Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1312 conjugacy classes of subgroups.
The subgroup lattice has 828 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D53⋊#444 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20291478 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20291337 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20290877 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20290863 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20290755 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20290714 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20290603 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20290562 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #20290493 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #578×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | D53⋊#131 | C22 | 1 | 2 | yes | — |
| 13 | #16811692 | C22 | 1 | 2 | yes | — |
| 14 | #16811670 | — | 2 | 1 | no | — |
| 15 | #16811669 | — | 2 | 1 | no | — |
| 16 | #16811668 | — | 2 | 2 | no | — |
| 17 | #16811664 | — | 2 | 1 | no | — |
| 18 | #16811663 | — | 2 | 1 | no | — |
| 19 | SD16×#6157 | — | 2 | 2 | no | — |
| 20 | D53⋊#108 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#13133285 | C22 | 1 | 1 | yes | characteristic |
| 22 | D53⋊#104 | C22 | 1 | 1 | yes | characteristic |
| 23 | D53⋊#104 | C22 | 1 | 2 | yes | — |
| 24 | #16811616 | — | 2 | 2 | no | — |
| 25 | #16811616 | C22 | 1 | 2 | yes | — |
| 26 | #16811614 | — | 2 | 2 | no | — |
| 27 | #16811614 | C22 | 1 | 2 | yes | — |
| 28 | #16811614 | C22 | 1 | 2 | yes | — |
| 29 | #16811613 | — | 2 | 2 | no | — |
| 30 | #16811613 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#13133280 | — | 2 | 2 | no | — |
| 32 | C2×#13133280 | C22 | 1 | 2 | yes | — |
| 33 | D53⋊#101 | C22 | 1 | 2 | yes | — |
| 34 | #16811586 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#13133271 | C22 | 1 | 1 | yes | characteristic |
| 36 | (C2×#6157)⋊Q8 | C22 | 1 | 2 | yes | — |
| 37 | #16811502 | C22 | 1 | 2 | yes | — |
| 38 | #16811498 | C22 | 1 | 1 | yes | characteristic |
| 39 | #16811495 | C22 | 1 | 1 | yes | characteristic |
| 40 | 2−1+4×D53 | C22 | 1 | 2 | yes | — |
| 41 | #16811440 | C4 | 1 | 1 | yes | characteristic, complemented |
| 42 | #16811439 | — | 2 | 2 | no | — |
| 43 | #16811439 | C4 | 1 | 2 | yes | complemented |
| 44 | #16811438 | C4 | 1 | 2 | yes | complemented |
| 45 | #16811437 | — | 2 | 1 | no | — |
| 46 | #16811437 | C4 | 1 | 1 | yes | characteristic, complemented |
| 47 | #16811436 | — | 2 | 1 | no | — |
| 48 | #16811436 | C4 | 1 | 1 | yes | characteristic, complemented |
| 49 | #137×D53 | — | 2 | 2 | no | — |
| 50 | #137×D53 | C22 | 1 | 2 | yes | — |
| 51 | #135×D53 | — | 2 | 1 | no | — |
| 52 | #135×D53 | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×Q16×D53 | — | 2 | 1 | no | — |
| 54 | C2×Q16×D53 | C22 | 1 | 1 | yes | characteristic |
| 55 | #131×D53 | C22 | 1 | 1 | yes | characteristic |
| 56 | C53×#578 | C4 | 1 | 1 | yes | characteristic, complemented |
| 57 | #13133305 | — | 2 | 2 | no | — |
| 58 | #13133304 | — | 2 | 2 | no | — |
| 59 | #13133304 | — | 4 | 2 | no | — |
| 60 | D53⋊M16 | — | 2 | 2 | no | — |
| 61 | D53⋊M16 | C23 | 1 | 1 | yes | characteristic |
| 62 | D53⋊M16 | C23 | 1 | 2 | yes | — |
| 63 | C2×D53⋊C8 | — | 2 | 2 | no | — |
| 64 | C2×D53⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 65 | Q8×#6157 | — | 2 | 2 | no | — |
| 66 | D4×#6157 | — | 2 | 2 | no | — |
| 67 | D4×#6157 | — | 4 | 2 | no | — |
| 68 | #13133296 | — | 2 | 2 | no | — |
| 69 | #13133296 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×C4⋊#6157 | — | 2 | 2 | no | — |
| 71 | C2×C4⋊#6157 | C23 | 1 | 2 | yes | — |
| 72 | C2×C4×#6157 | C23 | 1 | 1 | yes | characteristic |
| 73 | #13133288 | — | 2 | 1 | no | — |
| 74 | #13133287 | — | 2 | 1 | no | — |
| 75 | #13133285 | — | 2 | 1 | no | — |
| 76 | #13133285 | — | 2 | 1 | no | — |
| 77 | #13133282 | — | 2 | 2 | no | — |
| 78 | #13133282 | — | 2 | 1 | no | — |
| 79 | #13133281 | — | 2 | 2 | no | — |
| 80 | #13133281 | — | 2 | 1 | no | — |
| 81 | #13133280 | — | 2 | 2 | no | — |
| 82 | #13133280 | — | 2 | 2 | no | — |
| 83 | #13133280 | — | 2 | 2 | no | — |
| 84 | #13133280 | — | 2 | 2 | no | — |
| 85 | #13133280 | — | 2 | 2 | no | — |
| 86 | #13133280 | — | 2 | 2 | no | — |
| 87 | #13133280 | D4 | 1 | 2 | yes | — |
| 88 | #13133279 | — | 2 | 2 | no | — |
| 89 | #13133279 | — | 2 | 2 | no | — |
| 90 | #13133279 | D4 | 1 | 2 | yes | — |
| 91 | #13133278 | — | 4 | 2 | no | — |
| 92 | #13133271 | — | 2 | 1 | no | — |
| 93 | #13133271 | — | 2 | 1 | no | — |
| 94 | #13133271 | — | 2 | 1 | no | — |
| 95 | C8×#6157 | — | 2 | 1 | no | — |
| 96 | (C2×#6157)⋊C4 | — | 4 | 2 | no | — |
| 97 | #13133265 | — | 2 | 2 | no | — |
| 98 | #13133265 | — | 2 | 2 | no | — |
| 99 | #13133265 | C2×C4 | 1 | 2 | yes | complemented |
| 100 | #13133264 | — | 2 | 2 | no | — |
| 101 | #13133264 | — | 2 | 2 | no | — |
| 102 | #13133264 | — | 4 | 2 | no | — |
| 103 | #13133264 | C2×C4 | 1 | 2 | yes | complemented |
| 104 | #13133264 | C2×C4 | 1 | 2 | yes | complemented |
| 105 | #41×D53 | — | 2 | 2 | no | — |
| 106 | #41×D53 | — | 2 | 2 | no | — |
| 107 | #41×D53 | — | 4 | 2 | no | — |
| 108 | #41×D53 | C23 | 1 | 2 | yes | — |
| 109 | #41×D53 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×Q8×D53 | — | 2 | 2 | no | — |
| 111 | C2×Q8×D53 | — | 2 | 2 | no | — |
| 112 | C2×Q8×D53 | C23 | 1 | 2 | yes | — |
| 113 | #13133250 | — | 2 | 2 | no | — |
| 114 | #13133250 | C2×C4 | 1 | 2 | yes | complemented |
| 115 | #13133249 | — | 2 | 2 | no | — |
| 116 | #13133249 | — | 2 | 2 | no | — |
| 117 | #13133249 | — | 2 | 2 | no | — |
| 118 | #13133248 | — | 2 | 2 | no | — |
| 119 | #13133248 | C2×C4 | 1 | 2 | yes | complemented |
| 120 | #13133247 | — | 2 | 2 | no | — |
| 121 | #13133247 | C2×C4 | 1 | 2 | yes | complemented |
| 122 | #13133246 | — | 2 | 2 | no | — |
| 123 | #13133246 | — | 2 | 2 | no | — |
| 124 | #13133246 | — | 2 | 2 | no | — |
| 125 | #13133240 | — | 2 | 1 | no | — |
| 126 | #13133240 | D4 | 1 | 1 | yes | characteristic |
| 127 | #13133239 | — | 2 | 1 | no | — |
| 128 | #13133239 | C2×C4 | 1 | 1 | yes | characteristic |
| 129 | #13133238 | — | 2 | 2 | no | — |
| 130 | #13133238 | D4 | 1 | 2 | yes | — |
| 131 | #13133237 | — | 2 | 2 | no | — |
| 132 | #13133237 | C2×C4 | 1 | 2 | yes | — |
| 133 | #13133236 | — | 2 | 1 | no | — |
| 134 | #13133236 | D4 | 1 | 1 | yes | characteristic |
| 135 | C2×Dic212 | — | 2 | 1 | no | — |
| 136 | C2×Dic212 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 137 | C2×#11719925 | — | 2 | 2 | no | — |
| 138 | C2×#11719925 | C2×C4 | 1 | 2 | yes | complemented |
| 139 | Q16×D53 | — | 2 | 1 | no | — |
| 140 | Q16×D53 | — | 2 | 2 | no | — |
| 141 | Q16×D53 | — | 2 | 1 | no | — |
| 142 | Q16×D53 | — | 2 | 1 | no | — |
| 143 | Q16×D53 | — | 2 | 1 | no | — |
| 144 | Q16×D53 | — | 2 | 1 | no | — |
| 145 | Q16×D53 | — | 2 | 1 | no | — |
| 146 | Q16×D53 | — | 2 | 2 | no | — |
| 147 | Q16×D53 | D4 | 1 | 1 | yes | characteristic |
| 148 | SD16×D53 | — | 2 | 2 | no | — |
| 149 | SD16×D53 | D4 | 1 | 2 | yes | — |
| 150 | D8×D53 | D4 | 1 | 1 | yes | characteristic |
| 151 | #13133225 | — | 2 | 1 | no | — |
| 152 | #13133225 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 153 | #13133224 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 154 | #13133223 | — | 2 | 1 | no | — |
| 155 | #13133223 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 156 | M16×D53 | — | 2 | 1 | no | — |
| 157 | M16×D53 | C23 | 1 | 1 | yes | characteristic |
| 158 | C2×C8×D53 | — | 2 | 1 | no | — |
| 159 | C2×C8×D53 | C23 | 1 | 1 | yes | characteristic |
| 160 | 2−1+4×C53 | C2×C4 | 1 | 2 | yes | complemented |
| 161 | #137×C53 | — | 2 | 2 | no | — |
| 162 | #137×C53 | C2×C4 | 1 | 2 | yes | complemented |
| 163 | #135×C53 | — | 2 | 1 | no | — |
| 164 | #135×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 165 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 166 | C2×Q16×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 167 | #131×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 168 | C22×#6157 | — | 2 | 1 | no | — |
| 169 | C22×#6157 | — | 2 | 2 | no | — |
| 170 | C22×#6157 | — | 4 | 2 | no | — |
| 171 | #41×C53 | — | 2 | 2 | no | — |
| 172 | #41×C53 | — | 2 | 2 | no | — |
| 173 | #41×C53 | — | 4 | 2 | no | — |
| 174 | #41×C53 | C22×C4 | 1 | 2 | yes | — |
| 175 | #41×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 176 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 177 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 178 | C2×Q8×C53 | C22×C4 | 1 | 2 | yes | — |
| 179 | #11719949 | — | 2 | 2 | no | — |
| 180 | #11719949 | — | 2 | 2 | no | — |
| 181 | #11719949 | — | 4 | 2 | no | — |
| 182 | #11719949 | C2×D4 | 1 | 2 | yes | — |
| 183 | #11719949 | #41 | 1 | 1 | yes | characteristic |
| 184 | Q8×D53 | — | 2 | 2 | no | — |
| 185 | Q8×D53 | — | 2 | 2 | no | — |
| 186 | Q8×D53 | — | 2 | 2 | no | — |
| 187 | Q8×D53 | — | 2 | 2 | no | — |
| 188 | Q8×D53 | — | 2 | 2 | no | — |
| 189 | Q8×D53 | — | 2 | 2 | no | — |
| 190 | Q8×D53 | — | 2 | 2 | no | — |
| 191 | Q8×D53 | — | 2 | 2 | no | — |
| 192 | Q8×D53 | — | 4 | 2 | no | — |
| 193 | Q8×D53 | — | 4 | 2 | no | — |
| 194 | Q8×D53 | — | 4 | 2 | no | — |
| 195 | Q8×D53 | C2×D4 | 1 | 2 | yes | — |
| 196 | Q8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | #11719947 | — | 2 | 1 | no | — |
| 198 | #11719947 | — | 2 | 2 | no | — |
| 199 | #11719947 | — | 2 | 2 | no | — |
| 200 | #11719947 | — | 2 | 2 | no | — |
| 201 | #11719947 | — | 4 | 2 | no | — |
| 202 | #11719947 | — | 4 | 2 | no | — |
| 203 | #11719947 | — | 4 | 2 | no | — |
| 204 | #11719947 | — | 4 | 2 | no | — |
| 205 | #11719947 | — | 4 | 2 | no | — |
| 206 | #11719947 | C2×D4 | 1 | 2 | yes | — |
| 207 | #11719947 | #41 | 1 | 1 | yes | characteristic |
| 208 | D4×D53 | — | 2 | 1 | no | — |
| 209 | D4×D53 | — | 2 | 2 | no | — |
| 210 | D4×D53 | — | 4 | 2 | no | — |
| 211 | D4×D53 | C2×D4 | 1 | 2 | yes | — |
| 212 | D4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | #11719945 | — | 2 | 1 | no | — |
| 214 | #11719945 | — | 2 | 2 | no | — |
| 215 | #11719945 | — | 2 | 2 | no | — |
| 216 | #11719945 | — | 2 | 2 | no | — |
| 217 | #11719945 | — | 4 | 2 | no | — |
| 218 | #11719945 | — | 4 | 2 | no | — |
| 219 | #11719945 | — | 4 | 2 | no | — |
| 220 | #11719945 | — | 4 | 2 | no | — |
| 221 | #11719945 | — | 4 | 2 | no | — |
| 222 | #11719945 | C22×C4 | 1 | 2 | yes | — |
| 223 | #11719945 | C22×C4 | 1 | 1 | yes | characteristic |
| 224 | C2×C4×D53 | — | 2 | 1 | no | — |
| 225 | C2×C4×D53 | — | 2 | 2 | no | — |
| 226 | C2×C4×D53 | — | 2 | 2 | no | — |
| 227 | C2×C4×D53 | — | 4 | 2 | no | — |
| 228 | C2×C4×D53 | — | 4 | 2 | no | — |
| 229 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 230 | C2×Dic106 | — | 2 | 2 | no | — |
| 231 | C2×Dic106 | — | 2 | 2 | no | — |
| 232 | C2×Dic106 | — | 2 | 2 | no | — |
| 233 | C2×Dic106 | — | 4 | 2 | no | — |
| 234 | C2×Dic106 | — | 4 | 2 | no | — |
| 235 | C2×Dic106 | C22×C4 | 1 | 2 | yes | — |
| 236 | C22⋊#6157 | — | 2 | 1 | no | — |
| 237 | C22⋊#6157 | — | 4 | 2 | no | — |
| 238 | #11719940 | — | 2 | 1 | no | — |
| 239 | #11719940 | — | 2 | 2 | no | — |
| 240 | #11719940 | — | 4 | 2 | no | — |
| 241 | C2×#88324 | — | 2 | 1 | no | — |
| 242 | C2×#88324 | — | 4 | 2 | no | — |
| 243 | C4⋊#6157 | — | 2 | 2 | no | — |
| 244 | C4⋊#6157 | — | 2 | 2 | no | — |
| 245 | C4⋊#6157 | — | 4 | 2 | no | — |
| 246 | C4⋊#6157 | C2×D4 | 1 | 2 | yes | — |
| 247 | C4×#6157 | — | 2 | 1 | no | — |
| 248 | C4×#6157 | — | 2 | 1 | no | — |
| 249 | C4×#6157 | — | 2 | 1 | no | — |
| 250 | C4×#6157 | — | 4 | 2 | no | — |
| 251 | #11719936 | — | 2 | 2 | no | — |
| 252 | #11719936 | — | 2 | 1 | no | — |
| 253 | #11719936 | — | 4 | 2 | no | — |
| 254 | D53⋊C8 | — | 2 | 1 | no | — |
| 255 | D53⋊C8 | — | 2 | 1 | no | — |
| 256 | D53⋊C8 | — | 2 | 2 | no | — |
| 257 | D53⋊C8 | — | 4 | 2 | no | — |
| 258 | D53⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 259 | Q16×C53 | — | 2 | 2 | no | — |
| 260 | Q16×C53 | — | 2 | 1 | no | — |
| 261 | Q16×C53 | — | 2 | 1 | no | — |
| 262 | Q16×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 263 | SD16×C53 | — | 2 | 2 | no | — |
| 264 | SD16×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 265 | D8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 266 | M16×C53 | — | 2 | 1 | no | — |
| 267 | M16×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 268 | C2×C8×C53 | — | 2 | 1 | no | — |
| 269 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 270 | #11719925 | — | 2 | 2 | no | — |
| 271 | #11719925 | — | 2 | 2 | no | — |
| 272 | #11719925 | — | 2 | 2 | no | — |
| 273 | #11719925 | — | 2 | 2 | no | — |
| 274 | #11719925 | C22⋊C4 | 1 | 2 | yes | — |
| 275 | #11719924 | — | 2 | 2 | no | — |
| 276 | #11719924 | C22⋊C4 | 1 | 2 | yes | — |
| 277 | #11719923 | — | 2 | 2 | no | — |
| 278 | #11719923 | C22⋊C4 | 1 | 2 | yes | — |
| 279 | #11719922 | C22⋊C4 | 1 | 2 | yes | — |
| 280 | #11719917 | — | 2 | 1 | no | — |
| 281 | #11719917 | C22×C4 | 1 | 1 | yes | characteristic |
| 282 | C2×#88322 | — | 2 | 1 | no | — |
| 283 | C2×#88322 | C22×C4 | 1 | 1 | yes | characteristic |
| 284 | Dic212 | — | 2 | 2 | no | — |
| 285 | Dic212 | — | 2 | 1 | no | — |
| 286 | Dic212 | — | 2 | 1 | no | — |
| 287 | Dic212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 288 | D424 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 289 | #11719913 | — | 2 | 2 | no | — |
| 290 | #11719913 | C22⋊C4 | 1 | 2 | yes | — |
| 291 | #11719912 | — | 2 | 1 | no | — |
| 292 | #11719912 | — | 2 | 1 | no | — |
| 293 | #11719912 | — | 2 | 1 | no | — |
| 294 | C8×D53 | — | 2 | 1 | no | — |
| 295 | C8×D53 | — | 2 | 1 | no | — |
| 296 | C8×D53 | — | 2 | 1 | no | — |
| 297 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 300 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 301 | C22×D53 | — | 2 | 2 | no | — |
| 302 | C22×D53 | — | 2 | 1 | no | — |
| 303 | C22×D53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 304 | C2×#6157 | — | 2 | 2 | no | — |
| 305 | C2×#6157 | — | 4 | 2 | no | — |
| 306 | C2×#6157 | — | 4 | 2 | no | — |
| 307 | C2×#6157 | — | 4 | 1 | no | — |
| 308 | C2×#6157 | — | 8 | 2 | no | — |
| 309 | C2×#6157 | — | 16 | 2 | no | — |
| 310 | Q8×C53 | — | 2 | 2 | no | — |
| 311 | Q8×C53 | — | 2 | 2 | no | — |
| 312 | Q8×C53 | — | 4 | 2 | no | — |
| 313 | Q8×C53 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 314 | Q8×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 315 | D4×C53 | — | 2 | 1 | no | — |
| 316 | D4×C53 | — | 2 | 2 | no | — |
| 317 | D4×C53 | — | 4 | 2 | no | — |
| 318 | D4×C53 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 319 | D4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 320 | C2×C4×C53 | — | 2 | 1 | no | — |
| 321 | C2×C4×C53 | — | 2 | 2 | no | — |
| 322 | C2×C4×C53 | — | 2 | 2 | no | — |
| 323 | C2×C4×C53 | — | 4 | 2 | no | — |
| 324 | C2×C4×C53 | — | 4 | 2 | no | — |
| 325 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 326 | C22⋊D53 | — | 2 | 1 | no | — |
| 327 | C22⋊D53 | — | 2 | 2 | no | — |
| 328 | C22⋊D53 | — | 2 | 1 | no | — |
| 329 | C22⋊D53 | — | 2 | 2 | no | — |
| 330 | C22⋊D53 | — | 2 | 1 | no | — |
| 331 | C22⋊D53 | — | 2 | 2 | no | — |
| 332 | C22⋊D53 | — | 4 | 2 | no | — |
| 333 | C22⋊D53 | — | 4 | 2 | no | — |
| 334 | C2×Dic53 | — | 2 | 2 | no | — |
| 335 | C2×Dic53 | — | 2 | 1 | no | — |
| 336 | C2×Dic53 | — | 2 | 2 | no | — |
| 337 | C2×Dic53 | — | 4 | 2 | no | — |
| 338 | C2×Dic53 | — | 4 | 2 | no | — |
| 339 | C2×Dic53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 340 | D212 | — | 2 | 1 | no | — |
| 341 | D212 | — | 2 | 2 | no | — |
| 342 | D212 | — | 4 | 2 | no | — |
| 343 | D212 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 344 | D212 | C4×D4 | 1 | 1 | yes | characteristic |
| 345 | C4×D53 | — | 2 | 2 | no | — |
| 346 | C4×D53 | — | 2 | 1 | no | — |
| 347 | C4×D53 | — | 2 | 1 | no | — |
| 348 | C4×D53 | — | 2 | 2 | no | — |
| 349 | C4×D53 | — | 2 | 2 | no | — |
| 350 | C4×D53 | — | 2 | 1 | no | — |
| 351 | C4×D53 | — | 4 | 2 | no | — |
| 352 | C4×D53 | — | 4 | 2 | no | — |
| 353 | C4×D53 | — | 4 | 2 | no | — |
| 354 | C4×D53 | — | 4 | 2 | no | — |
| 355 | C4×D53 | — | 4 | 2 | no | — |
| 356 | C4×D53 | — | 4 | 2 | no | — |
| 357 | C4×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 358 | C4×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 359 | C4×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 360 | C4×D53 | C2×#41 | 1 | 1 | yes | characteristic |
| 361 | Dic106 | — | 2 | 1 | no | — |
| 362 | Dic106 | — | 2 | 2 | no | — |
| 363 | Dic106 | — | 2 | 2 | no | — |
| 364 | Dic106 | — | 2 | 2 | no | — |
| 365 | Dic106 | — | 4 | 2 | no | — |
| 366 | Dic106 | — | 4 | 2 | no | — |
| 367 | Dic106 | — | 4 | 2 | no | — |
| 368 | Dic106 | — | 4 | 2 | no | — |
| 369 | Dic106 | — | 4 | 2 | no | — |
| 370 | Dic106 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 371 | Dic106 | C4×D4 | 1 | 1 | yes | characteristic |
| 372 | #88324 | — | 2 | 2 | no | — |
| 373 | #88324 | — | 4 | 2 | no | — |
| 374 | #88324 | — | 4 | 1 | no | — |
| 375 | C8×C53 | — | 2 | 1 | no | — |
| 376 | C8×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 377 | C8×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 378 | #88322 | — | 2 | 1 | no | — |
| 379 | #88322 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 380 | #88322 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 381 | #22465 | — | 53 | 1 | no | maximal, Sylow |
| 382 | C22×C53 | — | 2 | 1 | no | — |
| 383 | C22×C53 | — | 2 | 2 | no | — |
| 384 | C22×C53 | #518 | 1 | 1 | yes | characteristic |
| 385 | C2×D53 | — | 2 | 2 | no | — |
| 386 | C2×D53 | — | 2 | 1 | no | — |
| 387 | C2×D53 | — | 2 | 2 | no | — |
| 388 | C2×D53 | — | 4 | 2 | no | — |
| 389 | C2×D53 | — | 4 | 2 | no | — |
| 390 | C2×D53 | — | 4 | 2 | no | — |
| 391 | C2×D53 | D42 | 1 | 1 | yes | characteristic |
| 392 | C2×D53 | #546 | 1 | 1 | yes | characteristic |
| 393 | #6157 | — | 4 | 2 | no | — |
| 394 | #6157 | — | 8 | 1 | no | — |
| 395 | #6157 | — | 8 | 2 | no | — |
| 396 | C4×C53 | — | 2 | 1 | no | — |
| 397 | C4×C53 | — | 2 | 2 | no | — |
| 398 | C4×C53 | — | 4 | 2 | no | — |
| 399 | C4×C53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 400 | C4×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 401 | Dic53 | — | 2 | 1 | no | — |
| 402 | Dic53 | — | 2 | 2 | no | — |
| 403 | Dic53 | — | 4 | 2 | no | — |
| 404 | Dic53 | D42 | 1 | 1 | yes | characteristic |
| 405 | Dic53 | #546 | 1 | 1 | yes | characteristic |
| 406 | C2×#578 | — | 53 | 1 | no | — |
| 407 | C2×#444 | — | 53 | 1 | no | — |
| 408 | #2952 | — | 53 | 1 | no | — |
| 409 | #2898 | — | 53 | 2 | no | — |
| 410 | #1979 | — | 53 | 1 | no | — |
| 411 | #1971 | — | 53 | 1 | no | — |
| 412 | #1908 | — | 53 | 2 | no | — |
| 413 | #1882 | — | 53 | 2 | no | — |
| 414 | #1815 | — | 53 | 1 | no | — |
| 415 | #1793 | — | 53 | 2 | no | — |
| 416 | #1765 | — | 53 | 1 | no | — |
| 417 | C2×C53 | — | 2 | 1 | no | — |
| 418 | C2×C53 | — | 4 | 2 | no | — |
| 419 | C2×C53 | — | 4 | 1 | no | — |
| 420 | C2×C53 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 421 | D53 | — | 2 | 1 | no | — |
| 422 | D53 | — | 4 | 1 | no | — |
| 423 | D53 | — | 4 | 2 | no | — |
| 424 | D53 | #3289 | 1 | 2 | yes | — |
| 425 | C2×2−1+4 | — | 53 | 2 | no | — |
| 426 | #578 | — | 53 | 2 | no | — |
| 427 | #578 | — | 53 | 2 | no | — |
| 428 | #578 | — | 53 | 1 | no | — |
| 429 | #578 | — | 53 | 1 | no | — |
| 430 | #578 | — | 53 | 1 | no | — |
| 431 | #578 | — | 106 | 1 | no | — |
| 432 | #578 | — | 106 | 1 | no | — |
| 433 | #578 | — | 106 | 2 | no | — |
| 434 | #578 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 435 | C2×#137 | — | 53 | 2 | no | — |
| 436 | C2×#137 | — | 106 | 2 | no | — |
| 437 | C2×#135 | — | 53 | 1 | no | — |
| 438 | C2×#135 | — | 106 | 1 | no | — |
| 439 | C22×Q16 | — | 53 | 1 | no | — |
| 440 | C22×Q16 | — | 106 | 1 | no | — |
| 441 | C2×#131 | — | 53 | 1 | no | — |
| 442 | C2×#131 | — | 53 | 2 | no | — |
| 443 | #520 | — | 53 | 2 | no | — |
| 444 | #444 | — | 106 | 2 | no | — |
| 445 | #444 | — | 106 | 1 | no | — |
| 446 | #444 | — | 106 | 1 | no | — |
| 447 | #442 | — | 106 | 1 | no | — |
| 448 | #441 | — | 106 | 1 | no | — |
| 449 | C4×SD16 | — | 106 | 2 | no | — |
| 450 | C2×#108 | — | 53 | 1 | no | — |
| 451 | C2×#106 | — | 53 | 1 | no | — |
| 452 | C2×#104 | — | 53 | 1 | no | — |
| 453 | C2×#104 | — | 53 | 2 | no | — |
| 454 | #419 | — | 53 | 2 | no | — |
| 455 | #419 | — | 106 | 2 | no | — |
| 456 | #417 | — | 53 | 2 | no | — |
| 457 | #417 | — | 53 | 2 | no | — |
| 458 | #417 | — | 106 | 2 | no | — |
| 459 | #416 | — | 53 | 1 | no | — |
| 460 | #416 | — | 106 | 2 | no | — |
| 461 | C2×#103 | — | 53 | 2 | no | — |
| 462 | C2×#103 | — | 106 | 2 | no | — |
| 463 | C2×#101 | — | 53 | 2 | no | — |
| 464 | #405 | — | 53 | 1 | no | — |
| 465 | C2×#97 | — | 53 | 1 | no | — |
| 466 | #391 | — | 53 | 2 | no | — |
| 467 | #343 | — | 53 | 2 | no | — |
| 468 | #341 | — | 53 | 1 | no | — |
| 469 | #339 | — | 53 | 1 | no | — |
| 470 | C53 | #22465 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 471 | 2−1+4 | — | 53 | 2 | no | — |
| 472 | 2−1+4 | — | 53 | 2 | no | — |
| 473 | 2−1+4 | — | 53 | 2 | no | — |
| 474 | 2−1+4 | — | 106 | 2 | no | — |
| 475 | 2−1+4 | — | 106 | 2 | no | — |
| 476 | 2−1+4 | — | 106 | 2 | no | — |
| 477 | 2−1+4 | — | 106 | 2 | no | — |
| 478 | 2−1+4 | — | 212 | 2 | no | — |
| 479 | 2−1+4 | C2×#6157 | 1 | 2 | yes | complemented |
| 480 | C2×#41 | — | 53 | 2 | no | — |
| 481 | C2×#41 | — | 53 | 1 | no | — |
| 482 | C2×#41 | — | 106 | 2 | no | — |
| 483 | C2×#41 | — | 106 | 2 | no | — |
| 484 | C2×#41 | — | 212 | 2 | no | — |
| 485 | C22×Q8 | — | 53 | 2 | no | — |
| 486 | C22×Q8 | — | 106 | 2 | no | — |
| 487 | C22×Q8 | — | 106 | 2 | no | — |
| 488 | #137 | — | 2 | 2 | no | — |
| 489 | #137 | — | 53 | 2 | no | — |
| 490 | #137 | — | 53 | 2 | no | — |
| 491 | #137 | — | 53 | 2 | no | — |
| 492 | #137 | — | 106 | 2 | no | — |
| 493 | #137 | — | 106 | 2 | no | — |
| 494 | #137 | — | 106 | 2 | no | — |
| 495 | #137 | — | 106 | 2 | no | — |
| 496 | #137 | — | 106 | 2 | no | — |
| 497 | #137 | — | 106 | 2 | no | — |
| 498 | #137 | — | 106 | 2 | no | — |
| 499 | #137 | — | 106 | 2 | no | — |
| 500 | #137 | — | 106 | 2 | no | — |
| 501 | #137 | C2×#6157 | 1 | 2 | yes | complemented |
| 502 | #135 | — | 2 | 1 | no | — |
| 503 | #135 | — | 53 | 2 | no | — |
| 504 | #135 | — | 53 | 1 | no | — |
| 505 | #135 | — | 53 | 2 | no | — |
| 506 | #135 | — | 53 | 1 | no | — |
| 507 | #135 | — | 53 | 1 | no | — |
| 508 | #135 | — | 106 | 1 | no | — |
| 509 | #135 | — | 106 | 2 | no | — |
| 510 | #135 | — | 106 | 1 | no | — |
| 511 | #135 | — | 106 | 2 | no | — |
| 512 | #135 | — | 106 | 1 | no | — |
| 513 | #135 | C2×#6157 | 1 | 1 | yes | characteristic |
| 514 | C2×Q16 | — | 2 | 1 | no | — |
| 515 | C2×Q16 | — | 53 | 1 | no | — |
| 516 | C2×Q16 | — | 53 | 2 | no | — |
| 517 | C2×Q16 | — | 53 | 1 | no | — |
| 518 | C2×Q16 | — | 106 | 1 | no | — |
| 519 | C2×Q16 | — | 106 | 1 | no | — |
| 520 | C2×Q16 | — | 106 | 1 | no | — |
| 521 | C2×Q16 | — | 106 | 1 | no | — |
| 522 | C2×Q16 | — | 106 | 1 | no | — |
| 523 | C2×Q16 | — | 106 | 2 | no | — |
| 524 | C2×Q16 | — | 106 | 1 | no | — |
| 525 | C2×Q16 | — | 106 | 2 | no | — |
| 526 | C2×Q16 | — | 106 | 2 | no | — |
| 527 | C2×Q16 | — | 106 | 1 | no | — |
| 528 | C2×Q16 | C2×#6157 | 1 | 1 | yes | characteristic, complemented |
| 529 | C2×SD16 | — | 53 | 2 | no | — |
| 530 | C2×SD16 | — | 106 | 2 | no | — |
| 531 | C2×D8 | — | 53 | 1 | no | — |
| 532 | #131 | — | 53 | 1 | no | — |
| 533 | #131 | — | 53 | 1 | no | — |
| 534 | #131 | — | 53 | 1 | no | — |
| 535 | #131 | — | 106 | 1 | no | — |
| 536 | #131 | — | 106 | 1 | no | — |
| 537 | #131 | — | 106 | 2 | no | — |
| 538 | #131 | — | 106 | 2 | no | — |
| 539 | #131 | — | 212 | 2 | no | — |
| 540 | #131 | C2×#6157 | 1 | 1 | yes | characteristic, complemented |
| 541 | C2×M16 | — | 53 | 1 | no | — |
| 542 | C2×M16 | — | 53 | 2 | no | — |
| 543 | C2×M16 | — | 53 | 1 | no | — |
| 544 | C2×M16 | — | 106 | 1 | no | — |
| 545 | C2×M16 | — | 106 | 2 | no | — |
| 546 | C22×C8 | — | 53 | 1 | no | — |
| 547 | C22×C8 | — | 53 | 1 | no | — |
| 548 | C22×C8 | — | 106 | 1 | no | — |
| 549 | C22×C8 | — | 106 | 2 | no | — |
| 550 | C4×Q8 | — | 106 | 2 | no | — |
| 551 | C4×D4 | — | 106 | 2 | no | — |
| 552 | C4×D4 | — | 212 | 2 | no | — |
| 553 | #117 | — | 53 | 1 | no | — |
| 554 | #117 | — | 106 | 2 | no | — |
| 555 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 556 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 557 | C2×C42 | — | 53 | 1 | no | — |
| 558 | #108 | — | 106 | 1 | no | — |
| 559 | #108 | — | 106 | 1 | no | — |
| 560 | #106 | — | 106 | 1 | no | — |
| 561 | #106 | — | 106 | 1 | no | — |
| 562 | #104 | — | 106 | 2 | no | — |
| 563 | #104 | — | 106 | 2 | no | — |
| 564 | #104 | — | 106 | 1 | no | — |
| 565 | #104 | — | 106 | 1 | no | — |
| 566 | #103 | — | 53 | 2 | no | — |
| 567 | #103 | — | 106 | 2 | no | — |
| 568 | #103 | — | 106 | 2 | no | — |
| 569 | #103 | — | 106 | 2 | no | — |
| 570 | #103 | — | 106 | 2 | no | — |
| 571 | #103 | — | 106 | 2 | no | — |
| 572 | #103 | — | 106 | 2 | no | — |
| 573 | #102 | — | 53 | 2 | no | — |
| 574 | #102 | — | 106 | 2 | no | — |
| 575 | #102 | — | 106 | 2 | no | — |
| 576 | #101 | — | 212 | 2 | no | — |
| 577 | #97 | — | 106 | 1 | no | — |
| 578 | #97 | — | 106 | 1 | no | — |
| 579 | #97 | — | 106 | 1 | no | — |
| 580 | C4×C8 | — | 106 | 1 | no | — |
| 581 | #95 | — | 212 | 2 | no | — |
| 582 | #41 | — | 2 | 2 | no | — |
| 583 | #41 | — | 2 | 2 | no | — |
| 584 | #41 | — | 4 | 2 | no | — |
| 585 | #41 | — | 53 | 2 | no | — |
| 586 | #41 | — | 53 | 1 | no | — |
| 587 | #41 | — | 53 | 2 | no | — |
| 588 | #41 | — | 53 | 1 | no | — |
| 589 | #41 | — | 53 | 1 | no | — |
| 590 | #41 | — | 53 | 2 | no | — |
| 591 | #41 | — | 106 | 1 | no | — |
| 592 | #41 | — | 106 | 2 | no | — |
| 593 | #41 | — | 106 | 2 | no | — |
| 594 | #41 | — | 106 | 2 | no | — |
| 595 | #41 | — | 106 | 2 | no | — |
| 596 | #41 | — | 106 | 1 | no | — |
| 597 | #41 | — | 106 | 2 | no | — |
| 598 | #41 | — | 106 | 2 | no | — |
| 599 | #41 | — | 106 | 2 | no | — |
| 600 | #41 | — | 106 | 2 | no | — |
| 601 | #41 | — | 212 | 2 | no | — |
| 602 | #41 | — | 212 | 2 | no | — |
| 603 | #41 | — | 212 | 2 | no | — |
| 604 | #41 | — | 212 | 2 | no | — |
| 605 | #41 | — | 212 | 2 | no | — |
| 606 | #41 | — | 212 | 2 | no | — |
| 607 | #41 | — | 212 | 2 | no | — |
| 608 | #41 | — | 212 | 2 | no | — |
| 609 | #41 | — | 212 | 2 | no | — |
| 610 | #41 | — | 212 | 2 | no | — |
| 611 | #41 | — | 212 | 2 | no | — |
| 612 | #41 | C22×#6157 | 1 | 2 | yes | — |
| 613 | #41 | C22×#6157 | 1 | 1 | yes | characteristic |
| 614 | C2×Q8 | — | 2 | 2 | no | — |
| 615 | C2×Q8 | — | 2 | 2 | no | — |
| 616 | C2×Q8 | — | 53 | 2 | no | — |
| 617 | C2×Q8 | — | 53 | 1 | no | — |
| 618 | C2×Q8 | — | 53 | 2 | no | — |
| 619 | C2×Q8 | — | 106 | 2 | no | — |
| 620 | C2×Q8 | — | 106 | 2 | no | — |
| 621 | C2×Q8 | — | 106 | 2 | no | — |
| 622 | C2×Q8 | — | 106 | 2 | no | — |
| 623 | C2×Q8 | — | 106 | 2 | no | — |
| 624 | C2×Q8 | — | 106 | 2 | no | — |
| 625 | C2×Q8 | — | 106 | 2 | no | — |
| 626 | C2×Q8 | — | 106 | 2 | no | — |
| 627 | C2×Q8 | — | 106 | 2 | no | — |
| 628 | C2×Q8 | — | 106 | 2 | no | — |
| 629 | C2×Q8 | — | 106 | 2 | no | — |
| 630 | C2×Q8 | — | 212 | 2 | no | — |
| 631 | C2×Q8 | — | 212 | 2 | no | — |
| 632 | C2×Q8 | — | 212 | 2 | no | — |
| 633 | C2×Q8 | — | 212 | 2 | no | — |
| 634 | C2×Q8 | — | 212 | 2 | no | — |
| 635 | C2×Q8 | C22×#6157 | 1 | 2 | yes | — |
| 636 | C2×D4 | — | 53 | 2 | no | — |
| 637 | C2×D4 | — | 53 | 1 | no | — |
| 638 | C2×D4 | — | 106 | 2 | no | — |
| 639 | C2×D4 | — | 106 | 1 | no | — |
| 640 | C2×D4 | — | 212 | 2 | no | — |
| 641 | C22×C4 | — | 53 | 1 | no | — |
| 642 | C22×C4 | — | 106 | 2 | no | — |
| 643 | C22×C4 | — | 106 | 1 | no | — |
| 644 | C22×C4 | — | 106 | 2 | no | — |
| 645 | C22×C4 | — | 106 | 2 | no | — |
| 646 | C22×C4 | — | 106 | 1 | no | — |
| 647 | C22×C4 | — | 212 | 2 | no | — |
| 648 | C22×C4 | — | 212 | 2 | no | — |
| 649 | C22×C4 | — | 212 | 2 | no | — |
| 650 | Q16 | — | 2 | 2 | no | — |
| 651 | Q16 | — | 2 | 1 | no | — |
| 652 | Q16 | — | 2 | 1 | no | — |
| 653 | Q16 | — | 53 | 2 | no | — |
| 654 | Q16 | — | 53 | 1 | no | — |
| 655 | Q16 | — | 106 | 2 | no | — |
| 656 | Q16 | — | 106 | 2 | no | — |
| 657 | Q16 | — | 106 | 2 | no | — |
| 658 | Q16 | — | 106 | 2 | no | — |
| 659 | Q16 | — | 106 | 2 | no | — |
| 660 | Q16 | — | 106 | 1 | no | — |
| 661 | Q16 | — | 106 | 1 | no | — |
| 662 | Q16 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 663 | SD16 | — | 2 | 2 | no | — |
| 664 | SD16 | — | 53 | 2 | no | — |
| 665 | SD16 | — | 53 | 2 | no | — |
| 666 | SD16 | — | 53 | 2 | no | — |
| 667 | SD16 | — | 106 | 2 | no | — |
| 668 | SD16 | — | 106 | 2 | no | — |
| 669 | SD16 | — | 106 | 2 | no | — |
| 670 | SD16 | C22⋊#6157 | 1 | 2 | yes | — |
| 671 | D8 | — | 53 | 2 | no | — |
| 672 | D8 | — | 53 | 1 | no | — |
| 673 | D8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 674 | M16 | — | 2 | 1 | no | — |
| 675 | M16 | — | 53 | 1 | no | — |
| 676 | M16 | — | 106 | 1 | no | — |
| 677 | M16 | — | 106 | 1 | no | — |
| 678 | M16 | — | 106 | 1 | no | — |
| 679 | M16 | — | 106 | 1 | no | — |
| 680 | M16 | — | 106 | 2 | no | — |
| 681 | M16 | — | 106 | 1 | no | — |
| 682 | M16 | — | 106 | 1 | no | — |
| 683 | M16 | — | 106 | 2 | no | — |
| 684 | M16 | — | 212 | 2 | no | — |
| 685 | M16 | — | 212 | 2 | no | — |
| 686 | M16 | C22×#6157 | 1 | 1 | yes | characteristic |
| 687 | C2×C8 | — | 2 | 1 | no | — |
| 688 | C2×C8 | — | 53 | 1 | no | — |
| 689 | C2×C8 | — | 53 | 1 | no | — |
| 690 | C2×C8 | — | 53 | 1 | no | — |
| 691 | C2×C8 | — | 53 | 1 | no | — |
| 692 | C2×C8 | — | 53 | 1 | no | — |
| 693 | C2×C8 | — | 53 | 2 | no | — |
| 694 | C2×C8 | — | 106 | 1 | no | — |
| 695 | C2×C8 | — | 106 | 1 | no | — |
| 696 | C2×C8 | — | 106 | 1 | no | — |
| 697 | C2×C8 | — | 106 | 1 | no | — |
| 698 | C2×C8 | — | 106 | 1 | no | — |
| 699 | C2×C8 | — | 106 | 1 | no | — |
| 700 | C2×C8 | — | 106 | 1 | no | — |
| 701 | C2×C8 | — | 106 | 2 | no | — |
| 702 | C2×C8 | — | 212 | 2 | no | — |
| 703 | C2×C8 | — | 212 | 2 | no | — |
| 704 | C2×C8 | C22×#6157 | 1 | 1 | yes | characteristic |
| 705 | C4⋊C4 | — | 53 | 2 | no | — |
| 706 | C4⋊C4 | — | 106 | 2 | no | — |
| 707 | C4⋊C4 | — | 106 | 2 | no | — |
| 708 | C4⋊C4 | — | 212 | 2 | no | — |
| 709 | C22⋊C4 | — | 106 | 1 | no | — |
| 710 | C22⋊C4 | — | 212 | 2 | no | — |
| 711 | C42 | — | 106 | 1 | no | — |
| 712 | C42 | — | 106 | 1 | no | — |
| 713 | C42 | — | 106 | 1 | no | — |
| 714 | C42 | — | 212 | 2 | no | — |
| 715 | C23 | — | 53 | 1 | no | — |
| 716 | C23 | — | 106 | 2 | no | — |
| 717 | C23 | — | 106 | 1 | no | — |
| 718 | Q8 | — | 2 | 2 | no | — |
| 719 | Q8 | — | 2 | 2 | no | — |
| 720 | Q8 | — | 4 | 2 | no | — |
| 721 | Q8 | — | 53 | 2 | no | — |
| 722 | Q8 | — | 53 | 1 | no | — |
| 723 | Q8 | — | 106 | 1 | no | — |
| 724 | Q8 | — | 106 | 2 | no | — |
| 725 | Q8 | — | 106 | 2 | no | — |
| 726 | Q8 | — | 106 | 2 | no | — |
| 727 | Q8 | — | 212 | 2 | no | — |
| 728 | Q8 | — | 212 | 2 | no | — |
| 729 | Q8 | — | 212 | 2 | no | — |
| 730 | Q8 | — | 212 | 2 | no | — |
| 731 | Q8 | — | 212 | 2 | no | — |
| 732 | Q8 | C2×C22⋊#6157 | 1 | 2 | yes | — |
| 733 | Q8 | D4×#6157 | 1 | 1 | yes | characteristic |
| 734 | D4 | — | 2 | 1 | no | — |
| 735 | D4 | — | 2 | 2 | no | — |
| 736 | D4 | — | 4 | 2 | no | — |
| 737 | D4 | — | 53 | 2 | no | — |
| 738 | D4 | — | 53 | 1 | no | — |
| 739 | D4 | — | 106 | 2 | no | — |
| 740 | D4 | — | 106 | 1 | no | — |
| 741 | D4 | — | 106 | 2 | no | — |
| 742 | D4 | — | 106 | 1 | no | — |
| 743 | D4 | — | 106 | 2 | no | — |
| 744 | D4 | — | 106 | 1 | no | — |
| 745 | D4 | — | 106 | 2 | no | — |
| 746 | D4 | — | 106 | 1 | no | — |
| 747 | D4 | — | 212 | 2 | no | — |
| 748 | D4 | — | 212 | 2 | no | — |
| 749 | D4 | — | 212 | 2 | no | — |
| 750 | D4 | C2×C22⋊#6157 | 1 | 2 | yes | — |
| 751 | D4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 752 | C2×C4 | — | 2 | 1 | no | — |
| 753 | C2×C4 | — | 2 | 2 | no | — |
| 754 | C2×C4 | — | 2 | 2 | no | — |
| 755 | C2×C4 | — | 4 | 2 | no | — |
| 756 | C2×C4 | — | 4 | 2 | no | — |
| 757 | C2×C4 | — | 53 | 1 | no | — |
| 758 | C2×C4 | — | 53 | 1 | no | — |
| 759 | C2×C4 | — | 53 | 1 | no | — |
| 760 | C2×C4 | — | 53 | 1 | no | — |
| 761 | C2×C4 | — | 53 | 1 | no | — |
| 762 | C2×C4 | — | 848 | 2 | no | — |
| 763 | C2×C4 | — | 106 | 2 | no | — |
| 764 | C2×C4 | — | 106 | 1 | no | — |
| 765 | C2×C4 | — | 106 | 2 | no | — |
| 766 | C2×C4 | — | 106 | 1 | no | — |
| 767 | C2×C4 | — | 106 | 2 | no | — |
| 768 | C2×C4 | — | 106 | 1 | no | — |
| 769 | C2×C4 | — | 106 | 1 | no | — |
| 770 | C2×C4 | — | 106 | 2 | no | — |
| 771 | C2×C4 | — | 106 | 2 | no | — |
| 772 | C2×C4 | — | 106 | 2 | no | — |
| 773 | C2×C4 | — | 424 | 2 | no | — |
| 774 | C2×C4 | — | 212 | 2 | no | — |
| 775 | C2×C4 | — | 212 | 2 | no | — |
| 776 | C2×C4 | — | 212 | 2 | no | — |
| 777 | C2×C4 | — | 212 | 2 | no | — |
| 778 | C2×C4 | — | 212 | 2 | no | — |
| 779 | C2×C4 | — | 212 | 2 | no | — |
| 780 | C2×C4 | — | 212 | 2 | no | — |
| 781 | C2×C4 | — | 212 | 2 | no | — |
| 782 | C2×C4 | — | 212 | 1 | no | — |
| 783 | C2×C4 | — | 212 | 2 | no | — |
| 784 | C2×C4 | — | 212 | 2 | no | — |
| 785 | C2×C4 | C23×#6157 | 1 | 1 | yes | characteristic |
| 786 | C8 | — | 2 | 1 | no | — |
| 787 | C8 | — | 53 | 1 | no | — |
| 788 | C8 | — | 53 | 1 | no | — |
| 789 | C8 | — | 106 | 2 | no | — |
| 790 | C8 | — | 106 | 1 | no | — |
| 791 | C8 | — | 212 | 2 | no | — |
| 792 | C8 | — | 212 | 1 | no | — |
| 793 | C8 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 794 | C8 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 795 | C22 | — | 2 | 1 | no | — |
| 796 | C22 | — | 2 | 2 | no | — |
| 797 | C22 | — | 53 | 1 | no | — |
| 798 | C22 | — | 53 | 1 | no | — |
| 799 | C22 | — | 106 | 2 | no | — |
| 800 | C22 | — | 106 | 1 | no | — |
| 801 | C22 | — | 106 | 2 | no | — |
| 802 | C22 | — | 212 | 2 | no | — |
| 803 | C22 | — | 212 | 2 | no | — |
| 804 | C22 | — | 212 | 2 | no | — |
| 805 | C22 | #16811690 | 1 | 1 | yes | characteristic |
| 806 | C4 | — | 2 | 1 | no | — |
| 807 | C4 | — | 2 | 2 | no | — |
| 808 | C4 | — | 4 | 2 | no | — |
| 809 | C4 | — | 53 | 1 | no | — |
| 810 | C4 | — | 53 | 1 | no | — |
| 811 | C4 | — | 106 | 1 | no | — |
| 812 | C4 | — | 106 | 2 | no | — |
| 813 | C4 | — | 424 | 2 | no | — |
| 814 | C4 | — | 424 | 1 | no | — |
| 815 | C4 | — | 212 | 2 | no | — |
| 816 | C4 | — | 212 | 2 | no | — |
| 817 | C4 | C22×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 818 | C4 | C2×D4×#6157 | 1 | 1 | yes | characteristic |
| 819 | C2 | — | 2 | 1 | no | — |
| 820 | C2 | — | 4 | 1 | no | — |
| 821 | C2 | — | 4 | 2 | no | — |
| 822 | C2 | — | 53 | 2 | no | — |
| 823 | C2 | — | 106 | 1 | no | — |
| 824 | C2 | — | 212 | 1 | no | — |
| 825 | C2 | — | 212 | 2 | no | — |
| 826 | C2 | D4×C22⋊#6157 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D53⋊#444 | C2 | semidirect |
| 2. #20291478 | C2 | semidirect |
| 3. #20291337 | C2 | semidirect |
| 4. #20290877 | C2 | semidirect |
| 5. #20290863 | C2 | semidirect |
| 6. #20290755 | C2 | semidirect |
| 7. #20290714 | C2 | semidirect |
| 8. #20290603 | C2 | semidirect |
| 9. #20290562 | C2 | semidirect |
| 10. #20290493 | C2 | semidirect |
| 41. #16811440 | C4 | semidirect |
| 43. #16811439 | C4 | semidirect |
| 44. #16811438 | C4 | semidirect |
| 46. #16811437 | C4 | semidirect |
| 48. #16811436 | C4 | semidirect |
| 56. C53×#578 | C4 | semidirect |
| 99. #13133265 | C2×C4 | semidirect |
| 103. #13133264 | C2×C4 | semidirect |
| 104. #13133264 | C2×C4 | semidirect |
| 114. #13133250 | C2×C4 | semidirect |
| 119. #13133248 | C2×C4 | semidirect |
| 121. #13133247 | C2×C4 | semidirect |
| 136. C2×Dic212 | C2×C4 | semidirect |
| 138. C2×#11719925 | C2×C4 | semidirect |
| 152. #13133225 | C2×C4 | semidirect |
| 153. #13133224 | C2×C4 | semidirect |
| 155. #13133223 | C2×C4 | semidirect |
| 160. 2−1+4×C53 | C2×C4 | semidirect |
| 162. #137×C53 | C2×C4 | semidirect |
| 166. C2×Q16×C53 | C2×C4 | semidirect |
| 167. #131×C53 | C2×C4 | semidirect |
| 434. #578 | #6157 | semidirect |
| 470. C53 | #22465 | semidirect |
| 479. 2−1+4 | C2×#6157 | semidirect |
| 501. #137 | C2×#6157 | semidirect |
| 528. C2×Q16 | C2×#6157 | semidirect |
| 540. #131 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#444 | 2 |
| #20291478 | 2 |
| #20291337 | 2 |
| #20290877 | 2 |
| #20290863 | 2 |
| #20290755 | 2 |
| #20290714 | 2 |
| #20290603 | 2 |
| #20290562 | 2 |
| #20290493 | 2 |
| #578×D53 | 2 |
| #22465 | 53 |