← #35197257
Subgroups — #35197257
Order 20224.
6616 conjugacy classes of subgroups.
The subgroup lattice has 640 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #23777906 | C2 | 1 | 6 | yes | maximal, complemented |
| 2 | #23777827 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #23777675 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #23777660 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #23777505 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #23777472 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #23777311 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #23777286 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #23777276 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #23776696 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C79×#3444 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #19099312 | C22 | 1 | 12 | yes | complemented |
| 13 | #19099306 | C22 | 1 | 4 | yes | — |
| 14 | #19099302 | C22 | 1 | 12 | yes | complemented |
| 15 | #19099300 | C22 | 1 | 4 | yes | complemented |
| 16 | #19099298 | C22 | 1 | 12 | yes | complemented |
| 17 | #19099297 | C22 | 1 | 12 | yes | complemented |
| 18 | #19099291 | C22 | 1 | 12 | yes | complemented |
| 19 | #19099286 | C22 | 1 | 12 | yes | complemented |
| 20 | #19099283 | C22 | 1 | 12 | yes | — |
| 21 | #19099278 | C22 | 1 | 12 | yes | complemented |
| 22 | #19099275 | C22 | 1 | 12 | yes | complemented |
| 23 | #19099273 | C22 | 1 | 12 | yes | complemented |
| 24 | #19099259 | C22 | 1 | 12 | yes | complemented |
| 25 | #19099259 | C22 | 1 | 12 | yes | complemented |
| 26 | #19099258 | C22 | 1 | 24 | yes | complemented |
| 27 | #19099253 | C22 | 1 | 12 | yes | complemented |
| 28 | #19099253 | C22 | 1 | 12 | yes | complemented |
| 29 | #19099245 | C22 | 1 | 24 | yes | complemented |
| 30 | #19099243 | C22 | 1 | 12 | yes | complemented |
| 31 | #19099241 | C22 | 1 | 12 | yes | — |
| 32 | #19099234 | C22 | 1 | 12 | yes | — |
| 33 | #19099222 | C22 | 1 | 12 | yes | complemented |
| 34 | #19099222 | C22 | 1 | 12 | yes | complemented |
| 35 | #19099218 | C22 | 1 | 12 | yes | complemented |
| 36 | #19099209 | C22 | 1 | 12 | yes | — |
| 37 | #19099209 | C22 | 1 | 12 | yes | complemented |
| 38 | #19099184 | C22 | 1 | 12 | yes | complemented |
| 39 | #19099184 | C22 | 1 | 12 | yes | complemented |
| 40 | #19099183 | C22 | 1 | 24 | yes | complemented |
| 41 | #19099175 | C22 | 1 | 6 | yes | complemented |
| 42 | #19099175 | C22 | 1 | 6 | yes | complemented |
| 43 | #19099168 | C22 | 1 | 6 | yes | — |
| 44 | #19099168 | C22 | 1 | 6 | yes | complemented |
| 45 | #19099163 | C22 | 1 | 24 | yes | complemented |
| 46 | #19099159 | C22 | 1 | 24 | yes | complemented |
| 47 | #19099145 | C22 | 1 | 24 | yes | — |
| 48 | #19099141 | C22 | 1 | 12 | yes | complemented |
| 49 | #19099134 | C22 | 1 | 6 | yes | — |
| 50 | #19099127 | C22 | 1 | 6 | yes | — |
| 51 | #19099120 | C22 | 1 | 3 | yes | complemented |
| 52 | #19099120 | C22 | 1 | 3 | yes | complemented |
| 53 | #19099120 | C22 | 1 | 6 | yes | complemented |
| 54 | #19099113 | C22 | 1 | 6 | yes | — |
| 55 | #19099113 | C22 | 1 | 6 | yes | complemented |
| 56 | C2×#14579161 | C22 | 1 | 3 | yes | complemented |
| 57 | C2×#14579158 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #19099097 | C22 | 1 | 12 | yes | complemented |
| 59 | #19099097 | C22 | 1 | 12 | yes | complemented |
| 60 | #19099096 | C22 | 1 | 24 | yes | complemented |
| 61 | #126×D79 | C22 | 1 | 8 | yes | complemented |
| 62 | #19099074 | C22 | 1 | 12 | yes | complemented |
| 63 | #19099043 | C22 | 1 | 12 | yes | complemented |
| 64 | #19099040 | C22 | 1 | 6 | yes | complemented |
| 65 | #19099037 | C22 | 1 | 6 | yes | complemented |
| 66 | C4×#11929624 | C22 | 1 | 12 | yes | complemented |
| 67 | #533×C79 | C22 | 1 | 3 | yes | complemented |
| 68 | #532×C79 | C22 | 1 | 3 | yes | — |
| 69 | #529×C79 | C22 | 1 | 6 | yes | — |
| 70 | #529×C79 | C22 | 1 | 6 | yes | complemented |
| 71 | #525×C79 | C22 | 1 | 3 | yes | — |
| 72 | #525×C79 | C22 | 1 | 3 | yes | complemented |
| 73 | C4×#41×C79 | C22 | 1 | 3 | yes | — |
| 74 | C4×#41×C79 | C22 | 1 | 3 | yes | complemented |
| 75 | C22×C42×C79 | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | C2×#11929624 | C23 | 1 | 12 | yes | — |
| 77 | C2×#11929624 | C23 | 1 | 12 | yes | — |
| 78 | C22×Dic158 | C23 | 1 | 6 | yes | — |
| 79 | C22×D316 | C23 | 1 | 6 | yes | — |
| 80 | #14579161 | C23 | 1 | 6 | yes | — |
| 81 | #14579161 | C23 | 1 | 12 | yes | — |
| 82 | #14579161 | C23 | 1 | 6 | yes | — |
| 83 | #14579159 | C23 | 1 | 12 | yes | — |
| 84 | #14579158 | C23 | 1 | 6 | yes | — |
| 85 | #14579158 | C23 | 1 | 2 | yes | — |
| 86 | #14579157 | C23 | 1 | 12 | yes | — |
| 87 | #14579156 | C23 | 1 | 24 | yes | — |
| 88 | #14579156 | C23 | 1 | 24 | yes | — |
| 89 | #14579155 | C23 | 1 | 8 | yes | — |
| 90 | #14579155 | C23 | 1 | 8 | yes | — |
| 91 | #14579154 | C23 | 1 | 24 | yes | — |
| 92 | #14579154 | C23 | 1 | 24 | yes | — |
| 93 | #14579153 | C23 | 1 | 6 | yes | — |
| 94 | #14579153 | C23 | 1 | 6 | yes | — |
| 95 | #14579153 | C23 | 1 | 12 | yes | — |
| 96 | #14579151 | C23 | 1 | 24 | yes | — |
| 97 | #14579151 | C23 | 1 | 24 | yes | — |
| 98 | #14579150 | C23 | 1 | 12 | yes | — |
| 99 | #14579149 | C23 | 1 | 12 | yes | — |
| 100 | #14579149 | C23 | 1 | 12 | yes | — |
| 101 | #14579148 | C23 | 1 | 12 | yes | — |
| 102 | #14579147 | C23 | 1 | 24 | yes | — |
| 103 | #14579147 | C23 | 1 | 24 | yes | — |
| 104 | #14579146 | C23 | 1 | 24 | yes | — |
| 105 | #14579146 | C23 | 1 | 24 | yes | — |
| 106 | #14579144 | C23 | 1 | 24 | yes | — |
| 107 | #14579143 | C23 | 1 | 24 | yes | — |
| 108 | #14579143 | C23 | 1 | 24 | yes | — |
| 109 | #14579142 | C23 | 1 | 12 | yes | — |
| 110 | #14579142 | C23 | 1 | 12 | yes | — |
| 111 | #14579140 | C23 | 1 | 12 | yes | — |
| 112 | #14579140 | C23 | 1 | 12 | yes | — |
| 113 | #14579140 | C23 | 1 | 12 | yes | — |
| 114 | #14579140 | C23 | 1 | 12 | yes | — |
| 115 | #14579139 | C23 | 1 | 24 | yes | — |
| 116 | #14579139 | C23 | 1 | 24 | yes | — |
| 117 | #14579137 | C23 | 1 | 24 | yes | — |
| 118 | #14579135 | C23 | 1 | 12 | yes | — |
| 119 | #14579135 | C23 | 1 | 12 | yes | — |
| 120 | #14579135 | C23 | 1 | 12 | yes | — |
| 121 | #14579135 | C23 | 1 | 12 | yes | — |
| 122 | #14579134 | C23 | 1 | 24 | yes | — |
| 123 | #14579134 | C23 | 1 | 24 | yes | — |
| 124 | #14579133 | C23 | 1 | 24 | yes | — |
| 125 | #14579133 | C23 | 1 | 24 | yes | — |
| 126 | #14579132 | C23 | 1 | 24 | yes | — |
| 127 | #14579130 | C23 | 1 | 8 | yes | — |
| 128 | #14579129 | C23 | 1 | 12 | yes | — |
| 129 | #14579129 | C23 | 1 | 12 | yes | — |
| 130 | C4×Dic158 | C23 | 1 | 12 | yes | — |
| 131 | C4×Dic158 | C23 | 1 | 12 | yes | — |
| 132 | C4×Dic158 | C23 | 1 | 12 | yes | — |
| 133 | C4×Dic158 | C23 | 1 | 12 | yes | — |
| 134 | #14579126 | C23 | 1 | 24 | yes | — |
| 135 | C4×D316 | C23 | 1 | 12 | yes | — |
| 136 | C4×D316 | C23 | 1 | 12 | yes | — |
| 137 | C4×D316 | C23 | 1 | 12 | yes | — |
| 138 | C4×D316 | C23 | 1 | 12 | yes | — |
| 139 | #14579123 | C23 | 1 | 24 | yes | — |
| 140 | C4×C22⋊D79 | C23 | 1 | 24 | yes | — |
| 141 | C4×C22⋊D79 | C23 | 1 | 24 | yes | — |
| 142 | (C22⋊D79)⋊C4 | C23 | 1 | 24 | yes | — |
| 143 | (C22⋊D79)⋊C4 | C23 | 1 | 24 | yes | — |
| 144 | #14579120 | C23 | 1 | 6 | yes | — |
| 145 | #14579120 | C23 | 1 | 12 | yes | — |
| 146 | #14579120 | C23 | 1 | 6 | yes | — |
| 147 | #14579119 | C23 | 1 | 24 | yes | — |
| 148 | #14579118 | C23 | 1 | 24 | yes | — |
| 149 | #14579117 | C23 | 1 | 24 | yes | — |
| 150 | C2×C4⋊Dic79 | C23 | 1 | 12 | yes | — |
| 151 | C4⋊C4×D79 | C23 | 1 | 24 | yes | — |
| 152 | C22⋊C4×D79 | C23 | 1 | 24 | yes | — |
| 153 | C42×D79 | C23 | 1 | 8 | yes | — |
| 154 | C2×#41×C79 | C23 | 1 | 3 | yes | — |
| 155 | C2×#41×C79 | C23 | 1 | 3 | yes | — |
| 156 | C23×C4×C79 | C23 | 1 | 3 | yes | — |
| 157 | C4⋊Q8×C79 | C23 | 1 | 3 | yes | — |
| 158 | #127×C79 | C23 | 1 | 1 | yes | characteristic |
| 159 | #126×C79 | C23 | 1 | 2 | yes | — |
| 160 | #126×C79 | C23 | 1 | 6 | yes | — |
| 161 | #125×C79 | C23 | 1 | 6 | yes | — |
| 162 | #124×C79 | C23 | 1 | 3 | yes | — |
| 163 | #124×C79 | C23 | 1 | 3 | yes | — |
| 164 | #123×C79 | C23 | 1 | 3 | yes | — |
| 165 | #123×C79 | C23 | 1 | 3 | yes | — |
| 166 | #123×C79 | C23 | 1 | 6 | yes | — |
| 167 | C22⋊Q8×C79 | C23 | 1 | 6 | yes | — |
| 168 | C22⋊Q8×C79 | C23 | 1 | 6 | yes | — |
| 169 | #121×C79 | C23 | 1 | 6 | yes | — |
| 170 | #121×C79 | C23 | 1 | 6 | yes | — |
| 171 | #120×C79 | C23 | 1 | 1 | yes | characteristic |
| 172 | #120×C79 | C23 | 1 | 3 | yes | — |
| 173 | C4×Q8×C79 | C23 | 1 | 6 | yes | — |
| 174 | C4×Q8×C79 | C23 | 1 | 6 | yes | — |
| 175 | C4×D4×C79 | C23 | 1 | 6 | yes | — |
| 176 | C4×D4×C79 | C23 | 1 | 6 | yes | — |
| 177 | C4×D4×C79 | C23 | 1 | 6 | yes | — |
| 178 | C4×D4×C79 | C23 | 1 | 6 | yes | — |
| 179 | C4×D4×C79 | C23 | 1 | 6 | yes | — |
| 180 | C4×D4×C79 | C23 | 1 | 6 | yes | — |
| 181 | #117×C79 | C23 | 1 | 3 | yes | — |
| 182 | #117×C79 | C23 | 1 | 3 | yes | — |
| 183 | #117×C79 | C23 | 1 | 3 | yes | — |
| 184 | #117×C79 | C23 | 1 | 3 | yes | — |
| 185 | #117×C79 | C23 | 1 | 6 | yes | — |
| 186 | C2×C42×C79 | C23 | 1 | 3 | yes | — |
| 187 | C2×C42×C79 | C23 | 1 | 6 | yes | — |
| 188 | C2×C42×C79 | C23 | 1 | 3 | yes | — |
| 189 | C2×C42×C79 | C23 | 1 | 1 | yes | characteristic |
| 190 | C2×C42×C79 | C23 | 1 | 3 | yes | — |
| 191 | C23×D79 | C24 | 1 | 4 | yes | — |
| 192 | #11929624 | — | 4 | 24 | no | — |
| 193 | #11929624 | — | 4 | 24 | no | — |
| 194 | C2×Dic158 | — | 4 | 12 | no | — |
| 195 | C2×Dic158 | C24 | 1 | 12 | yes | — |
| 196 | C2×Dic158 | C24 | 1 | 12 | yes | — |
| 197 | C2×D316 | — | 4 | 12 | no | — |
| 198 | C2×D316 | C24 | 1 | 12 | yes | — |
| 199 | C2×D316 | C24 | 1 | 12 | yes | — |
| 200 | C2×C22⋊D79 | C24 | 1 | 24 | yes | — |
| 201 | C2×C22⋊D79 | C24 | 1 | 24 | yes | — |
| 202 | C22×Dic79 | C24 | 1 | 12 | yes | — |
| 203 | C2×C4×D79 | C24 | 1 | 24 | yes | — |
| 204 | C2×C4×D79 | C24 | 1 | 24 | yes | — |
| 205 | C4⋊Dic79 | C24 | 1 | 24 | yes | — |
| 206 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 207 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 208 | Dic79⋊C4 | C24 | 1 | 24 | yes | — |
| 209 | Dic79⋊C4 | C24 | 1 | 24 | yes | — |
| 210 | Dic79⋊C4 | C24 | 1 | 24 | yes | — |
| 211 | Dic79⋊C4 | C24 | 1 | 24 | yes | — |
| 212 | C22⋊Dic79 | C24 | 1 | 12 | yes | — |
| 213 | C22⋊Dic79 | C24 | 1 | 12 | yes | — |
| 214 | C22⋊Dic79 | C24 | 1 | 24 | yes | — |
| 215 | (C2×D79)⋊C4 | C24 | 1 | 24 | yes | — |
| 216 | (C2×D79)⋊C4 | C24 | 1 | 24 | yes | — |
| 217 | (C2×D79)⋊C4 | C24 | 1 | 24 | yes | — |
| 218 | (C2×D79)⋊C4 | C24 | 1 | 24 | yes | — |
| 219 | C4×Dic79 | C24 | 1 | 24 | yes | — |
| 220 | C4×Dic79 | C24 | 1 | 12 | yes | — |
| 221 | C4×Dic79 | C24 | 1 | 12 | yes | — |
| 222 | C24×C79 | C24 | 1 | 1 | yes | characteristic |
| 223 | #41×C79 | — | 4 | 6 | no | — |
| 224 | #41×C79 | — | 4 | 6 | no | — |
| 225 | C2×Q8×C79 | C24 | 1 | 3 | yes | — |
| 226 | C2×Q8×C79 | C24 | 1 | 3 | yes | — |
| 227 | C2×D4×C79 | C24 | 1 | 3 | yes | — |
| 228 | C2×D4×C79 | C24 | 1 | 6 | yes | — |
| 229 | C2×D4×C79 | C24 | 1 | 3 | yes | — |
| 230 | C2×D4×C79 | C24 | 1 | 3 | yes | — |
| 231 | C2×D4×C79 | C24 | 1 | 3 | yes | — |
| 232 | C22×C4×C79 | — | 4 | 6 | no | — |
| 233 | C22×C4×C79 | C24 | 1 | 3 | yes | — |
| 234 | C22×C4×C79 | C24 | 1 | 6 | yes | — |
| 235 | C22×C4×C79 | C24 | 1 | 6 | yes | — |
| 236 | C22×C4×C79 | C24 | 1 | 3 | yes | — |
| 237 | C22×C4×C79 | C24 | 1 | 3 | yes | — |
| 238 | C22×C4×C79 | C24 | 1 | 6 | yes | — |
| 239 | C22×C4×C79 | C24 | 1 | 3 | yes | — |
| 240 | C4⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 241 | C4⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 242 | C4⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 243 | C4⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 244 | C4⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 245 | C4⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 246 | C22⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 247 | C22⋊C4×C79 | C24 | 1 | 3 | yes | — |
| 248 | C22⋊C4×C79 | C24 | 1 | 3 | yes | — |
| 249 | C22⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 250 | C22⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 251 | C22⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 252 | C22⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 253 | C42×C79 | C24 | 1 | 1 | yes | characteristic |
| 254 | C42×C79 | C24 | 1 | 3 | yes | — |
| 255 | C42×C79 | C24 | 1 | 6 | yes | — |
| 256 | C42×C79 | C24 | 1 | 3 | yes | — |
| 257 | C42×C79 | C24 | 1 | 2 | yes | — |
| 258 | C42×C79 | C24 | 1 | 1 | yes | characteristic |
| 259 | C42×C79 | C24 | 1 | 3 | yes | — |
| 260 | C42×C79 | C24 | 1 | 6 | yes | — |
| 261 | C42×C79 | C24 | 1 | 3 | yes | — |
| 262 | C23×C79 | — | 4 | 3 | no | — |
| 263 | C23×C79 | C25 | 1 | 1 | yes | characteristic |
| 264 | C23×C79 | C25 | 1 | 3 | yes | — |
| 265 | C23×C79 | C25 | 1 | 3 | yes | — |
| 266 | C22×D79 | — | 4 | 12 | no | — |
| 267 | C22×D79 | C25 | 1 | 8 | yes | — |
| 268 | Q8×C79 | — | 4 | 3 | no | — |
| 269 | Q8×C79 | — | 4 | 3 | no | — |
| 270 | D4×C79 | — | 4 | 3 | no | — |
| 271 | D4×C79 | — | 4 | 3 | no | — |
| 272 | D4×C79 | — | 4 | 3 | no | — |
| 273 | D4×C79 | — | 4 | 6 | no | — |
| 274 | D4×C79 | — | 4 | 3 | no | — |
| 275 | C2×C4×C79 | — | 2 | 6 | no | — |
| 276 | C2×C4×C79 | — | 2 | 6 | no | — |
| 277 | C2×C4×C79 | — | 2 | 12 | no | — |
| 278 | C2×C4×C79 | — | 2 | 12 | no | — |
| 279 | C2×C4×C79 | — | 2 | 6 | no | — |
| 280 | C2×C4×C79 | — | 4 | 6 | no | — |
| 281 | C2×C4×C79 | — | 4 | 3 | no | — |
| 282 | C2×C4×C79 | C25 | 1 | 3 | yes | — |
| 283 | C2×C4×C79 | C25 | 1 | 6 | yes | — |
| 284 | C2×C4×C79 | C25 | 1 | 3 | yes | — |
| 285 | C2×C4×C79 | C25 | 1 | 3 | yes | — |
| 286 | C2×C4×C79 | C25 | 1 | 6 | yes | — |
| 287 | C2×C4×C79 | C25 | 1 | 3 | yes | — |
| 288 | C22⋊D79 | — | 4 | 24 | no | — |
| 289 | C22⋊D79 | — | 4 | 24 | no | — |
| 290 | C2×Dic79 | — | 4 | 12 | no | — |
| 291 | C2×Dic79 | C25 | 1 | 24 | yes | — |
| 292 | D316 | — | 2 | 24 | no | — |
| 293 | D316 | — | 4 | 12 | no | — |
| 294 | C4×D79 | — | 4 | 24 | no | — |
| 295 | C4×D79 | — | 4 | 24 | no | — |
| 296 | Dic158 | — | 2 | 24 | no | — |
| 297 | Dic158 | — | 4 | 12 | no | — |
| 298 | C22×C79 | — | 2 | 6 | no | — |
| 299 | C22×C79 | — | 2 | 6 | no | — |
| 300 | C22×C79 | — | 2 | 3 | no | — |
| 301 | C22×C79 | — | 2 | 3 | no | — |
| 302 | C22×C79 | — | 2 | 3 | no | — |
| 303 | C22×C79 | — | 4 | 4 | no | — |
| 304 | C22×C79 | C26 | 1 | 1 | yes | characteristic |
| 305 | C2×D79 | — | 2 | 24 | no | — |
| 306 | C2×D79 | — | 16 | 4 | no | — |
| 307 | C4×C79 | — | 2 | 3 | no | — |
| 308 | C4×C79 | — | 2 | 6 | no | — |
| 309 | C4×C79 | — | 2 | 3 | no | — |
| 310 | C4×C79 | — | 2 | 6 | no | — |
| 311 | C4×C79 | — | 2 | 3 | no | — |
| 312 | C4×C79 | #585 | 1 | 6 | yes | — |
| 313 | Dic79 | — | 2 | 24 | no | — |
| 314 | #62839 | — | 79 | 1 | no | maximal, Sylow |
| 315 | C2×C79 | — | 4 | 1 | no | — |
| 316 | C2×C79 | — | 4 | 3 | no | — |
| 317 | C2×C79 | — | 4 | 3 | no | — |
| 318 | C2×C79 | C2×#585 | 1 | 3 | yes | — |
| 319 | D79 | — | 4 | 8 | no | — |
| 320 | #3557 | — | 79 | 6 | no | — |
| 321 | #3551 | — | 79 | 6 | no | — |
| 322 | #3540 | — | 79 | 6 | no | — |
| 323 | #3539 | — | 79 | 6 | no | — |
| 324 | #3524 | — | 79 | 12 | no | — |
| 325 | #3521 | — | 79 | 12 | no | — |
| 326 | #3511 | — | 79 | 6 | no | — |
| 327 | #3509 | — | 79 | 3 | no | — |
| 328 | #3508 | — | 79 | 3 | no | — |
| 329 | #3444 | — | 79 | 2 | no | — |
| 330 | #3444 | D79 | 1 | 1 | yes | characteristic, complemented |
| 331 | C79 | #62839 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 332 | #563 | — | 79 | 12 | no | — |
| 333 | H(3,𝔽4) | — | 79 | 4 | no | — |
| 334 | #560 | — | 79 | 4 | no | — |
| 335 | #560 | — | 79 | 12 | no | — |
| 336 | #559 | — | 79 | 12 | no | — |
| 337 | #559 | — | 79 | 12 | no | — |
| 338 | #557 | — | 79 | 12 | no | — |
| 339 | #556 | — | 79 | 12 | no | — |
| 340 | #556 | — | 79 | 12 | no | — |
| 341 | #555 | — | 79 | 12 | no | — |
| 342 | #555 | — | 79 | 12 | no | — |
| 343 | #554 | — | 79 | 12 | no | — |
| 344 | #553 | — | 79 | 24 | no | — |
| 345 | #553 | — | 79 | 12 | no | — |
| 346 | #553 | — | 79 | 12 | no | — |
| 347 | #552 | — | 79 | 24 | no | — |
| 348 | #552 | — | 79 | 12 | no | — |
| 349 | #552 | — | 79 | 12 | no | — |
| 350 | #551 | — | 79 | 12 | no | — |
| 351 | #551 | — | 79 | 12 | no | — |
| 352 | #550 | — | 79 | 12 | no | — |
| 353 | #548 | — | 79 | 12 | no | — |
| 354 | #548 | — | 79 | 12 | no | — |
| 355 | #547 | — | 79 | 12 | no | — |
| 356 | #546 | — | 79 | 12 | no | — |
| 357 | #546 | — | 79 | 12 | no | — |
| 358 | #542 | — | 79 | 24 | no | — |
| 359 | #542 | — | 79 | 12 | no | — |
| 360 | #542 | — | 79 | 12 | no | — |
| 361 | #541 | — | 79 | 6 | no | — |
| 362 | #541 | — | 79 | 6 | no | — |
| 363 | #540 | — | 79 | 24 | no | — |
| 364 | #540 | — | 79 | 6 | no | — |
| 365 | #540 | — | 79 | 6 | no | — |
| 366 | #539 | — | 79 | 24 | no | — |
| 367 | #538 | — | 79 | 24 | no | — |
| 368 | #537 | — | 79 | 12 | no | — |
| 369 | #536 | — | 79 | 6 | no | — |
| 370 | #535 | — | 79 | 6 | no | — |
| 371 | #533 | — | 79 | 6 | no | — |
| 372 | #533 | — | 79 | 3 | no | — |
| 373 | #533 | — | 79 | 3 | no | — |
| 374 | #533 | C2×D79 | 1 | 3 | yes | complemented |
| 375 | #532 | — | 79 | 6 | no | — |
| 376 | #532 | — | 79 | 6 | no | — |
| 377 | #532 | C2×D79 | 1 | 3 | yes | — |
| 378 | C2×C4⋊Q8 | — | 79 | 3 | no | — |
| 379 | C2×#127 | — | 79 | 1 | no | — |
| 380 | #529 | — | 79 | 24 | no | — |
| 381 | #529 | — | 79 | 12 | no | — |
| 382 | #529 | — | 79 | 12 | no | — |
| 383 | #529 | C2×D79 | 1 | 6 | yes | — |
| 384 | #529 | C2×D79 | 1 | 6 | yes | complemented |
| 385 | C2×#126 | — | 79 | 8 | no | — |
| 386 | #525 | — | 79 | 12 | no | — |
| 387 | #525 | C2×D79 | 1 | 3 | yes | — |
| 388 | #525 | C2×D79 | 1 | 3 | yes | complemented |
| 389 | #520 | — | 79 | 12 | no | — |
| 390 | #519 | — | 79 | 6 | no | — |
| 391 | #518 | — | 79 | 6 | no | — |
| 392 | C4×#41 | — | 79 | 12 | no | — |
| 393 | C4×#41 | C2×D79 | 1 | 3 | yes | — |
| 394 | C4×#41 | C2×D79 | 1 | 3 | yes | complemented |
| 395 | C22×C42 | C2×D79 | 1 | 1 | yes | characteristic, complemented |
| 396 | C2×#41 | — | 79 | 12 | no | — |
| 397 | C2×#41 | — | 79 | 12 | no | — |
| 398 | C2×#41 | C22×D79 | 1 | 3 | yes | — |
| 399 | C2×#41 | C22×D79 | 1 | 3 | yes | — |
| 400 | C22×Q8 | — | 79 | 6 | no | — |
| 401 | C22×D4 | — | 79 | 6 | no | — |
| 402 | C23×C4 | C22×D79 | 1 | 3 | yes | — |
| 403 | C4⋊Q8 | — | 79 | 12 | no | — |
| 404 | C4⋊Q8 | — | 79 | 6 | no | — |
| 405 | C4⋊Q8 | — | 79 | 6 | no | — |
| 406 | C4⋊Q8 | — | 79 | 12 | no | — |
| 407 | C4⋊Q8 | C22×D79 | 1 | 3 | yes | — |
| 408 | #127 | — | 79 | 12 | no | — |
| 409 | #127 | — | 79 | 2 | no | — |
| 410 | #127 | — | 79 | 6 | no | — |
| 411 | #127 | C22×D79 | 1 | 1 | yes | characteristic |
| 412 | #126 | — | 79 | 24 | no | — |
| 413 | #126 | — | 79 | 24 | no | — |
| 414 | #126 | — | 79 | 24 | no | — |
| 415 | #126 | — | 79 | 24 | no | — |
| 416 | #126 | — | 79 | 8 | no | — |
| 417 | #126 | — | 79 | 8 | no | — |
| 418 | #126 | C22×D79 | 1 | 2 | yes | — |
| 419 | #126 | C22×D79 | 1 | 6 | yes | — |
| 420 | #125 | — | 79 | 24 | no | — |
| 421 | #125 | — | 79 | 24 | no | — |
| 422 | #125 | — | 79 | 12 | no | — |
| 423 | #125 | — | 79 | 6 | no | — |
| 424 | #125 | — | 79 | 6 | no | — |
| 425 | #125 | C22×D79 | 1 | 6 | yes | — |
| 426 | #124 | — | 79 | 12 | no | — |
| 427 | #124 | — | 79 | 12 | no | — |
| 428 | #124 | — | 79 | 24 | no | — |
| 429 | #124 | — | 79 | 24 | no | — |
| 430 | #124 | — | 79 | 12 | no | — |
| 431 | #124 | — | 79 | 12 | no | — |
| 432 | #124 | C22×D79 | 1 | 3 | yes | — |
| 433 | #124 | C22×D79 | 1 | 3 | yes | — |
| 434 | #123 | — | 79 | 12 | no | — |
| 435 | #123 | — | 79 | 12 | no | — |
| 436 | #123 | — | 79 | 24 | no | — |
| 437 | #123 | — | 79 | 24 | no | — |
| 438 | #123 | — | 79 | 24 | no | — |
| 439 | #123 | — | 79 | 24 | no | — |
| 440 | #123 | — | 79 | 24 | no | — |
| 441 | #123 | C22×D79 | 1 | 3 | yes | — |
| 442 | #123 | C22×D79 | 1 | 3 | yes | — |
| 443 | #123 | C22×D79 | 1 | 6 | yes | — |
| 444 | C22⋊Q8 | — | 79 | 24 | no | — |
| 445 | C22⋊Q8 | — | 79 | 12 | no | — |
| 446 | C22⋊Q8 | — | 79 | 12 | no | — |
| 447 | C22⋊Q8 | — | 79 | 12 | no | — |
| 448 | C22⋊Q8 | — | 79 | 12 | no | — |
| 449 | C22⋊Q8 | — | 79 | 24 | no | — |
| 450 | C22⋊Q8 | — | 79 | 24 | no | — |
| 451 | C22⋊Q8 | C22×D79 | 1 | 6 | yes | — |
| 452 | C22⋊Q8 | C22×D79 | 1 | 6 | yes | — |
| 453 | #121 | — | 79 | 24 | no | — |
| 454 | #121 | — | 79 | 24 | no | — |
| 455 | #121 | — | 79 | 24 | no | — |
| 456 | #121 | — | 79 | 12 | no | — |
| 457 | #121 | — | 79 | 12 | no | — |
| 458 | #121 | — | 79 | 12 | no | — |
| 459 | #121 | — | 79 | 12 | no | — |
| 460 | #121 | — | 79 | 24 | no | — |
| 461 | #121 | — | 79 | 24 | no | — |
| 462 | #121 | C22×D79 | 1 | 6 | yes | — |
| 463 | #121 | C22×D79 | 1 | 6 | yes | — |
| 464 | #120 | — | 79 | 8 | no | — |
| 465 | #120 | — | 79 | 12 | no | — |
| 466 | #120 | — | 79 | 12 | no | — |
| 467 | #120 | C22×D79 | 1 | 1 | yes | characteristic |
| 468 | #120 | C22×D79 | 1 | 3 | yes | — |
| 469 | C4×Q8 | — | 79 | 24 | no | — |
| 470 | C4×Q8 | — | 79 | 12 | no | — |
| 471 | C4×Q8 | — | 79 | 12 | no | — |
| 472 | C4×Q8 | — | 79 | 12 | no | — |
| 473 | C4×Q8 | — | 79 | 12 | no | — |
| 474 | C4×Q8 | C22×D79 | 1 | 6 | yes | — |
| 475 | C4×Q8 | C22×D79 | 1 | 6 | yes | — |
| 476 | C4×D4 | — | 79 | 24 | no | — |
| 477 | C4×D4 | — | 79 | 24 | no | — |
| 478 | C4×D4 | — | 79 | 24 | no | — |
| 479 | C4×D4 | — | 79 | 24 | no | — |
| 480 | C4×D4 | — | 79 | 24 | no | — |
| 481 | C4×D4 | — | 79 | 12 | no | — |
| 482 | C4×D4 | — | 79 | 12 | no | — |
| 483 | C4×D4 | — | 79 | 12 | no | — |
| 484 | C4×D4 | — | 79 | 12 | no | — |
| 485 | C4×D4 | C22×D79 | 1 | 6 | yes | — |
| 486 | C4×D4 | C22×D79 | 1 | 6 | yes | — |
| 487 | C4×D4 | C22×D79 | 1 | 6 | yes | — |
| 488 | C4×D4 | C22×D79 | 1 | 6 | yes | — |
| 489 | C4×D4 | C22×D79 | 1 | 6 | yes | — |
| 490 | C4×D4 | C22×D79 | 1 | 6 | yes | — |
| 491 | #117 | — | 79 | 12 | no | — |
| 492 | #117 | — | 79 | 6 | no | — |
| 493 | #117 | — | 79 | 6 | no | — |
| 494 | #117 | — | 79 | 24 | no | — |
| 495 | #117 | — | 79 | 24 | no | — |
| 496 | #117 | — | 79 | 24 | no | — |
| 497 | #117 | C22×D79 | 1 | 3 | yes | — |
| 498 | #117 | C22×D79 | 1 | 3 | yes | — |
| 499 | #117 | C22×D79 | 1 | 3 | yes | — |
| 500 | #117 | C22×D79 | 1 | 6 | yes | — |
| 501 | #117 | C22×D79 | 1 | 3 | yes | — |
| 502 | C2×C4⋊C4 | — | 79 | 12 | no | — |
| 503 | C2×C4⋊C4 | — | 79 | 24 | no | — |
| 504 | C2×C22⋊C4 | — | 79 | 24 | no | — |
| 505 | C2×C42 | — | 79 | 8 | no | — |
| 506 | C2×C42 | C22×D79 | 1 | 6 | yes | — |
| 507 | C2×C42 | C22×D79 | 1 | 1 | yes | characteristic |
| 508 | C2×C42 | C22×D79 | 1 | 3 | yes | — |
| 509 | C2×C42 | C22×D79 | 1 | 3 | yes | — |
| 510 | C2×C42 | C22×D79 | 1 | 3 | yes | — |
| 511 | C24 | — | 79 | 4 | no | — |
| 512 | C24 | C23×D79 | 1 | 1 | yes | characteristic |
| 513 | #41 | — | 4 | 6 | no | — |
| 514 | #41 | — | 4 | 6 | no | — |
| 515 | #41 | — | 316 | 24 | no | — |
| 516 | #41 | — | 316 | 24 | no | — |
| 517 | C2×Q8 | — | 316 | 12 | no | — |
| 518 | C2×Q8 | — | 79 | 12 | no | — |
| 519 | C2×Q8 | — | 79 | 12 | no | — |
| 520 | C2×Q8 | C23×D79 | 1 | 3 | yes | — |
| 521 | C2×Q8 | C23×D79 | 1 | 3 | yes | — |
| 522 | C2×D4 | — | 316 | 12 | no | — |
| 523 | C2×D4 | — | 79 | 24 | no | — |
| 524 | C2×D4 | — | 79 | 24 | no | — |
| 525 | C2×D4 | — | 79 | 12 | no | — |
| 526 | C2×D4 | — | 79 | 12 | no | — |
| 527 | C2×D4 | C23×D79 | 1 | 3 | yes | — |
| 528 | C2×D4 | C23×D79 | 1 | 3 | yes | — |
| 529 | C2×D4 | C23×D79 | 1 | 6 | yes | — |
| 530 | C2×D4 | C23×D79 | 1 | 3 | yes | — |
| 531 | C2×D4 | C23×D79 | 1 | 3 | yes | — |
| 532 | C22×C4 | — | 4 | 6 | no | — |
| 533 | C22×C4 | — | 79 | 12 | no | — |
| 534 | C22×C4 | — | 79 | 24 | no | — |
| 535 | C22×C4 | — | 79 | 24 | no | — |
| 536 | C22×C4 | C23×D79 | 1 | 6 | yes | — |
| 537 | C22×C4 | C23×D79 | 1 | 3 | yes | — |
| 538 | C22×C4 | C23×D79 | 1 | 6 | yes | — |
| 539 | C22×C4 | C23×D79 | 1 | 3 | yes | — |
| 540 | C22×C4 | C23×D79 | 1 | 3 | yes | — |
| 541 | C22×C4 | C23×D79 | 1 | 3 | yes | — |
| 542 | C22×C4 | C23×D79 | 1 | 6 | yes | — |
| 543 | C4⋊C4 | — | 79 | 24 | no | — |
| 544 | C4⋊C4 | — | 79 | 24 | no | — |
| 545 | C4⋊C4 | — | 79 | 24 | no | — |
| 546 | C4⋊C4 | — | 79 | 24 | no | — |
| 547 | C4⋊C4 | — | 79 | 24 | no | — |
| 548 | C4⋊C4 | — | 79 | 12 | no | — |
| 549 | C4⋊C4 | — | 79 | 12 | no | — |
| 550 | C4⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 551 | C4⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 552 | C4⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 553 | C4⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 554 | C4⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 555 | C4⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 556 | C22⋊C4 | — | 79 | 12 | no | — |
| 557 | C22⋊C4 | — | 79 | 12 | no | — |
| 558 | C22⋊C4 | — | 79 | 24 | no | — |
| 559 | C22⋊C4 | — | 79 | 24 | no | — |
| 560 | C22⋊C4 | — | 79 | 24 | no | — |
| 561 | C22⋊C4 | — | 79 | 24 | no | — |
| 562 | C22⋊C4 | — | 79 | 24 | no | — |
| 563 | C22⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 564 | C22⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 565 | C22⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 566 | C22⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 567 | C22⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 568 | C22⋊C4 | C23×D79 | 1 | 3 | yes | — |
| 569 | C22⋊C4 | C23×D79 | 1 | 3 | yes | — |
| 570 | C42 | — | 79 | 24 | no | — |
| 571 | C42 | — | 79 | 12 | no | — |
| 572 | C42 | — | 79 | 12 | no | — |
| 573 | C42 | C23×D79 | 1 | 2 | yes | — |
| 574 | C42 | C23×D79 | 1 | 1 | yes | characteristic |
| 575 | C42 | C23×D79 | 1 | 3 | yes | — |
| 576 | C42 | C23×D79 | 1 | 3 | yes | — |
| 577 | C42 | C23×D79 | 1 | 6 | yes | — |
| 578 | C42 | C23×D79 | 1 | 1 | yes | characteristic |
| 579 | C42 | C23×D79 | 1 | 3 | yes | — |
| 580 | C42 | C23×D79 | 1 | 6 | yes | — |
| 581 | C42 | C23×D79 | 1 | 3 | yes | — |
| 582 | C23 | — | 4 | 3 | no | — |
| 583 | C23 | — | 316 | 12 | no | — |
| 584 | C23 | — | 79 | 8 | no | — |
| 585 | C23 | C24×D79 | 1 | 1 | yes | characteristic |
| 586 | C23 | C24×D79 | 1 | 3 | yes | — |
| 587 | C23 | C24×D79 | 1 | 3 | yes | — |
| 588 | Q8 | — | 4 | 3 | no | — |
| 589 | Q8 | — | 4 | 3 | no | — |
| 590 | Q8 | — | 316 | 12 | no | — |
| 591 | Q8 | — | 158 | 24 | no | — |
| 592 | D4 | — | 4 | 3 | no | — |
| 593 | D4 | — | 4 | 3 | no | — |
| 594 | D4 | — | 4 | 6 | no | — |
| 595 | D4 | — | 4 | 3 | no | — |
| 596 | D4 | — | 4 | 3 | no | — |
| 597 | D4 | — | 316 | 12 | no | — |
| 598 | D4 | — | 316 | 24 | no | — |
| 599 | D4 | — | 316 | 24 | no | — |
| 600 | D4 | — | 158 | 24 | no | — |
| 601 | C2×C4 | — | 2 | 6 | no | — |
| 602 | C2×C4 | — | 2 | 12 | no | — |
| 603 | C2×C4 | — | 2 | 6 | no | — |
| 604 | C2×C4 | — | 2 | 6 | no | — |
| 605 | C2×C4 | — | 2 | 12 | no | — |
| 606 | C2×C4 | — | 4 | 3 | no | — |
| 607 | C2×C4 | — | 4 | 6 | no | — |
| 608 | C2×C4 | — | 316 | 24 | no | — |
| 609 | C2×C4 | — | 316 | 24 | no | — |
| 610 | C2×C4 | — | 316 | 12 | no | — |
| 611 | C2×C4 | — | 79 | 24 | no | — |
| 612 | C2×C4 | C24×D79 | 1 | 6 | yes | — |
| 613 | C2×C4 | C24×D79 | 1 | 3 | yes | — |
| 614 | C2×C4 | C24×D79 | 1 | 3 | yes | — |
| 615 | C2×C4 | C24×D79 | 1 | 3 | yes | — |
| 616 | C2×C4 | C24×D79 | 1 | 6 | yes | — |
| 617 | C2×C4 | C24×D79 | 1 | 3 | yes | — |
| 618 | C22 | — | 2 | 3 | no | — |
| 619 | C22 | — | 2 | 6 | no | — |
| 620 | C22 | — | 2 | 3 | no | — |
| 621 | C22 | — | 2 | 6 | no | — |
| 622 | C22 | — | 2 | 3 | no | — |
| 623 | C22 | — | 4 | 4 | no | — |
| 624 | C22 | — | 158 | 24 | no | — |
| 625 | C22 | — | 1264 | 4 | no | — |
| 626 | C22 | C25×D79 | 1 | 1 | yes | characteristic |
| 627 | C4 | — | 2 | 6 | no | — |
| 628 | C4 | — | 2 | 3 | no | — |
| 629 | C4 | — | 2 | 6 | no | — |
| 630 | C4 | — | 2 | 3 | no | — |
| 631 | C4 | — | 2 | 3 | no | — |
| 632 | C4 | — | 158 | 24 | no | — |
| 633 | C4 | #19099399 | 1 | 6 | yes | — |
| 634 | C2 | — | 4 | 3 | no | — |
| 635 | C2 | — | 4 | 1 | no | — |
| 636 | C2 | — | 4 | 3 | no | — |
| 637 | C2 | — | 316 | 8 | no | — |
| 638 | C2 | C2×#19099399 | 1 | 3 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta