Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1430 conjugacy classes of subgroups.
The subgroup lattice has 638 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#19099131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#19098922 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#19098910 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23769224 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23764638 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #23764633 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #23764223 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #23763339 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #23763329 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #23763167 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C79×#1958 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#11929625 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×D4×D79 | C22 | 1 | 1 | yes | characteristic |
| 14 | #19099131 | — | 2 | 4 | no | — |
| 15 | #19099131 | — | 2 | 4 | no | — |
| 16 | C2×#14579161 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#14579158 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#14579157 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#14579150 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#14579134 | — | 2 | 1 | no | — |
| 21 | C2×#14579134 | — | 2 | 1 | no | — |
| 22 | C2×#14579131 | — | 2 | 1 | no | — |
| 23 | C2×#14579131 | — | 2 | 1 | no | — |
| 24 | C2×#14579118 | C22 | 1 | 1 | yes | characteristic |
| 25 | #19098922 | — | 2 | 4 | no | — |
| 26 | #19098910 | — | 2 | 4 | no | — |
| 27 | C2×#14579085 | C22 | 1 | 2 | yes | complemented |
| 28 | C2×#14579083 | C22 | 1 | 2 | yes | — |
| 29 | C2×#14579083 | C22 | 1 | 2 | yes | complemented |
| 30 | C2×#14579082 | C22 | 1 | 2 | yes | — |
| 31 | C2×#14579081 | C22 | 1 | 2 | yes | — |
| 32 | C2×#14579081 | C22 | 1 | 2 | yes | complemented |
| 33 | C2×(C2×D79)⋊C8 | C22 | 1 | 2 | yes | — |
| 34 | C2×#14579072 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #19098503 | — | 2 | 1 | no | — |
| 36 | #19098500 | — | 2 | 1 | no | — |
| 37 | #19098484 | — | 2 | 1 | no | — |
| 38 | #19098476 | — | 2 | 1 | no | — |
| 39 | #19098462 | C22 | 1 | 2 | yes | complemented |
| 40 | #19098420 | C22 | 1 | 2 | yes | — |
| 41 | #19098317 | C22 | 1 | 2 | yes | complemented |
| 42 | C2×#124×C79 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#103×C79 | C22 | 1 | 2 | yes | complemented |
| 44 | C2×#102×C79 | C22 | 1 | 2 | yes | — |
| 45 | C2×C4×C8×C79 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #382×C79 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | C24×D79 | — | 2 | 1 | no | — |
| 48 | C2×#11929625 | — | 2 | 2 | no | — |
| 49 | C2×#11929625 | — | 2 | 2 | no | — |
| 50 | C2×#11929625 | — | 2 | 4 | no | — |
| 51 | C2×#11929625 | — | 4 | 2 | no | — |
| 52 | C22×Dic158 | — | 2 | 1 | no | — |
| 53 | C22×D316 | — | 2 | 1 | no | — |
| 54 | C22×D316 | — | 2 | 1 | no | — |
| 55 | C22×D316 | — | 2 | 1 | no | — |
| 56 | C22×D316 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×D316 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 59 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 60 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 61 | C2×D4×D79 | — | 2 | 2 | no | — |
| 62 | C2×D4×D79 | — | 2 | 2 | no | — |
| 63 | C2×D4×D79 | — | 2 | 4 | no | — |
| 64 | C2×D4×D79 | — | 4 | 2 | no | — |
| 65 | C22×C4×D79 | — | 2 | 1 | no | — |
| 66 | C22×C4×D79 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×C79⋊C8 | C23 | 1 | 2 | yes | — |
| 68 | #14579161 | — | 2 | 2 | no | — |
| 69 | #14579161 | — | 2 | 2 | no | — |
| 70 | #14579158 | — | 2 | 2 | no | — |
| 71 | #14579158 | D4 | 1 | 4 | yes | — |
| 72 | #14579157 | — | 2 | 2 | no | — |
| 73 | #14579157 | — | 2 | 2 | no | — |
| 74 | #14579150 | — | 2 | 2 | no | — |
| 75 | #14579150 | — | 2 | 2 | no | — |
| 76 | #14579134 | — | 2 | 8 | no | — |
| 77 | #14579134 | — | 2 | 8 | no | — |
| 78 | #14579131 | — | 2 | 8 | no | — |
| 79 | #14579131 | — | 2 | 8 | no | — |
| 80 | #14579118 | — | 2 | 2 | no | — |
| 81 | #14579118 | — | 2 | 2 | no | — |
| 82 | C2×C4⋊Dic79 | — | 2 | 1 | no | — |
| 83 | C2×C4⋊Dic79 | — | 2 | 2 | no | — |
| 84 | C2×C4⋊Dic79 | C23 | 1 | 2 | yes | — |
| 85 | C2×Dic79⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×Dic79⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 87 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 88 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 89 | C2×(C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 90 | C2×(C2×D79)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 91 | C2×(C2×D79)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 92 | C2×C4×Dic79 | C23 | 1 | 1 | yes | characteristic |
| 93 | #14579085 | — | 2 | 4 | no | — |
| 94 | #14579083 | — | 2 | 4 | no | — |
| 95 | #14579083 | — | 2 | 4 | no | — |
| 96 | #14579082 | — | 2 | 4 | no | — |
| 97 | #14579081 | — | 4 | 2 | no | — |
| 98 | #14579081 | — | 4 | 2 | no | — |
| 99 | (C2×D79)⋊C8 | — | 2 | 4 | no | — |
| 100 | #14579072 | — | 2 | 2 | no | — |
| 101 | C79⋊#95 | — | 2 | 2 | no | — |
| 102 | C79⋊#95 | — | 2 | 2 | no | — |
| 103 | C22×Q8×C79 | C23 | 1 | 1 | yes | characteristic |
| 104 | C22×D4×C79 | C23 | 1 | 1 | yes | characteristic |
| 105 | C22×C8×C79 | C23 | 1 | 2 | yes | — |
| 106 | #124×C79 | — | 2 | 2 | no | — |
| 107 | #124×C79 | D4 | 1 | 4 | yes | — |
| 108 | C2×C4⋊C4×C79 | C23 | 1 | 2 | yes | — |
| 109 | C2×C22⋊C4×C79 | — | 2 | 1 | no | — |
| 110 | C2×C22⋊C4×C79 | — | 2 | 1 | no | — |
| 111 | C2×C42×C79 | C23 | 1 | 1 | yes | characteristic |
| 112 | #103×C79 | — | 4 | 2 | no | — |
| 113 | #102×C79 | — | 4 | 2 | no | — |
| 114 | C4×C8×C79 | — | 2 | 2 | no | — |
| 115 | #95×C79 | — | 2 | 1 | no | — |
| 116 | #95×C79 | — | 2 | 1 | no | — |
| 117 | C23×D79 | — | 2 | 1 | no | — |
| 118 | C23×D79 | — | 2 | 1 | no | — |
| 119 | C23×D79 | — | 2 | 4 | no | — |
| 120 | C23×D79 | — | 4 | 2 | no | — |
| 121 | C23×D79 | — | 4 | 2 | no | — |
| 122 | C23×D79 | — | 8 | 2 | no | — |
| 123 | C23×D79 | — | 8 | 2 | no | — |
| 124 | C23×D79 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | #11929625 | — | 4 | 8 | no | — |
| 126 | #11929625 | — | 4 | 8 | no | — |
| 127 | C2×Dic158 | — | 4 | 2 | no | — |
| 128 | C2×Dic158 | — | 8 | 2 | no | — |
| 129 | C2×D316 | — | 2 | 4 | no | — |
| 130 | C2×D316 | — | 2 | 4 | no | — |
| 131 | C2×D316 | — | 2 | 4 | no | — |
| 132 | C2×D316 | — | 2 | 1 | no | — |
| 133 | C2×D316 | — | 2 | 1 | no | — |
| 134 | C2×D316 | — | 2 | 2 | no | — |
| 135 | C2×D316 | — | 2 | 2 | no | — |
| 136 | C2×D316 | — | 2 | 2 | no | — |
| 137 | C2×D316 | — | 2 | 2 | no | — |
| 138 | C2×D316 | — | 4 | 2 | no | — |
| 139 | C2×D316 | — | 4 | 2 | no | — |
| 140 | C2×D316 | — | 8 | 2 | no | — |
| 141 | C2×D316 | — | 8 | 2 | no | — |
| 142 | C2×D316 | C2×D4 | 1 | 2 | yes | — |
| 143 | C2×D316 | C2×D4 | 1 | 2 | yes | — |
| 144 | C2×C22⋊D79 | — | 2 | 4 | no | — |
| 145 | C2×C22⋊D79 | — | 2 | 4 | no | — |
| 146 | C2×C22⋊D79 | — | 2 | 4 | no | — |
| 147 | C2×C22⋊D79 | — | 4 | 2 | no | — |
| 148 | C2×C22⋊D79 | — | 4 | 2 | no | — |
| 149 | C2×C22⋊D79 | — | 8 | 2 | no | — |
| 150 | C2×C22⋊D79 | — | 8 | 2 | no | — |
| 151 | D4×D79 | — | 4 | 8 | no | — |
| 152 | D4×D79 | — | 4 | 8 | no | — |
| 153 | C22×Dic79 | — | 2 | 2 | no | — |
| 154 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×C4×D79 | — | 2 | 4 | no | — |
| 158 | C2×C4×D79 | — | 2 | 1 | no | — |
| 159 | C2×C4×D79 | — | 2 | 1 | no | — |
| 160 | C2×C4×D79 | — | 2 | 2 | no | — |
| 161 | C2×C4×D79 | — | 4 | 2 | no | — |
| 162 | C2×C4×D79 | — | 4 | 2 | no | — |
| 163 | C2×C4×D79 | #41 | 1 | 4 | yes | — |
| 164 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 165 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 166 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 167 | C4⋊Dic79 | — | 2 | 2 | no | — |
| 168 | C4⋊Dic79 | — | 2 | 2 | no | — |
| 169 | C4⋊Dic79 | — | 4 | 2 | no | — |
| 170 | C4⋊Dic79 | — | 8 | 2 | no | — |
| 171 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 172 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 173 | (C2×D79)⋊C4 | — | 2 | 4 | no | — |
| 174 | (C2×D79)⋊C4 | — | 2 | 4 | no | — |
| 175 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 176 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 177 | (C2×D79)⋊C4 | — | 8 | 2 | no | — |
| 178 | C4×Dic79 | — | 2 | 1 | no | — |
| 179 | C4×Dic79 | — | 2 | 1 | no | — |
| 180 | C24×C79 | — | 2 | 1 | no | — |
| 181 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 182 | C2×Q8×C79 | — | 2 | 2 | no | — |
| 183 | C2×Q8×C79 | — | 2 | 2 | no | — |
| 184 | C2×Q8×C79 | C2×D4 | 1 | 2 | yes | — |
| 185 | C2×D4×C79 | — | 2 | 1 | no | — |
| 186 | C2×D4×C79 | — | 2 | 2 | no | — |
| 187 | C2×D4×C79 | — | 2 | 2 | no | — |
| 188 | C2×D4×C79 | C2×D4 | 1 | 2 | yes | — |
| 189 | C22×C4×C79 | — | 2 | 1 | no | — |
| 190 | C22×C4×C79 | — | 2 | 2 | no | — |
| 191 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C22×C4×C79 | C24 | 1 | 1 | yes | characteristic |
| 194 | C2×C8×C79 | — | 2 | 2 | no | — |
| 195 | C2×C8×C79 | — | 2 | 2 | no | — |
| 196 | C2×C8×C79 | — | 2 | 2 | no | — |
| 197 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 198 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 199 | C22⋊C4×C79 | — | 2 | 4 | no | — |
| 200 | C22⋊C4×C79 | — | 2 | 4 | no | — |
| 201 | C42×C79 | C2×D4 | 1 | 2 | yes | — |
| 202 | C42×C79 | C2×D4 | 1 | 2 | yes | — |
| 203 | C23×C79 | — | 2 | 2 | no | — |
| 204 | C23×C79 | — | 4 | 1 | no | — |
| 205 | C23×C79 | — | 4 | 1 | no | — |
| 206 | C23×C79 | — | 4 | 2 | no | — |
| 207 | C23×C79 | — | 4 | 2 | no | — |
| 208 | C23×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 209 | C22×D79 | — | 2 | 1 | no | — |
| 210 | C22×D79 | — | 2 | 1 | no | — |
| 211 | C22×D79 | — | 2 | 2 | no | — |
| 212 | C22×D79 | — | 2 | 2 | no | — |
| 213 | C22×D79 | — | 2 | 2 | no | — |
| 214 | C22×D79 | — | 2 | 2 | no | — |
| 215 | C22×D79 | — | 4 | 8 | no | — |
| 216 | C22×D79 | — | 4 | 1 | no | — |
| 217 | C22×D79 | — | 4 | 1 | no | — |
| 218 | C22×D79 | — | 4 | 1 | no | — |
| 219 | C22×D79 | — | 4 | 1 | no | — |
| 220 | C22×D79 | — | 4 | 2 | no | — |
| 221 | C22×D79 | — | 4 | 2 | no | — |
| 222 | C22×D79 | — | 4 | 2 | no | — |
| 223 | C22×D79 | — | 4 | 2 | no | — |
| 224 | C22×D79 | — | 8 | 8 | no | — |
| 225 | C22×D79 | — | 8 | 4 | no | — |
| 226 | C22×D79 | — | 8 | 4 | no | — |
| 227 | C22×D79 | — | 8 | 8 | no | — |
| 228 | C22×D79 | #124 | 1 | 2 | yes | — |
| 229 | Q8×C79 | — | 2 | 4 | no | — |
| 230 | Q8×C79 | — | 4 | 2 | no | — |
| 231 | D4×C79 | — | 2 | 4 | no | — |
| 232 | D4×C79 | — | 4 | 2 | no | — |
| 233 | C2×C4×C79 | — | 2 | 2 | no | — |
| 234 | C2×C4×C79 | — | 2 | 2 | no | — |
| 235 | C2×C4×C79 | — | 2 | 2 | no | — |
| 236 | C2×C4×C79 | — | 4 | 1 | no | — |
| 237 | C2×C4×C79 | — | 4 | 1 | no | — |
| 238 | C2×C4×C79 | — | 4 | 2 | no | — |
| 239 | C2×C4×C79 | — | 4 | 2 | no | — |
| 240 | C2×C4×C79 | — | 4 | 2 | no | — |
| 241 | C2×C4×C79 | #120 | 1 | 2 | yes | — |
| 242 | C2×C4×C79 | #120 | 1 | 2 | yes | — |
| 243 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C79 | C2×#41 | 1 | 2 | yes | — |
| 246 | C2×C4×C79 | H(5,𝔽2) | 1 | 2 | yes | — |
| 247 | C22⋊D79 | — | 4 | 8 | no | — |
| 248 | C22⋊D79 | — | 8 | 4 | no | — |
| 249 | C22⋊D79 | — | 8 | 4 | no | — |
| 250 | C2×Dic79 | — | 2 | 1 | no | — |
| 251 | C2×Dic79 | — | 2 | 1 | no | — |
| 252 | C2×Dic79 | — | 2 | 1 | no | — |
| 253 | C2×Dic79 | — | 2 | 1 | no | — |
| 254 | C2×Dic79 | — | 2 | 2 | no | — |
| 255 | C2×Dic79 | — | 2 | 2 | no | — |
| 256 | C2×Dic79 | — | 4 | 2 | no | — |
| 257 | C2×Dic79 | — | 4 | 2 | no | — |
| 258 | C2×Dic79 | — | 4 | 2 | no | — |
| 259 | C2×Dic79 | #124 | 1 | 2 | yes | — |
| 260 | D316 | — | 2 | 4 | no | — |
| 261 | D316 | — | 2 | 4 | no | — |
| 262 | D316 | — | 4 | 8 | no | — |
| 263 | D316 | — | 4 | 2 | no | — |
| 264 | D316 | — | 4 | 2 | no | — |
| 265 | D316 | — | 8 | 4 | no | — |
| 266 | D316 | — | 8 | 4 | no | — |
| 267 | C4×D79 | — | 2 | 4 | no | — |
| 268 | C4×D79 | — | 2 | 4 | no | — |
| 269 | C4×D79 | — | 4 | 8 | no | — |
| 270 | Dic158 | — | 8 | 4 | no | — |
| 271 | C8×C79 | — | 4 | 2 | no | — |
| 272 | C79⋊C8 | — | 4 | 2 | no | — |
| 273 | C22×C79 | — | 4 | 2 | no | — |
| 274 | C22×C79 | — | 4 | 2 | no | — |
| 275 | C22×C79 | — | 4 | 2 | no | — |
| 276 | C22×C79 | — | 8 | 2 | no | — |
| 277 | C22×C79 | — | 8 | 2 | no | — |
| 278 | C22×C79 | C2×#120 | 1 | 1 | yes | characteristic |
| 279 | C22×C79 | C2×#124 | 1 | 1 | yes | characteristic |
| 280 | C22×C79 | #535 | 1 | 1 | yes | characteristic |
| 281 | C22×C79 | #576 | 1 | 2 | yes | — |
| 282 | C22×C79 | #577 | 1 | 2 | yes | — |
| 283 | C2×D79 | — | 2 | 4 | no | — |
| 284 | C2×D79 | — | 2 | 2 | no | — |
| 285 | C2×D79 | — | 4 | 2 | no | — |
| 286 | C2×D79 | — | 4 | 1 | no | — |
| 287 | C2×D79 | — | 4 | 1 | no | — |
| 288 | C2×D79 | — | 4 | 2 | no | — |
| 289 | C2×D79 | — | 4 | 2 | no | — |
| 290 | C2×D79 | — | 4 | 2 | no | — |
| 291 | C2×D79 | — | 4 | 2 | no | — |
| 292 | C2×D79 | — | 4 | 2 | no | — |
| 293 | C2×D79 | — | 4 | 2 | no | — |
| 294 | C2×D79 | — | 8 | 16 | no | — |
| 295 | C2×D79 | — | 8 | 2 | no | — |
| 296 | C2×D79 | — | 8 | 2 | no | — |
| 297 | C2×D79 | — | 8 | 2 | no | — |
| 298 | C2×D79 | — | 8 | 2 | no | — |
| 299 | C4×C79 | — | 2 | 2 | no | — |
| 300 | C4×C79 | — | 2 | 2 | no | — |
| 301 | C4×C79 | — | 4 | 2 | no | — |
| 302 | C4×C79 | — | 8 | 2 | no | — |
| 303 | C4×C79 | #546 | 1 | 2 | yes | — |
| 304 | C4×C79 | #546 | 1 | 2 | yes | — |
| 305 | Dic79 | — | 2 | 2 | no | — |
| 306 | Dic79 | — | 4 | 1 | no | — |
| 307 | Dic79 | — | 4 | 1 | no | — |
| 308 | Dic79 | — | 8 | 2 | no | — |
| 309 | #25865 | — | 79 | 1 | no | maximal, Sylow |
| 310 | C2×C79 | — | 8 | 2 | no | — |
| 311 | C2×C79 | #2435 | 1 | 1 | yes | characteristic |
| 312 | C2×C79 | #3008 | 1 | 1 | yes | characteristic |
| 313 | C2×C79 | #3009 | 1 | 1 | yes | characteristic |
| 314 | C2×C79 | #3136 | 1 | 2 | yes | — |
| 315 | C2×C79 | #3224 | 1 | 2 | yes | — |
| 316 | D79 | — | 4 | 2 | no | — |
| 317 | D79 | — | 8 | 2 | no | — |
| 318 | D79 | — | 8 | 2 | no | — |
| 319 | C2×#535 | — | 79 | 1 | no | — |
| 320 | C2×#489 | — | 79 | 1 | no | — |
| 321 | C2×#486 | — | 79 | 1 | no | — |
| 322 | #2628 | — | 79 | 1 | no | — |
| 323 | #2042 | — | 79 | 2 | no | — |
| 324 | #2041 | — | 79 | 2 | no | — |
| 325 | #1961 | — | 79 | 1 | no | — |
| 326 | #1958 | D79 | 1 | 1 | yes | characteristic, complemented |
| 327 | #1788 | — | 79 | 2 | no | — |
| 328 | #1786 | — | 79 | 2 | no | — |
| 329 | #1750 | — | 79 | 1 | no | — |
| 330 | C79 | #25865 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 331 | C22×#41 | — | 79 | 1 | no | — |
| 332 | C23×D4 | — | 79 | 1 | no | — |
| 333 | #535 | — | 158 | 4 | no | — |
| 334 | #535 | — | 158 | 4 | no | — |
| 335 | C2×C4⋊Q8 | — | 79 | 1 | no | — |
| 336 | C2×#127 | — | 79 | 1 | no | — |
| 337 | C2×#127 | — | 79 | 1 | no | — |
| 338 | C2×#124 | — | 79 | 1 | no | — |
| 339 | C2×#124 | C2×D79 | 1 | 1 | yes | characteristic |
| 340 | C2×#121 | — | 158 | 1 | no | — |
| 341 | C2×#121 | — | 158 | 1 | no | — |
| 342 | C2×#120 | — | 158 | 1 | no | — |
| 343 | C2×#120 | — | 158 | 1 | no | — |
| 344 | C2×#117 | — | 79 | 1 | no | — |
| 345 | #489 | — | 158 | 4 | no | — |
| 346 | #486 | — | 158 | 4 | no | — |
| 347 | C2×#103 | — | 79 | 2 | no | — |
| 348 | C2×#103 | C2×D79 | 1 | 2 | yes | complemented |
| 349 | C2×#102 | — | 79 | 2 | no | — |
| 350 | C2×#102 | — | 79 | 2 | no | — |
| 351 | C2×#102 | — | 79 | 2 | no | — |
| 352 | C2×#102 | — | 79 | 2 | no | — |
| 353 | C2×#102 | — | 79 | 2 | no | — |
| 354 | C2×#102 | C2×D79 | 1 | 2 | yes | — |
| 355 | C2×C22⋊C8 | — | 79 | 2 | no | — |
| 356 | C2×#97 | — | 79 | 1 | no | — |
| 357 | C2×C4×C8 | C2×D79 | 1 | 1 | yes | characteristic, complemented |
| 358 | #400 | — | 158 | 1 | no | — |
| 359 | #399 | — | 158 | 1 | no | — |
| 360 | #395 | — | 158 | 1 | no | — |
| 361 | #393 | — | 158 | 1 | no | — |
| 362 | #389 | — | 79 | 2 | no | — |
| 363 | #382 | C2×D79 | 1 | 1 | yes | characteristic, complemented |
| 364 | #380 | — | 79 | 2 | no | — |
| 365 | #336 | — | 79 | 2 | no | — |
| 366 | C25 | — | 158 | 1 | no | — |
| 367 | C2×#41 | — | 316 | 2 | no | — |
| 368 | C2×#41 | — | 158 | 4 | no | — |
| 369 | C2×#41 | — | 158 | 2 | no | — |
| 370 | C2×#41 | — | 158 | 2 | no | — |
| 371 | C22×Q8 | — | 158 | 1 | no | — |
| 372 | C22×Q8 | C22×D79 | 1 | 1 | yes | characteristic |
| 373 | C22×D4 | — | 316 | 2 | no | — |
| 374 | C22×D4 | — | 79 | 1 | no | — |
| 375 | C22×D4 | — | 79 | 1 | no | — |
| 376 | C22×D4 | — | 158 | 1 | no | — |
| 377 | C22×D4 | — | 158 | 4 | no | — |
| 378 | C22×D4 | — | 158 | 1 | no | — |
| 379 | C22×D4 | — | 158 | 1 | no | — |
| 380 | C22×D4 | — | 158 | 1 | no | — |
| 381 | C22×D4 | — | 158 | 2 | no | — |
| 382 | C22×D4 | — | 158 | 2 | no | — |
| 383 | C22×D4 | — | 158 | 1 | no | — |
| 384 | C22×D4 | — | 158 | 1 | no | — |
| 385 | C22×D4 | C22×D79 | 1 | 1 | yes | characteristic |
| 386 | C23×C4 | — | 79 | 1 | no | — |
| 387 | C23×C4 | — | 158 | 1 | no | — |
| 388 | C22×C8 | — | 79 | 2 | no | — |
| 389 | C22×C8 | C22×D79 | 1 | 2 | yes | — |
| 390 | C4⋊Q8 | — | 158 | 2 | no | — |
| 391 | C4⋊Q8 | — | 158 | 2 | no | — |
| 392 | #127 | — | 79 | 4 | no | — |
| 393 | #127 | — | 158 | 2 | no | — |
| 394 | #127 | — | 158 | 2 | no | — |
| 395 | #127 | — | 158 | 2 | no | — |
| 396 | #124 | — | 2 | 2 | no | — |
| 397 | #124 | — | 158 | 2 | no | — |
| 398 | #124 | — | 158 | 2 | no | — |
| 399 | #124 | D316 | 1 | 4 | yes | — |
| 400 | #121 | — | 158 | 8 | no | — |
| 401 | #121 | — | 158 | 8 | no | — |
| 402 | #120 | — | 158 | 8 | no | — |
| 403 | #120 | — | 158 | 8 | no | — |
| 404 | #117 | — | 158 | 2 | no | — |
| 405 | #117 | — | 158 | 2 | no | — |
| 406 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 407 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 408 | C2×C4⋊C4 | — | 79 | 2 | no | — |
| 409 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 410 | C2×C4⋊C4 | — | 158 | 2 | no | — |
| 411 | C2×C4⋊C4 | C22×D79 | 1 | 2 | yes | — |
| 412 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 413 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 414 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 415 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 416 | C2×C22⋊C4 | — | 158 | 2 | no | — |
| 417 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 418 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 419 | C2×C42 | — | 79 | 1 | no | — |
| 420 | C2×C42 | C22×D79 | 1 | 1 | yes | characteristic |
| 421 | #103 | — | 4 | 2 | no | — |
| 422 | #103 | — | 158 | 4 | no | — |
| 423 | #102 | — | 4 | 2 | no | — |
| 424 | #102 | — | 316 | 2 | no | — |
| 425 | #102 | — | 316 | 2 | no | — |
| 426 | #102 | — | 158 | 4 | no | — |
| 427 | #102 | — | 158 | 4 | no | — |
| 428 | #102 | — | 158 | 4 | no | — |
| 429 | C22⋊C8 | — | 158 | 4 | no | — |
| 430 | #97 | — | 158 | 2 | no | — |
| 431 | C4×C8 | — | 2 | 2 | no | — |
| 432 | #95 | — | 2 | 1 | no | — |
| 433 | #95 | — | 2 | 1 | no | — |
| 434 | #95 | — | 158 | 2 | no | — |
| 435 | #95 | — | 158 | 2 | no | — |
| 436 | C24 | — | 2 | 1 | no | — |
| 437 | C24 | — | 316 | 2 | no | — |
| 438 | C24 | — | 316 | 2 | no | — |
| 439 | C24 | — | 79 | 1 | no | — |
| 440 | C24 | — | 632 | 2 | no | — |
| 441 | C24 | — | 632 | 2 | no | — |
| 442 | C24 | — | 158 | 4 | no | — |
| 443 | C24 | — | 158 | 1 | no | — |
| 444 | C24 | — | 158 | 1 | no | — |
| 445 | #41 | — | 316 | 8 | no | — |
| 446 | #41 | — | 316 | 8 | no | — |
| 447 | C2×Q8 | — | 2 | 1 | no | — |
| 448 | C2×Q8 | — | 2 | 2 | no | — |
| 449 | C2×Q8 | — | 2 | 2 | no | — |
| 450 | C2×Q8 | — | 316 | 2 | no | — |
| 451 | C2×Q8 | — | 632 | 2 | no | — |
| 452 | C2×Q8 | C2×D316 | 1 | 2 | yes | — |
| 453 | C2×D4 | — | 2 | 2 | no | — |
| 454 | C2×D4 | — | 2 | 2 | no | — |
| 455 | C2×D4 | — | 2 | 1 | no | — |
| 456 | C2×D4 | — | 316 | 2 | no | — |
| 457 | C2×D4 | — | 316 | 2 | no | — |
| 458 | C2×D4 | — | 316 | 2 | no | — |
| 459 | C2×D4 | — | 316 | 8 | no | — |
| 460 | C2×D4 | — | 316 | 8 | no | — |
| 461 | C2×D4 | — | 316 | 2 | no | — |
| 462 | C2×D4 | — | 79 | 2 | no | — |
| 463 | C2×D4 | — | 79 | 2 | no | — |
| 464 | C2×D4 | — | 632 | 2 | no | — |
| 465 | C2×D4 | — | 632 | 2 | no | — |
| 466 | C2×D4 | — | 632 | 2 | no | — |
| 467 | C2×D4 | — | 632 | 2 | no | — |
| 468 | C2×D4 | — | 158 | 4 | no | — |
| 469 | C2×D4 | — | 158 | 4 | no | — |
| 470 | C2×D4 | — | 158 | 4 | no | — |
| 471 | C2×D4 | — | 158 | 4 | no | — |
| 472 | C2×D4 | — | 158 | 2 | no | — |
| 473 | C2×D4 | — | 158 | 2 | no | — |
| 474 | C2×D4 | — | 158 | 2 | no | — |
| 475 | C2×D4 | — | 158 | 2 | no | — |
| 476 | C2×D4 | — | 158 | 4 | no | — |
| 477 | C2×D4 | — | 158 | 4 | no | — |
| 478 | C2×D4 | — | 158 | 1 | no | — |
| 479 | C2×D4 | — | 158 | 1 | no | — |
| 480 | C2×D4 | C2×D316 | 1 | 2 | yes | — |
| 481 | C22×C4 | — | 2 | 1 | no | — |
| 482 | C22×C4 | — | 2 | 2 | no | — |
| 483 | C22×C4 | — | 316 | 2 | no | — |
| 484 | C22×C4 | — | 316 | 2 | no | — |
| 485 | C22×C4 | — | 79 | 1 | no | — |
| 486 | C22×C4 | — | 79 | 4 | no | — |
| 487 | C22×C4 | — | 79 | 1 | no | — |
| 488 | C22×C4 | — | 79 | 1 | no | — |
| 489 | C22×C4 | — | 158 | 4 | no | — |
| 490 | C22×C4 | — | 158 | 2 | no | — |
| 491 | C22×C4 | — | 158 | 2 | no | — |
| 492 | C22×C4 | — | 158 | 1 | no | — |
| 493 | C22×C4 | — | 158 | 1 | no | — |
| 494 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 495 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 496 | C22×C4 | C23×D79 | 1 | 1 | yes | characteristic |
| 497 | C2×C8 | — | 2 | 2 | no | — |
| 498 | C2×C8 | — | 2 | 2 | no | — |
| 499 | C2×C8 | — | 2 | 2 | no | — |
| 500 | C2×C8 | — | 158 | 2 | no | — |
| 501 | C2×C8 | — | 158 | 2 | no | — |
| 502 | C2×C8 | — | 158 | 2 | no | — |
| 503 | C4⋊C4 | — | 2 | 2 | no | — |
| 504 | C4⋊C4 | — | 2 | 2 | no | — |
| 505 | C4⋊C4 | — | 316 | 2 | no | — |
| 506 | C4⋊C4 | — | 632 | 2 | no | — |
| 507 | C4⋊C4 | — | 158 | 2 | no | — |
| 508 | C4⋊C4 | — | 158 | 2 | no | — |
| 509 | C4⋊C4 | — | 158 | 2 | no | — |
| 510 | C4⋊C4 | — | 158 | 2 | no | — |
| 511 | C22⋊C4 | — | 2 | 4 | no | — |
| 512 | C22⋊C4 | — | 2 | 4 | no | — |
| 513 | C22⋊C4 | — | 632 | 2 | no | — |
| 514 | C22⋊C4 | — | 158 | 4 | no | — |
| 515 | C22⋊C4 | — | 158 | 4 | no | — |
| 516 | C22⋊C4 | — | 158 | 2 | no | — |
| 517 | C22⋊C4 | — | 158 | 2 | no | — |
| 518 | C42 | — | 158 | 1 | no | — |
| 519 | C42 | — | 158 | 1 | no | — |
| 520 | C42 | D4×D79 | 1 | 2 | yes | — |
| 521 | C42 | C2×D316 | 1 | 2 | yes | — |
| 522 | C23 | — | 2 | 2 | no | — |
| 523 | C23 | — | 4 | 1 | no | — |
| 524 | C23 | — | 4 | 2 | no | — |
| 525 | C23 | — | 4 | 2 | no | — |
| 526 | C23 | — | 4 | 1 | no | — |
| 527 | C23 | — | 316 | 8 | no | — |
| 528 | C23 | — | 316 | 1 | no | — |
| 529 | C23 | — | 316 | 1 | no | — |
| 530 | C23 | — | 316 | 2 | no | — |
| 531 | C23 | — | 316 | 2 | no | — |
| 532 | C23 | — | 316 | 2 | no | — |
| 533 | C23 | — | 316 | 2 | no | — |
| 534 | C23 | — | 316 | 1 | no | — |
| 535 | C23 | — | 316 | 1 | no | — |
| 536 | C23 | — | 79 | 2 | no | — |
| 537 | C23 | — | 632 | 4 | no | — |
| 538 | C23 | — | 632 | 4 | no | — |
| 539 | C23 | — | 632 | 8 | no | — |
| 540 | C23 | — | 632 | 8 | no | — |
| 541 | C23 | — | 158 | 2 | no | — |
| 542 | C23 | — | 158 | 2 | no | — |
| 543 | C23 | — | 158 | 1 | no | — |
| 544 | C23 | — | 158 | 2 | no | — |
| 545 | C23 | — | 158 | 2 | no | — |
| 546 | C23 | — | 158 | 1 | no | — |
| 547 | C23 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 548 | Q8 | — | 2 | 4 | no | — |
| 549 | Q8 | — | 4 | 2 | no | — |
| 550 | Q8 | — | 632 | 4 | no | — |
| 551 | D4 | — | 2 | 4 | no | — |
| 552 | D4 | — | 4 | 2 | no | — |
| 553 | D4 | — | 316 | 8 | no | — |
| 554 | D4 | — | 316 | 8 | no | — |
| 555 | D4 | — | 316 | 2 | no | — |
| 556 | D4 | — | 316 | 2 | no | — |
| 557 | D4 | — | 632 | 4 | no | — |
| 558 | D4 | — | 632 | 4 | no | — |
| 559 | D4 | — | 632 | 4 | no | — |
| 560 | D4 | — | 632 | 4 | no | — |
| 561 | D4 | — | 158 | 4 | no | — |
| 562 | D4 | — | 158 | 4 | no | — |
| 563 | C2×C4 | — | 2 | 2 | no | — |
| 564 | C2×C4 | — | 2 | 2 | no | — |
| 565 | C2×C4 | — | 2 | 2 | no | — |
| 566 | C2×C4 | — | 4 | 1 | no | — |
| 567 | C2×C4 | — | 4 | 1 | no | — |
| 568 | C2×C4 | — | 4 | 2 | no | — |
| 569 | C2×C4 | — | 4 | 2 | no | — |
| 570 | C2×C4 | — | 4 | 2 | no | — |
| 571 | C2×C4 | — | 316 | 8 | no | — |
| 572 | C2×C4 | — | 316 | 2 | no | — |
| 573 | C2×C4 | — | 316 | 2 | no | — |
| 574 | C2×C4 | — | 316 | 2 | no | — |
| 575 | C2×C4 | — | 79 | 2 | no | — |
| 576 | C2×C4 | — | 158 | 1 | no | — |
| 577 | C2×C4 | — | 158 | 1 | no | — |
| 578 | C2×C4 | — | 158 | 2 | no | — |
| 579 | C2×C4 | — | 158 | 2 | no | — |
| 580 | C2×C4 | — | 158 | 1 | no | — |
| 581 | C2×C4 | — | 158 | 1 | no | — |
| 582 | C2×C4 | — | 158 | 4 | no | — |
| 583 | C2×C4 | — | 158 | 4 | no | — |
| 584 | C2×C4 | #14579131 | 1 | 2 | yes | — |
| 585 | C2×C4 | #14579131 | 1 | 2 | yes | — |
| 586 | C2×C4 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 587 | C2×C4 | C22×D316 | 1 | 1 | yes | characteristic |
| 588 | C2×C4 | #41×D79 | 1 | 2 | yes | — |
| 589 | C2×C4 | #14579206 | 1 | 2 | yes | — |
| 590 | C8 | — | 4 | 2 | no | — |
| 591 | C8 | — | 316 | 2 | no | — |
| 592 | C22 | — | 4 | 2 | no | — |
| 593 | C22 | — | 4 | 2 | no | — |
| 594 | C22 | — | 4 | 2 | no | — |
| 595 | C22 | — | 8 | 2 | no | — |
| 596 | C22 | — | 8 | 2 | no | — |
| 597 | C22 | — | 316 | 1 | no | — |
| 598 | C22 | — | 316 | 2 | no | — |
| 599 | C22 | — | 316 | 1 | no | — |
| 600 | C22 | — | 316 | 2 | no | — |
| 601 | C22 | — | 316 | 2 | no | — |
| 602 | C22 | — | 316 | 2 | no | — |
| 603 | C22 | — | 316 | 2 | no | — |
| 604 | C22 | — | 316 | 2 | no | — |
| 605 | C22 | — | 316 | 2 | no | — |
| 606 | C22 | — | 632 | 16 | no | — |
| 607 | C22 | — | 632 | 2 | no | — |
| 608 | C22 | — | 632 | 2 | no | — |
| 609 | C22 | — | 632 | 2 | no | — |
| 610 | C22 | — | 632 | 2 | no | — |
| 611 | C22 | — | 158 | 2 | no | — |
| 612 | C22 | — | 158 | 4 | no | — |
| 613 | C22 | C2×#14579131 | 1 | 1 | yes | characteristic |
| 614 | C22 | #124×D79 | 1 | 1 | yes | characteristic |
| 615 | C22 | #19099126 | 1 | 1 | yes | characteristic |
| 616 | C22 | #19099365 | 1 | 2 | yes | — |
| 617 | C22 | #19099370 | 1 | 2 | yes | — |
| 618 | C4 | — | 2 | 2 | no | — |
| 619 | C4 | — | 2 | 2 | no | — |
| 620 | C4 | — | 4 | 2 | no | — |
| 621 | C4 | — | 8 | 2 | no | — |
| 622 | C4 | — | 316 | 1 | no | — |
| 623 | C4 | — | 316 | 1 | no | — |
| 624 | C4 | — | 632 | 2 | no | — |
| 625 | C4 | — | 158 | 2 | no | — |
| 626 | C4 | #19099208 | 1 | 2 | yes | — |
| 627 | C4 | #19099210 | 1 | 2 | yes | — |
| 628 | C2 | — | 8 | 2 | no | — |
| 629 | C2 | — | 316 | 2 | no | — |
| 630 | C2 | — | 632 | 2 | no | — |
| 631 | C2 | — | 632 | 2 | no | — |
| 632 | C2 | #23767050 | 1 | 1 | yes | characteristic |
| 633 | C2 | #23772671 | 1 | 1 | yes | characteristic |
| 634 | C2 | #23772680 | 1 | 1 | yes | characteristic |
| 635 | C2 | #23773753 | 1 | 2 | yes | — |
| 636 | C2 | #23774487 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19098922 | C2 | semidirect |
| 3. C2×#19098910 | C2 | semidirect |
| 4. #23769224 | C2 | semidirect |
| 5. #23764638 | C2 | semidirect |
| 6. #23764633 | C2 | semidirect |
| 7. #23764223 | C2 | semidirect |
| 8. #23763339 | C2 | semidirect |
| 9. #23763329 | C2 | semidirect |
| 10. #23763167 | C2 | semidirect |
| 11. C79×#1958 | C2 | semidirect |
| 16. C2×#14579161 | C22 | semidirect |
| 27. C2×#14579085 | C22 | semidirect |
| 29. C2×#14579083 | C22 | semidirect |
| 32. C2×#14579081 | C22 | semidirect |
| 34. C2×#14579072 | C22 | semidirect |
| 39. #19098462 | C22 | semidirect |
| 41. #19098317 | C22 | semidirect |
| 43. C2×#103×C79 | C22 | semidirect |
| 45. C2×C4×C8×C79 | C22 | semidirect |
| 46. #382×C79 | C22 | semidirect |
| 326. #1958 | D79 | semidirect |
| 330. C79 | #25865 | semidirect |
| 348. C2×#103 | C2×D79 | semidirect |
| 357. C2×C4×C8 | C2×D79 | semidirect |
| 363. #382 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099131 | 2 |
| C2×#19098922 | 2 |
| C2×#19098910 | 2 |
| #23769224 | 2 |
| #23764638 | 2 |
| #23764633 | 2 |
| #23764223 | 2 |
| #23763339 | 2 |
| #23763329 | 2 |
| #23763167 | 2 |
| C79×#1958 | 2 |
| #25865 | 79 |