Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
6588 conjugacy classes of subgroups.
The subgroup lattice has 600 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23777935 | C2 | 1 | 12 | yes | maximal, complemented |
| 2 | #23777934 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #23777933 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #23777800 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #23777799 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #23777547 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #23777407 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #23777406 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #23777400 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #23777225 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | C79×#3504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C79⋊#564 | C22 | 1 | 1 | yes | characteristic |
| 13 | #19099317 | C22 | 1 | 6 | yes | — |
| 14 | #19099314 | C22 | 1 | 12 | yes | — |
| 15 | #19099312 | C22 | 1 | 12 | yes | — |
| 16 | #19099311 | C22 | 1 | 3 | yes | — |
| 17 | #19099311 | C22 | 1 | 6 | yes | — |
| 18 | #19099309 | C22 | 1 | 12 | yes | — |
| 19 | #19099309 | C22 | 1 | 24 | yes | — |
| 20 | #19099292 | C22 | 1 | 2 | yes | — |
| 21 | #19099289 | C22 | 1 | 4 | yes | — |
| 22 | #19099274 | C22 | 1 | 12 | yes | — |
| 23 | #19099273 | C22 | 1 | 12 | yes | — |
| 24 | #19099269 | C22 | 1 | 12 | yes | — |
| 25 | #19099269 | C22 | 1 | 12 | yes | — |
| 26 | #19099266 | C22 | 1 | 12 | yes | — |
| 27 | #19099266 | C22 | 1 | 12 | yes | — |
| 28 | #19099263 | C22 | 1 | 12 | yes | — |
| 29 | #19099261 | C22 | 1 | 12 | yes | — |
| 30 | #19099257 | C22 | 1 | 12 | yes | — |
| 31 | #19099235 | C22 | 1 | 12 | yes | — |
| 32 | #19099235 | C22 | 1 | 4 | yes | — |
| 33 | #19099235 | C22 | 1 | 2 | yes | — |
| 34 | #19099234 | C22 | 1 | 12 | yes | — |
| 35 | #19099234 | C22 | 1 | 6 | yes | — |
| 36 | #19099232 | C22 | 1 | 4 | yes | — |
| 37 | #19099218 | C22 | 1 | 6 | yes | — |
| 38 | #19099216 | C22 | 1 | 12 | yes | — |
| 39 | #19099216 | C22 | 1 | 12 | yes | — |
| 40 | #19099215 | C22 | 1 | 24 | yes | — |
| 41 | #19099214 | C22 | 1 | 24 | yes | — |
| 42 | #19099214 | C22 | 1 | 12 | yes | — |
| 43 | #19099193 | C22 | 1 | 12 | yes | — |
| 44 | #19099190 | C22 | 1 | 12 | yes | — |
| 45 | #19099169 | C22 | 1 | 12 | yes | — |
| 46 | #19099169 | C22 | 1 | 12 | yes | — |
| 47 | #19099168 | C22 | 1 | 12 | yes | — |
| 48 | #19099164 | C22 | 1 | 12 | yes | — |
| 49 | #19099164 | C22 | 1 | 12 | yes | — |
| 50 | #19099161 | C22 | 1 | 24 | yes | — |
| 51 | #19099160 | C22 | 1 | 12 | yes | — |
| 52 | #19099159 | C22 | 1 | 24 | yes | — |
| 53 | #19099144 | C22 | 1 | 12 | yes | — |
| 54 | #19099143 | C22 | 1 | 24 | yes | — |
| 55 | #19099143 | C22 | 1 | 24 | yes | — |
| 56 | #19099117 | C22 | 1 | 12 | yes | — |
| 57 | #19099114 | C22 | 1 | 12 | yes | — |
| 58 | #19099113 | C22 | 1 | 6 | yes | — |
| 59 | #19099110 | C22 | 1 | 12 | yes | — |
| 60 | #19099100 | C22 | 1 | 12 | yes | — |
| 61 | #19099097 | C22 | 1 | 6 | yes | — |
| 62 | #19099091 | C22 | 1 | 12 | yes | — |
| 63 | #125×D79 | C22 | 1 | 12 | yes | — |
| 64 | #19099045 | C22 | 1 | 4 | yes | — |
| 65 | #19099045 | C22 | 1 | 4 | yes | — |
| 66 | C4×#11929625 | C22 | 1 | 4 | yes | — |
| 67 | #557×C79 | C22 | 1 | 4 | yes | — |
| 68 | #554×C79 | C22 | 1 | 12 | yes | — |
| 69 | #544×C79 | C22 | 1 | 6 | yes | — |
| 70 | #533×C79 | C22 | 1 | 3 | yes | — |
| 71 | C2×#125×C79 | C22 | 1 | 3 | yes | — |
| 72 | #520×C79 | C22 | 1 | 2 | yes | — |
| 73 | C4×#41×C79 | C22 | 1 | 1 | yes | characteristic |
| 74 | C2×#11929625 | C23 | 1 | 4 | yes | — |
| 75 | C2×#11929625 | C23 | 1 | 24 | yes | — |
| 76 | C2×#11929624 | C23 | 1 | 12 | yes | — |
| 77 | C2×#11929624 | C23 | 1 | 24 | yes | — |
| 78 | #14579161 | C23 | 1 | 6 | yes | — |
| 79 | #14579160 | C23 | 1 | 12 | yes | — |
| 80 | #14579160 | C23 | 1 | 12 | yes | — |
| 81 | #14579159 | C23 | 1 | 12 | yes | — |
| 82 | #14579158 | C23 | 1 | 12 | yes | — |
| 83 | #14579158 | C23 | 1 | 6 | yes | — |
| 84 | #14579157 | C23 | 1 | 12 | yes | — |
| 85 | #14579156 | C23 | 1 | 12 | yes | — |
| 86 | #14579156 | C23 | 1 | 12 | yes | — |
| 87 | #14579156 | C23 | 1 | 12 | yes | — |
| 88 | #14579155 | C23 | 1 | 12 | yes | — |
| 89 | #14579154 | C23 | 1 | 12 | yes | — |
| 90 | #14579153 | C23 | 1 | 12 | yes | — |
| 91 | #14579153 | C23 | 1 | 2 | yes | — |
| 92 | #14579152 | C23 | 1 | 12 | yes | — |
| 93 | #14579152 | C23 | 1 | 12 | yes | — |
| 94 | #14579152 | C23 | 1 | 4 | yes | — |
| 95 | #14579151 | C23 | 1 | 24 | yes | — |
| 96 | #14579151 | C23 | 1 | 4 | yes | — |
| 97 | #14579151 | C23 | 1 | 12 | yes | — |
| 98 | #14579151 | C23 | 1 | 4 | yes | — |
| 99 | #14579150 | C23 | 1 | 12 | yes | — |
| 100 | #14579149 | C23 | 1 | 6 | yes | — |
| 101 | #14579147 | C23 | 1 | 12 | yes | — |
| 102 | #14579146 | C23 | 1 | 24 | yes | — |
| 103 | #14579146 | C23 | 1 | 24 | yes | — |
| 104 | #14579146 | C23 | 1 | 24 | yes | — |
| 105 | #14579146 | C23 | 1 | 12 | yes | — |
| 106 | #14579146 | C23 | 1 | 12 | yes | — |
| 107 | #14579146 | C23 | 1 | 12 | yes | — |
| 108 | #14579144 | C23 | 1 | 24 | yes | — |
| 109 | #14579144 | C23 | 1 | 12 | yes | — |
| 110 | #14579143 | C23 | 1 | 24 | yes | — |
| 111 | #14579143 | C23 | 1 | 12 | yes | — |
| 112 | #14579141 | C23 | 1 | 12 | yes | — |
| 113 | #14579141 | C23 | 1 | 24 | yes | — |
| 114 | #14579140 | C23 | 1 | 6 | yes | — |
| 115 | #14579139 | C23 | 1 | 12 | yes | — |
| 116 | #14579139 | C23 | 1 | 12 | yes | — |
| 117 | #14579139 | C23 | 1 | 24 | yes | — |
| 118 | #14579139 | C23 | 1 | 24 | yes | — |
| 119 | #14579139 | C23 | 1 | 12 | yes | — |
| 120 | #14579137 | C23 | 1 | 12 | yes | — |
| 121 | #14579137 | C23 | 1 | 24 | yes | — |
| 122 | #14579137 | C23 | 1 | 12 | yes | — |
| 123 | #14579136 | C23 | 1 | 24 | yes | — |
| 124 | #14579136 | C23 | 1 | 24 | yes | — |
| 125 | #14579136 | C23 | 1 | 12 | yes | — |
| 126 | #14579136 | C23 | 1 | 24 | yes | — |
| 127 | #14579136 | C23 | 1 | 12 | yes | — |
| 128 | #14579136 | C23 | 1 | 12 | yes | — |
| 129 | #14579136 | C23 | 1 | 12 | yes | — |
| 130 | #14579135 | C23 | 1 | 12 | yes | — |
| 131 | #14579135 | C23 | 1 | 24 | yes | — |
| 132 | #14579135 | C23 | 1 | 6 | yes | — |
| 133 | #14579135 | C23 | 1 | 12 | yes | — |
| 134 | #14579134 | C23 | 1 | 24 | yes | — |
| 135 | #14579134 | C23 | 1 | 24 | yes | — |
| 136 | #14579134 | C23 | 1 | 24 | yes | — |
| 137 | #14579134 | C23 | 1 | 12 | yes | — |
| 138 | #14579132 | C23 | 1 | 12 | yes | — |
| 139 | Q8×Dic79 | C23 | 1 | 4 | yes | — |
| 140 | C4×Dic158 | C23 | 1 | 6 | yes | — |
| 141 | C4×Dic158 | C23 | 1 | 12 | yes | — |
| 142 | C4×D316 | C23 | 1 | 12 | yes | — |
| 143 | C4×D316 | C23 | 1 | 12 | yes | — |
| 144 | C4×D316 | C23 | 1 | 12 | yes | — |
| 145 | C4×D316 | C23 | 1 | 12 | yes | — |
| 146 | C4×D316 | C23 | 1 | 12 | yes | — |
| 147 | C4×D316 | C23 | 1 | 6 | yes | — |
| 148 | #14579123 | C23 | 1 | 24 | yes | — |
| 149 | #14579123 | C23 | 1 | 12 | yes | — |
| 150 | #14579123 | C23 | 1 | 12 | yes | — |
| 151 | #14579123 | C23 | 1 | 12 | yes | — |
| 152 | C4×C22⋊D79 | C23 | 1 | 24 | yes | — |
| 153 | C4×C22⋊D79 | C23 | 1 | 12 | yes | — |
| 154 | #14579119 | C23 | 1 | 12 | yes | — |
| 155 | #14579118 | C23 | 1 | 12 | yes | — |
| 156 | #14579118 | C23 | 1 | 12 | yes | — |
| 157 | C4⋊C4×D79 | C23 | 1 | 24 | yes | — |
| 158 | C4⋊C4×D79 | C23 | 1 | 24 | yes | — |
| 159 | C4⋊C4×D79 | C23 | 1 | 12 | yes | — |
| 160 | C4⋊C4×D79 | C23 | 1 | 12 | yes | — |
| 161 | C42×D79 | C23 | 1 | 12 | yes | — |
| 162 | C2×#41×C79 | C23 | 1 | 1 | yes | characteristic |
| 163 | C4⋊Q8×C79 | C23 | 1 | 12 | yes | — |
| 164 | C4⋊Q8×C79 | C23 | 1 | 6 | yes | — |
| 165 | #125×C79 | C23 | 1 | 6 | yes | — |
| 166 | #125×C79 | C23 | 1 | 12 | yes | — |
| 167 | #125×C79 | C23 | 1 | 12 | yes | — |
| 168 | #125×C79 | C23 | 1 | 3 | yes | — |
| 169 | #125×C79 | C23 | 1 | 1 | yes | characteristic |
| 170 | C22⋊Q8×C79 | C23 | 1 | 12 | yes | — |
| 171 | C22⋊Q8×C79 | C23 | 1 | 24 | yes | — |
| 172 | C4×Q8×C79 | C23 | 1 | 2 | yes | — |
| 173 | C4×Q8×C79 | C23 | 1 | 4 | yes | — |
| 174 | C4×Q8×C79 | C23 | 1 | 12 | yes | — |
| 175 | C4×D4×C79 | C23 | 1 | 6 | yes | — |
| 176 | C4×D4×C79 | C23 | 1 | 12 | yes | — |
| 177 | #117×C79 | C23 | 1 | 6 | yes | — |
| 178 | #117×C79 | C23 | 1 | 3 | yes | — |
| 179 | C2×C4⋊C4×C79 | C23 | 1 | 12 | yes | — |
| 180 | C2×C4⋊C4×C79 | C23 | 1 | 6 | yes | — |
| 181 | C2×C42×C79 | C23 | 1 | 3 | yes | — |
| 182 | #11929625 | — | 2 | 16 | no | — |
| 183 | #11929625 | — | 8 | 24 | no | — |
| 184 | #11929624 | — | 8 | 24 | no | — |
| 185 | #11929624 | — | 8 | 12 | no | — |
| 186 | C2×Dic158 | C24 | 1 | 6 | yes | — |
| 187 | C2×Dic158 | C24 | 1 | 12 | yes | — |
| 188 | C2×D316 | C24 | 1 | 12 | yes | — |
| 189 | C2×D316 | C24 | 1 | 6 | yes | — |
| 190 | C2×D316 | C24 | 1 | 24 | yes | — |
| 191 | C2×D316 | C24 | 1 | 12 | yes | — |
| 192 | C2×D316 | C24 | 1 | 12 | yes | — |
| 193 | C2×C22⋊D79 | C24 | 1 | 24 | yes | — |
| 194 | C2×C22⋊D79 | C24 | 1 | 12 | yes | — |
| 195 | C2×C4×D79 | C24 | 1 | 12 | yes | — |
| 196 | C2×C4×D79 | C24 | 1 | 12 | yes | — |
| 197 | C2×C4×D79 | C24 | 1 | 24 | yes | — |
| 198 | C2×C4×D79 | C24 | 1 | 24 | yes | — |
| 199 | C2×C4×D79 | C24 | 1 | 12 | yes | — |
| 200 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 201 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 202 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 203 | C4⋊Dic79 | C24 | 1 | 4 | yes | — |
| 204 | C4⋊Dic79 | C24 | 1 | 2 | yes | — |
| 205 | C4⋊Dic79 | C24 | 1 | 2 | yes | — |
| 206 | Dic79⋊C4 | C24 | 1 | 12 | yes | — |
| 207 | Dic79⋊C4 | C24 | 1 | 12 | yes | — |
| 208 | Dic79⋊C4 | C24 | 1 | 24 | yes | — |
| 209 | Dic79⋊C4 | C24 | 1 | 12 | yes | — |
| 210 | Dic79⋊C4 | C24 | 1 | 12 | yes | — |
| 211 | Dic79⋊C4 | C24 | 1 | 4 | yes | — |
| 212 | Dic79⋊C4 | C24 | 1 | 4 | yes | — |
| 213 | Dic79⋊C4 | C24 | 1 | 4 | yes | — |
| 214 | Dic79⋊C4 | C24 | 1 | 4 | yes | — |
| 215 | C22⋊Dic79 | C24 | 1 | 12 | yes | — |
| 216 | (C2×D79)⋊C4 | C24 | 1 | 12 | yes | — |
| 217 | (C2×D79)⋊C4 | C24 | 1 | 12 | yes | — |
| 218 | (C2×D79)⋊C4 | C24 | 1 | 12 | yes | — |
| 219 | (C2×D79)⋊C4 | C24 | 1 | 12 | yes | — |
| 220 | (C2×D79)⋊C4 | C24 | 1 | 24 | yes | — |
| 221 | (C2×D79)⋊C4 | C24 | 1 | 12 | yes | — |
| 222 | (C2×D79)⋊C4 | C24 | 1 | 12 | yes | — |
| 223 | (C2×D79)⋊C4 | C24 | 1 | 12 | yes | — |
| 224 | (C2×D79)⋊C4 | C24 | 1 | 12 | yes | — |
| 225 | C4×Dic79 | C24 | 1 | 4 | yes | — |
| 226 | C4×Dic79 | C24 | 1 | 12 | yes | — |
| 227 | C4×Dic79 | C24 | 1 | 12 | yes | — |
| 228 | #41×C79 | — | 2 | 4 | no | — |
| 229 | C2×Q8×C79 | C24 | 1 | 12 | yes | — |
| 230 | C2×Q8×C79 | C24 | 1 | 1 | yes | characteristic |
| 231 | C2×D4×C79 | C24 | 1 | 3 | yes | — |
| 232 | C22×C4×C79 | C24 | 1 | 3 | yes | — |
| 233 | C22×C4×C79 | C24 | 1 | 6 | yes | — |
| 234 | C22×C4×C79 | C24 | 1 | 12 | yes | — |
| 235 | C4⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 236 | C4⋊C4×C79 | C24 | 1 | 12 | yes | — |
| 237 | C4⋊C4×C79 | C24 | 1 | 12 | yes | — |
| 238 | C4⋊C4×C79 | C24 | 1 | 24 | yes | — |
| 239 | C4⋊C4×C79 | C24 | 1 | 2 | yes | — |
| 240 | C4⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 241 | C4⋊C4×C79 | C24 | 1 | 4 | yes | — |
| 242 | C4⋊C4×C79 | C24 | 1 | 12 | yes | — |
| 243 | C22⋊C4×C79 | C24 | 1 | 12 | yes | — |
| 244 | C22⋊C4×C79 | C24 | 1 | 6 | yes | — |
| 245 | C42×C79 | C24 | 1 | 1 | yes | characteristic |
| 246 | C42×C79 | C24 | 1 | 3 | yes | — |
| 247 | C42×C79 | C24 | 1 | 6 | yes | — |
| 248 | C42×C79 | C24 | 1 | 12 | yes | — |
| 249 | C23×C79 | C25 | 1 | 3 | yes | — |
| 250 | C22×D79 | C25 | 1 | 12 | yes | — |
| 251 | Q8×C79 | — | 4 | 12 | no | — |
| 252 | Q8×C79 | 2−1+4 | 1 | 4 | yes | — |
| 253 | D4×C79 | — | 2 | 6 | no | — |
| 254 | C2×C4×C79 | — | 2 | 6 | no | — |
| 255 | C2×C4×C79 | — | 4 | 6 | no | — |
| 256 | C2×C4×C79 | — | 4 | 12 | no | — |
| 257 | C2×C4×C79 | C25 | 1 | 12 | yes | — |
| 258 | C2×C4×C79 | C25 | 1 | 4 | yes | — |
| 259 | C2×C4×C79 | C25 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C79 | C25 | 1 | 2 | yes | — |
| 261 | C2×C4×C79 | C25 | 1 | 6 | yes | — |
| 262 | C2×C4×C79 | C25 | 1 | 3 | yes | — |
| 263 | C22⋊D79 | — | 4 | 12 | no | — |
| 264 | C22⋊D79 | — | 4 | 24 | no | — |
| 265 | C2×Dic79 | C25 | 1 | 4 | yes | — |
| 266 | C2×Dic79 | C25 | 1 | 4 | yes | — |
| 267 | C2×Dic79 | C25 | 1 | 12 | yes | — |
| 268 | D316 | — | 2 | 24 | no | — |
| 269 | D316 | — | 4 | 6 | no | — |
| 270 | D316 | — | 4 | 24 | no | — |
| 271 | D316 | — | 4 | 12 | no | — |
| 272 | D316 | — | 4 | 12 | no | — |
| 273 | C4×D79 | — | 2 | 24 | no | — |
| 274 | C4×D79 | — | 4 | 12 | no | — |
| 275 | C4×D79 | — | 4 | 24 | no | — |
| 276 | C4×D79 | — | 4 | 24 | no | — |
| 277 | C4×D79 | — | 4 | 12 | no | — |
| 278 | Dic158 | — | 4 | 12 | no | — |
| 279 | Dic158 | — | 4 | 6 | no | — |
| 280 | C22×C79 | — | 2 | 3 | no | — |
| 281 | C22×C79 | — | 2 | 6 | no | — |
| 282 | C22×C79 | C26 | 1 | 1 | yes | characteristic |
| 283 | C2×D79 | — | 2 | 12 | no | — |
| 284 | C2×D79 | — | 2 | 12 | no | — |
| 285 | C2×D79 | — | 2 | 12 | no | — |
| 286 | C4×C79 | — | 2 | 1 | no | — |
| 287 | C4×C79 | — | 2 | 2 | no | — |
| 288 | C4×C79 | — | 2 | 12 | no | — |
| 289 | C4×C79 | — | 2 | 6 | no | — |
| 290 | C4×C79 | — | 2 | 4 | no | — |
| 291 | C4×C79 | C2×2−1+4 | 1 | 6 | yes | — |
| 292 | Dic79 | — | 2 | 4 | no | — |
| 293 | Dic79 | — | 2 | 4 | no | — |
| 294 | Dic79 | — | 2 | 12 | no | — |
| 295 | #63070 | — | 79 | 1 | no | maximal, Sylow |
| 296 | C2×C79 | — | 4 | 3 | no | — |
| 297 | C2×C79 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 298 | C2×C79 | H(7,𝔽2) | 1 | 2 | yes | — |
| 299 | D79 | — | 4 | 12 | no | — |
| 300 | #3559 | — | 79 | 12 | no | — |
| 301 | #3559 | — | 79 | 12 | no | — |
| 302 | #3559 | — | 79 | 6 | no | — |
| 303 | #3548 | — | 79 | 12 | no | — |
| 304 | #3548 | — | 79 | 3 | no | — |
| 305 | #3531 | — | 79 | 3 | no | — |
| 306 | #3517 | — | 79 | 4 | no | — |
| 307 | #3517 | — | 79 | 4 | no | — |
| 308 | #3517 | — | 79 | 2 | no | — |
| 309 | #3504 | — | 79 | 4 | no | — |
| 310 | #3504 | D79 | 1 | 1 | yes | characteristic, complemented |
| 311 | C79 | #63070 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 312 | #564 | — | 79 | 1 | no | — |
| 313 | #563 | — | 79 | 12 | no | — |
| 314 | #563 | — | 79 | 6 | no | — |
| 315 | #563 | — | 79 | 12 | no | — |
| 316 | #562 | — | 79 | 3 | no | — |
| 317 | #562 | — | 79 | 6 | no | — |
| 318 | #562 | — | 79 | 12 | no | — |
| 319 | #562 | — | 79 | 24 | no | — |
| 320 | #557 | — | 79 | 4 | no | — |
| 321 | #557 | — | 79 | 2 | no | — |
| 322 | #557 | C2×D79 | 1 | 4 | yes | — |
| 323 | #554 | — | 79 | 12 | no | — |
| 324 | #554 | — | 79 | 12 | no | — |
| 325 | #554 | — | 79 | 12 | no | — |
| 326 | #554 | — | 79 | 12 | no | — |
| 327 | #554 | C2×D79 | 1 | 12 | yes | — |
| 328 | #553 | — | 79 | 12 | no | — |
| 329 | #553 | — | 79 | 12 | no | — |
| 330 | #553 | — | 79 | 12 | no | — |
| 331 | #553 | — | 79 | 12 | no | — |
| 332 | #553 | — | 79 | 12 | no | — |
| 333 | #550 | — | 79 | 4 | no | — |
| 334 | #550 | — | 79 | 4 | no | — |
| 335 | #550 | — | 79 | 2 | no | — |
| 336 | #550 | — | 79 | 12 | no | — |
| 337 | #550 | — | 79 | 12 | no | — |
| 338 | #550 | — | 79 | 6 | no | — |
| 339 | #547 | — | 79 | 12 | no | — |
| 340 | #547 | — | 79 | 12 | no | — |
| 341 | #547 | — | 79 | 24 | no | — |
| 342 | #547 | — | 79 | 6 | no | — |
| 343 | #547 | — | 79 | 12 | no | — |
| 344 | #547 | — | 79 | 24 | no | — |
| 345 | #544 | — | 79 | 12 | no | — |
| 346 | #544 | — | 79 | 12 | no | — |
| 347 | #544 | C2×D79 | 1 | 6 | yes | — |
| 348 | #540 | — | 79 | 12 | no | — |
| 349 | #540 | — | 79 | 12 | no | — |
| 350 | #540 | — | 79 | 12 | no | — |
| 351 | #540 | — | 79 | 12 | no | — |
| 352 | #540 | — | 79 | 12 | no | — |
| 353 | #539 | — | 79 | 24 | no | — |
| 354 | #539 | — | 79 | 24 | no | — |
| 355 | #539 | — | 79 | 12 | no | — |
| 356 | #537 | — | 79 | 24 | no | — |
| 357 | #537 | — | 79 | 24 | no | — |
| 358 | #537 | — | 79 | 12 | no | — |
| 359 | #533 | — | 79 | 12 | no | — |
| 360 | #533 | C2×D79 | 1 | 3 | yes | — |
| 361 | #532 | — | 79 | 12 | no | — |
| 362 | #532 | — | 79 | 12 | no | — |
| 363 | #532 | — | 79 | 6 | no | — |
| 364 | #529 | — | 79 | 12 | no | — |
| 365 | #529 | — | 79 | 12 | no | — |
| 366 | #529 | — | 79 | 6 | no | — |
| 367 | C2×#125 | — | 79 | 12 | no | — |
| 368 | C2×#125 | C2×D79 | 1 | 3 | yes | — |
| 369 | #520 | — | 79 | 4 | no | — |
| 370 | #520 | — | 79 | 4 | no | — |
| 371 | #520 | C2×D79 | 1 | 2 | yes | — |
| 372 | C4×#41 | — | 79 | 4 | no | — |
| 373 | C4×#41 | C2×D79 | 1 | 1 | yes | characteristic |
| 374 | C2×#41 | — | 79 | 24 | no | — |
| 375 | C2×#41 | — | 79 | 4 | no | — |
| 376 | C2×#41 | — | 79 | 24 | no | — |
| 377 | C2×#41 | — | 79 | 12 | no | — |
| 378 | C2×#41 | C22×D79 | 1 | 1 | yes | characteristic |
| 379 | C4⋊Q8 | — | 79 | 12 | no | — |
| 380 | C4⋊Q8 | — | 79 | 12 | no | — |
| 381 | C4⋊Q8 | — | 79 | 12 | no | — |
| 382 | C4⋊Q8 | — | 79 | 6 | no | — |
| 383 | C4⋊Q8 | C22×D79 | 1 | 12 | yes | — |
| 384 | C4⋊Q8 | C22×D79 | 1 | 6 | yes | — |
| 385 | #127 | — | 79 | 12 | no | — |
| 386 | #127 | — | 79 | 12 | no | — |
| 387 | #127 | — | 79 | 6 | no | — |
| 388 | #126 | — | 79 | 12 | no | — |
| 389 | #126 | — | 79 | 12 | no | — |
| 390 | #126 | — | 79 | 12 | no | — |
| 391 | #126 | — | 79 | 12 | no | — |
| 392 | #126 | — | 79 | 12 | no | — |
| 393 | #125 | — | 79 | 12 | no | — |
| 394 | #125 | — | 79 | 24 | no | — |
| 395 | #125 | — | 79 | 12 | no | — |
| 396 | #125 | — | 79 | 12 | no | — |
| 397 | #125 | — | 79 | 4 | no | — |
| 398 | #125 | — | 79 | 4 | no | — |
| 399 | #125 | — | 79 | 4 | no | — |
| 400 | #125 | — | 79 | 12 | no | — |
| 401 | #125 | — | 79 | 2 | no | — |
| 402 | #125 | C22×D79 | 1 | 12 | yes | — |
| 403 | #125 | C22×D79 | 1 | 3 | yes | — |
| 404 | #125 | C22×D79 | 1 | 6 | yes | — |
| 405 | #125 | C22×D79 | 1 | 12 | yes | — |
| 406 | #125 | C22×D79 | 1 | 1 | yes | characteristic |
| 407 | #124 | — | 79 | 12 | no | — |
| 408 | #124 | — | 79 | 12 | no | — |
| 409 | #124 | — | 79 | 6 | no | — |
| 410 | #123 | — | 79 | 12 | no | — |
| 411 | #123 | — | 79 | 24 | no | — |
| 412 | #123 | — | 79 | 12 | no | — |
| 413 | #123 | — | 79 | 12 | no | — |
| 414 | #123 | — | 79 | 12 | no | — |
| 415 | #123 | — | 79 | 24 | no | — |
| 416 | #123 | — | 79 | 24 | no | — |
| 417 | #123 | — | 79 | 24 | no | — |
| 418 | #123 | — | 79 | 12 | no | — |
| 419 | #123 | — | 79 | 24 | no | — |
| 420 | C22⋊Q8 | — | 79 | 12 | no | — |
| 421 | C22⋊Q8 | — | 79 | 12 | no | — |
| 422 | C22⋊Q8 | — | 79 | 24 | no | — |
| 423 | C22⋊Q8 | — | 79 | 6 | no | — |
| 424 | C22⋊Q8 | — | 79 | 12 | no | — |
| 425 | C22⋊Q8 | — | 79 | 12 | no | — |
| 426 | C22⋊Q8 | — | 79 | 12 | no | — |
| 427 | C22⋊Q8 | — | 79 | 12 | no | — |
| 428 | C22⋊Q8 | — | 79 | 24 | no | — |
| 429 | C22⋊Q8 | — | 79 | 24 | no | — |
| 430 | C22⋊Q8 | — | 79 | 24 | no | — |
| 431 | C22⋊Q8 | C22×D79 | 1 | 12 | yes | — |
| 432 | C22⋊Q8 | C22×D79 | 1 | 24 | yes | — |
| 433 | #121 | — | 79 | 12 | no | — |
| 434 | #121 | — | 79 | 6 | no | — |
| 435 | #121 | — | 79 | 12 | no | — |
| 436 | #121 | — | 79 | 12 | no | — |
| 437 | #121 | — | 79 | 24 | no | — |
| 438 | #121 | — | 79 | 12 | no | — |
| 439 | #121 | — | 79 | 24 | no | — |
| 440 | #121 | — | 79 | 12 | no | — |
| 441 | #121 | — | 79 | 12 | no | — |
| 442 | #121 | — | 79 | 12 | no | — |
| 443 | #121 | — | 79 | 24 | no | — |
| 444 | #121 | — | 79 | 24 | no | — |
| 445 | #121 | — | 79 | 12 | no | — |
| 446 | #121 | — | 79 | 24 | no | — |
| 447 | #121 | — | 79 | 24 | no | — |
| 448 | #121 | — | 79 | 24 | no | — |
| 449 | C4×Q8 | — | 79 | 4 | no | — |
| 450 | C4×Q8 | — | 79 | 12 | no | — |
| 451 | C4×Q8 | — | 79 | 6 | no | — |
| 452 | C4×Q8 | C22×D79 | 1 | 4 | yes | — |
| 453 | C4×Q8 | C22×D79 | 1 | 2 | yes | — |
| 454 | C4×Q8 | C22×D79 | 1 | 12 | yes | — |
| 455 | C4×D4 | — | 79 | 12 | no | — |
| 456 | C4×D4 | — | 79 | 24 | no | — |
| 457 | C4×D4 | — | 79 | 12 | no | — |
| 458 | C4×D4 | — | 79 | 12 | no | — |
| 459 | C4×D4 | — | 79 | 12 | no | — |
| 460 | C4×D4 | — | 79 | 24 | no | — |
| 461 | C4×D4 | — | 79 | 12 | no | — |
| 462 | C4×D4 | — | 79 | 12 | no | — |
| 463 | C4×D4 | — | 79 | 12 | no | — |
| 464 | C4×D4 | — | 79 | 12 | no | — |
| 465 | C4×D4 | — | 79 | 6 | no | — |
| 466 | C4×D4 | — | 79 | 12 | no | — |
| 467 | C4×D4 | C22×D79 | 1 | 6 | yes | — |
| 468 | C4×D4 | C22×D79 | 1 | 12 | yes | — |
| 469 | #117 | — | 79 | 12 | no | — |
| 470 | #117 | — | 79 | 12 | no | — |
| 471 | #117 | — | 79 | 12 | no | — |
| 472 | #117 | C22×D79 | 1 | 3 | yes | — |
| 473 | #117 | C22×D79 | 1 | 6 | yes | — |
| 474 | C2×C4⋊C4 | — | 79 | 12 | no | — |
| 475 | C2×C4⋊C4 | — | 79 | 12 | no | — |
| 476 | C2×C4⋊C4 | — | 79 | 24 | no | — |
| 477 | C2×C4⋊C4 | — | 79 | 24 | no | — |
| 478 | C2×C4⋊C4 | C22×D79 | 1 | 6 | yes | — |
| 479 | C2×C4⋊C4 | C22×D79 | 1 | 12 | yes | — |
| 480 | C2×C42 | — | 79 | 12 | no | — |
| 481 | C2×C42 | C22×D79 | 1 | 3 | yes | — |
| 482 | #41 | — | 2 | 4 | no | — |
| 483 | #41 | — | 632 | 12 | no | — |
| 484 | #41 | — | 632 | 24 | no | — |
| 485 | #41 | — | 632 | 24 | no | — |
| 486 | #41 | — | 158 | 16 | no | — |
| 487 | C2×Q8 | — | 79 | 12 | no | — |
| 488 | C2×Q8 | — | 79 | 6 | no | — |
| 489 | C2×Q8 | C23×D79 | 1 | 12 | yes | — |
| 490 | C2×Q8 | C23×D79 | 1 | 1 | yes | characteristic |
| 491 | C2×D4 | — | 79 | 24 | no | — |
| 492 | C2×D4 | — | 79 | 12 | no | — |
| 493 | C2×D4 | — | 79 | 24 | no | — |
| 494 | C2×D4 | — | 79 | 12 | no | — |
| 495 | C2×D4 | — | 79 | 12 | no | — |
| 496 | C2×D4 | — | 79 | 6 | no | — |
| 497 | C2×D4 | — | 79 | 12 | no | — |
| 498 | C2×D4 | C23×D79 | 1 | 3 | yes | — |
| 499 | C22×C4 | — | 79 | 12 | no | — |
| 500 | C22×C4 | — | 79 | 12 | no | — |
| 501 | C22×C4 | — | 79 | 24 | no | — |
| 502 | C22×C4 | — | 79 | 24 | no | — |
| 503 | C22×C4 | — | 79 | 12 | no | — |
| 504 | C22×C4 | C23×D79 | 1 | 3 | yes | — |
| 505 | C22×C4 | C23×D79 | 1 | 6 | yes | — |
| 506 | C22×C4 | C23×D79 | 1 | 12 | yes | — |
| 507 | C4⋊C4 | — | 79 | 12 | no | — |
| 508 | C4⋊C4 | — | 79 | 12 | no | — |
| 509 | C4⋊C4 | — | 79 | 24 | no | — |
| 510 | C4⋊C4 | — | 79 | 12 | no | — |
| 511 | C4⋊C4 | — | 79 | 12 | no | — |
| 512 | C4⋊C4 | — | 79 | 4 | no | — |
| 513 | C4⋊C4 | — | 79 | 4 | no | — |
| 514 | C4⋊C4 | — | 79 | 4 | no | — |
| 515 | C4⋊C4 | — | 79 | 4 | no | — |
| 516 | C4⋊C4 | — | 79 | 12 | no | — |
| 517 | C4⋊C4 | — | 79 | 12 | no | — |
| 518 | C4⋊C4 | — | 79 | 12 | no | — |
| 519 | C4⋊C4 | — | 79 | 4 | no | — |
| 520 | C4⋊C4 | — | 79 | 2 | no | — |
| 521 | C4⋊C4 | — | 79 | 2 | no | — |
| 522 | C4⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 523 | C4⋊C4 | C23×D79 | 1 | 12 | yes | — |
| 524 | C4⋊C4 | C23×D79 | 1 | 12 | yes | — |
| 525 | C4⋊C4 | C23×D79 | 1 | 24 | yes | — |
| 526 | C4⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 527 | C4⋊C4 | C23×D79 | 1 | 12 | yes | — |
| 528 | C4⋊C4 | C23×D79 | 1 | 2 | yes | — |
| 529 | C4⋊C4 | C23×D79 | 1 | 4 | yes | — |
| 530 | C22⋊C4 | — | 79 | 12 | no | — |
| 531 | C22⋊C4 | — | 79 | 12 | no | — |
| 532 | C22⋊C4 | — | 79 | 12 | no | — |
| 533 | C22⋊C4 | — | 79 | 12 | no | — |
| 534 | C22⋊C4 | — | 79 | 12 | no | — |
| 535 | C22⋊C4 | — | 79 | 24 | no | — |
| 536 | C22⋊C4 | — | 79 | 12 | no | — |
| 537 | C22⋊C4 | — | 79 | 12 | no | — |
| 538 | C22⋊C4 | — | 79 | 12 | no | — |
| 539 | C22⋊C4 | — | 79 | 12 | no | — |
| 540 | C22⋊C4 | C23×D79 | 1 | 12 | yes | — |
| 541 | C22⋊C4 | C23×D79 | 1 | 6 | yes | — |
| 542 | C42 | — | 79 | 4 | no | — |
| 543 | C42 | — | 79 | 12 | no | — |
| 544 | C42 | — | 79 | 12 | no | — |
| 545 | C42 | C23×D79 | 1 | 12 | yes | — |
| 546 | C42 | C23×D79 | 1 | 1 | yes | characteristic |
| 547 | C42 | C23×D79 | 1 | 6 | yes | — |
| 548 | C42 | C23×D79 | 1 | 3 | yes | — |
| 549 | C23 | — | 79 | 12 | no | — |
| 550 | C23 | C24×D79 | 1 | 3 | yes | — |
| 551 | Q8 | — | 4 | 12 | no | — |
| 552 | Q8 | — | 316 | 6 | no | — |
| 553 | Q8 | — | 316 | 12 | no | — |
| 554 | Q8 | #14579209 | 1 | 4 | yes | — |
| 555 | D4 | — | 2 | 6 | no | — |
| 556 | D4 | — | 316 | 6 | no | — |
| 557 | D4 | — | 316 | 24 | no | — |
| 558 | D4 | — | 316 | 12 | no | — |
| 559 | D4 | — | 316 | 12 | no | — |
| 560 | D4 | — | 316 | 24 | no | — |
| 561 | D4 | — | 316 | 12 | no | — |
| 562 | D4 | — | 158 | 24 | no | — |
| 563 | C2×C4 | — | 2 | 6 | no | — |
| 564 | C2×C4 | — | 4 | 6 | no | — |
| 565 | C2×C4 | — | 4 | 12 | no | — |
| 566 | C2×C4 | — | 316 | 24 | no | — |
| 567 | C2×C4 | — | 316 | 12 | no | — |
| 568 | C2×C4 | — | 316 | 24 | no | — |
| 569 | C2×C4 | — | 316 | 12 | no | — |
| 570 | C2×C4 | — | 79 | 4 | no | — |
| 571 | C2×C4 | — | 79 | 4 | no | — |
| 572 | C2×C4 | — | 79 | 12 | no | — |
| 573 | C2×C4 | — | 158 | 24 | no | — |
| 574 | C2×C4 | C24×D79 | 1 | 4 | yes | — |
| 575 | C2×C4 | C24×D79 | 1 | 12 | yes | — |
| 576 | C2×C4 | C24×D79 | 1 | 1 | yes | characteristic |
| 577 | C2×C4 | C24×D79 | 1 | 2 | yes | — |
| 578 | C2×C4 | C24×D79 | 1 | 6 | yes | — |
| 579 | C2×C4 | C24×D79 | 1 | 3 | yes | — |
| 580 | C22 | — | 2 | 3 | no | — |
| 581 | C22 | — | 2 | 6 | no | — |
| 582 | C22 | — | 158 | 12 | no | — |
| 583 | C22 | — | 158 | 12 | no | — |
| 584 | C22 | — | 158 | 12 | no | — |
| 585 | C22 | C25×D79 | 1 | 1 | yes | characteristic |
| 586 | C4 | — | 2 | 1 | no | — |
| 587 | C4 | — | 2 | 2 | no | — |
| 588 | C4 | — | 2 | 12 | no | — |
| 589 | C4 | — | 2 | 6 | no | — |
| 590 | C4 | — | 2 | 4 | no | — |
| 591 | C4 | — | 158 | 4 | no | — |
| 592 | C4 | — | 158 | 12 | no | — |
| 593 | C4 | — | 158 | 4 | no | — |
| 594 | C4 | C2×#14579209 | 1 | 6 | yes | — |
| 595 | C2 | — | 4 | 3 | no | — |
| 596 | C2 | — | 316 | 12 | no | — |
| 597 | C2 | C22×#14579209 | 1 | 1 | yes | characteristic |
| 598 | C2 | #23778211 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D79 |
| commutator, socle, cosocle | C22×C79 | C26 |
| Fitting | C79×#3504 | C2 |
| hypercenter | #3504 | D79 |
| hypocenter | C79 | #63070 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ #3504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23777935 | C2 | semidirect |
| 2. #23777934 | C2 | semidirect |
| 3. #23777933 | C2 | semidirect |
| 4. #23777800 | C2 | semidirect |
| 5. #23777799 | C2 | semidirect |
| 6. #23777547 | C2 | semidirect |
| 7. #23777407 | C2 | semidirect |
| 8. #23777406 | C2 | semidirect |
| 9. #23777400 | C2 | semidirect |
| 10. #23777225 | C2 | semidirect |
| 11. C79×#3504 | C2 | semidirect |
| 310. #3504 | D79 | semidirect |
| 311. C79 | #63070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777935 | 2 |
| #23777934 | 2 |
| #23777933 | 2 |
| #23777800 | 2 |
| #23777799 | 2 |
| #23777547 | 2 |
| #23777407 | 2 |
| #23777406 | 2 |
| #23777400 | 2 |
| #23777225 | 2 |
| C79×#3504 | 2 |
| #63070 | 79 |