Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
6184 conjugacy classes of subgroups.
The subgroup lattice has 530 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23778009 | C2 | 1 | 10 | yes | maximal, complemented |
| 2 | #23778009 | C2 | 1 | 10 | yes | maximal, complemented |
| 3 | #23778006 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #23777894 | C2 | 1 | 5 | yes | maximal, complemented |
| 5 | #23777857 | C2 | 1 | 5 | yes | maximal, complemented |
| 6 | #23777856 | C2 | 1 | 5 | yes | maximal, complemented |
| 7 | #23777548 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #564×D79 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #23777372 | C2 | 1 | 10 | yes | maximal, complemented |
| 10 | #23777224 | C2 | 1 | 5 | yes | maximal, complemented |
| 11 | C2×#564×C79 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C79⋊#564 | C22 | 1 | 5 | yes | — |
| 13 | C79⋊#564 | C22 | 1 | 10 | yes | — |
| 14 | C79⋊#564 | C22 | 1 | 10 | yes | — |
| 15 | #19099317 | C22 | 1 | 10 | yes | — |
| 16 | #19099317 | C22 | 1 | 10 | yes | — |
| 17 | #19099317 | C22 | 1 | 10 | yes | — |
| 18 | #19099311 | C22 | 1 | 5 | yes | — |
| 19 | #19099290 | C22 | 1 | 10 | yes | — |
| 20 | #19099290 | C22 | 1 | 20 | yes | — |
| 21 | #19099290 | C22 | 1 | 20 | yes | — |
| 22 | #19099269 | C22 | 1 | 20 | yes | — |
| 23 | #19099269 | C22 | 1 | 10 | yes | — |
| 24 | #19099268 | C22 | 1 | 20 | yes | — |
| 25 | #19099268 | C22 | 1 | 10 | yes | — |
| 26 | #19099266 | C22 | 1 | 10 | yes | — |
| 27 | #19099261 | C22 | 1 | 10 | yes | — |
| 28 | #19099251 | C22 | 1 | 20 | yes | — |
| 29 | #19099251 | C22 | 1 | 10 | yes | — |
| 30 | #19099248 | C22 | 1 | 10 | yes | — |
| 31 | #19099248 | C22 | 1 | 20 | yes | — |
| 32 | #19099245 | C22 | 1 | 20 | yes | — |
| 33 | #19099245 | C22 | 1 | 20 | yes | — |
| 34 | #19099245 | C22 | 1 | 20 | yes | — |
| 35 | #19099214 | C22 | 1 | 10 | yes | — |
| 36 | #19099194 | C22 | 1 | 10 | yes | — |
| 37 | #19099193 | C22 | 1 | 10 | yes | — |
| 38 | #19099193 | C22 | 1 | 10 | yes | — |
| 39 | #19099193 | C22 | 1 | 20 | yes | — |
| 40 | #19099176 | C22 | 1 | 20 | yes | — |
| 41 | #19099172 | C22 | 1 | 20 | yes | — |
| 42 | #19099172 | C22 | 1 | 20 | yes | — |
| 43 | #19099172 | C22 | 1 | 20 | yes | — |
| 44 | #19099172 | C22 | 1 | 20 | yes | — |
| 45 | #19099161 | C22 | 1 | 20 | yes | — |
| 46 | #19099161 | C22 | 1 | 20 | yes | — |
| 47 | #19099160 | C22 | 1 | 20 | yes | — |
| 48 | #19099120 | C22 | 1 | 5 | yes | — |
| 49 | #19099119 | C22 | 1 | 5 | yes | — |
| 50 | #19099119 | C22 | 1 | 10 | yes | — |
| 51 | #19099119 | C22 | 1 | 5 | yes | — |
| 52 | #19099098 | C22 | 1 | 10 | yes | — |
| 53 | #19099098 | C22 | 1 | 10 | yes | — |
| 54 | #19099097 | C22 | 1 | 10 | yes | — |
| 55 | #125×D79 | C22 | 1 | 5 | yes | — |
| 56 | #125×D79 | C22 | 1 | 10 | yes | — |
| 57 | #125×D79 | C22 | 1 | 5 | yes | — |
| 58 | #19099044 | C22 | 1 | 10 | yes | — |
| 59 | C4×#11929624 | C22 | 1 | 5 | yes | — |
| 60 | #564×C79 | C22 | 1 | 1 | yes | characteristic |
| 61 | #564×C79 | C22 | 1 | 5 | yes | — |
| 62 | #564×C79 | C22 | 1 | 10 | yes | — |
| 63 | C2×#125×C79 | C22 | 1 | 5 | yes | — |
| 64 | C2×#125×C79 | C22 | 1 | 10 | yes | — |
| 65 | C2×#11929624 | C23 | 1 | 5 | yes | — |
| 66 | #14579161 | C23 | 1 | 10 | yes | — |
| 67 | #14579160 | C23 | 1 | 10 | yes | — |
| 68 | #14579160 | C23 | 1 | 10 | yes | — |
| 69 | #14579160 | C23 | 1 | 20 | yes | — |
| 70 | #14579160 | C23 | 1 | 20 | yes | — |
| 71 | #14579160 | C23 | 1 | 10 | yes | — |
| 72 | #14579160 | C23 | 1 | 10 | yes | — |
| 73 | #14579156 | C23 | 1 | 20 | yes | — |
| 74 | #14579156 | C23 | 1 | 20 | yes | — |
| 75 | #14579156 | C23 | 1 | 20 | yes | — |
| 76 | #14579156 | C23 | 1 | 20 | yes | — |
| 77 | #14579156 | C23 | 1 | 20 | yes | — |
| 78 | #14579156 | C23 | 1 | 20 | yes | — |
| 79 | #14579155 | C23 | 1 | 20 | yes | — |
| 80 | #14579153 | C23 | 1 | 5 | yes | — |
| 81 | #14579153 | C23 | 1 | 5 | yes | — |
| 82 | #14579153 | C23 | 1 | 10 | yes | — |
| 83 | #14579152 | C23 | 1 | 10 | yes | — |
| 84 | #14579152 | C23 | 1 | 10 | yes | — |
| 85 | #14579152 | C23 | 1 | 20 | yes | — |
| 86 | #14579152 | C23 | 1 | 20 | yes | — |
| 87 | #14579152 | C23 | 1 | 10 | yes | — |
| 88 | #14579152 | C23 | 1 | 10 | yes | — |
| 89 | #14579151 | C23 | 1 | 20 | yes | — |
| 90 | #14579151 | C23 | 1 | 20 | yes | — |
| 91 | #14579151 | C23 | 1 | 20 | yes | — |
| 92 | #14579151 | C23 | 1 | 20 | yes | — |
| 93 | #14579151 | C23 | 1 | 20 | yes | — |
| 94 | #14579151 | C23 | 1 | 20 | yes | — |
| 95 | #14579151 | C23 | 1 | 20 | yes | — |
| 96 | #14579151 | C23 | 1 | 20 | yes | — |
| 97 | #14579149 | C23 | 1 | 10 | yes | — |
| 98 | #14579146 | C23 | 1 | 20 | yes | — |
| 99 | #14579146 | C23 | 1 | 20 | yes | — |
| 100 | #14579146 | C23 | 1 | 20 | yes | — |
| 101 | #14579146 | C23 | 1 | 20 | yes | — |
| 102 | #14579144 | C23 | 1 | 20 | yes | — |
| 103 | #14579141 | C23 | 1 | 20 | yes | — |
| 104 | #14579141 | C23 | 1 | 20 | yes | — |
| 105 | #14579141 | C23 | 1 | 10 | yes | — |
| 106 | #14579141 | C23 | 1 | 10 | yes | — |
| 107 | #14579140 | C23 | 1 | 20 | yes | — |
| 108 | #14579140 | C23 | 1 | 10 | yes | — |
| 109 | #14579139 | C23 | 1 | 20 | yes | — |
| 110 | #14579139 | C23 | 1 | 20 | yes | — |
| 111 | #14579139 | C23 | 1 | 20 | yes | — |
| 112 | #14579139 | C23 | 1 | 20 | yes | — |
| 113 | #14579139 | C23 | 1 | 20 | yes | — |
| 114 | #14579139 | C23 | 1 | 20 | yes | — |
| 115 | #14579136 | C23 | 1 | 10 | yes | — |
| 116 | #14579136 | C23 | 1 | 10 | yes | — |
| 117 | #14579135 | C23 | 1 | 10 | yes | — |
| 118 | C4×Dic158 | C23 | 1 | 20 | yes | — |
| 119 | C4×Dic158 | C23 | 1 | 10 | yes | — |
| 120 | C4×Dic158 | C23 | 1 | 10 | yes | — |
| 121 | #14579126 | C23 | 1 | 10 | yes | — |
| 122 | #14579126 | C23 | 1 | 20 | yes | — |
| 123 | #14579126 | C23 | 1 | 20 | yes | — |
| 124 | #14579126 | C23 | 1 | 20 | yes | — |
| 125 | #14579126 | C23 | 1 | 10 | yes | — |
| 126 | C4×D316 | C23 | 1 | 10 | yes | — |
| 127 | C4×D316 | C23 | 1 | 10 | yes | — |
| 128 | #14579123 | C23 | 1 | 10 | yes | — |
| 129 | #14579123 | C23 | 1 | 20 | yes | — |
| 130 | #14579123 | C23 | 1 | 10 | yes | — |
| 131 | C4×C22⋊D79 | C23 | 1 | 10 | yes | — |
| 132 | C4×C22⋊D79 | C23 | 1 | 20 | yes | — |
| 133 | C4×C22⋊D79 | C23 | 1 | 10 | yes | — |
| 134 | #14579120 | C23 | 1 | 5 | yes | — |
| 135 | #14579120 | C23 | 1 | 10 | yes | — |
| 136 | #14579119 | C23 | 1 | 10 | yes | — |
| 137 | #14579119 | C23 | 1 | 10 | yes | — |
| 138 | #14579119 | C23 | 1 | 10 | yes | — |
| 139 | #14579119 | C23 | 1 | 20 | yes | — |
| 140 | #14579119 | C23 | 1 | 10 | yes | — |
| 141 | #14579118 | C23 | 1 | 20 | yes | — |
| 142 | #14579118 | C23 | 1 | 5 | yes | — |
| 143 | #14579118 | C23 | 1 | 5 | yes | — |
| 144 | C4⋊C4×D79 | C23 | 1 | 10 | yes | — |
| 145 | C4⋊C4×D79 | C23 | 1 | 20 | yes | — |
| 146 | C4⋊C4×D79 | C23 | 1 | 10 | yes | — |
| 147 | C4⋊C4×D79 | C23 | 1 | 10 | yes | — |
| 148 | C4⋊C4×D79 | C23 | 1 | 10 | yes | — |
| 149 | C42×D79 | C23 | 1 | 5 | yes | — |
| 150 | C42×D79 | C23 | 1 | 5 | yes | — |
| 151 | #125×C79 | C23 | 1 | 20 | yes | — |
| 152 | #125×C79 | C23 | 1 | 20 | yes | — |
| 153 | #125×C79 | C23 | 1 | 10 | yes | — |
| 154 | #125×C79 | C23 | 1 | 10 | yes | — |
| 155 | #125×C79 | C23 | 1 | 20 | yes | — |
| 156 | #125×C79 | C23 | 1 | 10 | yes | — |
| 157 | #125×C79 | C23 | 1 | 5 | yes | — |
| 158 | #125×C79 | C23 | 1 | 5 | yes | — |
| 159 | #125×C79 | C23 | 1 | 10 | yes | — |
| 160 | #125×C79 | C23 | 1 | 10 | yes | — |
| 161 | C2×C4⋊C4×C79 | C23 | 1 | 10 | yes | — |
| 162 | C2×C4⋊C4×C79 | C23 | 1 | 10 | yes | — |
| 163 | C2×C4⋊C4×C79 | C23 | 1 | 10 | yes | — |
| 164 | C2×C42×C79 | C23 | 1 | 5 | yes | — |
| 165 | #11929624 | — | 2 | 20 | no | — |
| 166 | C2×Dic158 | C24 | 1 | 5 | yes | — |
| 167 | C2×Dic158 | C24 | 1 | 20 | yes | — |
| 168 | C2×Dic158 | C24 | 1 | 10 | yes | — |
| 169 | C2×D316 | C24 | 1 | 5 | yes | — |
| 170 | C2×D316 | C24 | 1 | 10 | yes | — |
| 171 | C2×C22⋊D79 | C24 | 1 | 5 | yes | — |
| 172 | C2×C22⋊D79 | C24 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×D79 | C24 | 1 | 5 | yes | — |
| 174 | C2×C4×D79 | C24 | 1 | 5 | yes | — |
| 175 | C2×C4×D79 | C24 | 1 | 10 | yes | — |
| 176 | C2×C4×D79 | C24 | 1 | 10 | yes | — |
| 177 | C2×C4×D79 | C24 | 1 | 20 | yes | — |
| 178 | C4⋊Dic79 | C24 | 1 | 10 | yes | — |
| 179 | C4⋊Dic79 | C24 | 1 | 10 | yes | — |
| 180 | C4⋊Dic79 | C24 | 1 | 10 | yes | — |
| 181 | C4⋊Dic79 | C24 | 1 | 20 | yes | — |
| 182 | C4⋊Dic79 | C24 | 1 | 10 | yes | — |
| 183 | C4⋊Dic79 | C24 | 1 | 10 | yes | — |
| 184 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 185 | Dic79⋊C4 | C24 | 1 | 20 | yes | — |
| 186 | Dic79⋊C4 | C24 | 1 | 20 | yes | — |
| 187 | Dic79⋊C4 | C24 | 1 | 20 | yes | — |
| 188 | Dic79⋊C4 | C24 | 1 | 20 | yes | — |
| 189 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 190 | Dic79⋊C4 | C24 | 1 | 20 | yes | — |
| 191 | Dic79⋊C4 | C24 | 1 | 20 | yes | — |
| 192 | C22⋊Dic79 | C24 | 1 | 10 | yes | — |
| 193 | (C2×D79)⋊C4 | C24 | 1 | 10 | yes | — |
| 194 | (C2×D79)⋊C4 | C24 | 1 | 20 | yes | — |
| 195 | (C2×D79)⋊C4 | C24 | 1 | 20 | yes | — |
| 196 | (C2×D79)⋊C4 | C24 | 1 | 10 | yes | — |
| 197 | (C2×D79)⋊C4 | C24 | 1 | 20 | yes | — |
| 198 | (C2×D79)⋊C4 | C24 | 1 | 20 | yes | — |
| 199 | C4×Dic79 | C24 | 1 | 5 | yes | — |
| 200 | C4×Dic79 | C24 | 1 | 5 | yes | — |
| 201 | C4×Dic79 | C24 | 1 | 10 | yes | — |
| 202 | C4×Dic79 | C24 | 1 | 10 | yes | — |
| 203 | C4×Dic79 | C24 | 1 | 20 | yes | — |
| 204 | C4×Dic79 | C24 | 1 | 20 | yes | — |
| 205 | C22×C4×C79 | C24 | 1 | 5 | yes | — |
| 206 | C22×C4×C79 | C24 | 1 | 10 | yes | — |
| 207 | C4⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 208 | C4⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 209 | C4⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 210 | C4⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 211 | C4⋊C4×C79 | C24 | 1 | 20 | yes | — |
| 212 | C4⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 213 | C4⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 214 | C4⋊C4×C79 | C24 | 1 | 20 | yes | — |
| 215 | C4⋊C4×C79 | C24 | 1 | 20 | yes | — |
| 216 | C42×C79 | C24 | 1 | 5 | yes | — |
| 217 | C42×C79 | C24 | 1 | 5 | yes | — |
| 218 | C42×C79 | C24 | 1 | 10 | yes | — |
| 219 | C23×C79 | C25 | 1 | 1 | yes | characteristic |
| 220 | C22×D79 | C25 | 1 | 5 | yes | — |
| 221 | C22×D79 | C25 | 1 | 1 | yes | characteristic |
| 222 | C2×C4×C79 | — | 2 | 10 | no | — |
| 223 | C2×C4×C79 | — | 4 | 10 | no | — |
| 224 | C2×C4×C79 | C25 | 1 | 5 | yes | — |
| 225 | C2×C4×C79 | C25 | 1 | 5 | yes | — |
| 226 | C2×C4×C79 | C25 | 1 | 10 | yes | — |
| 227 | C2×C4×C79 | C25 | 1 | 10 | yes | — |
| 228 | C22⋊D79 | — | 2 | 10 | no | — |
| 229 | C22⋊D79 | 2−1+4 | 1 | 4 | yes | — |
| 230 | C2×Dic79 | C25 | 1 | 10 | yes | — |
| 231 | C2×Dic79 | C25 | 1 | 5 | yes | — |
| 232 | C2×Dic79 | C25 | 1 | 10 | yes | — |
| 233 | C2×Dic79 | C25 | 1 | 1 | yes | characteristic |
| 234 | D316 | — | 2 | 10 | no | — |
| 235 | D316 | — | 4 | 10 | no | — |
| 236 | C4×D79 | — | 2 | 10 | no | — |
| 237 | C4×D79 | — | 2 | 10 | no | — |
| 238 | C4×D79 | — | 4 | 10 | no | — |
| 239 | C4×D79 | — | 4 | 20 | no | — |
| 240 | C4×D79 | — | 4 | 10 | no | — |
| 241 | Dic158 | — | 2 | 10 | no | — |
| 242 | Dic158 | — | 4 | 10 | no | — |
| 243 | Dic158 | — | 4 | 20 | no | — |
| 244 | C22×C79 | — | 2 | 2 | no | — |
| 245 | C22×C79 | C2×2−1+4 | 1 | 2 | yes | — |
| 246 | C22×C79 | C26 | 1 | 1 | yes | characteristic |
| 247 | C2×D79 | — | 2 | 2 | no | — |
| 248 | C2×D79 | — | 2 | 5 | no | — |
| 249 | C2×D79 | — | 2 | 10 | no | — |
| 250 | C2×D79 | C2×2−1+4 | 1 | 2 | yes | — |
| 251 | C4×C79 | — | 2 | 5 | no | — |
| 252 | C4×C79 | — | 2 | 5 | no | — |
| 253 | C4×C79 | — | 2 | 10 | no | — |
| 254 | C4×C79 | — | 2 | 10 | no | — |
| 255 | Dic79 | — | 2 | 5 | no | — |
| 256 | Dic79 | — | 2 | 10 | no | — |
| 257 | Dic79 | — | 2 | 10 | no | — |
| 258 | Dic79 | C2×2−1+4 | 1 | 2 | yes | — |
| 259 | #63067 | — | 79 | 1 | no | maximal, Sylow |
| 260 | C2×C79 | — | 2 | 2 | no | — |
| 261 | C2×C79 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 262 | C2×C79 | 2−1+6 | 1 | 2 | yes | — |
| 263 | D79 | — | 2 | 2 | no | — |
| 264 | D79 | — | 4 | 5 | no | — |
| 265 | #3563 | — | 79 | 10 | no | — |
| 266 | #3563 | — | 79 | 10 | no | — |
| 267 | #3563 | — | 79 | 10 | no | — |
| 268 | #3556 | — | 79 | 5 | no | — |
| 269 | #3553 | — | 79 | 5 | no | — |
| 270 | #3553 | — | 79 | 5 | no | — |
| 271 | #3531 | — | 79 | 1 | no | — |
| 272 | C2×#564 | — | 79 | 1 | no | — |
| 273 | C2×#564 | D79 | 1 | 1 | yes | characteristic, complemented |
| 274 | #3515 | — | 79 | 10 | no | — |
| 275 | #3504 | — | 79 | 5 | no | — |
| 276 | C79 | #63067 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 277 | #564 | — | 79 | 5 | no | — |
| 278 | #564 | — | 79 | 10 | no | — |
| 279 | #564 | — | 79 | 10 | no | — |
| 280 | #564 | C2×D79 | 1 | 1 | yes | characteristic |
| 281 | #564 | C2×D79 | 1 | 5 | yes | — |
| 282 | #564 | C2×D79 | 1 | 10 | yes | — |
| 283 | #563 | — | 79 | 10 | no | — |
| 284 | #563 | — | 79 | 10 | no | — |
| 285 | #563 | — | 79 | 10 | no | — |
| 286 | #562 | — | 79 | 5 | no | — |
| 287 | #557 | — | 79 | 20 | no | — |
| 288 | #557 | — | 79 | 10 | no | — |
| 289 | #557 | — | 79 | 20 | no | — |
| 290 | #554 | — | 79 | 20 | no | — |
| 291 | #554 | — | 79 | 10 | no | — |
| 292 | #554 | — | 79 | 10 | no | — |
| 293 | #554 | — | 79 | 20 | no | — |
| 294 | #553 | — | 79 | 10 | no | — |
| 295 | #553 | — | 79 | 10 | no | — |
| 296 | #552 | — | 79 | 20 | no | — |
| 297 | #552 | — | 79 | 20 | no | — |
| 298 | #552 | — | 79 | 20 | no | — |
| 299 | #552 | — | 79 | 10 | no | — |
| 300 | #552 | — | 79 | 20 | no | — |
| 301 | #552 | — | 79 | 20 | no | — |
| 302 | #552 | — | 79 | 10 | no | — |
| 303 | #547 | — | 79 | 10 | no | — |
| 304 | #544 | — | 79 | 10 | no | — |
| 305 | #544 | — | 79 | 10 | no | — |
| 306 | #544 | — | 79 | 20 | no | — |
| 307 | #544 | — | 79 | 10 | no | — |
| 308 | #541 | — | 79 | 20 | no | — |
| 309 | #541 | — | 79 | 20 | no | — |
| 310 | #541 | — | 79 | 20 | no | — |
| 311 | #541 | — | 79 | 20 | no | — |
| 312 | #541 | — | 79 | 20 | no | — |
| 313 | #539 | — | 79 | 20 | no | — |
| 314 | #539 | — | 79 | 20 | no | — |
| 315 | #539 | — | 79 | 20 | no | — |
| 316 | #533 | — | 79 | 5 | no | — |
| 317 | #533 | — | 79 | 5 | no | — |
| 318 | #533 | — | 79 | 10 | no | — |
| 319 | #533 | — | 79 | 5 | no | — |
| 320 | #529 | — | 79 | 10 | no | — |
| 321 | #529 | — | 79 | 10 | no | — |
| 322 | #529 | — | 79 | 10 | no | — |
| 323 | C2×#125 | — | 79 | 5 | no | — |
| 324 | C2×#125 | — | 79 | 5 | no | — |
| 325 | C2×#125 | — | 79 | 10 | no | — |
| 326 | C2×#125 | C2×D79 | 1 | 5 | yes | — |
| 327 | C2×#125 | C2×D79 | 1 | 10 | yes | — |
| 328 | #520 | — | 79 | 10 | no | — |
| 329 | C4×#41 | — | 79 | 5 | no | — |
| 330 | C2×#41 | — | 79 | 5 | no | — |
| 331 | C4⋊Q8 | — | 79 | 10 | no | — |
| 332 | C4⋊Q8 | — | 79 | 10 | no | — |
| 333 | C4⋊Q8 | — | 79 | 10 | no | — |
| 334 | C4⋊Q8 | — | 79 | 10 | no | — |
| 335 | C4⋊Q8 | — | 79 | 20 | no | — |
| 336 | C4⋊Q8 | — | 79 | 20 | no | — |
| 337 | C4⋊Q8 | — | 79 | 10 | no | — |
| 338 | #126 | — | 79 | 20 | no | — |
| 339 | #126 | — | 79 | 20 | no | — |
| 340 | #126 | — | 79 | 20 | no | — |
| 341 | #126 | — | 79 | 20 | no | — |
| 342 | #126 | — | 79 | 20 | no | — |
| 343 | #126 | — | 79 | 20 | no | — |
| 344 | #126 | — | 79 | 20 | no | — |
| 345 | #125 | — | 79 | 20 | no | — |
| 346 | #125 | — | 79 | 20 | no | — |
| 347 | #125 | — | 79 | 10 | no | — |
| 348 | #125 | — | 79 | 10 | no | — |
| 349 | #125 | — | 79 | 10 | no | — |
| 350 | #125 | — | 79 | 20 | no | — |
| 351 | #125 | — | 79 | 20 | no | — |
| 352 | #125 | — | 79 | 10 | no | — |
| 353 | #125 | — | 79 | 20 | no | — |
| 354 | #125 | — | 79 | 20 | no | — |
| 355 | #125 | — | 79 | 20 | no | — |
| 356 | #125 | — | 79 | 20 | no | — |
| 357 | #125 | — | 79 | 20 | no | — |
| 358 | #125 | — | 79 | 20 | no | — |
| 359 | #125 | — | 79 | 5 | no | — |
| 360 | #125 | — | 79 | 10 | no | — |
| 361 | #125 | — | 79 | 5 | no | — |
| 362 | #125 | C22×D79 | 1 | 10 | yes | — |
| 363 | #125 | C22×D79 | 1 | 5 | yes | — |
| 364 | #125 | C22×D79 | 1 | 5 | yes | — |
| 365 | #125 | C22×D79 | 1 | 10 | yes | — |
| 366 | #125 | C22×D79 | 1 | 20 | yes | — |
| 367 | #125 | C22×D79 | 1 | 20 | yes | — |
| 368 | #125 | C22×D79 | 1 | 10 | yes | — |
| 369 | #125 | C22×D79 | 1 | 10 | yes | — |
| 370 | #125 | C22×D79 | 1 | 20 | yes | — |
| 371 | #125 | C22×D79 | 1 | 10 | yes | — |
| 372 | #124 | — | 79 | 10 | no | — |
| 373 | #123 | — | 79 | 20 | no | — |
| 374 | #123 | — | 79 | 20 | no | — |
| 375 | #123 | — | 79 | 20 | no | — |
| 376 | #123 | — | 79 | 20 | no | — |
| 377 | #123 | — | 79 | 20 | no | — |
| 378 | C22⋊Q8 | — | 79 | 10 | no | — |
| 379 | C22⋊Q8 | — | 79 | 20 | no | — |
| 380 | C22⋊Q8 | — | 79 | 10 | no | — |
| 381 | C22⋊Q8 | — | 79 | 10 | no | — |
| 382 | C22⋊Q8 | — | 79 | 20 | no | — |
| 383 | C22⋊Q8 | — | 79 | 20 | no | — |
| 384 | C22⋊Q8 | — | 79 | 20 | no | — |
| 385 | C22⋊Q8 | — | 79 | 20 | no | — |
| 386 | C22⋊Q8 | — | 79 | 20 | no | — |
| 387 | C22⋊Q8 | — | 79 | 20 | no | — |
| 388 | C22⋊Q8 | — | 79 | 20 | no | — |
| 389 | C22⋊Q8 | — | 79 | 20 | no | — |
| 390 | #121 | — | 79 | 10 | no | — |
| 391 | #121 | — | 79 | 10 | no | — |
| 392 | #121 | — | 79 | 10 | no | — |
| 393 | C4×Q8 | — | 79 | 20 | no | — |
| 394 | C4×Q8 | — | 79 | 10 | no | — |
| 395 | C4×Q8 | — | 79 | 10 | no | — |
| 396 | C4×Q8 | — | 79 | 20 | no | — |
| 397 | C4×Q8 | — | 79 | 20 | no | — |
| 398 | C4×Q8 | — | 79 | 10 | no | — |
| 399 | C4×Q8 | — | 79 | 10 | no | — |
| 400 | C4×Q8 | — | 79 | 20 | no | — |
| 401 | C4×D4 | — | 79 | 10 | no | — |
| 402 | C4×D4 | — | 79 | 10 | no | — |
| 403 | C4×D4 | — | 79 | 20 | no | — |
| 404 | C4×D4 | — | 79 | 20 | no | — |
| 405 | C4×D4 | — | 79 | 10 | no | — |
| 406 | C4×D4 | — | 79 | 10 | no | — |
| 407 | C4×D4 | — | 79 | 10 | no | — |
| 408 | C4×D4 | — | 79 | 10 | no | — |
| 409 | #117 | — | 79 | 5 | no | — |
| 410 | #117 | — | 79 | 10 | no | — |
| 411 | #117 | — | 79 | 10 | no | — |
| 412 | #117 | — | 79 | 10 | no | — |
| 413 | #117 | — | 79 | 20 | no | — |
| 414 | #117 | — | 79 | 10 | no | — |
| 415 | #117 | — | 79 | 10 | no | — |
| 416 | #117 | — | 79 | 5 | no | — |
| 417 | #117 | — | 79 | 5 | no | — |
| 418 | #117 | — | 79 | 20 | no | — |
| 419 | C2×C4⋊C4 | — | 79 | 10 | no | — |
| 420 | C2×C4⋊C4 | — | 79 | 10 | no | — |
| 421 | C2×C4⋊C4 | — | 79 | 10 | no | — |
| 422 | C2×C4⋊C4 | — | 79 | 10 | no | — |
| 423 | C2×C4⋊C4 | — | 79 | 20 | no | — |
| 424 | C2×C4⋊C4 | C22×D79 | 1 | 10 | yes | — |
| 425 | C2×C4⋊C4 | C22×D79 | 1 | 10 | yes | — |
| 426 | C2×C4⋊C4 | C22×D79 | 1 | 10 | yes | — |
| 427 | C2×C42 | — | 79 | 5 | no | — |
| 428 | C2×C42 | — | 79 | 5 | no | — |
| 429 | C2×C42 | C22×D79 | 1 | 5 | yes | — |
| 430 | #41 | — | 158 | 20 | no | — |
| 431 | C2×Q8 | — | 79 | 20 | no | — |
| 432 | C2×Q8 | — | 79 | 10 | no | — |
| 433 | C2×Q8 | — | 79 | 5 | no | — |
| 434 | C2×D4 | — | 79 | 1 | no | — |
| 435 | C2×D4 | — | 79 | 5 | no | — |
| 436 | C2×D4 | — | 79 | 10 | no | — |
| 437 | C2×D4 | — | 79 | 5 | no | — |
| 438 | C22×C4 | — | 79 | 10 | no | — |
| 439 | C22×C4 | — | 79 | 10 | no | — |
| 440 | C22×C4 | — | 79 | 20 | no | — |
| 441 | C22×C4 | — | 79 | 5 | no | — |
| 442 | C22×C4 | — | 79 | 5 | no | — |
| 443 | C22×C4 | C23×D79 | 1 | 5 | yes | — |
| 444 | C22×C4 | C23×D79 | 1 | 10 | yes | — |
| 445 | C4⋊C4 | — | 79 | 10 | no | — |
| 446 | C4⋊C4 | — | 79 | 20 | no | — |
| 447 | C4⋊C4 | — | 79 | 20 | no | — |
| 448 | C4⋊C4 | — | 79 | 20 | no | — |
| 449 | C4⋊C4 | — | 79 | 20 | no | — |
| 450 | C4⋊C4 | — | 79 | 10 | no | — |
| 451 | C4⋊C4 | — | 79 | 20 | no | — |
| 452 | C4⋊C4 | — | 79 | 20 | no | — |
| 453 | C4⋊C4 | — | 79 | 10 | no | — |
| 454 | C4⋊C4 | — | 79 | 10 | no | — |
| 455 | C4⋊C4 | — | 79 | 10 | no | — |
| 456 | C4⋊C4 | — | 79 | 20 | no | — |
| 457 | C4⋊C4 | — | 79 | 10 | no | — |
| 458 | C4⋊C4 | — | 79 | 10 | no | — |
| 459 | C4⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 460 | C4⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 461 | C4⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 462 | C4⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 463 | C4⋊C4 | C23×D79 | 1 | 20 | yes | — |
| 464 | C4⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 465 | C4⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 466 | C4⋊C4 | C23×D79 | 1 | 20 | yes | — |
| 467 | C4⋊C4 | C23×D79 | 1 | 20 | yes | — |
| 468 | C22⋊C4 | — | 79 | 10 | no | — |
| 469 | C22⋊C4 | — | 79 | 10 | no | — |
| 470 | C22⋊C4 | — | 79 | 20 | no | — |
| 471 | C22⋊C4 | — | 79 | 20 | no | — |
| 472 | C22⋊C4 | — | 79 | 20 | no | — |
| 473 | C22⋊C4 | — | 79 | 20 | no | — |
| 474 | C22⋊C4 | — | 79 | 10 | no | — |
| 475 | C42 | — | 79 | 5 | no | — |
| 476 | C42 | — | 79 | 10 | no | — |
| 477 | C42 | — | 79 | 5 | no | — |
| 478 | C42 | — | 79 | 10 | no | — |
| 479 | C42 | — | 79 | 20 | no | — |
| 480 | C42 | — | 79 | 20 | no | — |
| 481 | C42 | C23×D79 | 1 | 5 | yes | — |
| 482 | C42 | C23×D79 | 1 | 5 | yes | — |
| 483 | C42 | C23×D79 | 1 | 10 | yes | — |
| 484 | C23 | — | 79 | 1 | no | — |
| 485 | C23 | — | 79 | 5 | no | — |
| 486 | C23 | C24×D79 | 1 | 1 | yes | characteristic |
| 487 | Q8 | — | 316 | 10 | no | — |
| 488 | Q8 | — | 316 | 20 | no | — |
| 489 | Q8 | — | 158 | 10 | no | — |
| 490 | D4 | — | 316 | 10 | no | — |
| 491 | D4 | — | 79 | 4 | no | — |
| 492 | D4 | — | 158 | 10 | no | — |
| 493 | D4 | — | 158 | 10 | no | — |
| 494 | C2×C4 | — | 2 | 10 | no | — |
| 495 | C2×C4 | — | 4 | 10 | no | — |
| 496 | C2×C4 | — | 316 | 10 | no | — |
| 497 | C2×C4 | — | 316 | 10 | no | — |
| 498 | C2×C4 | — | 316 | 20 | no | — |
| 499 | C2×C4 | — | 79 | 1 | no | — |
| 500 | C2×C4 | — | 79 | 10 | no | — |
| 501 | C2×C4 | — | 79 | 5 | no | — |
| 502 | C2×C4 | — | 79 | 10 | no | — |
| 503 | C2×C4 | — | 158 | 10 | no | — |
| 504 | C2×C4 | — | 158 | 10 | no | — |
| 505 | C2×C4 | C24×D79 | 1 | 5 | yes | — |
| 506 | C2×C4 | C24×D79 | 1 | 5 | yes | — |
| 507 | C2×C4 | C24×D79 | 1 | 10 | yes | — |
| 508 | C2×C4 | C24×D79 | 1 | 10 | yes | — |
| 509 | C22 | — | 2 | 2 | no | — |
| 510 | C22 | — | 79 | 2 | no | — |
| 511 | C22 | — | 158 | 5 | no | — |
| 512 | C22 | — | 158 | 10 | no | — |
| 513 | C22 | — | 158 | 2 | no | — |
| 514 | C22 | 2−1+4×D79 | 1 | 2 | yes | — |
| 515 | C22 | C25×D79 | 1 | 1 | yes | characteristic |
| 516 | C4 | — | 2 | 5 | no | — |
| 517 | C4 | — | 2 | 5 | no | — |
| 518 | C4 | — | 2 | 10 | no | — |
| 519 | C4 | — | 2 | 10 | no | — |
| 520 | C4 | — | 79 | 2 | no | — |
| 521 | C4 | — | 158 | 5 | no | — |
| 522 | C4 | — | 158 | 10 | no | — |
| 523 | C4 | — | 158 | 10 | no | — |
| 524 | C2 | — | 2 | 2 | no | — |
| 525 | C2 | — | 316 | 5 | no | — |
| 526 | C2 | — | 158 | 2 | no | — |
| 527 | C2 | C2×2−1+4×D79 | 1 | 1 | yes | characteristic |
| 528 | C2 | #23778212 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D79 |
| commutator, socle, cosocle | C22×C79 | C26 |
| Fitting | C2×#564×C79 | C2 |
| hypercenter | C2×#564 | D79 |
| hypocenter | C79 | #63067 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×#564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23778009 | C2 | semidirect |
| 2. #23778009 | C2 | semidirect |
| 3. #23778006 | C2 | semidirect |
| 4. #23777894 | C2 | semidirect |
| 5. #23777857 | C2 | semidirect |
| 6. #23777856 | C2 | semidirect |
| 7. #23777548 | C2 | semidirect |
| 8. #564×D79 | C2 | semidirect |
| 9. #23777372 | C2 | semidirect |
| 10. #23777224 | C2 | semidirect |
| 11. C2×#564×C79 | C2 | semidirect |
| 273. C2×#564 | D79 | semidirect |
| 276. C79 | #63067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778009 | 2 |
| #23778006 | 2 |
| #23777894 | 2 |
| #23777857 | 2 |
| #23777856 | 2 |
| #23777548 | 2 |
| #564×D79 | 2 |
| #23777372 | 2 |
| #23777224 | 2 |
| C2×#564×C79 | 2 |
| #63067 | 79 |