Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
976 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23777189 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #23765083 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #23765063 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23765054 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23763371 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #23763368 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C79×#2123 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14579209 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×#14579207 | C22 | 1 | 1 | yes | characteristic |
| 10 | #19099223 | — | 2 | 1 | no | — |
| 11 | #19099223 | — | 2 | 1 | no | — |
| 12 | #19099205 | — | 2 | 2 | no | — |
| 13 | #19099205 | — | 2 | 2 | no | — |
| 14 | #19099204 | — | 2 | 1 | no | — |
| 15 | #19099204 | — | 2 | 1 | no | — |
| 16 | #19099138 | — | 2 | 1 | no | — |
| 17 | #19099132 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #19099131 | — | 2 | 1 | no | — |
| 19 | #19099114 | — | 2 | 1 | no | — |
| 20 | #19099109 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#14579150 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #124×D79 | — | 2 | 1 | no | — |
| 23 | #19099031 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #19098581 | — | 2 | 1 | no | — |
| 25 | #19098579 | — | 2 | 1 | no | — |
| 26 | #19098569 | — | 2 | 1 | no | — |
| 27 | #19098567 | — | 2 | 1 | no | — |
| 28 | #19098547 | C22 | 1 | 1 | yes | characteristic |
| 29 | #19098537 | C22 | 1 | 1 | yes | characteristic |
| 30 | #19098361 | — | 2 | 1 | no | — |
| 31 | #19098359 | — | 2 | 1 | no | — |
| 32 | #19098357 | — | 2 | 1 | no | — |
| 33 | #19098355 | — | 2 | 1 | no | — |
| 34 | #19098353 | — | 2 | 2 | no | — |
| 35 | #536×C79 | C22 | 1 | 1 | yes | characteristic |
| 36 | #413×C79 | C22 | 1 | 1 | yes | characteristic |
| 37 | #410×C79 | C22 | 1 | 1 | yes | characteristic |
| 38 | #352×C79 | — | 2 | 2 | no | — |
| 39 | #14579209 | — | 4 | 2 | no | — |
| 40 | #14579209 | — | 4 | 2 | no | — |
| 41 | #14579207 | — | 4 | 2 | no | — |
| 42 | #14579207 | — | 4 | 2 | no | — |
| 43 | C2×#11929625 | — | 2 | 1 | no | — |
| 44 | C2×#11929625 | — | 2 | 1 | no | — |
| 45 | C2×#11929625 | — | 2 | 1 | no | — |
| 46 | C2×#11929624 | — | 2 | 2 | no | — |
| 47 | C2×#11929624 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C2×#11929624 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×#11929624 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×#11929624 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×Q8×D79 | — | 2 | 1 | no | — |
| 52 | C2×Q8×D79 | — | 2 | 1 | no | — |
| 53 | C22×D316 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C22×D316 | D4 | 1 | 1 | yes | characteristic |
| 55 | C22×D316 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×D4×D79 | — | 2 | 1 | no | — |
| 57 | C2×D4×D79 | — | 2 | 1 | no | — |
| 58 | C2×D4×D79 | — | 2 | 1 | no | — |
| 59 | C2×#11929608 | — | 2 | 1 | no | — |
| 60 | #14579159 | D4 | 1 | 1 | yes | characteristic |
| 61 | #14579158 | — | 2 | 1 | no | — |
| 62 | #14579157 | D4 | 1 | 1 | yes | characteristic |
| 63 | #14579150 | — | 2 | 1 | no | — |
| 64 | #14579150 | — | 2 | 1 | no | — |
| 65 | #14579150 | — | 2 | 1 | no | — |
| 66 | #14579150 | — | 2 | 1 | no | — |
| 67 | #14579150 | D4 | 1 | 1 | yes | characteristic |
| 68 | #14579149 | — | 2 | 1 | no | — |
| 69 | #14579148 | D4 | 1 | 1 | yes | characteristic |
| 70 | #14579147 | — | 2 | 2 | no | — |
| 71 | #14579147 | — | 2 | 2 | no | — |
| 72 | #14579146 | — | 2 | 2 | no | — |
| 73 | #14579146 | — | 2 | 2 | no | — |
| 74 | #14579139 | — | 2 | 2 | no | — |
| 75 | #14579139 | — | 2 | 2 | no | — |
| 76 | #14579136 | — | 2 | 2 | no | — |
| 77 | #14579136 | — | 2 | 2 | no | — |
| 78 | #14579136 | — | 2 | 1 | no | — |
| 79 | #14579136 | — | 2 | 1 | no | — |
| 80 | #14579134 | — | 2 | 2 | no | — |
| 81 | #14579134 | — | 2 | 2 | no | — |
| 82 | #14579133 | — | 2 | 1 | no | — |
| 83 | #14579133 | — | 2 | 1 | no | — |
| 84 | #14579131 | — | 2 | 2 | no | — |
| 85 | #14579131 | — | 2 | 2 | no | — |
| 86 | #14579131 | — | 2 | 2 | no | — |
| 87 | #14579126 | — | 2 | 1 | no | — |
| 88 | #14579123 | — | 2 | 2 | no | — |
| 89 | #14579123 | — | 2 | 2 | no | — |
| 90 | #14579123 | — | 2 | 1 | no | — |
| 91 | C4×C22⋊D79 | — | 2 | 1 | no | — |
| 92 | C4×C22⋊D79 | — | 2 | 1 | no | — |
| 93 | (C22⋊D79)⋊C4 | — | 2 | 2 | no | — |
| 94 | #14579120 | — | 2 | 1 | no | — |
| 95 | #14579118 | — | 2 | 1 | no | — |
| 96 | C2×(C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 97 | C22⋊C4×D79 | — | 2 | 2 | no | — |
| 98 | C22⋊C4×D79 | — | 2 | 2 | no | — |
| 99 | C2×C4×Dic79 | C2×C4 | 1 | 1 | yes | characteristic |
| 100 | C42×D79 | — | 2 | 1 | no | — |
| 101 | #14579089 | — | 4 | 2 | no | — |
| 102 | #14579087 | — | 4 | 2 | no | — |
| 103 | #14579083 | — | 4 | 2 | no | — |
| 104 | #14579081 | — | 4 | 2 | no | — |
| 105 | #14579080 | — | 2 | 1 | no | — |
| 106 | #14579078 | — | 2 | 1 | no | — |
| 107 | #14579076 | — | 2 | 1 | no | — |
| 108 | #14579076 | — | 2 | 1 | no | — |
| 109 | C2×#41×C79 | C23 | 1 | 1 | yes | characteristic |
| 110 | C22×Q8×C79 | C2×C4 | 1 | 1 | yes | characteristic |
| 111 | C2×M16×C79 | — | 2 | 1 | no | — |
| 112 | C4⋊Q8×C79 | — | 2 | 1 | no | — |
| 113 | #124×C79 | — | 2 | 1 | no | — |
| 114 | #123×C79 | D4 | 1 | 2 | yes | — |
| 115 | #123×C79 | D4 | 1 | 2 | yes | — |
| 116 | C22⋊Q8×C79 | — | 2 | 1 | no | — |
| 117 | C22⋊Q8×C79 | — | 2 | 1 | no | — |
| 118 | #117×C79 | — | 2 | 1 | no | — |
| 119 | #117×C79 | C2×C4 | 1 | 1 | yes | characteristic |
| 120 | #101×C79 | — | 2 | 1 | no | — |
| 121 | #100×C79 | — | 2 | 1 | no | — |
| 122 | #99×C79 | — | 2 | 1 | no | — |
| 123 | #99×C79 | — | 2 | 1 | no | — |
| 124 | C23×D79 | — | 2 | 1 | no | — |
| 125 | C23×D79 | — | 2 | 1 | no | — |
| 126 | C23×D79 | — | 2 | 1 | no | — |
| 127 | #11929625 | — | 4 | 4 | no | — |
| 128 | #11929625 | — | 4 | 4 | no | — |
| 129 | #11929625 | — | 4 | 2 | no | — |
| 130 | #11929625 | — | 4 | 2 | no | — |
| 131 | #11929624 | — | 2 | 2 | no | — |
| 132 | #11929624 | — | 2 | 2 | no | — |
| 133 | #11929624 | — | 2 | 2 | no | — |
| 134 | #11929624 | — | 2 | 2 | no | — |
| 135 | #11929624 | — | 4 | 8 | no | — |
| 136 | #11929624 | — | 4 | 1 | no | — |
| 137 | #11929624 | — | 4 | 1 | no | — |
| 138 | #11929624 | — | 4 | 1 | no | — |
| 139 | #11929624 | — | 4 | 1 | no | — |
| 140 | C2×Dic158 | — | 2 | 2 | no | — |
| 141 | C2×Dic158 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 142 | C2×Dic158 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 143 | Q8×D79 | — | 4 | 2 | no | — |
| 144 | Q8×D79 | — | 4 | 4 | no | — |
| 145 | Q8×D79 | — | 4 | 2 | no | — |
| 146 | C2×D316 | — | 2 | 2 | no | — |
| 147 | C2×D316 | — | 2 | 2 | no | — |
| 148 | C2×D316 | — | 2 | 2 | no | — |
| 149 | C2×D316 | — | 2 | 2 | no | — |
| 150 | C2×D316 | — | 2 | 2 | no | — |
| 151 | C2×D316 | — | 2 | 1 | no | — |
| 152 | C2×D316 | — | 2 | 1 | no | — |
| 153 | C2×D316 | — | 2 | 1 | no | — |
| 154 | C2×D316 | — | 4 | 1 | no | — |
| 155 | C2×D316 | — | 4 | 1 | no | — |
| 156 | C2×D316 | — | 4 | 1 | no | — |
| 157 | C2×D316 | — | 4 | 1 | no | — |
| 158 | C2×D316 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 159 | C2×D316 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 160 | C2×D316 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 161 | C2×D316 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 162 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 163 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 164 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 165 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 166 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 167 | C2×C22⋊D79 | — | 2 | 1 | no | — |
| 168 | D4×D79 | — | 4 | 4 | no | — |
| 169 | D4×D79 | — | 4 | 4 | no | — |
| 170 | D4×D79 | — | 4 | 4 | no | — |
| 171 | C22×Dic79 | — | 2 | 1 | no | — |
| 172 | C2×C4×D79 | — | 2 | 2 | no | — |
| 173 | C2×C4×D79 | — | 2 | 2 | no | — |
| 174 | C2×C4×D79 | — | 2 | 2 | no | — |
| 175 | C2×C4×D79 | — | 2 | 1 | no | — |
| 176 | C2×C4×D79 | — | 2 | 1 | no | — |
| 177 | C2×C4×D79 | — | 2 | 1 | no | — |
| 178 | C2×C4×D79 | — | 2 | 1 | no | — |
| 179 | #11929608 | — | 4 | 1 | no | — |
| 180 | #11929608 | — | 4 | 1 | no | — |
| 181 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 182 | C4⋊Dic79 | — | 4 | 1 | no | — |
| 183 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 184 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 185 | Dic79⋊C4 | — | 2 | 1 | no | — |
| 186 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 187 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 188 | C22⋊Dic79 | — | 4 | 1 | no | — |
| 189 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 190 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 191 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 192 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 193 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 194 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 195 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 196 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 197 | (C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 198 | C4×Dic79 | — | 2 | 2 | no | — |
| 199 | C4×Dic79 | — | 2 | 1 | no | — |
| 200 | C4×Dic79 | — | 4 | 1 | no | — |
| 201 | C4×Dic79 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 202 | C4×Dic79 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 203 | #41×C79 | — | 4 | 1 | no | — |
| 204 | #41×C79 | — | 4 | 1 | no | — |
| 205 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 206 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 207 | C2×Q8×C79 | — | 4 | 1 | no | — |
| 208 | C2×Q8×C79 | — | 4 | 1 | no | — |
| 209 | C2×Q8×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C22×C4×C79 | C22⋊C4 | 1 | 2 | yes | — |
| 214 | C22×C4×C79 | C22×C4 | 1 | 1 | yes | characteristic |
| 215 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | M16×C79 | — | 4 | 1 | no | — |
| 218 | M16×C79 | — | 4 | 1 | no | — |
| 219 | C2×C8×C79 | — | 4 | 1 | no | — |
| 220 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 221 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 222 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 223 | C4⋊C4×C79 | — | 4 | 1 | no | — |
| 224 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 225 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 226 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 227 | C22⋊C4×C79 | C22⋊C4 | 1 | 2 | yes | — |
| 228 | C42×C79 | — | 2 | 1 | no | — |
| 229 | C42×C79 | — | 4 | 1 | no | — |
| 230 | C23×C79 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 231 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 232 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 233 | C22×D79 | — | 2 | 1 | no | — |
| 234 | C22×D79 | — | 2 | 1 | no | — |
| 235 | C22×D79 | — | 2 | 1 | no | — |
| 236 | C22×D79 | — | 2 | 1 | no | — |
| 237 | C22×D79 | — | 4 | 2 | no | — |
| 238 | C22×D79 | — | 4 | 2 | no | — |
| 239 | C22×D79 | — | 4 | 2 | no | — |
| 240 | C22×D79 | — | 8 | 2 | no | — |
| 241 | C22×D79 | — | 8 | 2 | no | — |
| 242 | C22×D79 | — | 8 | 2 | no | — |
| 243 | Q8×C79 | — | 4 | 1 | no | — |
| 244 | Q8×C79 | — | 4 | 2 | no | — |
| 245 | Q8×C79 | — | 4 | 1 | no | — |
| 246 | Q8×C79 | — | 4 | 1 | no | — |
| 247 | D4×C79 | — | 4 | 1 | no | — |
| 248 | D4×C79 | — | 4 | 1 | no | — |
| 249 | D4×C79 | — | 4 | 1 | no | — |
| 250 | C2×C4×C79 | — | 2 | 1 | no | — |
| 251 | C2×C4×C79 | — | 2 | 1 | no | — |
| 252 | C2×C4×C79 | — | 2 | 1 | no | — |
| 253 | C2×C4×C79 | — | 2 | 1 | no | — |
| 254 | C2×C4×C79 | — | 2 | 1 | no | — |
| 255 | C2×C4×C79 | — | 2 | 1 | no | — |
| 256 | C2×C4×C79 | — | 2 | 2 | no | — |
| 257 | C2×C4×C79 | — | 2 | 2 | no | — |
| 258 | C2×C4×C79 | — | 4 | 2 | no | — |
| 259 | C2×C4×C79 | — | 8 | 1 | no | — |
| 260 | C2×C4×C79 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C79 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 262 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 264 | C22⋊D79 | — | 2 | 4 | no | — |
| 265 | C22⋊D79 | — | 4 | 2 | no | — |
| 266 | C22⋊D79 | — | 4 | 2 | no | — |
| 267 | C22⋊D79 | — | 4 | 2 | no | — |
| 268 | C22⋊D79 | — | 8 | 1 | no | — |
| 269 | C22⋊D79 | — | 8 | 1 | no | — |
| 270 | C2×Dic79 | — | 2 | 1 | no | — |
| 271 | C2×Dic79 | — | 2 | 1 | no | — |
| 272 | C2×Dic79 | — | 2 | 1 | no | — |
| 273 | C2×Dic79 | — | 2 | 1 | no | — |
| 274 | C2×Dic79 | — | 8 | 1 | no | — |
| 275 | C2×Dic79 | — | 8 | 1 | no | — |
| 276 | D316 | — | 2 | 1 | no | — |
| 277 | D316 | — | 2 | 1 | no | — |
| 278 | D316 | — | 2 | 1 | no | — |
| 279 | D316 | — | 2 | 1 | no | — |
| 280 | D316 | — | 2 | 1 | no | — |
| 281 | D316 | — | 4 | 2 | no | — |
| 282 | D316 | — | 4 | 2 | no | — |
| 283 | D316 | — | 4 | 1 | no | — |
| 284 | D316 | — | 4 | 2 | no | — |
| 285 | D316 | — | 4 | 4 | no | — |
| 286 | D316 | — | 8 | 2 | no | — |
| 287 | D316 | — | 8 | 2 | no | — |
| 288 | D316 | #99 | 1 | 2 | yes | — |
| 289 | C4×D79 | — | 2 | 4 | no | — |
| 290 | C4×D79 | — | 4 | 2 | no | — |
| 291 | C4×D79 | — | 4 | 2 | no | — |
| 292 | C4×D79 | — | 4 | 4 | no | — |
| 293 | C4×D79 | — | 4 | 4 | no | — |
| 294 | C4×D79 | — | 4 | 1 | no | — |
| 295 | C4×D79 | — | 4 | 1 | no | — |
| 296 | C4×D79 | — | 8 | 2 | no | — |
| 297 | Dic158 | — | 2 | 1 | no | — |
| 298 | Dic158 | — | 4 | 4 | no | — |
| 299 | Dic158 | — | 4 | 1 | no | — |
| 300 | Dic158 | #99 | 1 | 2 | yes | — |
| 301 | C8×C79 | — | 8 | 1 | no | — |
| 302 | C79⋊C8 | — | 8 | 1 | no | — |
| 303 | C22×C79 | — | 2 | 1 | no | — |
| 304 | C22×C79 | — | 2 | 1 | no | — |
| 305 | C22×C79 | — | 2 | 1 | no | — |
| 306 | C22×C79 | — | 4 | 1 | no | — |
| 307 | C22×C79 | — | 4 | 1 | no | — |
| 308 | C22×C79 | — | 4 | 1 | no | — |
| 309 | C22×C79 | #379 | 1 | 1 | yes | characteristic |
| 310 | C2×D79 | — | 2 | 2 | no | — |
| 311 | C2×D79 | — | 4 | 2 | no | — |
| 312 | C2×D79 | — | 4 | 1 | no | — |
| 313 | C2×D79 | — | 4 | 1 | no | — |
| 314 | C2×D79 | — | 4 | 2 | no | — |
| 315 | C2×D79 | — | 4 | 2 | no | — |
| 316 | C2×D79 | — | 4 | 1 | no | — |
| 317 | C2×D79 | — | 4 | 1 | no | — |
| 318 | C2×D79 | — | 4 | 1 | no | — |
| 319 | C2×D79 | — | 16 | 2 | no | — |
| 320 | C2×D79 | — | 16 | 2 | no | — |
| 321 | C2×D79 | — | 16 | 2 | no | — |
| 322 | C4×C79 | — | 2 | 1 | no | — |
| 323 | C4×C79 | — | 2 | 1 | no | — |
| 324 | C4×C79 | — | 2 | 1 | no | — |
| 325 | C4×C79 | — | 4 | 2 | no | — |
| 326 | C4×C79 | — | 4 | 2 | no | — |
| 327 | C4×C79 | — | 16 | 1 | no | — |
| 328 | C4×C79 | C2×#99 | 1 | 1 | yes | characteristic |
| 329 | C4×C79 | C2×#99 | 1 | 1 | yes | characteristic |
| 330 | Dic79 | — | 2 | 2 | no | — |
| 331 | Dic79 | — | 4 | 1 | no | — |
| 332 | Dic79 | — | 4 | 1 | no | — |
| 333 | Dic79 | — | 4 | 1 | no | — |
| 334 | Dic79 | — | 16 | 1 | no | — |
| 335 | #12716 | — | 79 | 1 | no | maximal, Sylow |
| 336 | C2×C79 | — | 2 | 1 | no | — |
| 337 | C2×C79 | — | 4 | 1 | no | — |
| 338 | C2×C79 | — | 4 | 1 | no | — |
| 339 | C2×C79 | — | 4 | 1 | no | — |
| 340 | C2×C79 | #1781 | 1 | 1 | yes | characteristic |
| 341 | D79 | — | 4 | 2 | no | — |
| 342 | D79 | — | 8 | 1 | no | — |
| 343 | D79 | — | 8 | 1 | no | — |
| 344 | D79 | — | 8 | 1 | no | — |
| 345 | #3500 | — | 79 | 1 | no | — |
| 346 | #2132 | — | 79 | 1 | no | — |
| 347 | #2126 | — | 79 | 1 | no | — |
| 348 | #2123 | — | 79 | 1 | no | — |
| 349 | #2123 | D79 | 1 | 1 | yes | characteristic, complemented |
| 350 | #1795 | — | 79 | 1 | no | — |
| 351 | #1795 | — | 79 | 1 | no | — |
| 352 | C79 | #12716 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 353 | C2×2−1+4 | — | 79 | 1 | no | — |
| 354 | C2×H(5,𝔽2) | — | 79 | 1 | no | — |
| 355 | #548 | — | 158 | 1 | no | — |
| 356 | #548 | — | 158 | 1 | no | — |
| 357 | #546 | — | 158 | 1 | no | — |
| 358 | #546 | — | 158 | 1 | no | — |
| 359 | #546 | — | 158 | 2 | no | — |
| 360 | #546 | — | 158 | 2 | no | — |
| 361 | #536 | — | 158 | 1 | no | — |
| 362 | #536 | C2×D79 | 1 | 1 | yes | characteristic |
| 363 | #535 | — | 79 | 1 | no | — |
| 364 | #535 | — | 158 | 1 | no | — |
| 365 | #532 | — | 79 | 1 | no | — |
| 366 | #532 | — | 158 | 1 | no | — |
| 367 | C2×#124 | — | 79 | 1 | no | — |
| 368 | C2×#124 | — | 158 | 1 | no | — |
| 369 | C4×#41 | — | 79 | 1 | no | — |
| 370 | #421 | — | 158 | 1 | no | — |
| 371 | #421 | — | 158 | 1 | no | — |
| 372 | #418 | — | 158 | 1 | no | — |
| 373 | #418 | — | 158 | 1 | no | — |
| 374 | #413 | — | 79 | 1 | no | — |
| 375 | #413 | C2×D79 | 1 | 1 | yes | characteristic |
| 376 | #410 | — | 79 | 1 | no | — |
| 377 | #410 | C2×D79 | 1 | 1 | yes | characteristic |
| 378 | #356 | — | 158 | 1 | no | — |
| 379 | #355 | — | 158 | 1 | no | — |
| 380 | #354 | — | 158 | 1 | no | — |
| 381 | #353 | — | 158 | 1 | no | — |
| 382 | #352 | — | 2 | 2 | no | — |
| 383 | #352 | — | 158 | 2 | no | — |
| 384 | 2−1+4 | — | 316 | 2 | no | — |
| 385 | 2−1+4 | — | 316 | 2 | no | — |
| 386 | H(5,𝔽2) | — | 316 | 2 | no | — |
| 387 | H(5,𝔽2) | — | 316 | 2 | no | — |
| 388 | C2×#41 | — | 79 | 1 | no | — |
| 389 | C2×#41 | — | 79 | 1 | no | — |
| 390 | C2×#41 | — | 79 | 1 | no | — |
| 391 | C2×#41 | — | 79 | 1 | no | — |
| 392 | C2×#41 | — | 158 | 1 | no | — |
| 393 | C2×#41 | — | 158 | 1 | no | — |
| 394 | C2×#41 | — | 158 | 1 | no | — |
| 395 | C2×#41 | — | 158 | 2 | no | — |
| 396 | C2×#41 | C22×D79 | 1 | 1 | yes | characteristic |
| 397 | C22×Q8 | — | 158 | 1 | no | — |
| 398 | C22×Q8 | — | 158 | 1 | no | — |
| 399 | C22×Q8 | C4×D79 | 1 | 1 | yes | characteristic |
| 400 | C22×D4 | — | 79 | 1 | no | — |
| 401 | C22×D4 | — | 79 | 1 | no | — |
| 402 | C22×D4 | — | 79 | 1 | no | — |
| 403 | C22×D4 | — | 158 | 1 | no | — |
| 404 | C22×D4 | — | 158 | 1 | no | — |
| 405 | C22×D4 | — | 158 | 1 | no | — |
| 406 | C2×M16 | — | 2 | 1 | no | — |
| 407 | C2×M16 | — | 158 | 1 | no | — |
| 408 | C4⋊Q8 | — | 2 | 1 | no | — |
| 409 | C4⋊Q8 | — | 79 | 1 | no | — |
| 410 | #127 | — | 79 | 1 | no | — |
| 411 | #127 | — | 158 | 1 | no | — |
| 412 | #124 | — | 2 | 1 | no | — |
| 413 | #124 | — | 79 | 1 | no | — |
| 414 | #124 | — | 79 | 1 | no | — |
| 415 | #124 | — | 158 | 1 | no | — |
| 416 | #124 | — | 158 | 1 | no | — |
| 417 | #124 | — | 158 | 1 | no | — |
| 418 | #124 | — | 158 | 2 | no | — |
| 419 | #124 | — | 158 | 2 | no | — |
| 420 | #124 | — | 158 | 1 | no | — |
| 421 | #124 | — | 158 | 1 | no | — |
| 422 | #123 | — | 158 | 2 | no | — |
| 423 | #123 | — | 158 | 2 | no | — |
| 424 | #123 | D316 | 1 | 2 | yes | — |
| 425 | #123 | C22⋊D79 | 1 | 2 | yes | — |
| 426 | C22⋊Q8 | — | 2 | 1 | no | — |
| 427 | C22⋊Q8 | — | 2 | 1 | no | — |
| 428 | C22⋊Q8 | — | 158 | 2 | no | — |
| 429 | C22⋊Q8 | — | 158 | 2 | no | — |
| 430 | #121 | — | 158 | 2 | no | — |
| 431 | #121 | — | 158 | 2 | no | — |
| 432 | #121 | — | 158 | 1 | no | — |
| 433 | #121 | — | 158 | 1 | no | — |
| 434 | #121 | — | 158 | 2 | no | — |
| 435 | #121 | — | 158 | 2 | no | — |
| 436 | #121 | — | 158 | 1 | no | — |
| 437 | #121 | — | 158 | 1 | no | — |
| 438 | #120 | — | 158 | 2 | no | — |
| 439 | #120 | — | 158 | 2 | no | — |
| 440 | #120 | — | 158 | 2 | no | — |
| 441 | C4×Q8 | — | 158 | 1 | no | — |
| 442 | C4×D4 | — | 158 | 1 | no | — |
| 443 | C4×D4 | — | 158 | 2 | no | — |
| 444 | C4×D4 | — | 158 | 2 | no | — |
| 445 | C4×D4 | — | 158 | 1 | no | — |
| 446 | C4×D4 | — | 158 | 1 | no | — |
| 447 | C4×D4 | — | 158 | 2 | no | — |
| 448 | #117 | — | 2 | 1 | no | — |
| 449 | #117 | — | 158 | 1 | no | — |
| 450 | #117 | — | 158 | 1 | no | — |
| 451 | #117 | C4×D79 | 1 | 1 | yes | characteristic |
| 452 | C2×C22⋊C4 | — | 158 | 2 | no | — |
| 453 | C2×C22⋊C4 | — | 158 | 2 | no | — |
| 454 | C2×C22⋊C4 | — | 158 | 2 | no | — |
| 455 | C2×C42 | — | 79 | 1 | no | — |
| 456 | C2×C42 | — | 158 | 1 | no | — |
| 457 | #104 | — | 316 | 2 | no | — |
| 458 | #104 | — | 316 | 2 | no | — |
| 459 | #102 | — | 316 | 2 | no | — |
| 460 | #102 | — | 316 | 2 | no | — |
| 461 | #101 | — | 2 | 1 | no | — |
| 462 | #101 | — | 158 | 1 | no | — |
| 463 | #100 | — | 2 | 1 | no | — |
| 464 | #100 | — | 158 | 1 | no | — |
| 465 | #99 | — | 2 | 1 | no | — |
| 466 | #99 | — | 2 | 1 | no | — |
| 467 | #99 | — | 158 | 1 | no | — |
| 468 | #99 | — | 158 | 1 | no | — |
| 469 | C24 | — | 158 | 1 | no | — |
| 470 | C24 | — | 158 | 1 | no | — |
| 471 | C24 | — | 158 | 1 | no | — |
| 472 | #41 | — | 4 | 1 | no | — |
| 473 | #41 | — | 4 | 1 | no | — |
| 474 | #41 | — | 316 | 1 | no | — |
| 475 | #41 | — | 316 | 1 | no | — |
| 476 | #41 | — | 316 | 1 | no | — |
| 477 | #41 | — | 316 | 1 | no | — |
| 478 | #41 | — | 316 | 8 | no | — |
| 479 | #41 | — | 316 | 2 | no | — |
| 480 | #41 | — | 316 | 2 | no | — |
| 481 | #41 | — | 316 | 4 | no | — |
| 482 | #41 | — | 316 | 4 | no | — |
| 483 | #41 | — | 158 | 2 | no | — |
| 484 | #41 | — | 158 | 2 | no | — |
| 485 | #41 | — | 158 | 2 | no | — |
| 486 | #41 | — | 158 | 2 | no | — |
| 487 | C2×Q8 | — | 2 | 1 | no | — |
| 488 | C2×Q8 | — | 2 | 1 | no | — |
| 489 | C2×Q8 | — | 4 | 1 | no | — |
| 490 | C2×Q8 | — | 4 | 1 | no | — |
| 491 | C2×Q8 | — | 316 | 2 | no | — |
| 492 | C2×Q8 | — | 316 | 2 | no | — |
| 493 | C2×Q8 | — | 316 | 4 | no | — |
| 494 | C2×Q8 | — | 79 | 1 | no | — |
| 495 | C2×Q8 | — | 79 | 1 | no | — |
| 496 | C2×Q8 | — | 158 | 2 | no | — |
| 497 | C2×Q8 | D4×D79 | 1 | 1 | yes | characteristic |
| 498 | C2×D4 | — | 316 | 1 | no | — |
| 499 | C2×D4 | — | 316 | 1 | no | — |
| 500 | C2×D4 | — | 316 | 1 | no | — |
| 501 | C2×D4 | — | 316 | 1 | no | — |
| 502 | C2×D4 | — | 316 | 4 | no | — |
| 503 | C2×D4 | — | 316 | 4 | no | — |
| 504 | C2×D4 | — | 316 | 4 | no | — |
| 505 | C2×D4 | — | 79 | 1 | no | — |
| 506 | C2×D4 | — | 79 | 1 | no | — |
| 507 | C2×D4 | — | 79 | 1 | no | — |
| 508 | C2×D4 | — | 79 | 1 | no | — |
| 509 | C2×D4 | — | 158 | 2 | no | — |
| 510 | C2×D4 | — | 158 | 2 | no | — |
| 511 | C2×D4 | — | 158 | 2 | no | — |
| 512 | C2×D4 | — | 158 | 2 | no | — |
| 513 | C2×D4 | — | 158 | 2 | no | — |
| 514 | C2×D4 | — | 158 | 1 | no | — |
| 515 | C2×D4 | — | 158 | 1 | no | — |
| 516 | C2×D4 | — | 158 | 1 | no | — |
| 517 | C2×D4 | — | 158 | 1 | no | — |
| 518 | C2×D4 | — | 158 | 1 | no | — |
| 519 | C2×D4 | — | 158 | 1 | no | — |
| 520 | C2×D4 | — | 158 | 1 | no | — |
| 521 | C2×D4 | — | 158 | 1 | no | — |
| 522 | C2×D4 | — | 158 | 1 | no | — |
| 523 | C2×D4 | D4×D79 | 1 | 1 | yes | characteristic |
| 524 | C2×D4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 525 | C2×D4 | C2×D316 | 1 | 1 | yes | characteristic |
| 526 | C22×C4 | — | 158 | 2 | no | — |
| 527 | C22×C4 | — | 158 | 2 | no | — |
| 528 | C22×C4 | — | 158 | 2 | no | — |
| 529 | C22×C4 | — | 158 | 1 | no | — |
| 530 | C22×C4 | — | 158 | 1 | no | — |
| 531 | C22×C4 | — | 158 | 1 | no | — |
| 532 | C22×C4 | — | 158 | 1 | no | — |
| 533 | C22×C4 | — | 158 | 1 | no | — |
| 534 | C22×C4 | (C2×D79)⋊C4 | 1 | 2 | yes | — |
| 535 | C22×C4 | C2×C4×D79 | 1 | 1 | yes | characteristic |
| 536 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 537 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 538 | M16 | — | 4 | 1 | no | — |
| 539 | M16 | — | 4 | 1 | no | — |
| 540 | M16 | — | 316 | 1 | no | — |
| 541 | M16 | — | 316 | 1 | no | — |
| 542 | C2×C8 | — | 4 | 1 | no | — |
| 543 | C2×C8 | — | 316 | 1 | no | — |
| 544 | C4⋊C4 | — | 2 | 1 | no | — |
| 545 | C4⋊C4 | — | 2 | 2 | no | — |
| 546 | C4⋊C4 | — | 2 | 2 | no | — |
| 547 | C4⋊C4 | — | 4 | 1 | no | — |
| 548 | C4⋊C4 | — | 316 | 1 | no | — |
| 549 | C4⋊C4 | — | 158 | 2 | no | — |
| 550 | C4⋊C4 | — | 158 | 1 | no | — |
| 551 | C4⋊C4 | — | 158 | 1 | no | — |
| 552 | C22⋊C4 | — | 2 | 2 | no | — |
| 553 | C22⋊C4 | — | 2 | 2 | no | — |
| 554 | C22⋊C4 | — | 4 | 1 | no | — |
| 555 | C22⋊C4 | — | 316 | 1 | no | — |
| 556 | C22⋊C4 | — | 158 | 2 | no | — |
| 557 | C22⋊C4 | — | 158 | 2 | no | — |
| 558 | C22⋊C4 | — | 158 | 2 | no | — |
| 559 | C22⋊C4 | — | 158 | 2 | no | — |
| 560 | C22⋊C4 | — | 158 | 2 | no | — |
| 561 | C22⋊C4 | — | 158 | 2 | no | — |
| 562 | C22⋊C4 | — | 158 | 2 | no | — |
| 563 | C22⋊C4 | — | 158 | 1 | no | — |
| 564 | C22⋊C4 | — | 158 | 1 | no | — |
| 565 | C22⋊C4 | — | 158 | 1 | no | — |
| 566 | C22⋊C4 | — | 158 | 1 | no | — |
| 567 | C22⋊C4 | (C2×D79)⋊C4 | 1 | 2 | yes | — |
| 568 | C42 | — | 2 | 1 | no | — |
| 569 | C42 | — | 4 | 1 | no | — |
| 570 | C42 | — | 316 | 1 | no | — |
| 571 | C42 | — | 79 | 1 | no | — |
| 572 | C42 | — | 79 | 1 | no | — |
| 573 | C42 | — | 158 | 2 | no | — |
| 574 | C42 | — | 158 | 1 | no | — |
| 575 | C23 | — | 316 | 2 | no | — |
| 576 | C23 | — | 316 | 2 | no | — |
| 577 | C23 | — | 316 | 2 | no | — |
| 578 | C23 | — | 632 | 2 | no | — |
| 579 | C23 | — | 632 | 2 | no | — |
| 580 | C23 | — | 632 | 2 | no | — |
| 581 | C23 | — | 158 | 1 | no | — |
| 582 | C23 | — | 158 | 1 | no | — |
| 583 | C23 | — | 158 | 1 | no | — |
| 584 | C23 | — | 158 | 1 | no | — |
| 585 | C23 | C2×(C2×D79)⋊C4 | 1 | 1 | yes | characteristic |
| 586 | C23 | #14579129 | 1 | 1 | yes | characteristic |
| 587 | C23 | #14579131 | 1 | 1 | yes | characteristic |
| 588 | Q8 | — | 4 | 1 | no | — |
| 589 | Q8 | — | 4 | 2 | no | — |
| 590 | Q8 | — | 4 | 1 | no | — |
| 591 | Q8 | — | 4 | 1 | no | — |
| 592 | Q8 | — | 316 | 1 | no | — |
| 593 | Q8 | — | 316 | 4 | no | — |
| 594 | Q8 | — | 79 | 2 | no | — |
| 595 | Q8 | — | 158 | 1 | no | — |
| 596 | D4 | — | 4 | 1 | no | — |
| 597 | D4 | — | 4 | 1 | no | — |
| 598 | D4 | — | 4 | 1 | no | — |
| 599 | D4 | — | 316 | 1 | no | — |
| 600 | D4 | — | 316 | 2 | no | — |
| 601 | D4 | — | 316 | 2 | no | — |
| 602 | D4 | — | 316 | 2 | no | — |
| 603 | D4 | — | 316 | 4 | no | — |
| 604 | D4 | — | 316 | 2 | no | — |
| 605 | D4 | — | 316 | 2 | no | — |
| 606 | D4 | — | 316 | 2 | no | — |
| 607 | D4 | — | 79 | 2 | no | — |
| 608 | D4 | — | 632 | 2 | no | — |
| 609 | D4 | — | 632 | 2 | no | — |
| 610 | D4 | — | 632 | 1 | no | — |
| 611 | D4 | — | 632 | 1 | no | — |
| 612 | D4 | — | 158 | 4 | no | — |
| 613 | D4 | — | 158 | 1 | no | — |
| 614 | D4 | — | 158 | 1 | no | — |
| 615 | D4 | — | 158 | 1 | no | — |
| 616 | D4 | — | 158 | 1 | no | — |
| 617 | D4 | — | 158 | 1 | no | — |
| 618 | C2×C4 | — | 2 | 1 | no | — |
| 619 | C2×C4 | — | 2 | 1 | no | — |
| 620 | C2×C4 | — | 2 | 1 | no | — |
| 621 | C2×C4 | — | 2 | 1 | no | — |
| 622 | C2×C4 | — | 2 | 1 | no | — |
| 623 | C2×C4 | — | 2 | 1 | no | — |
| 624 | C2×C4 | — | 2 | 2 | no | — |
| 625 | C2×C4 | — | 2 | 2 | no | — |
| 626 | C2×C4 | — | 4 | 2 | no | — |
| 627 | C2×C4 | — | 8 | 1 | no | — |
| 628 | C2×C4 | — | 316 | 2 | no | — |
| 629 | C2×C4 | — | 316 | 2 | no | — |
| 630 | C2×C4 | — | 316 | 4 | no | — |
| 631 | C2×C4 | — | 316 | 4 | no | — |
| 632 | C2×C4 | — | 316 | 1 | no | — |
| 633 | C2×C4 | — | 316 | 1 | no | — |
| 634 | C2×C4 | — | 632 | 2 | no | — |
| 635 | C2×C4 | — | 632 | 1 | no | — |
| 636 | C2×C4 | — | 632 | 1 | no | — |
| 637 | C2×C4 | — | 158 | 4 | no | — |
| 638 | C2×C4 | — | 158 | 1 | no | — |
| 639 | C2×C4 | — | 158 | 1 | no | — |
| 640 | C2×C4 | — | 158 | 1 | no | — |
| 641 | C2×C4 | — | 158 | 1 | no | — |
| 642 | C2×C4 | C22⋊C4×D79 | 1 | 1 | yes | characteristic |
| 643 | C2×C4 | C22⋊C4×D79 | 1 | 1 | yes | characteristic |
| 644 | C2×C4 | #14579129 | 1 | 1 | yes | characteristic |
| 645 | C2×C4 | #14579131 | 1 | 1 | yes | characteristic |
| 646 | C8 | — | 8 | 1 | no | — |
| 647 | C8 | — | 632 | 1 | no | — |
| 648 | C22 | — | 2 | 1 | no | — |
| 649 | C22 | — | 2 | 1 | no | — |
| 650 | C22 | — | 2 | 1 | no | — |
| 651 | C22 | — | 4 | 1 | no | — |
| 652 | C22 | — | 4 | 1 | no | — |
| 653 | C22 | — | 4 | 1 | no | — |
| 654 | C22 | — | 316 | 2 | no | — |
| 655 | C22 | — | 316 | 1 | no | — |
| 656 | C22 | — | 316 | 1 | no | — |
| 657 | C22 | — | 316 | 2 | no | — |
| 658 | C22 | — | 316 | 2 | no | — |
| 659 | C22 | — | 316 | 1 | no | — |
| 660 | C22 | — | 316 | 1 | no | — |
| 661 | C22 | — | 316 | 1 | no | — |
| 662 | C22 | — | 158 | 2 | no | — |
| 663 | C22 | — | 1264 | 2 | no | — |
| 664 | C22 | — | 1264 | 2 | no | — |
| 665 | C22 | — | 1264 | 2 | no | — |
| 666 | C22 | #19098418 | 1 | 1 | yes | characteristic |
| 667 | C4 | — | 2 | 1 | no | — |
| 668 | C4 | — | 2 | 1 | no | — |
| 669 | C4 | — | 2 | 1 | no | — |
| 670 | C4 | — | 4 | 2 | no | — |
| 671 | C4 | — | 4 | 2 | no | — |
| 672 | C4 | — | 16 | 1 | no | — |
| 673 | C4 | — | 316 | 1 | no | — |
| 674 | C4 | — | 316 | 1 | no | — |
| 675 | C4 | — | 316 | 1 | no | — |
| 676 | C4 | — | 158 | 2 | no | — |
| 677 | C4 | — | 1264 | 1 | no | — |
| 678 | C4 | #99×D79 | 1 | 1 | yes | characteristic |
| 679 | C4 | #99×D79 | 1 | 1 | yes | characteristic |
| 680 | C2 | — | 2 | 1 | no | — |
| 681 | C2 | — | 4 | 1 | no | — |
| 682 | C2 | — | 4 | 1 | no | — |
| 683 | C2 | — | 4 | 1 | no | — |
| 684 | C2 | — | 316 | 2 | no | — |
| 685 | C2 | — | 632 | 1 | no | — |
| 686 | C2 | — | 632 | 1 | no | — |
| 687 | C2 | — | 632 | 1 | no | — |
| 688 | C2 | #23763313 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23765083 | C2 | semidirect |
| 3. #23765063 | C2 | semidirect |
| 4. #23765054 | C2 | semidirect |
| 5. #23763371 | C2 | semidirect |
| 6. #23763368 | C2 | semidirect |
| 7. C79×#2123 | C2 | semidirect |
| 8. C2×#14579209 | C4 | semidirect |
| 17. #19099132 | C4 | semidirect |
| 21. C2×#14579150 | C4 | semidirect |
| 23. #19099031 | C4 | semidirect |
| 349. #2123 | D79 | semidirect |
| 352. C79 | #12716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777189 | 2 |
| #23765083 | 2 |
| #23765063 | 2 |
| #23765054 | 2 |
| #23763371 | 2 |
| #23763368 | 2 |
| C79×#2123 | 2 |
| #12716 | 79 |