | — | 79 | 2 | no | — |
| 446 | #1516 | — | 79 | 1 | no | — |
| 447 | #1510 | — | 79 | 1 | no | — |
| 448 | #1468 | — | 79 | 1 | no | — |
| 449 | C79 | #18225 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 450 | C23×Q8 | C2×D79 | 1 | 1 | yes | characteristic, complemented |
| 451 | C2×#137 | — | 2 | 1 | no | — |
| 452 | C22×SD16 | — | 158 | 1 | no | — |
| 453 | #562 | — | 158 | 1 | no | — |
| 454 | #560 | — | 158 | 1 | no | — |
| 455 | #553 | — | 158 | 1 | no | — |
| 456 | #551 | — | 158 | 1 | no | — |
| 457 | #546 | — | 158 | 1 | no | — |
| 458 | #546 | — | 158 | 1 | no | — |
| 459 | #546 | — | 158 | 1 | no | — |
| 460 | D42 | — | 158 | 1 | no | — |
| 461 | #540 | — | 158 | 1 | no | — |
| 462 | #539 | — | 79 | 1 | no | — |
| 463 | #539 | — | 158 | 1 | no | — |
| 464 | #538 | — | 79 | 1 | no | — |
| 465 | #538 | — | 158 | 1 | no | — |
| 466 | #537 | — | 79 | 1 | no | — |
| 467 | #534 | — | 79 | 1 | no | — |
| 468 | #534 | — | 158 | 1 | no | — |
| 469 | #525 | C2×D79 | 1 | 1 | yes | characteristic |
| 470 | C2×#123 | — | 79 | 1 | no | — |
| 471 | C2×#123 | — | 158 | 1 | no | — |
| 472 | C2×#121 | — | 79 | 1 | no | — |
| 473 | #451 | — | 2 | 1 | no | — |
| 474 | #451 | C2×D79 | 1 | 2 | yes | complemented |
| 475 | #448 | — | 2 | 1 | no | — |
| 476 | #448 | — | 79 | 2 | no | — |
| 477 | #448 | — | 79 | 2 | no | — |
| 478 | #448 | — | 158 | 1 | no | — |
| 479 | #448 | — | 158 | 1 | no | — |
| 480 | #448 | C2×D79 | 1 | 2 | yes | complemented |
| 481 | #419 | — | 2 | 1 | no | — |
| 482 | C2×#103 | — | 158 | 1 | no | — |
| 483 | #407 | C2×D79 | 1 | 1 | yes | characteristic, complemented |
| 484 | C2×C22⋊C8 | — | 79 | 1 | no | — |
| 485 | #395 | — | 79 | 2 | no | — |
| 486 | #395 | — | 158 | 1 | no | — |
| 487 | #393 | — | 79 | 2 | no | — |
| 488 | #393 | — | 158 | 1 | no | — |
| 489 | #381 | — | 79 | 1 | no | — |
| 490 | #381 | — | 158 | 1 | no | — |
| 491 | #328 | — | 79 | 2 | no | — |
| 492 | #327 | — | 79 | 2 | no | — |
| 493 | #327 | — | 79 | 2 | no | — |
| 494 | #327 | — | 79 | 2 | no | — |
| 495 | #324 | — | 79 | 2 | no | — |
| 496 | #323 | — | 79 | 2 | no | — |
| 497 | C2×#41 | — | 158 | 1 | no | — |
| 498 | C2×#41 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 499 | C22×Q8 | — | 2 | 1 | no | — |
| 500 | C22×Q8 | — | 2 | 1 | no | — |
| 501 | C22×Q8 | — | 2 | 1 | no | — |
| 502 | C22×Q8 | — | 2 | 1 | no | — |
| 503 | C22×Q8 | — | 2 | 1 | no | — |
| 504 | C22×Q8 | — | 4 | 4 | no | — |
| 505 | C22×Q8 | C22×D79 | 1 | 2 | yes | — |
| 506 | C22×D4 | — | 79 | 1 | no | — |
| 507 | C22×D4 | — | 79 | 1 | no | — |
| 508 | C22×D4 | — | 158 | 1 | no | — |
| 509 | C22×D4 | — | 158 | 1 | no | — |
| 510 | C22×D4 | — | 158 | 1 | no | — |
| 511 | C23×C4 | — | 2 | 1 | no | — |
| 512 | C23×C4 | C22×D79 | 1 | 1 | yes | characteristic |
| 513 | #137 | — | 4 | 4 | no | — |
| 514 | C2×Q16 | — | 2 | 2 | no | — |
| 515 | C2×SD16 | — | 2 | 2 | no | — |
| 516 | C2×SD16 | — | 316 | 4 | no | — |
| 517 | C2×SD16 | — | 158 | 2 | no | — |
| 518 | C2×SD16 | — | 158 | 2 | no | — |
| 519 | C2×M16 | — | 2 | 1 | no | — |
| 520 | C22×C8 | — | 158 | 1 | no | — |
| 521 | #127 | — | 158 | 1 | no | — |
| 522 | #126 | — | 158 | 1 | no | — |
| 523 | #126 | — | 158 | 1 | no | — |
| 524 | #126 | — | 158 | 1 | no | — |
| 525 | #126 | — | 158 | 1 | no | — |
| 526 | #125 | — | 158 | 1 | no | — |
| 527 | #125 | — | 158 | 1 | no | — |
| 528 | #124 | — | 158 | 1 | no | — |
| 529 | #124 | — | 158 | 1 | no | — |
| 530 | #124 | — | 158 | 1 | no | — |
| 531 | #123 | — | 2 | 1 | no | — |
| 532 | #123 | — | 316 | 4 | no | — |
| 533 | #123 | — | 158 | 1 | no | — |
| 534 | #123 | — | 158 | 1 | no | — |
| 535 | #123 | — | 158 | 1 | no | — |
| 536 | #123 | — | 158 | 1 | no | — |
| 537 | #123 | — | 158 | 1 | no | — |
| 538 | #123 | — | 158 | 1 | no | — |
| 539 | #123 | — | 158 | 1 | no | — |
| 540 | #123 | — | 158 | 1 | no | — |
| 541 | #123 | — | 158 | 1 | no | — |
| 542 | #123 | — | 158 | 1 | no | — |
| 543 | #123 | — | 158 | 1 | no | — |
| 544 | #123 | — | 158 | 1 | no | — |
| 545 | #123 | — | 158 | 1 | no | — |
| 546 | C22⋊Q8 | — | 158 | 1 | no | — |
| 547 | C22⋊Q8 | — | 158 | 1 | no | — |
| 548 | C22⋊Q8 | — | 158 | 1 | no | — |
| 549 | C22⋊Q8 | — | 158 | 1 | no | — |
| 550 | C22⋊Q8 | — | 158 | 1 | no | — |
| 551 | C22⋊Q8 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 552 | C22⋊Q8 | C22×D79 | 1 | 1 | yes | characteristic |
| 553 | #121 | — | 79 | 1 | no | — |
| 554 | #121 | — | 79 | 1 | no | — |
| 555 | #121 | — | 79 | 1 | no | — |
| 556 | #121 | — | 79 | 1 | no | — |
| 557 | #121 | — | 158 | 1 | no | — |
| 558 | #121 | — | 158 | 1 | no | — |
| 559 | #121 | — | 158 | 1 | no | — |
| 560 | #121 | — | 158 | 1 | no | — |
| 561 | #121 | — | 158 | 1 | no | — |
| 562 | #121 | — | 158 | 1 | no | — |
| 563 | #121 | — | 158 | 1 | no | — |
| 564 | #121 | — | 158 | 1 | no | — |
| 565 | #121 | — | 158 | 1 | no | — |
| 566 | #121 | — | 158 | 1 | no | — |
| 567 | #121 | — | 158 | 1 | no | — |
| 568 | #121 | — | 158 | 1 | no | — |
| 569 | #121 | — | 158 | 1 | no | — |
| 570 | #121 | — | 158 | 1 | no | — |
| 571 | #121 | — | 158 | 1 | no | — |
| 572 | #121 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 573 | #121 | C22×D79 | 1 | 1 | yes | characteristic |
| 574 | #120 | — | 2 | 1 | no | — |
| 575 | #120 | — | 158 | 1 | no | — |
| 576 | #120 | — | 158 | 1 | no | — |
| 577 | #120 | — | 158 | 1 | no | — |
| 578 | #120 | — | 158 | 1 | no | — |
| 579 | #120 | — | 158 | 1 | no | — |
| 580 | #120 | — | 158 | 1 | no | — |
| 581 | #120 | — | 158 | 1 | no | — |
| 582 | C4×D4 | — | 2 | 1 | no | — |
| 583 | C4×D4 | — | 2 | 1 | no | — |
| 584 | C4×D4 | — | 158 | 1 | no | — |
| 585 | C4×D4 | — | 158 | 1 | no | — |
| 586 | C4×D4 | — | 158 | 1 | no | — |
| 587 | C4×D4 | — | 158 | 1 | no | — |
| 588 | C4×D4 | — | 158 | 1 | no | — |
| 589 | C4×D4 | — | 158 | 1 | no | — |
| 590 | #117 | — | 158 | 1 | no | — |
| 591 | #117 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 592 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 593 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 594 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 595 | C2×C4⋊C4 | — | 158 | 2 | no | — |
| 596 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 597 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 598 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 599 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 600 | C2×C22⋊C4 | — | 158 | 2 | no | — |
| 601 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 602 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 603 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 604 | #103 | — | 2 | 2 | no | — |
| 605 | #103 | — | 2 | 2 | no | — |
| 606 | #103 | — | 158 | 2 | no | — |
| 607 | #103 | — | 158 | 2 | no | — |
| 608 | C22⋊C8 | — | 2 | 1 | no | — |
| 609 | C22⋊C8 | — | 79 | 2 | no | — |
| 610 | C22⋊C8 | — | 158 | 1 | no | — |
| 611 | C22⋊C8 | C22×D79 | 1 | 2 | yes | — |
| 612 | #95 | — | 79 | 2 | no | — |
| 613 | #95 | — | 158 | 2 | no | — |
| 614 | #95 | — | 158 | 2 | no | — |
| 615 | #95 | — | 158 | 1 | no | — |
| 616 | C24 | — | 79 | 1 | no | — |
| 617 | C24 | — | 158 | 1 | no | — |
| 618 | C24 | — | 158 | 1 | no | — |
| 619 | C24 | D4×D79 | 1 | 1 | yes | characteristic |
| 620 | #41 | — | 4 | 2 | no | — |
| 621 | #41 | — | 632 | 2 | no | — |
| 622 | C2×Q8 | — | 2 | 4 | no | — |
| 623 | C2×Q8 | — | 2 | 4 | no | — |
| 624 | C2×Q8 | — | 2 | 2 | no | — |
| 625 | C2×Q8 | — | 2 | 2 | no | — |
| 626 | C2×Q8 | — | 4 | 4 | no | — |
| 627 | C2×Q8 | — | 4 | 2 | no | — |
| 628 | C2×Q8 | — | 4 | 2 | no | — |
| 629 | C2×Q8 | — | 4 | 4 | no | — |
| 630 | C2×Q8 | — | 4 | 4 | no | — |
| 631 | C2×Q8 | — | 4 | 4 | no | — |
| 632 | C2×Q8 | — | 4 | 1 | no | — |
| 633 | C2×Q8 | — | 4 | 1 | no | — |
| 634 | C2×Q8 | — | 158 | 1 | no | — |
| 635 | C2×Q8 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 636 | C2×D4 | — | 2 | 1 | no | — |
| 637 | C2×D4 | — | 2 | 1 | no | — |
| 638 | C2×D4 | — | 2 | 1 | no | — |
| 639 | C2×D4 | — | 316 | 2 | no | — |
| 640 | C2×D4 | — | 316 | 2 | no | — |
| 641 | C2×D4 | — | 79 | 1 | no | — |
| 642 | C2×D4 | — | 79 | 1 | no | — |
| 643 | C2×D4 | — | 632 | 2 | no | — |
| 644 | C2×D4 | — | 632 | 2 | no | — |
| 645 | C2×D4 | — | 632 | 2 | no | — |
| 646 | C2×D4 | — | 158 | 1 | no | — |
| 647 | C2×D4 | — | 158 | 1 | no | — |
| 648 | C2×D4 | — | 158 | 1 | no | — |
| 649 | C2×D4 | — | 158 | 1 | no | — |
| 650 | C2×D4 | — | 158 | 1 | no | — |
| 651 | C2×D4 | — | 158 | 1 | no | — |
| 652 | C2×D4 | — | 158 | 1 | no | — |
| 653 | C2×D4 | — | 158 | 1 | no | — |
| 654 | C2×D4 | — | 158 | 1 | no | — |
| 655 | C2×D4 | — | 158 | 1 | no | — |
| 656 | C2×D4 | — | 158 | 1 | no | — |
| 657 | C2×D4 | — | 158 | 1 | no | — |
| 658 | C2×D4 | — | 158 | 1 | no | — |
| 659 | C2×D4 | — | 158 | 1 | no | — |
| 660 | C2×D4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 661 | C22×C4 | — | 2 | 4 | no | — |
| 662 | C22×C4 | — | 2 | 2 | no | — |
| 663 | C22×C4 | — | 2 | 1 | no | — |
| 664 | C22×C4 | — | 4 | 2 | no | — |
| 665 | C22×C4 | — | 4 | 2 | no | — |
| 666 | C22×C4 | — | 4 | 1 | no | — |
| 667 | C22×C4 | — | 4 | 1 | no | — |
| 668 | C22×C4 | — | 79 | 1 | no | — |
| 669 | C22×C4 | — | 79 | 1 | no | — |
| 670 | C22×C4 | — | 79 | 1 | no | — |
| 671 | C22×C4 | — | 158 | 1 | no | — |
| 672 | C22×C4 | — | 158 | 1 | no | — |
| 673 | C22×C4 | — | 158 | 1 | no | — |
| 674 | C22×C4 | — | 158 | 1 | no | — |
| 675 | C22×C4 | — | 158 | 2 | no | — |
| 676 | C22×C4 | — | 158 | 1 | no | — |
| 677 | C22×C4 | — | 158 | 1 | no | — |
| 678 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 679 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 680 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 681 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 682 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 683 | C22×C4 | C23×D79 | 1 | 1 | yes | characteristic |
| 684 | Q16 | — | 4 | 4 | no | — |
| 685 | SD16 | — | 4 | 4 | no | — |
| 686 | SD16 | — | 316 | 4 | no | — |
| 687 | SD16 | — | 316 | 4 | no | — |
| 688 | M16 | — | 4 | 2 | no | — |
| 689 | C2×C8 | — | 2 | 2 | no | — |
| 690 | C2×C8 | — | 316 | 2 | no | — |
| 691 | C2×C8 | — | 158 | 2 | no | — |
| 692 | C4⋊C4 | — | 2 | 1 | no | — |
| 693 | C4⋊C4 | — | 2 | 1 | no | — |
| 694 | C4⋊C4 | — | 316 | 4 | no | — |
| 695 | C4⋊C4 | — | 79 | 1 | no | — |
| 696 | C4⋊C4 | — | 79 | 1 | no | — |
| 697 | C4⋊C4 | — | 158 | 1 | no | — |
| 698 | C4⋊C4 | — | 158 | 1 | no | — |
| 699 | C4⋊C4 | — | 158 | 1 | no | — |
| 700 | C4⋊C4 | — | 158 | 1 | no | — |
| 701 | C4⋊C4 | — | 158 | 1 | no | — |
| 702 | C4⋊C4 | — | 158 | 1 | no | — |
| 703 | C4⋊C4 | — | 158 | 1 | no | — |
| 704 | C4⋊C4 | — | 158 | 1 | no | — |
| 705 | C4⋊C4 | — | 158 | 1 | no | — |
| 706 | C4⋊C4 | — | 158 | 1 | no | — |
| 707 | C4⋊C4 | — | 158 | 1 | no | — |
| 708 | C4⋊C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 709 | C4⋊C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 710 | C22⋊C4 | — | 2 | 1 | no | — |
| 711 | C22⋊C4 | — | 2 | 1 | no | — |
| 712 | C22⋊C4 | — | 2 | 1 | no | — |
| 713 | C22⋊C4 | — | 2 | 1 | no | — |
| 714 | C22⋊C4 | — | 2 | 1 | no | — |
| 715 | C22⋊C4 | — | 316 | 4 | no | — |
| 716 | C22⋊C4 | — | 316 | 2 | no | — |
| 717 | C22⋊C4 | — | 158 | 1 | no | — |
| 718 | C22⋊C4 | — | 158 | 1 | no | — |
| 719 | C22⋊C4 | — | 158 | 1 | no | — |
| 720 | C22⋊C4 | — | 158 | 1 | no | — |
| 721 | C22⋊C4 | — | 158 | 1 | no | — |
| 722 | C22⋊C4 | — | 158 | 1 | no | — |
| 723 | C22⋊C4 | — | 158 | 1 | no | — |
| 724 | C22⋊C4 | — | 158 | 1 | no | — |
| 725 | C22⋊C4 | — | 158 | 1 | no | — |
| 726 | C22⋊C4 | — | 158 | 1 | no | — |
| 727 | C22⋊C4 | — | 158 | 1 | no | — |
| 728 | C22⋊C4 | — | 158 | 1 | no | — |
| 729 | C22⋊C4 | — | 158 | 1 | no | — |
| 730 | C22⋊C4 | — | 158 | 1 | no | — |
| 731 | C22⋊C4 | — | 158 | 1 | no | — |
| 732 | C22⋊C4 | — | 158 | 1 | no | — |
| 733 | C22⋊C4 | — | 158 | 1 | no | — |
| 734 | C22⋊C4 | — | 158 | 1 | no | — |
| 735 | C22⋊C4 | — | 158 | 1 | no | — |
| 736 | C22⋊C4 | — | 158 | 1 | no | — |
| 737 | C42 | — | 2 | 1 | no | — |
| 738 | C42 | — | 158 | 1 | no | — |
| 739 | C42 | — | 158 | 1 | no | — |
| 740 | C23 | — | 2 | 2 | no | — |
| 741 | C23 | — | 2 | 2 | no | — |
| 742 | C23 | — | 2 | 1 | no | — |
| 743 | C23 | — | 4 | 1 | no | — |
| 744 | C23 | — | 316 | 1 | no | — |
| 745 | C23 | — | 316 | 1 | no | — |
| 746 | C23 | — | 316 | 2 | no | — |
| 747 | C23 | — | 632 | 1 | no | — |
| 748 | C23 | — | 632 | 1 | no | — |
| 749 | C23 | — | 632 | 1 | no | — |
| 750 | C23 | — | 632 | 1 | no | — |
| 751 | C23 | — | 632 | 1 | no | — |
| 752 | C23 | — | 158 | 1 | no | — |
| 753 | C23 | — | 158 | 1 | no | — |
| 754 | C23 | — | 158 | 1 | no | — |
| 755 | C23 | — | 158 | 2 | no | — |
| 756 | C23 | #14579129 | 1 | 1 | yes | characteristic |
| 757 | C23 | #14579129 | 1 | 1 | yes | characteristic |
| 758 | C23 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 759 | Q8 | — | 2 | 4 | no | — |
| 760 | Q8 | — | 2 | 4 | no | — |
| 761 | Q8 | — | 4 | 1 | no | — |
| 762 | Q8 | — | 4 | 2 | no | — |
| 763 | Q8 | — | 4 | 2 | no | — |
| 764 | Q8 | — | 4 | 4 | no | — |
| 765 | Q8 | — | 4 | 4 | no | — |
| 766 | Q8 | — | 632 | 1 | no | — |
| 767 | D4 | — | 4 | 1 | no | — |
| 768 | D4 | — | 4 | 2 | no | — |
| 769 | D4 | — | 4 | 2 | no | — |
| 770 | D4 | — | 8 | 1 | no | — |
| 771 | D4 | — | 316 | 1 | no | — |
| 772 | D4 | — | 316 | 1 | no | — |
| 773 | D4 | — | 316 | 2 | no | — |
| 774 | D4 | — | 316 | 2 | no | — |
| 775 | D4 | — | 316 | 2 | no | — |
| 776 | D4 | — | 632 | 1 | no | — |
| 777 | D4 | — | 632 | 1 | no | — |
| 778 | D4 | — | 632 | 1 | no | — |
| 779 | D4 | — | 632 | 1 | no | — |
| 780 | D4 | — | 632 | 1 | no | — |
| 781 | D4 | — | 632 | 1 | no | — |
| 782 | D4 | — | 632 | 1 | no | — |
| 783 | D4 | — | 632 | 1 | no | — |
| 784 | D4 | — | 632 | 1 | no | — |
| 785 | D4 | — | 632 | 1 | no | — |
| 786 | D4 | — | 632 | 1 | no | — |
| 787 | C2×C4 | — | 2 | 2 | no | — |
| 788 | C2×C4 | — | 2 | 2 | no | — |
| 789 | C2×C4 | — | 2 | 4 | no | — |
| 790 | C2×C4 | — | 2 | 1 | no | — |
| 791 | C2×C4 | — | 2 | 1 | no | — |
| 792 | C2×C4 | — | 2 | 1 | no | — |
| 793 | C2×C4 | — | 4 | 1 | no | — |
| 794 | C2×C4 | — | 4 | 1 | no | — |
| 795 | C2×C4 | — | 4 | 1 | no | — |
| 796 | C2×C4 | — | 4 | 1 | no | — |
| 797 | C2×C4 | — | 4 | 2 | no | — |
| 798 | C2×C4 | — | 4 | 4 | no | — |
| 799 | C2×C4 | — | 4 | 4 | no | — |
| 800 | C2×C4 | — | 4 | 2 | no | — |
| 801 | C2×C4 | — | 8 | 1 | no | — |
| 802 | C2×C4 | — | 316 | 1 | no | — |
| 803 | C2×C4 | — | 316 | 1 | no | — |
| 804 | C2×C4 | — | 316 | 2 | no | — |
| 805 | C2×C4 | — | 316 | 2 | no | — |
| 806 | C2×C4 | — | 316 | 2 | no | — |
| 807 | C2×C4 | — | 632 | 1 | no | — |
| 808 | C2×C4 | — | 632 | 1 | no | — |
| 809 | C2×C4 | — | 632 | 1 | no | — |
| 810 | C2×C4 | — | 632 | 1 | no | — |
| 811 | C2×C4 | — | 632 | 1 | no | — |
| 812 | C2×C4 | — | 632 | 1 | no | — |
| 813 | C2×C4 | — | 158 | 1 | no | — |
| 814 | C2×C4 | — | 158 | 1 | no | — |
| 815 | C2×C4 | — | 158 | 1 | no | — |
| 816 | C2×C4 | — | 158 | 1 | no | — |
| 817 | C2×C4 | — | 158 | 1 | no | — |
| 818 | C2×C4 | — | 158 | 2 | no | — |
| 819 | C2×C4 | #14579129 | 1 | 1 | yes | characteristic |
| 820 | C2×C4 | #14579129 | 1 | 1 | yes | characteristic |
| 821 | C2×C4 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 822 | C2×C4 | C22×C22⋊D79 | 1 | 1 | yes | characteristic |
| 823 | C8 | — | 4 | 2 | no | — |
| 824 | C8 | — | 316 | 2 | no | — |
| 825 | C22 | — | 2 | 1 | no | — |
| 826 | C22 | — | 2 | 1 | no | — |
| 827 | C22 | — | 2 | 1 | no | — |
| 828 | C22 | — | 2 | 1 | no | — |
| 829 | C22 | — | 2 | 1 | no | — |
| 830 | C22 | — | 2 | 1 | no | — |
| 831 | C22 | — | 2 | 1 | no | — |
| 832 | C22 | — | 4 | 4 | no | — |
| 833 | C22 | — | 4 | 1 | no | — |
| 834 | C22 | — | 4 | 1 | no | — |
| 835 | C22 | — | 4 | 1 | no | — |
| 836 | C22 | — | 316 | 1 | no | — |
| 837 | C22 | — | 316 | 1 | no | — |
| 838 | C22 | — | 316 | 1 | no | — |
| 839 | C22 | — | 316 | 1 | no | — |
| 840 | C22 | — | 316 | 1 | no | — |
| 841 | C22 | — | 316 | 1 | no | — |
| 842 | C22 | — | 316 | 1 | no | — |
| 843 | C22 | — | 316 | 1 | no | — |
| 844 | C22 | — | 316 | 1 | no | — |
| 845 | C22 | — | 632 | 2 | no | — |
| 846 | C22 | — | 1264 | 2 | no | — |
| 847 | C22 | — | 1264 | 2 | no | — |
| 848 | C22 | #19098749 | 1 | 2 | yes | — |
| 849 | C22 | C2×#14579129 | 1 | 1 | yes | characteristic |
| 850 | C22 | #19099372 | 1 | 2 | yes | — |
| 851 | C4 | — | 2 | 1 | no | — |
| 852 | C4 | — | 2 | 1 | no | — |
| 853 | C4 | — | 2 | 1 | no | — |
| 854 | C4 | — | 2 | 1 | no | — |
| 855 | C4 | — | 4 | 1 | no | — |
| 856 | C4 | — | 4 | 1 | no | — |
| 857 | C4 | — | 4 | 4 | no | — |
| 858 | C4 | — | 4 | 1 | no | — |
| 859 | C4 | — | 316 | 1 | no | — |
| 860 | C4 | — | 316 | 1 | no | — |
| 861 | C4 | — | 316 | 1 | no | — |
| 862 | C4 | — | 316 | 1 | no | — |
| 863 | C4 | — | 316 | 1 | no | — |
| 864 | C4 | — | 632 | 2 | no | — |
| 865 | C2 | — | 2 | 2 | no | — |
| 866 | C2 | — | 2 | 2 | no | — |
| 867 | C2 | — | 4 | 1 | no | — |
| 868 | C2 | — | 8 | 1 | no | — |
| 869 | C2 | — | 632 | 1 | no | — |
| 870 | C2 | — | 632 | 1 | no | — |
| 871 | C2 | — | 632 | 1 | no | — |
| 872 | C2 | #23772676 | 1 | 1 | yes | characteristic |
| 873 | C2 | #23772776 | 1 | 1 | yes | characteristic |
| 874 | C2 | C2×#19098749 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19098702 | C2 | semidirect |
| 3. #23769119 | C2 | semidirect |
| 4. #23762379 | C2 | semidirect |
| 5. #23762367 | C2 | semidirect |
| 6. #23762362 | C2 | semidirect |
| 7. #23762350 | C2 | semidirect |
| 8. #23761956 | C2 | semidirect |
| 9. #23761930 | C2 | semidirect |
| 10. #23761749 | C2 | semidirect |
| 11. C79×#3004 | C2 | semidirect |
| 35. #19098702 | C22 | semidirect |
| 37. C2×C22⋊(C79⋊C8) | C22 | semidirect |
| 39. #19098482 | C22 | semidirect |
| 41. #19098474 | C22 | semidirect |
| 43. #19098426 | C22 | semidirect |
| 44. #19098300 | C22 | semidirect |
| 46. #19098298 | C22 | semidirect |
| 47. #19098297 | C22 | semidirect |
| 48. #19098288 | C22 | semidirect |
| 49. #19098286 | C22 | semidirect |
| 50. C23×Q8×C79 | C22 | semidirect |
| 54. #451×C79 | C22 | semidirect |
| 56. #448×C79 | C22 | semidirect |
| 58. #407×C79 | C22 | semidirect |
| 439. #3004 | D79 | semidirect |
| 449. C79 | #18225 | semidirect |
| 450. C23×Q8 | C2×D79 | semidirect |
| 474. #451 | C2×D79 | semidirect |
| 480. #448 | C2×D79 | semidirect |
| 483. #407 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777584 | 2 |
| C2×#19098702 | 2 |
| #23769119 | 2 |
| #23762379 | 2 |
| #23762367 | 2 |
| #23762362 | 2 |
| #23762350 | 2 |
| #23761956 | 2 |
| #23761930 | 2 |
| #23761749 | 2 |
| C79×#3004 | 2 |
| #18225 | 79 |