Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
6274 conjugacy classes of subgroups.
The subgroup lattice has 938 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23778088 | C2 | 1 | 5 | yes | maximal, complemented |
| 2 | #23778087 | C2 | 1 | 5 | yes | maximal, complemented |
| 3 | #23778010 | C2 | 1 | 5 | yes | maximal, complemented |
| 4 | #23778000 | C2 | 1 | 5 | yes | maximal, complemented |
| 5 | #23777937 | C2 | 1 | 5 | yes | maximal, complemented |
| 6 | #23777928 | C2 | 1 | 5 | yes | maximal, complemented |
| 7 | #23777853 | C2 | 1 | 5 | yes | maximal, complemented |
| 8 | #23777851 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | #23777851 | C2 | 1 | 5 | yes | maximal, complemented |
| 10 | #23777548 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #564×D79 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #23777373 | C2 | 1 | 5 | yes | maximal, complemented |
| 13 | #23777366 | C2 | 1 | 5 | yes | maximal, complemented |
| 14 | #23777315 | C2 | 1 | 5 | yes | maximal, complemented |
| 15 | C79×#3531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C79⋊#564 | C22 | 1 | 5 | yes | — |
| 17 | C79⋊#564 | C22 | 1 | 5 | yes | — |
| 18 | C79⋊#564 | C22 | 1 | 5 | yes | — |
| 19 | C79⋊#564 | C22 | 1 | 5 | yes | — |
| 20 | #19099317 | C22 | 1 | 5 | yes | — |
| 21 | #19099317 | C22 | 1 | 5 | yes | — |
| 22 | #19099317 | C22 | 1 | 5 | yes | — |
| 23 | #19099313 | C22 | 1 | 5 | yes | — |
| 24 | #19099311 | C22 | 1 | 5 | yes | — |
| 25 | #19099307 | C22 | 1 | 5 | yes | — |
| 26 | #19099307 | C22 | 1 | 5 | yes | — |
| 27 | #19099307 | C22 | 1 | 5 | yes | — |
| 28 | #19099289 | C22 | 1 | 5 | yes | — |
| 29 | #19099288 | C22 | 1 | 5 | yes | — |
| 30 | #19099274 | C22 | 1 | 5 | yes | — |
| 31 | #19099274 | C22 | 1 | 5 | yes | — |
| 32 | #19099272 | C22 | 1 | 5 | yes | — |
| 33 | #19099271 | C22 | 1 | 5 | yes | — |
| 34 | #19099271 | C22 | 1 | 10 | yes | — |
| 35 | #19099267 | C22 | 1 | 10 | yes | — |
| 36 | #19099265 | C22 | 1 | 5 | yes | — |
| 37 | #19099264 | C22 | 1 | 10 | yes | — |
| 38 | #19099264 | C22 | 1 | 10 | yes | — |
| 39 | #19099263 | C22 | 1 | 5 | yes | — |
| 40 | #19099262 | C22 | 1 | 10 | yes | — |
| 41 | #19099258 | C22 | 1 | 10 | yes | — |
| 42 | #19099258 | C22 | 1 | 10 | yes | — |
| 43 | #19099257 | C22 | 1 | 5 | yes | — |
| 44 | #19099257 | C22 | 1 | 5 | yes | — |
| 45 | #19099256 | C22 | 1 | 10 | yes | — |
| 46 | #19099255 | C22 | 1 | 10 | yes | — |
| 47 | #19099255 | C22 | 1 | 5 | yes | — |
| 48 | #19099254 | C22 | 1 | 10 | yes | — |
| 49 | #19099254 | C22 | 1 | 5 | yes | — |
| 50 | #19099252 | C22 | 1 | 5 | yes | — |
| 51 | #19099252 | C22 | 1 | 5 | yes | — |
| 52 | #19099250 | C22 | 1 | 10 | yes | — |
| 53 | #19099249 | C22 | 1 | 10 | yes | — |
| 54 | #19099249 | C22 | 1 | 10 | yes | — |
| 55 | #19099247 | C22 | 1 | 10 | yes | — |
| 56 | #19099246 | C22 | 1 | 10 | yes | — |
| 57 | #19099246 | C22 | 1 | 10 | yes | — |
| 58 | #19099216 | C22 | 1 | 5 | yes | — |
| 59 | #19099215 | C22 | 1 | 10 | yes | — |
| 60 | #19099213 | C22 | 1 | 5 | yes | — |
| 61 | #19099211 | C22 | 1 | 10 | yes | — |
| 62 | #19099192 | C22 | 1 | 10 | yes | — |
| 63 | #19099190 | C22 | 1 | 10 | yes | — |
| 64 | #19099174 | C22 | 1 | 10 | yes | — |
| 65 | #19099173 | C22 | 1 | 5 | yes | — |
| 66 | #19099171 | C22 | 1 | 5 | yes | — |
| 67 | #19099171 | C22 | 1 | 10 | yes | — |
| 68 | #19099170 | C22 | 1 | 10 | yes | — |
| 69 | #19099170 | C22 | 1 | 10 | yes | — |
| 70 | #19099166 | C22 | 1 | 5 | yes | — |
| 71 | #19099165 | C22 | 1 | 10 | yes | — |
| 72 | #19099164 | C22 | 1 | 5 | yes | — |
| 73 | #19099163 | C22 | 1 | 10 | yes | — |
| 74 | #19099162 | C22 | 1 | 10 | yes | — |
| 75 | #19099159 | C22 | 1 | 10 | yes | — |
| 76 | #19099159 | C22 | 1 | 10 | yes | — |
| 77 | #19099159 | C22 | 1 | 10 | yes | — |
| 78 | #19099157 | C22 | 1 | 10 | yes | — |
| 79 | #19099157 | C22 | 1 | 10 | yes | — |
| 80 | #19099156 | C22 | 1 | 10 | yes | — |
| 81 | #19099155 | C22 | 1 | 10 | yes | — |
| 82 | #19099154 | C22 | 1 | 10 | yes | — |
| 83 | #19099154 | C22 | 1 | 10 | yes | — |
| 84 | #19099143 | C22 | 1 | 5 | yes | — |
| 85 | #19099142 | C22 | 1 | 5 | yes | — |
| 86 | #19099119 | C22 | 1 | 5 | yes | — |
| 87 | #19099112 | C22 | 1 | 5 | yes | — |
| 88 | #19099098 | C22 | 1 | 5 | yes | — |
| 89 | #19099098 | C22 | 1 | 5 | yes | — |
| 90 | #19099098 | C22 | 1 | 5 | yes | — |
| 91 | #19099097 | C22 | 1 | 5 | yes | — |
| 92 | #19099097 | C22 | 1 | 5 | yes | — |
| 93 | #19099092 | C22 | 1 | 5 | yes | — |
| 94 | #19099092 | C22 | 1 | 5 | yes | — |
| 95 | #19099092 | C22 | 1 | 5 | yes | — |
| 96 | C2×#14579153 | C22 | 1 | 5 | yes | — |
| 97 | #125×D79 | C22 | 1 | 5 | yes | — |
| 98 | #125×D79 | C22 | 1 | 5 | yes | — |
| 99 | #125×D79 | C22 | 1 | 5 | yes | — |
| 100 | #125×D79 | C22 | 1 | 5 | yes | — |
| 101 | #19099045 | C22 | 1 | 5 | yes | — |
| 102 | #19099042 | C22 | 1 | 5 | yes | — |
| 103 | C4×#11929624 | C22 | 1 | 5 | yes | — |
| 104 | #564×C79 | C22 | 1 | 1 | yes | characteristic |
| 105 | #563×C79 | C22 | 1 | 5 | yes | — |
| 106 | #563×C79 | C22 | 1 | 5 | yes | — |
| 107 | #562×C79 | C22 | 1 | 5 | yes | — |
| 108 | #533×C79 | C22 | 1 | 5 | yes | — |
| 109 | #529×C79 | C22 | 1 | 5 | yes | — |
| 110 | #529×C79 | C22 | 1 | 5 | yes | — |
| 111 | C2×#11929625 | C23 | 1 | 5 | yes | — |
| 112 | C2×#11929624 | C23 | 1 | 5 | yes | — |
| 113 | C2×#11929623 | C23 | 1 | 5 | yes | — |
| 114 | #14579160 | C23 | 1 | 5 | yes | — |
| 115 | #14579160 | C23 | 1 | 10 | yes | — |
| 116 | #14579160 | C23 | 1 | 5 | yes | — |
| 117 | #14579159 | C23 | 1 | 5 | yes | — |
| 118 | #14579159 | C23 | 1 | 10 | yes | — |
| 119 | #14579157 | C23 | 1 | 5 | yes | — |
| 120 | #14579156 | C23 | 1 | 10 | yes | — |
| 121 | #14579156 | C23 | 1 | 10 | yes | — |
| 122 | #14579156 | C23 | 1 | 10 | yes | — |
| 123 | #14579156 | C23 | 1 | 10 | yes | — |
| 124 | #14579156 | C23 | 1 | 10 | yes | — |
| 125 | #14579155 | C23 | 1 | 10 | yes | — |
| 126 | #14579155 | C23 | 1 | 10 | yes | — |
| 127 | #14579154 | C23 | 1 | 10 | yes | — |
| 128 | #14579154 | C23 | 1 | 10 | yes | — |
| 129 | #14579154 | C23 | 1 | 10 | yes | — |
| 130 | #14579154 | C23 | 1 | 10 | yes | — |
| 131 | #14579154 | C23 | 1 | 10 | yes | — |
| 132 | #14579153 | C23 | 1 | 10 | yes | — |
| 133 | #14579153 | C23 | 1 | 10 | yes | — |
| 134 | #14579153 | C23 | 1 | 5 | yes | — |
| 135 | #14579153 | C23 | 1 | 5 | yes | — |
| 136 | #14579153 | C23 | 1 | 5 | yes | — |
| 137 | #14579153 | C23 | 1 | 5 | yes | — |
| 138 | #14579153 | C23 | 1 | 5 | yes | — |
| 139 | #14579153 | C23 | 1 | 5 | yes | — |
| 140 | #14579152 | C23 | 1 | 5 | yes | — |
| 141 | #14579152 | C23 | 1 | 10 | yes | — |
| 142 | #14579152 | C23 | 1 | 5 | yes | — |
| 143 | #14579152 | C23 | 1 | 5 | yes | — |
| 144 | #14579152 | C23 | 1 | 10 | yes | — |
| 145 | #14579152 | C23 | 1 | 5 | yes | — |
| 146 | #14579152 | C23 | 1 | 5 | yes | — |
| 147 | #14579152 | C23 | 1 | 5 | yes | — |
| 148 | #14579152 | C23 | 1 | 5 | yes | — |
| 149 | #14579152 | C23 | 1 | 5 | yes | — |
| 150 | #14579151 | C23 | 1 | 10 | yes | — |
| 151 | #14579151 | C23 | 1 | 10 | yes | — |
| 152 | #14579151 | C23 | 1 | 10 | yes | — |
| 153 | #14579151 | C23 | 1 | 10 | yes | — |
| 154 | #14579151 | C23 | 1 | 10 | yes | — |
| 155 | #14579151 | C23 | 1 | 10 | yes | — |
| 156 | #14579151 | C23 | 1 | 10 | yes | — |
| 157 | #14579151 | C23 | 1 | 10 | yes | — |
| 158 | #14579151 | C23 | 1 | 10 | yes | — |
| 159 | #14579151 | C23 | 1 | 10 | yes | — |
| 160 | #14579151 | C23 | 1 | 10 | yes | — |
| 161 | #14579151 | C23 | 1 | 10 | yes | — |
| 162 | #14579149 | C23 | 1 | 5 | yes | — |
| 163 | #14579149 | C23 | 1 | 5 | yes | — |
| 164 | #14579146 | C23 | 1 | 10 | yes | — |
| 165 | #14579146 | C23 | 1 | 10 | yes | — |
| 166 | #14579146 | C23 | 1 | 10 | yes | — |
| 167 | #14579146 | C23 | 1 | 10 | yes | — |
| 168 | #14579145 | C23 | 1 | 10 | yes | — |
| 169 | #14579145 | C23 | 1 | 10 | yes | — |
| 170 | #14579145 | C23 | 1 | 10 | yes | — |
| 171 | #14579144 | C23 | 1 | 10 | yes | — |
| 172 | #14579144 | C23 | 1 | 10 | yes | — |
| 173 | #14579143 | C23 | 1 | 10 | yes | — |
| 174 | #14579143 | C23 | 1 | 10 | yes | — |
| 175 | #14579143 | C23 | 1 | 10 | yes | — |
| 176 | #14579143 | C23 | 1 | 10 | yes | — |
| 177 | #14579143 | C23 | 1 | 10 | yes | — |
| 178 | #14579143 | C23 | 1 | 10 | yes | — |
| 179 | #14579142 | C23 | 1 | 10 | yes | — |
| 180 | #14579141 | C23 | 1 | 5 | yes | — |
| 181 | #14579141 | C23 | 1 | 5 | yes | — |
| 182 | #14579141 | C23 | 1 | 10 | yes | — |
| 183 | #14579141 | C23 | 1 | 5 | yes | — |
| 184 | #14579140 | C23 | 1 | 5 | yes | — |
| 185 | #14579140 | C23 | 1 | 5 | yes | — |
| 186 | #14579139 | C23 | 1 | 10 | yes | — |
| 187 | #14579139 | C23 | 1 | 10 | yes | — |
| 188 | #14579139 | C23 | 1 | 10 | yes | — |
| 189 | #14579138 | C23 | 1 | 10 | yes | — |
| 190 | #14579138 | C23 | 1 | 10 | yes | — |
| 191 | #14579138 | C23 | 1 | 10 | yes | — |
| 192 | #14579138 | C23 | 1 | 10 | yes | — |
| 193 | #14579138 | C23 | 1 | 10 | yes | — |
| 194 | #14579137 | C23 | 1 | 5 | yes | — |
| 195 | #14579137 | C23 | 1 | 10 | yes | — |
| 196 | #14579137 | C23 | 1 | 10 | yes | — |
| 197 | #14579137 | C23 | 1 | 5 | yes | — |
| 198 | #14579137 | C23 | 1 | 5 | yes | — |
| 199 | #14579137 | C23 | 1 | 10 | yes | — |
| 200 | #14579136 | C23 | 1 | 5 | yes | — |
| 201 | #14579136 | C23 | 1 | 5 | yes | — |
| 202 | #14579136 | C23 | 1 | 5 | yes | — |
| 203 | #14579135 | C23 | 1 | 5 | yes | — |
| 204 | #14579135 | C23 | 1 | 5 | yes | — |
| 205 | #14579134 | C23 | 1 | 10 | yes | — |
| 206 | #14579134 | C23 | 1 | 10 | yes | — |
| 207 | #14579134 | C23 | 1 | 10 | yes | — |
| 208 | #14579134 | C23 | 1 | 10 | yes | — |
| 209 | #14579134 | C23 | 1 | 10 | yes | — |
| 210 | #14579133 | C23 | 1 | 10 | yes | — |
| 211 | #14579133 | C23 | 1 | 10 | yes | — |
| 212 | #14579133 | C23 | 1 | 10 | yes | — |
| 213 | #14579132 | C23 | 1 | 5 | yes | — |
| 214 | #14579132 | C23 | 1 | 5 | yes | — |
| 215 | #14579132 | C23 | 1 | 5 | yes | — |
| 216 | Q8×Dic79 | C23 | 1 | 5 | yes | — |
| 217 | Q8×Dic79 | C23 | 1 | 5 | yes | — |
| 218 | Q8×Dic79 | C23 | 1 | 5 | yes | — |
| 219 | C4×Dic158 | C23 | 1 | 5 | yes | — |
| 220 | C4×Dic158 | C23 | 1 | 5 | yes | — |
| 221 | C4×Dic158 | C23 | 1 | 5 | yes | — |
| 222 | C4×Dic158 | C23 | 1 | 5 | yes | — |
| 223 | #14579126 | C23 | 1 | 5 | yes | — |
| 224 | #14579126 | C23 | 1 | 5 | yes | — |
| 225 | #14579126 | C23 | 1 | 5 | yes | — |
| 226 | C4×D316 | C23 | 1 | 5 | yes | — |
| 227 | C4×D316 | C23 | 1 | 5 | yes | — |
| 228 | C4×D316 | C23 | 1 | 5 | yes | — |
| 229 | C4×D316 | C23 | 1 | 5 | yes | — |
| 230 | D4×Dic79 | C23 | 1 | 5 | yes | — |
| 231 | D4×Dic79 | C23 | 1 | 5 | yes | — |
| 232 | D4×Dic79 | C23 | 1 | 5 | yes | — |
| 233 | #14579123 | C23 | 1 | 5 | yes | — |
| 234 | #14579123 | C23 | 1 | 5 | yes | — |
| 235 | #14579123 | C23 | 1 | 10 | yes | — |
| 236 | #14579123 | C23 | 1 | 5 | yes | — |
| 237 | C4×C22⋊D79 | C23 | 1 | 5 | yes | — |
| 238 | C4×C22⋊D79 | C23 | 1 | 10 | yes | — |
| 239 | C4×C22⋊D79 | C23 | 1 | 5 | yes | — |
| 240 | C4×C22⋊D79 | C23 | 1 | 5 | yes | — |
| 241 | C4×C22⋊D79 | C23 | 1 | 10 | yes | — |
| 242 | C4×C22⋊D79 | C23 | 1 | 5 | yes | — |
| 243 | (C22⋊D79)⋊C4 | C23 | 1 | 10 | yes | — |
| 244 | (C22⋊D79)⋊C4 | C23 | 1 | 10 | yes | — |
| 245 | (C22⋊D79)⋊C4 | C23 | 1 | 10 | yes | — |
| 246 | (C22⋊D79)⋊C4 | C23 | 1 | 10 | yes | — |
| 247 | (C22⋊D79)⋊C4 | C23 | 1 | 10 | yes | — |
| 248 | #14579120 | C23 | 1 | 5 | yes | — |
| 249 | #14579119 | C23 | 1 | 10 | yes | — |
| 250 | #14579119 | C23 | 1 | 5 | yes | — |
| 251 | #14579119 | C23 | 1 | 5 | yes | — |
| 252 | #14579118 | C23 | 1 | 5 | yes | — |
| 253 | #14579118 | C23 | 1 | 10 | yes | — |
| 254 | #14579118 | C23 | 1 | 10 | yes | — |
| 255 | #14579118 | C23 | 1 | 5 | yes | — |
| 256 | #14579117 | C23 | 1 | 10 | yes | — |
| 257 | #14579117 | C23 | 1 | 10 | yes | — |
| 258 | #14579117 | C23 | 1 | 10 | yes | — |
| 259 | C2×C4⋊Dic79 | C23 | 1 | 5 | yes | — |
| 260 | C2×C4⋊Dic79 | C23 | 1 | 5 | yes | — |
| 261 | C2×Dic79⋊C4 | C23 | 1 | 10 | yes | — |
| 262 | C2×Dic79⋊C4 | C23 | 1 | 10 | yes | — |
| 263 | C4⋊C4×D79 | C23 | 1 | 5 | yes | — |
| 264 | C4⋊C4×D79 | C23 | 1 | 5 | yes | — |
| 265 | C4⋊C4×D79 | C23 | 1 | 5 | yes | — |
| 266 | C4⋊C4×D79 | C23 | 1 | 10 | yes | — |
| 267 | C4⋊C4×D79 | C23 | 1 | 5 | yes | — |
| 268 | C4⋊C4×D79 | C23 | 1 | 10 | yes | — |
| 269 | C4⋊C4×D79 | C23 | 1 | 5 | yes | — |
| 270 | C4⋊C4×D79 | C23 | 1 | 5 | yes | — |
| 271 | C4⋊C4×D79 | C23 | 1 | 5 | yes | — |
| 272 | C4⋊C4×D79 | C23 | 1 | 5 | yes | — |
| 273 | C42×D79 | C23 | 1 | 5 | yes | — |
| 274 | C42×D79 | C23 | 1 | 5 | yes | — |
| 275 | C4⋊Q8×C79 | C23 | 1 | 5 | yes | — |
| 276 | C4⋊Q8×C79 | C23 | 1 | 5 | yes | — |
| 277 | #126×C79 | C23 | 1 | 10 | yes | — |
| 278 | #126×C79 | C23 | 1 | 10 | yes | — |
| 279 | #125×C79 | C23 | 1 | 5 | yes | — |
| 280 | #125×C79 | C23 | 1 | 5 | yes | — |
| 281 | #125×C79 | C23 | 1 | 5 | yes | — |
| 282 | #125×C79 | C23 | 1 | 5 | yes | — |
| 283 | #124×C79 | C23 | 1 | 5 | yes | — |
| 284 | #124×C79 | C23 | 1 | 5 | yes | — |
| 285 | #123×C79 | C23 | 1 | 10 | yes | — |
| 286 | #123×C79 | C23 | 1 | 10 | yes | — |
| 287 | C22⋊Q8×C79 | C23 | 1 | 5 | yes | — |
| 288 | C22⋊Q8×C79 | C23 | 1 | 5 | yes | — |
| 289 | C22⋊Q8×C79 | C23 | 1 | 10 | yes | — |
| 290 | C22⋊Q8×C79 | C23 | 1 | 10 | yes | — |
| 291 | #121×C79 | C23 | 1 | 5 | yes | — |
| 292 | #121×C79 | C23 | 1 | 5 | yes | — |
| 293 | C4×Q8×C79 | C23 | 1 | 5 | yes | — |
| 294 | C4×Q8×C79 | C23 | 1 | 5 | yes | — |
| 295 | C4×D4×C79 | C23 | 1 | 5 | yes | — |
| 296 | C4×D4×C79 | C23 | 1 | 5 | yes | — |
| 297 | #117×C79 | C23 | 1 | 5 | yes | — |
| 298 | #117×C79 | C23 | 1 | 5 | yes | — |
| 299 | C2×C42×C79 | C23 | 1 | 5 | yes | — |
| 300 | #11929625 | — | 4 | 10 | no | — |
| 301 | #11929624 | — | 4 | 10 | no | — |
| 302 | #11929623 | — | 4 | 10 | no | — |
| 303 | C2×Dic158 | C24 | 1 | 5 | yes | — |
| 304 | C2×Dic158 | C24 | 1 | 5 | yes | — |
| 305 | C2×Dic158 | C24 | 1 | 5 | yes | — |
| 306 | C2×D316 | C24 | 1 | 5 | yes | — |
| 307 | C2×D316 | C24 | 1 | 5 | yes | — |
| 308 | C2×D316 | C24 | 1 | 5 | yes | — |
| 309 | C2×C22⋊D79 | C24 | 1 | 5 | yes | — |
| 310 | C2×C22⋊D79 | C24 | 1 | 5 | yes | — |
| 311 | C2×C22⋊D79 | C24 | 1 | 10 | yes | — |
| 312 | C2×C22⋊D79 | C24 | 1 | 10 | yes | — |
| 313 | C22×Dic79 | C24 | 1 | 10 | yes | — |
| 314 | C22×Dic79 | C24 | 1 | 10 | yes | — |
| 315 | C2×C4×D79 | C24 | 1 | 5 | yes | — |
| 316 | C2×C4×D79 | C24 | 1 | 5 | yes | — |
| 317 | C2×C4×D79 | C24 | 1 | 10 | yes | — |
| 318 | C2×C4×D79 | C24 | 1 | 5 | yes | — |
| 319 | C2×C4×D79 | C24 | 1 | 5 | yes | — |
| 320 | C2×C4×D79 | C24 | 1 | 5 | yes | — |
| 321 | C2×C4×D79 | C24 | 1 | 5 | yes | — |
| 322 | C2×C4×D79 | C24 | 1 | 10 | yes | — |
| 323 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 324 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 325 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 326 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 327 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 328 | C4⋊Dic79 | C24 | 1 | 10 | yes | — |
| 329 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 330 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 331 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 332 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 333 | C4⋊Dic79 | C24 | 1 | 10 | yes | — |
| 334 | C4⋊Dic79 | C24 | 1 | 5 | yes | — |
| 335 | Dic79⋊C4 | C24 | 1 | 5 | yes | — |
| 336 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 337 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 338 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 339 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 340 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 341 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 342 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 343 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 344 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 345 | Dic79⋊C4 | C24 | 1 | 5 | yes | — |
| 346 | Dic79⋊C4 | C24 | 1 | 5 | yes | — |
| 347 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 348 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 349 | Dic79⋊C4 | C24 | 1 | 10 | yes | — |
| 350 | Dic79⋊C4 | C24 | 1 | 5 | yes | — |
| 351 | C22⋊Dic79 | C24 | 1 | 5 | yes | — |
| 352 | C22⋊Dic79 | C24 | 1 | 10 | yes | — |
| 353 | C22⋊Dic79 | C24 | 1 | 5 | yes | — |
| 354 | C22⋊Dic79 | C24 | 1 | 10 | yes | — |
| 355 | (C2×D79)⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 356 | (C2×D79)⋊C4 | C24 | 1 | 5 | yes | — |
| 357 | (C2×D79)⋊C4 | C24 | 1 | 10 | yes | — |
| 358 | (C2×D79)⋊C4 | C24 | 1 | 10 | yes | — |
| 359 | (C2×D79)⋊C4 | C24 | 1 | 5 | yes | — |
| 360 | (C2×D79)⋊C4 | C24 | 1 | 5 | yes | — |
| 361 | (C2×D79)⋊C4 | C24 | 1 | 10 | yes | — |
| 362 | (C2×D79)⋊C4 | C24 | 1 | 10 | yes | — |
| 363 | (C2×D79)⋊C4 | C24 | 1 | 10 | yes | — |
| 364 | (C2×D79)⋊C4 | C24 | 1 | 10 | yes | — |
| 365 | C4×Dic79 | C24 | 1 | 5 | yes | — |
| 366 | C4×Dic79 | C24 | 1 | 5 | yes | — |
| 367 | C4×Dic79 | C24 | 1 | 5 | yes | — |
| 368 | C4×Dic79 | C24 | 1 | 5 | yes | — |
| 369 | C4×Dic79 | C24 | 1 | 5 | yes | — |
| 370 | C4×Dic79 | C24 | 1 | 5 | yes | — |
| 371 | C4×Dic79 | C24 | 1 | 10 | yes | — |
| 372 | C4×Dic79 | C24 | 1 | 10 | yes | — |
| 373 | C2×Q8×C79 | C24 | 1 | 5 | yes | — |
| 374 | C2×Q8×C79 | C24 | 1 | 5 | yes | — |
| 375 | C2×D4×C79 | C24 | 1 | 5 | yes | — |
| 376 | C2×D4×C79 | C24 | 1 | 5 | yes | — |
| 377 | C22×C4×C79 | C24 | 1 | 5 | yes | — |
| 378 | C22×C4×C79 | C24 | 1 | 5 | yes | — |
| 379 | C22×C4×C79 | C24 | 1 | 5 | yes | — |
| 380 | C4⋊C4×C79 | C24 | 1 | 5 | yes | — |
| 381 | C4⋊C4×C79 | C24 | 1 | 5 | yes | — |
| 382 | C4⋊C4×C79 | C24 | 1 | 5 | yes | — |
| 383 | C4⋊C4×C79 | C24 | 1 | 5 | yes | — |
| 384 | C4⋊C4×C79 | C24 | 1 | 5 | yes | — |
| 385 | C4⋊C4×C79 | C24 | 1 | 5 | yes | — |
| 386 | C4⋊C4×C79 | C24 | 1 | 5 | yes | — |
| 387 | C4⋊C4×C79 | C24 | 1 | 5 | yes | — |
| 388 | C4⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 389 | C4⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 390 | C22⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 391 | C22⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 392 | C22⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 393 | C22⋊C4×C79 | C24 | 1 | 10 | yes | — |
| 394 | C42×C79 | C24 | 1 | 5 | yes | — |
| 395 | C42×C79 | C24 | 1 | 5 | yes | — |
| 396 | C42×C79 | C24 | 1 | 5 | yes | — |
| 397 | C42×C79 | C24 | 1 | 5 | yes | — |
| 398 | C23×C79 | C25 | 1 | 5 | yes | — |
| 399 | C22×D79 | C25 | 1 | 5 | yes | — |
| 400 | C22×D79 | C25 | 1 | 1 | yes | characteristic |
| 401 | Q8×C79 | — | 4 | 5 | no | — |
| 402 | Q8×C79 | — | 4 | 5 | no | — |
| 403 | D4×C79 | — | 4 | 5 | no | — |
| 404 | D4×C79 | — | 4 | 5 | no | — |
| 405 | C2×C4×C79 | — | 4 | 5 | no | — |
| 406 | C2×C4×C79 | — | 4 | 5 | no | — |
| 407 | C2×C4×C79 | — | 4 | 5 | no | — |
| 408 | C2×C4×C79 | C25 | 1 | 5 | yes | — |
| 409 | C2×C4×C79 | C25 | 1 | 5 | yes | — |
| 410 | C2×C4×C79 | C25 | 1 | 5 | yes | — |
| 411 | C2×C4×C79 | C25 | 1 | 5 | yes | — |
| 412 | C2×C4×C79 | C25 | 1 | 5 | yes | — |
| 413 | C2×C4×C79 | C25 | 1 | 1 | yes | characteristic |
| 414 | C22⋊D79 | — | 2 | 10 | no | — |
| 415 | C22⋊D79 | — | 4 | 10 | no | — |
| 416 | C22⋊D79 | — | 4 | 10 | no | — |
| 417 | C22⋊D79 | — | 4 | 5 | no | — |
| 418 | C2×Dic79 | — | 4 | 10 | no | — |
| 419 | C2×Dic79 | — | 4 | 10 | no | — |
| 420 | C2×Dic79 | C25 | 1 | 1 | yes | characteristic |
| 421 | C2×Dic79 | C25 | 1 | 5 | yes | — |
| 422 | C2×Dic79 | C25 | 1 | 5 | yes | — |
| 423 | C2×Dic79 | C25 | 1 | 5 | yes | — |
| 424 | C2×Dic79 | C25 | 1 | 5 | yes | — |
| 425 | C2×Dic79 | C25 | 1 | 5 | yes | — |
| 426 | D316 | — | 2 | 10 | no | — |
| 427 | D316 | — | 4 | 5 | no | — |
| 428 | D316 | — | 4 | 5 | no | — |
| 429 | C4×D79 | — | 2 | 10 | no | — |
| 430 | C4×D79 | — | 4 | 5 | no | — |
| 431 | C4×D79 | — | 4 | 10 | no | — |
| 432 | C4×D79 | — | 4 | 5 | no | — |
| 433 | C4×D79 | — | 4 | 5 | no | — |
| 434 | C4×D79 | — | 4 | 5 | no | — |
| 435 | C4×D79 | — | 4 | 5 | no | — |
| 436 | C4×D79 | — | 4 | 10 | no | — |
| 437 | Dic158 | — | 4 | 5 | no | — |
| 438 | Dic158 | — | 4 | 5 | no | — |
| 439 | Dic158 | — | 4 | 5 | no | — |
| 440 | C22×C79 | — | 2 | 5 | no | — |
| 441 | C22×C79 | — | 2 | 5 | no | — |
| 442 | C22×C79 | — | 2 | 5 | no | — |
| 443 | C22×C79 | C26 | 1 | 1 | yes | characteristic |
| 444 | C2×D79 | — | 2 | 1 | no | — |
| 445 | C2×D79 | — | 2 | 1 | no | — |
| 446 | C2×D79 | — | 2 | 5 | no | — |
| 447 | C2×D79 | — | 2 | 5 | no | — |
| 448 | C2×D79 | — | 2 | 5 | no | — |
| 449 | C2×D79 | #585 | 1 | 2 | yes | — |
| 450 | C4×C79 | — | 2 | 5 | no | — |
| 451 | C4×C79 | — | 2 | 5 | no | — |
| 452 | C4×C79 | — | 2 | 1 | no | — |
| 453 | C4×C79 | — | 2 | 5 | no | — |
| 454 | C4×C79 | — | 2 | 5 | no | — |
| 455 | C4×C79 | — | 2 | 5 | no | — |
| 456 | Dic79 | — | 2 | 5 | no | — |
| 457 | Dic79 | — | 2 | 5 | no | — |
| 458 | Dic79 | — | 2 | 5 | no | — |
| 459 | Dic79 | — | 2 | 5 | no | — |
| 460 | Dic79 | — | 2 | 5 | no | — |
| 461 | Dic79 | — | 2 | 1 | no | — |
| 462 | #63068 | — | 79 | 1 | no | maximal, Sylow |
| 463 | C2×C79 | — | 4 | 5 | no | — |
| 464 | C2×C79 | C2×#585 | 1 | 1 | yes | characteristic |
| 465 | C2×C79 | 2−1+6 | 1 | 1 | yes | characteristic |
| 466 | C2×C79 | 2−1+6 | 1 | 1 | yes | characteristic |
| 467 | D79 | — | 2 | 2 | no | — |
| 468 | D79 | — | 4 | 5 | no | — |
| 469 | #3567 | — | 79 | 5 | no | — |
| 470 | #3567 | — | 79 | 5 | no | — |
| 471 | #3563 | — | 79 | 5 | no | — |
| 472 | #3563 | — | 79 | 5 | no | — |
| 473 | #3559 | — | 79 | 5 | no | — |
| 474 | #3559 | — | 79 | 5 | no | — |
| 475 | #3553 | — | 79 | 5 | no | — |
| 476 | #3553 | — | 79 | 5 | no | — |
| 477 | #3553 | — | 79 | 5 | no | — |
| 478 | #3531 | — | 79 | 1 | no | — |
| 479 | #3531 | D79 | 1 | 1 | yes | characteristic, complemented |
| 480 | C2×#564 | — | 79 | 1 | no | — |
| 481 | #3515 | — | 79 | 5 | no | — |
| 482 | #3515 | — | 79 | 5 | no | — |
| 483 | #3512 | — | 79 | 5 | no | — |
| 484 | C79 | #63068 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 485 | #564 | — | 79 | 5 | no | — |
| 486 | #564 | — | 79 | 5 | no | — |
| 487 | #564 | — | 79 | 5 | no | — |
| 488 | #564 | — | 79 | 5 | no | — |
| 489 | #564 | C2×D79 | 1 | 1 | yes | characteristic |
| 490 | #563 | — | 79 | 5 | no | — |
| 491 | #563 | — | 79 | 5 | no | — |
| 492 | #563 | — | 79 | 5 | no | — |
| 493 | #563 | — | 79 | 5 | no | — |
| 494 | #563 | C2×D79 | 1 | 5 | yes | — |
| 495 | #563 | C2×D79 | 1 | 5 | yes | — |
| 496 | #562 | — | 79 | 5 | no | — |
| 497 | #562 | — | 79 | 5 | no | — |
| 498 | #562 | — | 79 | 5 | no | — |
| 499 | #562 | — | 79 | 5 | no | — |
| 500 | #562 | C2×D79 | 1 | 5 | yes | — |
| 501 | #557 | — | 79 | 5 | no | — |
| 502 | #557 | — | 79 | 5 | no | — |
| 503 | #554 | — | 79 | 5 | no | — |
| 504 | #554 | — | 79 | 5 | no | — |
| 505 | #554 | — | 79 | 10 | no | — |
| 506 | #554 | — | 79 | 5 | no | — |
| 507 | #554 | — | 79 | 10 | no | — |
| 508 | #554 | — | 79 | 5 | no | — |
| 509 | #553 | — | 79 | 10 | no | — |
| 510 | #553 | — | 79 | 10 | no | — |
| 511 | #553 | — | 79 | 10 | no | — |
| 512 | #553 | — | 79 | 10 | no | — |
| 513 | #553 | — | 79 | 10 | no | — |
| 514 | #553 | — | 79 | 5 | no | — |
| 515 | #553 | — | 79 | 10 | no | — |
| 516 | #553 | — | 79 | 5 | no | — |
| 517 | #553 | — | 79 | 5 | no | — |
| 518 | #553 | — | 79 | 5 | no | — |
| 519 | #552 | — | 79 | 10 | no | — |
| 520 | #552 | — | 79 | 10 | no | — |
| 521 | #552 | — | 79 | 10 | no | — |
| 522 | #552 | — | 79 | 10 | no | — |
| 523 | #552 | — | 79 | 5 | no | — |
| 524 | #552 | — | 79 | 10 | no | — |
| 525 | #552 | — | 79 | 5 | no | — |
| 526 | #552 | — | 79 | 10 | no | — |
| 527 | #552 | — | 79 | 10 | no | — |
| 528 | #552 | — | 79 | 10 | no | — |
| 529 | #552 | — | 79 | 5 | no | — |
| 530 | #552 | — | 79 | 5 | no | — |
| 531 | #547 | — | 79 | 5 | no | — |
| 532 | #547 | — | 79 | 10 | no | — |
| 533 | #547 | — | 79 | 10 | no | — |
| 534 | #547 | — | 79 | 5 | no | — |
| 535 | #544 | — | 79 | 10 | no | — |
| 536 | #544 | — | 79 | 10 | no | — |
| 537 | #541 | — | 79 | 10 | no | — |
| 538 | #541 | — | 79 | 10 | no | — |
| 539 | #541 | — | 79 | 10 | no | — |
| 540 | #541 | — | 79 | 5 | no | — |
| 541 | #541 | — | 79 | 5 | no | — |
| 542 | #541 | — | 79 | 10 | no | — |
| 543 | #540 | — | 79 | 10 | no | — |
| 544 | #540 | — | 79 | 10 | no | — |
| 545 | #540 | — | 79 | 5 | no | — |
| 546 | #540 | — | 79 | 5 | no | — |
| 547 | #539 | — | 79 | 10 | no | — |
| 548 | #539 | — | 79 | 10 | no | — |
| 549 | #539 | — | 79 | 10 | no | — |
| 550 | #539 | — | 79 | 10 | no | — |
| 551 | #539 | — | 79 | 10 | no | — |
| 552 | #539 | — | 79 | 10 | no | — |
| 553 | #539 | — | 79 | 10 | no | — |
| 554 | #539 | — | 79 | 10 | no | — |
| 555 | #539 | — | 79 | 10 | no | — |
| 556 | #539 | — | 79 | 10 | no | — |
| 557 | #537 | — | 79 | 5 | no | — |
| 558 | #537 | — | 79 | 5 | no | — |
| 559 | #533 | — | 79 | 5 | no | — |
| 560 | #533 | C2×D79 | 1 | 5 | yes | — |
| 561 | #532 | — | 79 | 5 | no | — |
| 562 | #529 | — | 79 | 5 | no | — |
| 563 | #529 | — | 79 | 5 | no | — |
| 564 | #529 | — | 79 | 5 | no | — |
| 565 | #529 | — | 79 | 5 | no | — |
| 566 | #529 | — | 79 | 5 | no | — |
| 567 | #529 | — | 79 | 5 | no | — |
| 568 | #529 | — | 79 | 5 | no | — |
| 569 | #529 | — | 79 | 5 | no | — |
| 570 | #529 | C2×D79 | 1 | 5 | yes | — |
| 571 | #529 | C2×D79 | 1 | 5 | yes | — |
| 572 | C2×#125 | — | 79 | 5 | no | — |
| 573 | C2×#125 | — | 79 | 5 | no | — |
| 574 | C2×#125 | — | 79 | 5 | no | — |
| 575 | C2×#125 | — | 79 | 5 | no | — |
| 576 | C2×#125 | — | 79 | 5 | no | — |
| 577 | #520 | — | 79 | 5 | no | — |
| 578 | #520 | — | 79 | 5 | no | — |
| 579 | C4×#41 | — | 79 | 5 | no | — |
| 580 | C2×#41 | — | 79 | 5 | no | — |
| 581 | C2×#41 | — | 79 | 5 | no | — |
| 582 | C2×#41 | — | 79 | 5 | no | — |
| 583 | C4⋊Q8 | — | 79 | 5 | no | — |
| 584 | C4⋊Q8 | — | 79 | 10 | no | — |
| 585 | C4⋊Q8 | — | 79 | 5 | no | — |
| 586 | C4⋊Q8 | — | 79 | 5 | no | — |
| 587 | C4⋊Q8 | — | 79 | 10 | no | — |
| 588 | C4⋊Q8 | C22×D79 | 1 | 5 | yes | — |
| 589 | C4⋊Q8 | C22×D79 | 1 | 5 | yes | — |
| 590 | #127 | — | 79 | 5 | no | — |
| 591 | #126 | — | 79 | 10 | no | — |
| 592 | #126 | — | 79 | 10 | no | — |
| 593 | #126 | — | 79 | 10 | no | — |
| 594 | #126 | — | 79 | 10 | no | — |
| 595 | #126 | — | 79 | 10 | no | — |
| 596 | #126 | — | 79 | 10 | no | — |
| 597 | #126 | — | 79 | 10 | no | — |
| 598 | #126 | — | 79 | 10 | no | — |
| 599 | #126 | — | 79 | 10 | no | — |
| 600 | #126 | — | 79 | 10 | no | — |
| 601 | #126 | — | 79 | 10 | no | — |
| 602 | #126 | — | 79 | 10 | no | — |
| 603 | #126 | C22×D79 | 1 | 10 | yes | — |
| 604 | #126 | C22×D79 | 1 | 10 | yes | — |
| 605 | #125 | — | 79 | 10 | no | — |
| 606 | #125 | — | 79 | 5 | no | — |
| 607 | #125 | — | 79 | 5 | no | — |
| 608 | #125 | — | 79 | 5 | no | — |
| 609 | #125 | — | 79 | 5 | no | — |
| 610 | #125 | — | 79 | 10 | no | — |
| 611 | #125 | — | 79 | 10 | no | — |
| 612 | #125 | — | 79 | 10 | no | — |
| 613 | #125 | — | 79 | 10 | no | — |
| 614 | #125 | — | 79 | 10 | no | — |
| 615 | #125 | — | 79 | 5 | no | — |
| 616 | #125 | — | 79 | 5 | no | — |
| 617 | #125 | — | 79 | 10 | no | — |
| 618 | #125 | — | 79 | 10 | no | — |
| 619 | #125 | — | 79 | 5 | no | — |
| 620 | #125 | — | 79 | 5 | no | — |
| 621 | #125 | — | 79 | 10 | no | — |
| 622 | #125 | — | 79 | 10 | no | — |
| 623 | #125 | — | 79 | 10 | no | — |
| 624 | #125 | — | 79 | 10 | no | — |
| 625 | #125 | — | 79 | 10 | no | — |
| 626 | #125 | — | 79 | 10 | no | — |
| 627 | #125 | — | 79 | 5 | no | — |
| 628 | #125 | — | 79 | 5 | no | — |
| 629 | #125 | — | 79 | 5 | no | — |
| 630 | #125 | — | 79 | 5 | no | — |
| 631 | #125 | — | 79 | 10 | no | — |
| 632 | #125 | — | 79 | 10 | no | — |
| 633 | #125 | — | 79 | 5 | no | — |
| 634 | #125 | — | 79 | 5 | no | — |
| 635 | #125 | C22×D79 | 1 | 5 | yes | — |
| 636 | #125 | C22×D79 | 1 | 5 | yes | — |
| 637 | #125 | C22×D79 | 1 | 5 | yes | — |
| 638 | #125 | C22×D79 | 1 | 5 | yes | — |
| 639 | #124 | — | 79 | 5 | no | — |
| 640 | #124 | — | 79 | 5 | no | — |
| 641 | #124 | C22×D79 | 1 | 5 | yes | — |
| 642 | #124 | C22×D79 | 1 | 5 | yes | — |
| 643 | #123 | — | 79 | 10 | no | — |
| 644 | #123 | — | 79 | 10 | no | — |
| 645 | #123 | — | 79 | 10 | no | — |
| 646 | #123 | — | 79 | 10 | no | — |
| 647 | #123 | — | 79 | 10 | no | — |
| 648 | #123 | — | 79 | 10 | no | — |
| 649 | #123 | — | 79 | 10 | no | — |
| 650 | #123 | — | 79 | 10 | no | — |
| 651 | #123 | — | 79 | 10 | no | — |
| 652 | #123 | — | 79 | 10 | no | — |
| 653 | #123 | — | 79 | 10 | no | — |
| 654 | #123 | — | 79 | 10 | no | — |
| 655 | #123 | — | 79 | 10 | no | — |
| 656 | #123 | — | 79 | 10 | no | — |
| 657 | #123 | — | 79 | 10 | no | — |
| 658 | #123 | — | 79 | 10 | no | — |
| 659 | #123 | C22×D79 | 1 | 10 | yes | — |
| 660 | #123 | C22×D79 | 1 | 10 | yes | — |
| 661 | C22⋊Q8 | — | 79 | 5 | no | — |
| 662 | C22⋊Q8 | — | 79 | 5 | no | — |
| 663 | C22⋊Q8 | — | 79 | 5 | no | — |
| 664 | C22⋊Q8 | — | 79 | 10 | no | — |
| 665 | C22⋊Q8 | — | 79 | 10 | no | — |
| 666 | C22⋊Q8 | — | 79 | 10 | no | — |
| 667 | C22⋊Q8 | — | 79 | 5 | no | — |
| 668 | C22⋊Q8 | — | 79 | 5 | no | — |
| 669 | C22⋊Q8 | — | 79 | 5 | no | — |
| 670 | C22⋊Q8 | — | 79 | 5 | no | — |
| 671 | C22⋊Q8 | — | 79 | 5 | no | — |
| 672 | C22⋊Q8 | — | 79 | 10 | no | — |
| 673 | C22⋊Q8 | — | 79 | 10 | no | — |
| 674 | C22⋊Q8 | — | 79 | 10 | no | — |
| 675 | C22⋊Q8 | — | 79 | 10 | no | — |
| 676 | C22⋊Q8 | — | 79 | 10 | no | — |
| 677 | C22⋊Q8 | — | 79 | 10 | no | — |
| 678 | C22⋊Q8 | — | 79 | 10 | no | — |
| 679 | C22⋊Q8 | — | 79 | 10 | no | — |
| 680 | C22⋊Q8 | — | 79 | 10 | no | — |
| 681 | C22⋊Q8 | C22×D79 | 1 | 5 | yes | — |
| 682 | C22⋊Q8 | C22×D79 | 1 | 5 | yes | — |
| 683 | C22⋊Q8 | C22×D79 | 1 | 10 | yes | — |
| 684 | C22⋊Q8 | C22×D79 | 1 | 10 | yes | — |
| 685 | #121 | — | 79 | 5 | no | — |
| 686 | #121 | — | 79 | 5 | no | — |
| 687 | #121 | — | 79 | 5 | no | — |
| 688 | #121 | — | 79 | 10 | no | — |
| 689 | #121 | — | 79 | 10 | no | — |
| 690 | #121 | — | 79 | 10 | no | — |
| 691 | #121 | — | 79 | 5 | no | — |
| 692 | #121 | — | 79 | 5 | no | — |
| 693 | #121 | — | 79 | 5 | no | — |
| 694 | #121 | — | 79 | 5 | no | — |
| 695 | #121 | — | 79 | 5 | no | — |
| 696 | #121 | — | 79 | 10 | no | — |
| 697 | #121 | — | 79 | 10 | no | — |
| 698 | #121 | — | 79 | 10 | no | — |
| 699 | #121 | — | 79 | 10 | no | — |
| 700 | #121 | — | 79 | 10 | no | — |
| 701 | #121 | C22×D79 | 1 | 5 | yes | — |
| 702 | #121 | C22×D79 | 1 | 5 | yes | — |
| 703 | C4×Q8 | — | 79 | 5 | no | — |
| 704 | C4×Q8 | — | 79 | 5 | no | — |
| 705 | C4×Q8 | — | 79 | 5 | no | — |
| 706 | C4×Q8 | — | 79 | 5 | no | — |
| 707 | C4×Q8 | — | 79 | 5 | no | — |
| 708 | C4×Q8 | — | 79 | 5 | no | — |
| 709 | C4×Q8 | — | 79 | 5 | no | — |
| 710 | C4×Q8 | — | 79 | 5 | no | — |
| 711 | C4×Q8 | — | 79 | 5 | no | — |
| 712 | C4×Q8 | — | 79 | 5 | no | — |
| 713 | C4×Q8 | C22×D79 | 1 | 5 | yes | — |
| 714 | C4×Q8 | C22×D79 | 1 | 5 | yes | — |
| 715 | C4×D4 | — | 79 | 5 | no | — |
| 716 | C4×D4 | — | 79 | 5 | no | — |
| 717 | C4×D4 | — | 79 | 5 | no | — |
| 718 | C4×D4 | — | 79 | 5 | no | — |
| 719 | C4×D4 | — | 79 | 5 | no | — |
| 720 | C4×D4 | — | 79 | 5 | no | — |
| 721 | C4×D4 | — | 79 | 5 | no | — |
| 722 | C4×D4 | — | 79 | 10 | no | — |
| 723 | C4×D4 | — | 79 | 10 | no | — |
| 724 | C4×D4 | — | 79 | 5 | no | — |
| 725 | C4×D4 | — | 79 | 10 | no | — |
| 726 | C4×D4 | — | 79 | 5 | no | — |
| 727 | C4×D4 | — | 79 | 5 | no | — |
| 728 | C4×D4 | — | 79 | 10 | no | — |
| 729 | C4×D4 | — | 79 | 10 | no | — |
| 730 | C4×D4 | — | 79 | 10 | no | — |
| 731 | C4×D4 | — | 79 | 10 | no | — |
| 732 | C4×D4 | — | 79 | 10 | no | — |
| 733 | C4×D4 | — | 79 | 5 | no | — |
| 734 | C4×D4 | — | 79 | 5 | no | — |
| 735 | C4×D4 | — | 79 | 5 | no | — |
| 736 | C4×D4 | — | 79 | 5 | no | — |
| 737 | C4×D4 | C22×D79 | 1 | 5 | yes | — |
| 738 | C4×D4 | C22×D79 | 1 | 5 | yes | — |
| 739 | #117 | — | 79 | 5 | no | — |
| 740 | #117 | — | 79 | 5 | no | — |
| 741 | #117 | — | 79 | 5 | no | — |
| 742 | #117 | — | 79 | 10 | no | — |
| 743 | #117 | — | 79 | 10 | no | — |
| 744 | #117 | — | 79 | 10 | no | — |
| 745 | #117 | — | 79 | 10 | no | — |
| 746 | #117 | — | 79 | 5 | no | — |
| 747 | #117 | — | 79 | 5 | no | — |
| 748 | #117 | — | 79 | 10 | no | — |
| 749 | #117 | — | 79 | 10 | no | — |
| 750 | #117 | C22×D79 | 1 | 5 | yes | — |
| 751 | #117 | C22×D79 | 1 | 5 | yes | — |
| 752 | C2×C4⋊C4 | — | 79 | 10 | no | — |
| 753 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 754 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 755 | C2×C4⋊C4 | — | 79 | 10 | no | — |
| 756 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 757 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 758 | C2×C4⋊C4 | — | 79 | 10 | no | — |
| 759 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 760 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 761 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 762 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 763 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 764 | C2×C4⋊C4 | — | 79 | 5 | no | — |
| 765 | C2×C4⋊C4 | — | 79 | 10 | no | — |
| 766 | C2×C42 | — | 79 | 5 | no | — |
| 767 | C2×C42 | — | 79 | 5 | no | — |
| 768 | C2×C42 | C22×D79 | 1 | 5 | yes | — |
| 769 | #41 | — | 316 | 10 | no | — |
| 770 | #41 | — | 316 | 10 | no | — |
| 771 | #41 | — | 316 | 10 | no | — |
| 772 | C2×Q8 | — | 79 | 5 | no | — |
| 773 | C2×Q8 | — | 79 | 5 | no | — |
| 774 | C2×Q8 | — | 79 | 5 | no | — |
| 775 | C2×Q8 | C23×D79 | 1 | 5 | yes | — |
| 776 | C2×Q8 | C23×D79 | 1 | 5 | yes | — |
| 777 | C2×D4 | — | 79 | 10 | no | — |
| 778 | C2×D4 | — | 79 | 10 | no | — |
| 779 | C2×D4 | — | 79 | 5 | no | — |
| 780 | C2×D4 | — | 79 | 5 | no | — |
| 781 | C2×D4 | — | 79 | 5 | no | — |
| 782 | C2×D4 | — | 79 | 5 | no | — |
| 783 | C2×D4 | — | 79 | 5 | no | — |
| 784 | C2×D4 | C23×D79 | 1 | 5 | yes | — |
| 785 | C2×D4 | C23×D79 | 1 | 5 | yes | — |
| 786 | C22×C4 | — | 79 | 10 | no | — |
| 787 | C22×C4 | — | 79 | 10 | no | — |
| 788 | C22×C4 | — | 79 | 5 | no | — |
| 789 | C22×C4 | — | 79 | 5 | no | — |
| 790 | C22×C4 | — | 79 | 5 | no | — |
| 791 | C22×C4 | — | 79 | 5 | no | — |
| 792 | C22×C4 | — | 79 | 5 | no | — |
| 793 | C22×C4 | — | 79 | 10 | no | — |
| 794 | C22×C4 | — | 79 | 10 | no | — |
| 795 | C22×C4 | — | 79 | 5 | no | — |
| 796 | C22×C4 | C23×D79 | 1 | 5 | yes | — |
| 797 | C22×C4 | C23×D79 | 1 | 5 | yes | — |
| 798 | C22×C4 | C23×D79 | 1 | 5 | yes | — |
| 799 | C4⋊C4 | — | 79 | 5 | no | — |
| 800 | C4⋊C4 | — | 79 | 5 | no | — |
| 801 | C4⋊C4 | — | 79 | 5 | no | — |
| 802 | C4⋊C4 | — | 79 | 10 | no | — |
| 803 | C4⋊C4 | — | 79 | 10 | no | — |
| 804 | C4⋊C4 | — | 79 | 10 | no | — |
| 805 | C4⋊C4 | — | 79 | 10 | no | — |
| 806 | C4⋊C4 | — | 79 | 10 | no | — |
| 807 | C4⋊C4 | — | 79 | 10 | no | — |
| 808 | C4⋊C4 | — | 79 | 10 | no | — |
| 809 | C4⋊C4 | — | 79 | 10 | no | — |
| 810 | C4⋊C4 | — | 79 | 10 | no | — |
| 811 | C4⋊C4 | — | 79 | 10 | no | — |
| 812 | C4⋊C4 | — | 79 | 10 | no | — |
| 813 | C4⋊C4 | — | 79 | 10 | no | — |
| 814 | C4⋊C4 | — | 79 | 5 | no | — |
| 815 | C4⋊C4 | — | 79 | 5 | no | — |
| 816 | C4⋊C4 | — | 79 | 5 | no | — |
| 817 | C4⋊C4 | — | 79 | 5 | no | — |
| 818 | C4⋊C4 | — | 79 | 5 | no | — |
| 819 | C4⋊C4 | — | 79 | 5 | no | — |
| 820 | C4⋊C4 | — | 79 | 10 | no | — |
| 821 | C4⋊C4 | — | 79 | 5 | no | — |
| 822 | C4⋊C4 | — | 79 | 5 | no | — |
| 823 | C4⋊C4 | — | 79 | 10 | no | — |
| 824 | C4⋊C4 | — | 79 | 5 | no | — |
| 825 | C4⋊C4 | — | 79 | 5 | no | — |
| 826 | C4⋊C4 | — | 79 | 5 | no | — |
| 827 | C4⋊C4 | C23×D79 | 1 | 5 | yes | — |
| 828 | C4⋊C4 | C23×D79 | 1 | 5 | yes | — |
| 829 | C4⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 830 | C4⋊C4 | C23×D79 | 1 | 5 | yes | — |
| 831 | C4⋊C4 | C23×D79 | 1 | 5 | yes | — |
| 832 | C4⋊C4 | C23×D79 | 1 | 5 | yes | — |
| 833 | C4⋊C4 | C23×D79 | 1 | 5 | yes | — |
| 834 | C4⋊C4 | C23×D79 | 1 | 5 | yes | — |
| 835 | C4⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 836 | C4⋊C4 | C23×D79 | 1 | 5 | yes | — |
| 837 | C22⋊C4 | — | 79 | 5 | no | — |
| 838 | C22⋊C4 | — | 79 | 10 | no | — |
| 839 | C22⋊C4 | — | 79 | 5 | no | — |
| 840 | C22⋊C4 | — | 79 | 10 | no | — |
| 841 | C22⋊C4 | — | 79 | 1 | no | — |
| 842 | C22⋊C4 | — | 79 | 5 | no | — |
| 843 | C22⋊C4 | — | 79 | 10 | no | — |
| 844 | C22⋊C4 | — | 79 | 10 | no | — |
| 845 | C22⋊C4 | — | 79 | 10 | no | — |
| 846 | C22⋊C4 | — | 79 | 5 | no | — |
| 847 | C22⋊C4 | — | 79 | 5 | no | — |
| 848 | C22⋊C4 | — | 79 | 10 | no | — |
| 849 | C22⋊C4 | — | 79 | 10 | no | — |
| 850 | C22⋊C4 | — | 79 | 10 | no | — |
| 851 | C22⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 852 | C22⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 853 | C22⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 854 | C22⋊C4 | C23×D79 | 1 | 10 | yes | — |
| 855 | C42 | — | 79 | 5 | no | — |
| 856 | C42 | — | 79 | 5 | no | — |
| 857 | C42 | — | 79 | 5 | no | — |
| 858 | C42 | — | 79 | 5 | no | — |
| 859 | C42 | — | 79 | 5 | no | — |
| 860 | C42 | — | 79 | 5 | no | — |
| 861 | C42 | — | 79 | 10 | no | — |
| 862 | C42 | — | 79 | 10 | no | — |
| 863 | C42 | C23×D79 | 1 | 5 | yes | — |
| 864 | C42 | C23×D79 | 1 | 5 | yes | — |
| 865 | C42 | C23×D79 | 1 | 5 | yes | — |
| 866 | C42 | C23×D79 | 1 | 5 | yes | — |
| 867 | C23 | — | 79 | 1 | no | — |
| 868 | C23 | — | 79 | 5 | no | — |
| 869 | C23 | C24×D79 | 1 | 5 | yes | — |
| 870 | Q8 | — | 4 | 5 | no | — |
| 871 | Q8 | — | 4 | 5 | no | — |
| 872 | Q8 | — | 316 | 5 | no | — |
| 873 | Q8 | — | 316 | 5 | no | — |
| 874 | Q8 | — | 316 | 5 | no | — |
| 875 | D4 | — | 4 | 5 | no | — |
| 876 | D4 | — | 4 | 5 | no | — |
| 877 | D4 | — | 316 | 5 | no | — |
| 878 | D4 | — | 316 | 5 | no | — |
| 879 | D4 | — | 316 | 10 | no | — |
| 880 | D4 | — | 316 | 10 | no | — |
| 881 | D4 | — | 316 | 5 | no | — |
| 882 | D4 | — | 158 | 10 | no | — |
| 883 | D4 | — | 158 | 10 | no | — |
| 884 | C2×C4 | — | 4 | 5 | no | — |
| 885 | C2×C4 | — | 4 | 5 | no | — |
| 886 | C2×C4 | — | 4 | 5 | no | — |
| 887 | C2×C4 | — | 316 | 10 | no | — |
| 888 | C2×C4 | — | 316 | 5 | no | — |
| 889 | C2×C4 | — | 316 | 5 | no | — |
| 890 | C2×C4 | — | 316 | 5 | no | — |
| 891 | C2×C4 | — | 316 | 5 | no | — |
| 892 | C2×C4 | — | 316 | 5 | no | — |
| 893 | C2×C4 | — | 316 | 10 | no | — |
| 894 | C2×C4 | — | 316 | 10 | no | — |
| 895 | C2×C4 | — | 316 | 10 | no | — |
| 896 | C2×C4 | — | 79 | 1 | no | — |
| 897 | C2×C4 | — | 79 | 5 | no | — |
| 898 | C2×C4 | — | 79 | 5 | no | — |
| 899 | C2×C4 | — | 79 | 5 | no | — |
| 900 | C2×C4 | — | 79 | 5 | no | — |
| 901 | C2×C4 | — | 79 | 5 | no | — |
| 902 | C2×C4 | — | 158 | 10 | no | — |
| 903 | C2×C4 | C24×D79 | 1 | 5 | yes | — |
| 904 | C2×C4 | C24×D79 | 1 | 5 | yes | — |
| 905 | C2×C4 | C24×D79 | 1 | 5 | yes | — |
| 906 | C2×C4 | C24×D79 | 1 | 5 | yes | — |
| 907 | C2×C4 | C24×D79 | 1 | 5 | yes | — |
| 908 | C2×C4 | C24×D79 | 1 | 1 | yes | characteristic |
| 909 | C22 | — | 2 | 5 | no | — |
| 910 | C22 | — | 2 | 5 | no | — |
| 911 | C22 | — | 2 | 5 | no | — |
| 912 | C22 | — | 79 | 2 | no | — |
| 913 | C22 | — | 158 | 5 | no | — |
| 914 | C22 | — | 158 | 5 | no | — |
| 915 | C22 | — | 158 | 5 | no | — |
| 916 | C22 | — | 158 | 1 | no | — |
| 917 | C22 | — | 158 | 1 | no | — |
| 918 | C22 | C25×D79 | 1 | 1 | yes | characteristic |
| 919 | C4 | — | 2 | 5 | no | — |
| 920 | C4 | — | 2 | 5 | no | — |
| 921 | C4 | — | 2 | 1 | no | — |
| 922 | C4 | — | 2 | 5 | no | — |
| 923 | C4 | — | 2 | 5 | no | — |
| 924 | C4 | — | 2 | 5 | no | — |
| 925 | C4 | — | 158 | 5 | no | — |
| 926 | C4 | — | 158 | 5 | no | — |
| 927 | C4 | — | 158 | 5 | no | — |
| 928 | C4 | — | 158 | 5 | no | — |
| 929 | C4 | — | 158 | 1 | no | — |
| 930 | C4 | — | 158 | 5 | no | — |
| 931 | C2 | — | 4 | 5 | no | — |
| 932 | C2 | — | 316 | 5 | no | — |
| 933 | C2 | — | 158 | 2 | no | — |
| 934 | C2 | #585×D79 | 1 | 1 | yes | characteristic |
| 935 | C2 | #23778212 | 1 | 1 | yes | characteristic |
| 936 | C2 | #23778213 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D79 |
| commutator, socle, cosocle | C22×C79 | C26 |
| Fitting | C79×#3531 | C2 |
| hypercenter | #3531 | D79 |
| hypocenter | C79 | #63068 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ #3531 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23778088 | C2 | semidirect |
| 2. #23778087 | C2 | semidirect |
| 3. #23778010 | C2 | semidirect |
| 4. #23778000 | C2 | semidirect |
| 5. #23777937 | C2 | semidirect |
| 6. #23777928 | C2 | semidirect |
| 7. #23777853 | C2 | semidirect |
| 8. #23777851 | C2 | semidirect |
| 9. #23777851 | C2 | semidirect |
| 10. #23777548 | C2 | semidirect |
| 11. #564×D79 | C2 | semidirect |
| 12. #23777373 | C2 | semidirect |
| 13. #23777366 | C2 | semidirect |
| 14. #23777315 | C2 | semidirect |
| 15. C79×#3531 | C2 | semidirect |
| 479. #3531 | D79 | semidirect |
| 484. C79 | #63068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778088 | 2 |
| #23778087 | 2 |
| #23778010 | 2 |
| #23778000 | 2 |
| #23777937 | 2 |
| #23777928 | 2 |
| #23777853 | 2 |
| #23777851 | 2 |
| #23777548 | 2 |
| #564×D79 | 2 |
| #23777373 | 2 |
| #23777366 | 2 |
| #23777315 | 2 |
| C79×#3531 | 2 |
| #63068 | 79 |