Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1654 conjugacy classes of subgroups.
The subgroup lattice has 936 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D53⋊#568 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20291335 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#16811616 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×D53⋊#101 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20290755 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #20290419 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20290408 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#137×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #16811703 | — | 2 | 1 | no | — |
| 10 | #16811702 | — | 2 | 2 | no | — |
| 11 | #16811702 | — | 2 | 2 | no | — |
| 12 | #16811701 | — | 2 | 2 | no | — |
| 13 | #16811701 | — | 2 | 1 | no | — |
| 14 | D53⋊#131 | — | 2 | 2 | no | — |
| 15 | D53⋊#131 | C22 | 1 | 4 | yes | — |
| 16 | C2×D53⋊M16 | — | 2 | 2 | no | — |
| 17 | C2×D53⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×D53⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×D53⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#13133296 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16811616 | — | 2 | 2 | no | — |
| 22 | #16811616 | — | 2 | 2 | no | — |
| 23 | #16811616 | — | 2 | 1 | no | — |
| 24 | #16811615 | — | 2 | 1 | no | — |
| 25 | #16811614 | C22 | 1 | 4 | yes | — |
| 26 | #16811613 | — | 2 | 2 | no | — |
| 27 | C2×#13133280 | C22 | 1 | 4 | yes | complemented |
| 28 | D53⋊#101 | — | 2 | 2 | no | — |
| 29 | D53⋊#101 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×#13133278 | — | 2 | 2 | no | — |
| 31 | #16811502 | C22 | 1 | 4 | yes | complemented |
| 32 | #16811498 | C22 | 1 | 4 | yes | complemented |
| 33 | C2×#41×D53 | C22 | 1 | 1 | yes | characteristic |
| 34 | C22×Q8×D53 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#13133250 | C4 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×#13133249 | — | 2 | 1 | no | — |
| 37 | C2×#13133248 | C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×#13133247 | C4 | 1 | 1 | yes | characteristic, complemented |
| 39 | C2×#13133246 | — | 2 | 1 | no | — |
| 40 | #137×D53 | — | 2 | 2 | no | — |
| 41 | #137×D53 | — | 2 | 2 | no | — |
| 42 | #137×D53 | C4 | 1 | 4 | yes | complemented |
| 43 | #137×D53 | C22 | 1 | 4 | yes | — |
| 44 | C2×Q16×D53 | — | 2 | 1 | no | — |
| 45 | C2×SD16×D53 | — | 2 | 1 | no | — |
| 46 | C2×M16×D53 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×#137×C53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 48 | #13133305 | — | 2 | 4 | no | — |
| 49 | #13133305 | — | 2 | 4 | no | — |
| 50 | #13133304 | — | 2 | 8 | no | — |
| 51 | #13133304 | — | 2 | 4 | no | — |
| 52 | #13133304 | — | 2 | 4 | no | — |
| 53 | #13133304 | — | 2 | 8 | no | — |
| 54 | C2×#11719936 | — | 2 | 4 | no | — |
| 55 | C2×#11719936 | — | 2 | 1 | no | — |
| 56 | C2×#11719936 | — | 2 | 1 | no | — |
| 57 | C2×#11719936 | — | 2 | 1 | no | — |
| 58 | D53⋊M16 | — | 2 | 4 | no | — |
| 59 | D53⋊M16 | — | 2 | 4 | no | — |
| 60 | D53⋊M16 | — | 2 | 4 | no | — |
| 61 | D53⋊M16 | — | 2 | 1 | no | — |
| 62 | D53⋊M16 | — | 2 | 1 | no | — |
| 63 | D53⋊M16 | — | 2 | 1 | no | — |
| 64 | D53⋊M16 | — | 2 | 1 | no | — |
| 65 | D53⋊M16 | — | 2 | 1 | no | — |
| 66 | D53⋊M16 | — | 2 | 1 | no | — |
| 67 | D53⋊M16 | — | 2 | 1 | no | — |
| 68 | D53⋊M16 | D4 | 1 | 2 | yes | — |
| 69 | D53⋊M16 | D4 | 1 | 2 | yes | — |
| 70 | D53⋊M16 | D4 | 1 | 2 | yes | — |
| 71 | D53⋊M16 | C23 | 1 | 2 | yes | — |
| 72 | D53⋊M16 | C23 | 1 | 2 | yes | — |
| 73 | C2×#11719940 | — | 2 | 4 | no | — |
| 74 | C2×#11719940 | — | 2 | 1 | no | — |
| 75 | C2×#11719940 | — | 2 | 1 | no | — |
| 76 | C2×#11719940 | D4 | 1 | 2 | yes | — |
| 77 | C2×D53⋊C8 | — | 2 | 4 | no | — |
| 78 | C2×D53⋊C8 | — | 2 | 1 | no | — |
| 79 | C2×D53⋊C8 | — | 2 | 1 | no | — |
| 80 | C2×D53⋊C8 | C23 | 1 | 2 | yes | — |
| 81 | #13133296 | — | 2 | 1 | no | — |
| 82 | #13133296 | — | 2 | 1 | no | — |
| 83 | #13133296 | — | 2 | 1 | no | — |
| 84 | #13133296 | — | 2 | 1 | no | — |
| 85 | C2×C4⋊#6157 | C23 | 1 | 2 | yes | — |
| 86 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 87 | C2×C4×#6157 | — | 2 | 1 | no | — |
| 88 | #13133280 | — | 2 | 8 | no | — |
| 89 | #13133280 | — | 2 | 4 | no | — |
| 90 | #13133279 | — | 2 | 4 | no | — |
| 91 | #13133278 | — | 2 | 8 | no | — |
| 92 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 93 | C2×#11719945 | — | 2 | 1 | no | — |
| 94 | C2×#11719945 | C2×C4 | 1 | 1 | yes | characteristic |
| 95 | C2×#11719947 | — | 2 | 1 | no | — |
| 96 | C2×#11719947 | D4 | 1 | 1 | yes | characteristic |
| 97 | #41×D53 | — | 2 | 1 | no | — |
| 98 | #41×D53 | — | 2 | 1 | no | — |
| 99 | #41×D53 | — | 2 | 1 | no | — |
| 100 | #41×D53 | — | 2 | 1 | no | — |
| 101 | #41×D53 | C2×C4 | 1 | 2 | yes | — |
| 102 | #41×D53 | D4 | 1 | 2 | yes | — |
| 103 | #41×D53 | D4 | 1 | 2 | yes | — |
| 104 | #41×D53 | C23 | 1 | 2 | yes | — |
| 105 | C22×Dic106 | — | 2 | 1 | no | — |
| 106 | C22×Dic106 | C2×C4 | 1 | 1 | yes | characteristic |
| 107 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 108 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 109 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 110 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 111 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 112 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 113 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 114 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 115 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 116 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 117 | C2×Q8×D53 | C2×C4 | 1 | 2 | yes | — |
| 118 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 119 | C2×Q8×D53 | C23 | 1 | 2 | yes | — |
| 120 | C2×D4×D53 | — | 2 | 1 | no | — |
| 121 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 122 | C22×C4×D53 | — | 2 | 1 | no | — |
| 123 | C22×C4×D53 | — | 2 | 1 | no | — |
| 124 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 125 | #13133250 | — | 2 | 2 | no | — |
| 126 | #13133250 | C2×C4 | 1 | 4 | yes | — |
| 127 | #13133249 | — | 2 | 4 | no | — |
| 128 | #13133249 | — | 2 | 4 | no | — |
| 129 | #13133248 | — | 2 | 2 | no | — |
| 130 | #13133248 | C2×C4 | 1 | 4 | yes | — |
| 131 | #13133247 | — | 2 | 2 | no | — |
| 132 | #13133247 | C2×C4 | 1 | 4 | yes | — |
| 133 | #13133246 | — | 2 | 4 | no | — |
| 134 | #13133246 | — | 2 | 4 | no | — |
| 135 | C2×Dic212 | — | 2 | 1 | no | — |
| 136 | C2×#11719925 | — | 2 | 1 | no | — |
| 137 | C2×#11719925 | — | 2 | 1 | no | — |
| 138 | Q16×D53 | — | 2 | 4 | no | — |
| 139 | Q16×D53 | — | 2 | 4 | no | — |
| 140 | C2×#11719913 | — | 2 | 1 | no | — |
| 141 | C2×#11719923 | — | 2 | 1 | no | — |
| 142 | C2×#11719924 | — | 2 | 1 | no | — |
| 143 | SD16×D53 | — | 2 | 4 | no | — |
| 144 | SD16×D53 | — | 2 | 4 | no | — |
| 145 | C2×#11719917 | C2×C4 | 1 | 1 | yes | characteristic |
| 146 | C2×#11719912 | — | 2 | 1 | no | — |
| 147 | M16×D53 | — | 2 | 1 | no | — |
| 148 | M16×D53 | — | 2 | 1 | no | — |
| 149 | M16×D53 | C2×C4 | 1 | 2 | yes | — |
| 150 | M16×D53 | C23 | 1 | 2 | yes | — |
| 151 | C2×C8×D53 | — | 2 | 1 | no | — |
| 152 | C2×#41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 153 | C22×Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 154 | #137×C53 | — | 2 | 2 | no | — |
| 155 | #137×C53 | C2×C4 | 1 | 4 | yes | — |
| 156 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 157 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 158 | C2×M16×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 159 | C23×D53 | — | 2 | 1 | no | — |
| 160 | C23×D53 | #41 | 1 | 1 | yes | characteristic |
| 161 | C22×#6157 | — | 2 | 2 | no | — |
| 162 | #41×C53 | — | 2 | 1 | no | — |
| 163 | #41×C53 | — | 2 | 1 | no | — |
| 164 | #41×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 165 | #41×C53 | C22×C4 | 1 | 2 | yes | — |
| 166 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 167 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 168 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 169 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 170 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 171 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 172 | C2×Q8×C53 | C22×C4 | 1 | 2 | yes | — |
| 173 | C2×D4×C53 | — | 2 | 1 | no | — |
| 174 | C2×D4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 175 | C22×C4×C53 | — | 2 | 1 | no | — |
| 176 | C22×C4×C53 | — | 2 | 1 | no | — |
| 177 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 178 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 179 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 180 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 181 | C22×Dic53 | — | 2 | 1 | no | — |
| 182 | C22×Dic53 | — | 2 | 1 | no | — |
| 183 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | #11719949 | — | 2 | 1 | no | — |
| 185 | #11719949 | — | 2 | 1 | no | — |
| 186 | #11719949 | C22⋊C4 | 1 | 2 | yes | — |
| 187 | #11719949 | C2×D4 | 1 | 2 | yes | — |
| 188 | Q8×D53 | — | 2 | 1 | no | — |
| 189 | Q8×D53 | — | 2 | 1 | no | — |
| 190 | Q8×D53 | — | 2 | 2 | no | — |
| 191 | Q8×D53 | — | 2 | 2 | no | — |
| 192 | Q8×D53 | — | 2 | 2 | no | — |
| 193 | Q8×D53 | — | 2 | 2 | no | — |
| 194 | Q8×D53 | — | 2 | 2 | no | — |
| 195 | Q8×D53 | — | 2 | 2 | no | — |
| 196 | Q8×D53 | — | 2 | 2 | no | — |
| 197 | Q8×D53 | — | 2 | 2 | no | — |
| 198 | Q8×D53 | — | 4 | 1 | no | — |
| 199 | Q8×D53 | — | 4 | 1 | no | — |
| 200 | Q8×D53 | — | 4 | 1 | no | — |
| 201 | Q8×D53 | — | 4 | 1 | no | — |
| 202 | Q8×D53 | — | 4 | 1 | no | — |
| 203 | Q8×D53 | — | 4 | 1 | no | — |
| 204 | Q8×D53 | — | 4 | 1 | no | — |
| 205 | Q8×D53 | — | 4 | 1 | no | — |
| 206 | Q8×D53 | C22⋊C4 | 1 | 2 | yes | — |
| 207 | Q8×D53 | C2×D4 | 1 | 2 | yes | — |
| 208 | #11719947 | — | 2 | 2 | no | — |
| 209 | #11719947 | — | 2 | 2 | no | — |
| 210 | #11719947 | — | 2 | 2 | no | — |
| 211 | #11719947 | — | 2 | 2 | no | — |
| 212 | #11719947 | — | 2 | 1 | no | — |
| 213 | #11719947 | — | 2 | 1 | no | — |
| 214 | #11719947 | C22⋊C4 | 1 | 2 | yes | — |
| 215 | #11719947 | C2×D4 | 1 | 2 | yes | — |
| 216 | D4×D53 | — | 2 | 2 | no | — |
| 217 | D4×D53 | — | 2 | 2 | no | — |
| 218 | D4×D53 | — | 2 | 2 | no | — |
| 219 | D4×D53 | — | 2 | 2 | no | — |
| 220 | D4×D53 | — | 2 | 1 | no | — |
| 221 | D4×D53 | — | 2 | 1 | no | — |
| 222 | D4×D53 | C22⋊C4 | 1 | 2 | yes | — |
| 223 | D4×D53 | C2×D4 | 1 | 2 | yes | — |
| 224 | #11719945 | — | 2 | 1 | no | — |
| 225 | #11719945 | — | 2 | 1 | no | — |
| 226 | #11719945 | — | 2 | 2 | no | — |
| 227 | #11719945 | — | 2 | 2 | no | — |
| 228 | #11719945 | — | 2 | 2 | no | — |
| 229 | #11719945 | — | 2 | 2 | no | — |
| 230 | #11719945 | C22⋊C4 | 1 | 2 | yes | — |
| 231 | #11719945 | C22×C4 | 1 | 2 | yes | — |
| 232 | C2×D212 | — | 2 | 1 | no | — |
| 233 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×D53 | — | 2 | 1 | no | — |
| 235 | C2×C4×D53 | — | 2 | 1 | no | — |
| 236 | C2×C4×D53 | — | 2 | 1 | no | — |
| 237 | C2×C4×D53 | — | 2 | 2 | no | — |
| 238 | C2×C4×D53 | — | 2 | 2 | no | — |
| 239 | C2×C4×D53 | — | 2 | 2 | no | — |
| 240 | C2×C4×D53 | — | 2 | 2 | no | — |
| 241 | C2×C4×D53 | — | 2 | 2 | no | — |
| 242 | C2×C4×D53 | — | 2 | 2 | no | — |
| 243 | C2×C4×D53 | — | 4 | 1 | no | — |
| 244 | C2×C4×D53 | — | 4 | 1 | no | — |
| 245 | C2×C4×D53 | — | 4 | 1 | no | — |
| 246 | C2×C4×D53 | — | 4 | 1 | no | — |
| 247 | C2×C4×D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 252 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C2×C4×D53 | #41 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×D53 | #41 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×D53 | #41 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 259 | C2×Dic106 | — | 2 | 1 | no | — |
| 260 | C2×Dic106 | — | 2 | 1 | no | — |
| 261 | C2×Dic106 | — | 2 | 1 | no | — |
| 262 | C2×Dic106 | — | 2 | 1 | no | — |
| 263 | C2×Dic106 | — | 2 | 1 | no | — |
| 264 | C2×Dic106 | — | 2 | 1 | no | — |
| 265 | C2×Dic106 | — | 2 | 2 | no | — |
| 266 | C2×Dic106 | — | 2 | 2 | no | — |
| 267 | C2×Dic106 | — | 4 | 1 | no | — |
| 268 | C2×Dic106 | — | 4 | 1 | no | — |
| 269 | C2×Dic106 | — | 4 | 1 | no | — |
| 270 | C2×Dic106 | — | 4 | 1 | no | — |
| 271 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 272 | C2×Dic106 | C22×C4 | 1 | 2 | yes | — |
| 273 | C22⋊#6157 | — | 4 | 1 | no | — |
| 274 | C22⋊#6157 | — | 4 | 1 | no | — |
| 275 | #11719940 | — | 2 | 8 | no | — |
| 276 | #11719940 | — | 2 | 2 | no | — |
| 277 | #11719940 | — | 2 | 2 | no | — |
| 278 | #11719940 | — | 2 | 2 | no | — |
| 279 | #11719940 | — | 2 | 2 | no | — |
| 280 | #11719940 | — | 4 | 1 | no | — |
| 281 | #11719940 | C2×D4 | 1 | 4 | yes | — |
| 282 | C2×#88324 | — | 2 | 8 | no | — |
| 283 | C2×#88324 | — | 2 | 2 | no | — |
| 284 | C2×#88324 | — | 2 | 2 | no | — |
| 285 | C2×#88324 | — | 4 | 1 | no | — |
| 286 | C4⋊#6157 | — | 2 | 2 | no | — |
| 287 | C4⋊#6157 | — | 2 | 2 | no | — |
| 288 | C4×#6157 | — | 4 | 1 | no | — |
| 289 | C4×#6157 | — | 4 | 1 | no | — |
| 290 | #11719936 | — | 2 | 8 | no | — |
| 291 | #11719936 | — | 2 | 2 | no | — |
| 292 | #11719936 | — | 2 | 2 | no | — |
| 293 | #11719936 | — | 2 | 2 | no | — |
| 294 | #11719936 | — | 2 | 2 | no | — |
| 295 | #11719936 | — | 2 | 2 | no | — |
| 296 | #11719936 | — | 4 | 1 | no | — |
| 297 | D53⋊C8 | — | 2 | 8 | no | — |
| 298 | D53⋊C8 | — | 2 | 2 | no | — |
| 299 | D53⋊C8 | — | 2 | 2 | no | — |
| 300 | D53⋊C8 | — | 2 | 2 | no | — |
| 301 | D53⋊C8 | — | 2 | 2 | no | — |
| 302 | D53⋊C8 | — | 4 | 1 | no | — |
| 303 | D53⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 304 | Q16×C53 | — | 2 | 4 | no | — |
| 305 | SD16×C53 | — | 2 | 4 | no | — |
| 306 | M16×C53 | — | 2 | 1 | no | — |
| 307 | M16×C53 | C22×C4 | 1 | 2 | yes | — |
| 308 | C2×C8×C53 | — | 2 | 1 | no | — |
| 309 | #11719925 | — | 2 | 4 | no | — |
| 310 | #11719925 | — | 2 | 4 | no | — |
| 311 | #11719924 | — | 2 | 4 | no | — |
| 312 | #11719923 | — | 2 | 4 | no | — |
| 313 | #11719917 | — | 2 | 1 | no | — |
| 314 | #11719917 | C22×C4 | 1 | 2 | yes | — |
| 315 | C2×#88322 | — | 2 | 1 | no | — |
| 316 | Dic212 | — | 2 | 4 | no | — |
| 317 | #11719913 | — | 2 | 4 | no | — |
| 318 | #11719912 | — | 2 | 2 | no | — |
| 319 | #11719912 | — | 2 | 2 | no | — |
| 320 | C8×D53 | — | 2 | 2 | no | — |
| 321 | C8×D53 | — | 2 | 2 | no | — |
| 322 | C23×C53 | — | 2 | 1 | no | — |
| 323 | C23×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 324 | C22×D53 | — | 2 | 1 | no | — |
| 325 | C22×D53 | — | 2 | 2 | no | — |
| 326 | C22×D53 | — | 2 | 2 | no | — |
| 327 | C22×D53 | — | 4 | 2 | no | — |
| 328 | C22×D53 | — | 8 | 2 | no | — |
| 329 | C22×D53 | C4×D4 | 1 | 1 | yes | characteristic |
| 330 | C22×D53 | #121 | 1 | 1 | yes | characteristic |
| 331 | C22×D53 | #121 | 1 | 1 | yes | characteristic |
| 332 | C22×D53 | #123 | 1 | 1 | yes | characteristic |
| 333 | C22×D53 | #123 | 1 | 1 | yes | characteristic |
| 334 | C22×D53 | C2×#41 | 1 | 1 | yes | characteristic |
| 335 | C2×#6157 | — | 4 | 2 | no | — |
| 336 | C2×#6157 | — | 8 | 2 | no | — |
| 337 | Q8×C53 | — | 2 | 1 | no | — |
| 338 | Q8×C53 | — | 2 | 2 | no | — |
| 339 | Q8×C53 | — | 2 | 2 | no | — |
| 340 | Q8×C53 | — | 4 | 1 | no | — |
| 341 | Q8×C53 | — | 4 | 1 | no | — |
| 342 | Q8×C53 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 343 | D4×C53 | — | 2 | 2 | no | — |
| 344 | D4×C53 | — | 2 | 2 | no | — |
| 345 | D4×C53 | — | 2 | 1 | no | — |
| 346 | D4×C53 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 347 | C2×C4×C53 | — | 2 | 1 | no | — |
| 348 | C2×C4×C53 | — | 2 | 2 | no | — |
| 349 | C2×C4×C53 | — | 2 | 2 | no | — |
| 350 | C2×C4×C53 | — | 2 | 2 | no | — |
| 351 | C2×C4×C53 | — | 4 | 1 | no | — |
| 352 | C2×C4×C53 | — | 4 | 1 | no | — |
| 353 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 354 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 355 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 356 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 357 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 358 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 359 | C22⋊D53 | — | 2 | 2 | no | — |
| 360 | C22⋊D53 | — | 2 | 2 | no | — |
| 361 | C22⋊D53 | — | 2 | 2 | no | — |
| 362 | C22⋊D53 | — | 2 | 2 | no | — |
| 363 | C22⋊D53 | — | 2 | 2 | no | — |
| 364 | C22⋊D53 | — | 2 | 2 | no | — |
| 365 | C2×Dic53 | — | 2 | 1 | no | — |
| 366 | C2×Dic53 | — | 2 | 2 | no | — |
| 367 | C2×Dic53 | — | 2 | 2 | no | — |
| 368 | C2×Dic53 | — | 2 | 2 | no | — |
| 369 | C2×Dic53 | — | 4 | 1 | no | — |
| 370 | C2×Dic53 | — | 4 | 1 | no | — |
| 371 | C2×Dic53 | C4×D4 | 1 | 1 | yes | characteristic |
| 372 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 373 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 374 | C2×Dic53 | #121 | 1 | 1 | yes | characteristic |
| 375 | C2×Dic53 | #121 | 1 | 1 | yes | characteristic |
| 376 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 377 | D212 | — | 2 | 2 | no | — |
| 378 | D212 | — | 2 | 2 | no | — |
| 379 | D212 | — | 2 | 1 | no | — |
| 380 | D212 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 381 | C4×D53 | — | 2 | 2 | no | — |
| 382 | C4×D53 | — | 2 | 2 | no | — |
| 383 | C4×D53 | — | 2 | 2 | no | — |
| 384 | C4×D53 | — | 2 | 2 | no | — |
| 385 | C4×D53 | — | 2 | 2 | no | — |
| 386 | C4×D53 | — | 2 | 2 | no | — |
| 387 | C4×D53 | — | 4 | 2 | no | — |
| 388 | C4×D53 | — | 4 | 2 | no | — |
| 389 | C4×D53 | — | 4 | 2 | no | — |
| 390 | C4×D53 | — | 4 | 2 | no | — |
| 391 | C4×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 392 | C4×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 393 | C4×D53 | C4×D4 | 1 | 1 | yes | characteristic |
| 394 | C4×D53 | C4×D4 | 1 | 1 | yes | characteristic |
| 395 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 396 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 397 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 398 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 399 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 400 | C4×D53 | #121 | 1 | 1 | yes | characteristic |
| 401 | C4×D53 | #123 | 1 | 1 | yes | characteristic |
| 402 | C4×D53 | #123 | 1 | 1 | yes | characteristic |
| 403 | C4×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 404 | C4×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 405 | C4×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 406 | C4×D53 | C2×#41 | 1 | 1 | yes | characteristic |
| 407 | Dic106 | — | 2 | 1 | no | — |
| 408 | Dic106 | — | 2 | 2 | no | — |
| 409 | Dic106 | — | 2 | 2 | no | — |
| 410 | Dic106 | — | 2 | 2 | no | — |
| 411 | Dic106 | — | 2 | 2 | no | — |
| 412 | Dic106 | — | 4 | 1 | no | — |
| 413 | Dic106 | — | 4 | 1 | no | — |
| 414 | Dic106 | — | 4 | 2 | no | — |
| 415 | Dic106 | — | 4 | 2 | no | — |
| 416 | Dic106 | — | 4 | 2 | no | — |
| 417 | Dic106 | — | 4 | 2 | no | — |
| 418 | Dic106 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 419 | #88324 | — | 2 | 4 | no | — |
| 420 | #88324 | — | 2 | 4 | no | — |
| 421 | #88324 | — | 4 | 2 | no | — |
| 422 | C8×C53 | — | 2 | 2 | no | — |
| 423 | #88322 | — | 2 | 2 | no | — |
| 424 | #21006 | — | 53 | 1 | no | maximal, Sylow |
| 425 | C22×C53 | — | 2 | 2 | no | — |
| 426 | C22×C53 | — | 4 | 1 | no | — |
| 427 | C22×C53 | — | 8 | 1 | no | — |
| 428 | C22×C53 | #386 | 1 | 1 | yes | characteristic |
| 429 | C22×C53 | #386 | 1 | 1 | yes | characteristic |
| 430 | C22×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 431 | C2×D53 | — | 2 | 2 | no | — |
| 432 | C2×D53 | — | 2 | 2 | no | — |
| 433 | C2×D53 | — | 2 | 2 | no | — |
| 434 | C2×D53 | — | 2 | 2 | no | — |
| 435 | C2×D53 | — | 4 | 1 | no | — |
| 436 | C2×D53 | — | 4 | 1 | no | — |
| 437 | C2×D53 | — | 4 | 1 | no | — |
| 438 | C2×D53 | — | 4 | 4 | no | — |
| 439 | C2×D53 | — | 8 | 2 | no | — |
| 440 | C2×D53 | — | 8 | 1 | no | — |
| 441 | C2×D53 | #386 | 1 | 1 | yes | characteristic |
| 442 | C2×D53 | #386 | 1 | 1 | yes | characteristic |
| 443 | C2×D53 | C2×#121 | 1 | 1 | yes | characteristic |
| 444 | C2×D53 | C2×#123 | 1 | 1 | yes | characteristic |
| 445 | #6157 | — | 8 | 2 | no | — |
| 446 | C4×C53 | — | 2 | 2 | no | — |
| 447 | C4×C53 | — | 4 | 2 | no | — |
| 448 | C4×C53 | #386 | 1 | 1 | yes | characteristic |
| 449 | C4×C53 | #386 | 1 | 1 | yes | characteristic |
| 450 | C4×C53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 451 | C4×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 452 | Dic53 | — | 2 | 2 | no | — |
| 453 | Dic53 | — | 4 | 2 | no | — |
| 454 | Dic53 | #386 | 1 | 1 | yes | characteristic |
| 455 | Dic53 | #386 | 1 | 1 | yes | characteristic |
| 456 | Dic53 | C2×#120 | 1 | 1 | yes | characteristic |
| 457 | Dic53 | C2×#121 | 1 | 1 | yes | characteristic |
| 458 | C22×#137 | — | 53 | 1 | no | — |
| 459 | C2×#568 | — | 53 | 1 | no | — |
| 460 | #2896 | — | 53 | 1 | no | — |
| 461 | C2×#419 | — | 53 | 1 | no | — |
| 462 | C22×#101 | — | 53 | 1 | no | — |
| 463 | #1908 | — | 53 | 8 | no | — |
| 464 | #1742 | — | 53 | 1 | no | — |
| 465 | #1738 | — | 53 | 1 | no | — |
| 466 | C2×C53 | — | 2 | 1 | no | — |
| 467 | C2×C53 | — | 2 | 1 | no | — |
| 468 | C2×C53 | — | 2 | 1 | no | — |
| 469 | C2×C53 | — | 4 | 2 | no | — |
| 470 | C2×C53 | C2×#386 | 1 | 1 | yes | characteristic |
| 471 | D53 | — | 2 | 1 | no | — |
| 472 | D53 | — | 2 | 1 | no | — |
| 473 | D53 | — | 2 | 1 | no | — |
| 474 | D53 | — | 4 | 2 | no | — |
| 475 | D53 | #3069 | 1 | 2 | yes | — |
| 476 | C22×#41 | — | 53 | 1 | no | — |
| 477 | C23×Q8 | — | 53 | 1 | no | — |
| 478 | C2×#137 | — | 53 | 1 | no | — |
| 479 | C2×#137 | — | 53 | 1 | no | — |
| 480 | C2×#137 | — | 53 | 4 | no | — |
| 481 | C2×#137 | — | 53 | 4 | no | — |
| 482 | C2×#137 | — | 53 | 1 | no | — |
| 483 | C2×#137 | — | 106 | 1 | no | — |
| 484 | C2×#137 | — | 106 | 1 | no | — |
| 485 | C2×#137 | — | 106 | 2 | no | — |
| 486 | C2×#137 | — | 106 | 2 | no | — |
| 487 | C2×#137 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 488 | C22×Q16 | — | 106 | 1 | no | — |
| 489 | C22×SD16 | — | 106 | 1 | no | — |
| 490 | #568 | — | 106 | 2 | no | — |
| 491 | #568 | — | 106 | 2 | no | — |
| 492 | #568 | — | 106 | 1 | no | — |
| 493 | #568 | — | 106 | 2 | no | — |
| 494 | #568 | — | 106 | 1 | no | — |
| 495 | C2×#131 | — | 53 | 4 | no | — |
| 496 | C2×#131 | — | 106 | 2 | no | — |
| 497 | C22×M16 | — | 53 | 1 | no | — |
| 498 | C22×M16 | — | 53 | 1 | no | — |
| 499 | C22×M16 | — | 53 | 1 | no | — |
| 500 | C22×M16 | — | 53 | 1 | no | — |
| 501 | C22×M16 | — | 106 | 2 | no | — |
| 502 | C2×#117 | — | 53 | 1 | no | — |
| 503 | #419 | — | 106 | 2 | no | — |
| 504 | #419 | — | 106 | 2 | no | — |
| 505 | #419 | — | 106 | 1 | no | — |
| 506 | #418 | — | 106 | 1 | no | — |
| 507 | #417 | — | 53 | 4 | no | — |
| 508 | #416 | — | 106 | 2 | no | — |
| 509 | C2×#103 | — | 53 | 4 | no | — |
| 510 | C2×#101 | — | 53 | 4 | no | — |
| 511 | C2×#101 | — | 106 | 2 | no | — |
| 512 | C2×#101 | — | 106 | 2 | no | — |
| 513 | #343 | — | 53 | 4 | no | — |
| 514 | #341 | — | 53 | 4 | no | — |
| 515 | C53 | #21006 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 516 | C2×#41 | — | 53 | 2 | no | — |
| 517 | C2×#41 | — | 53 | 2 | no | — |
| 518 | C2×#41 | — | 53 | 2 | no | — |
| 519 | C2×#41 | — | 53 | 2 | no | — |
| 520 | C2×#41 | — | 53 | 1 | no | — |
| 521 | C2×#41 | — | 53 | 1 | no | — |
| 522 | C2×#41 | — | 53 | 1 | no | — |
| 523 | C2×#41 | — | 106 | 1 | no | — |
| 524 | C2×#41 | — | 106 | 1 | no | — |
| 525 | C2×#41 | — | 106 | 1 | no | — |
| 526 | C2×#41 | — | 106 | 1 | no | — |
| 527 | C2×#41 | — | 106 | 1 | no | — |
| 528 | C2×#41 | — | 106 | 1 | no | — |
| 529 | C2×#41 | C2×#6157 | 1 | 1 | yes | characteristic |
| 530 | C22×Q8 | — | 53 | 1 | no | — |
| 531 | C22×Q8 | — | 53 | 2 | no | — |
| 532 | C22×Q8 | — | 53 | 2 | no | — |
| 533 | C22×Q8 | — | 53 | 1 | no | — |
| 534 | C22×Q8 | — | 106 | 1 | no | — |
| 535 | C22×Q8 | — | 106 | 1 | no | — |
| 536 | C22×Q8 | — | 106 | 1 | no | — |
| 537 | C22×Q8 | — | 106 | 1 | no | — |
| 538 | C22×Q8 | — | 106 | 1 | no | — |
| 539 | C22×Q8 | — | 106 | 1 | no | — |
| 540 | C22×Q8 | — | 106 | 1 | no | — |
| 541 | C22×Q8 | — | 106 | 1 | no | — |
| 542 | C22×Q8 | — | 106 | 1 | no | — |
| 543 | C22×Q8 | — | 106 | 1 | no | — |
| 544 | C22×Q8 | — | 106 | 1 | no | — |
| 545 | C22×Q8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 546 | C22×D4 | — | 53 | 1 | no | — |
| 547 | C22×D4 | — | 106 | 1 | no | — |
| 548 | C23×C4 | — | 53 | 1 | no | — |
| 549 | C23×C4 | — | 106 | 1 | no | — |
| 550 | C23×C4 | — | 106 | 1 | no | — |
| 551 | #137 | — | 2 | 2 | no | — |
| 552 | #137 | — | 53 | 4 | no | — |
| 553 | #137 | — | 53 | 4 | no | — |
| 554 | #137 | — | 53 | 4 | no | — |
| 555 | #137 | — | 106 | 2 | no | — |
| 556 | #137 | — | 106 | 4 | no | — |
| 557 | #137 | — | 106 | 4 | no | — |
| 558 | #137 | — | 106 | 4 | no | — |
| 559 | #137 | — | 106 | 4 | no | — |
| 560 | #137 | — | 106 | 2 | no | — |
| 561 | #137 | — | 106 | 2 | no | — |
| 562 | #137 | C2×#6157 | 1 | 4 | yes | — |
| 563 | C2×Q16 | — | 2 | 1 | no | — |
| 564 | C2×Q16 | — | 106 | 1 | no | — |
| 565 | C2×Q16 | — | 106 | 4 | no | — |
| 566 | C2×Q16 | — | 106 | 4 | no | — |
| 567 | C2×Q16 | — | 106 | 1 | no | — |
| 568 | C2×Q16 | — | 106 | 1 | no | — |
| 569 | C2×SD16 | — | 2 | 1 | no | — |
| 570 | C2×SD16 | — | 106 | 1 | no | — |
| 571 | C2×SD16 | — | 106 | 4 | no | — |
| 572 | C2×SD16 | — | 106 | 4 | no | — |
| 573 | C2×SD16 | — | 106 | 1 | no | — |
| 574 | C2×SD16 | — | 106 | 1 | no | — |
| 575 | #131 | — | 106 | 8 | no | — |
| 576 | #131 | — | 106 | 4 | no | — |
| 577 | #131 | — | 106 | 4 | no | — |
| 578 | #131 | — | 106 | 8 | no | — |
| 579 | #131 | — | 106 | 4 | no | — |
| 580 | #131 | — | 106 | 4 | no | — |
| 581 | C2×M16 | — | 53 | 2 | no | — |
| 582 | C2×M16 | — | 53 | 2 | no | — |
| 583 | C2×M16 | — | 53 | 2 | no | — |
| 584 | C2×M16 | — | 53 | 2 | no | — |
| 585 | C2×M16 | — | 53 | 2 | no | — |
| 586 | C2×M16 | — | 53 | 1 | no | — |
| 587 | C2×M16 | — | 53 | 2 | no | — |
| 588 | C2×M16 | — | 53 | 2 | no | — |
| 589 | C2×M16 | — | 53 | 2 | no | — |
| 590 | C2×M16 | — | 106 | 1 | no | — |
| 591 | C2×M16 | — | 106 | 4 | no | — |
| 592 | C2×M16 | — | 106 | 1 | no | — |
| 593 | C2×M16 | — | 106 | 1 | no | — |
| 594 | C2×M16 | — | 106 | 1 | no | — |
| 595 | C2×M16 | — | 106 | 1 | no | — |
| 596 | C2×M16 | — | 106 | 1 | no | — |
| 597 | C2×M16 | — | 106 | 1 | no | — |
| 598 | C2×M16 | — | 106 | 1 | no | — |
| 599 | C2×M16 | — | 106 | 1 | no | — |
| 600 | C2×M16 | — | 106 | 1 | no | — |
| 601 | C2×M16 | — | 106 | 4 | no | — |
| 602 | C2×M16 | — | 106 | 4 | no | — |
| 603 | C2×M16 | — | 106 | 4 | no | — |
| 604 | C2×M16 | — | 106 | 4 | no | — |
| 605 | C2×M16 | — | 106 | 1 | no | — |
| 606 | C2×M16 | — | 106 | 1 | no | — |
| 607 | C2×M16 | — | 106 | 1 | no | — |
| 608 | C2×M16 | — | 106 | 1 | no | — |
| 609 | C2×M16 | — | 106 | 1 | no | — |
| 610 | C2×M16 | C2×#6157 | 1 | 1 | yes | characteristic |
| 611 | C22×C8 | — | 53 | 2 | no | — |
| 612 | C22×C8 | — | 106 | 1 | no | — |
| 613 | C22×C8 | — | 106 | 4 | no | — |
| 614 | C22×C8 | — | 106 | 1 | no | — |
| 615 | C22×C8 | — | 106 | 1 | no | — |
| 616 | #117 | — | 106 | 1 | no | — |
| 617 | #117 | — | 106 | 1 | no | — |
| 618 | #117 | — | 106 | 1 | no | — |
| 619 | #117 | — | 106 | 1 | no | — |
| 620 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 621 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 622 | C2×C42 | — | 106 | 1 | no | — |
| 623 | #103 | — | 106 | 8 | no | — |
| 624 | #103 | — | 106 | 4 | no | — |
| 625 | #102 | — | 106 | 4 | no | — |
| 626 | #101 | — | 106 | 8 | no | — |
| 627 | C24 | — | 53 | 1 | no | — |
| 628 | C24 | — | 106 | 1 | no | — |
| 629 | #41 | — | 2 | 1 | no | — |
| 630 | #41 | — | 2 | 1 | no | — |
| 631 | #41 | — | 53 | 2 | no | — |
| 632 | #41 | — | 53 | 2 | no | — |
| 633 | #41 | — | 53 | 2 | no | — |
| 634 | #41 | — | 53 | 2 | no | — |
| 635 | #41 | — | 53 | 2 | no | — |
| 636 | #41 | — | 53 | 2 | no | — |
| 637 | #41 | — | 106 | 2 | no | — |
| 638 | #41 | — | 106 | 2 | no | — |
| 639 | #41 | — | 106 | 2 | no | — |
| 640 | #41 | — | 106 | 2 | no | — |
| 641 | #41 | — | 106 | 2 | no | — |
| 642 | #41 | — | 106 | 2 | no | — |
| 643 | #41 | — | 106 | 1 | no | — |
| 644 | #41 | — | 106 | 2 | no | — |
| 645 | #41 | — | 106 | 2 | no | — |
| 646 | #41 | — | 106 | 1 | no | — |
| 647 | #41 | — | 106 | 1 | no | — |
| 648 | #41 | — | 106 | 1 | no | — |
| 649 | #41 | — | 106 | 1 | no | — |
| 650 | #41 | — | 106 | 1 | no | — |
| 651 | #41 | C22⋊#6157 | 1 | 2 | yes | — |
| 652 | #41 | C22×#6157 | 1 | 2 | yes | — |
| 653 | C2×Q8 | — | 2 | 1 | no | — |
| 654 | C2×Q8 | — | 2 | 1 | no | — |
| 655 | C2×Q8 | — | 2 | 1 | no | — |
| 656 | C2×Q8 | — | 2 | 1 | no | — |
| 657 | C2×Q8 | — | 2 | 1 | no | — |
| 658 | C2×Q8 | — | 53 | 2 | no | — |
| 659 | C2×Q8 | — | 53 | 2 | no | — |
| 660 | C2×Q8 | — | 53 | 1 | no | — |
| 661 | C2×Q8 | — | 53 | 2 | no | — |
| 662 | C2×Q8 | — | 106 | 1 | no | — |
| 663 | C2×Q8 | — | 106 | 2 | no | — |
| 664 | C2×Q8 | — | 106 | 2 | no | — |
| 665 | C2×Q8 | — | 106 | 1 | no | — |
| 666 | C2×Q8 | — | 106 | 1 | no | — |
| 667 | C2×Q8 | — | 106 | 2 | no | — |
| 668 | C2×Q8 | — | 106 | 2 | no | — |
| 669 | C2×Q8 | — | 106 | 2 | no | — |
| 670 | C2×Q8 | — | 106 | 2 | no | — |
| 671 | C2×Q8 | — | 106 | 2 | no | — |
| 672 | C2×Q8 | — | 106 | 2 | no | — |
| 673 | C2×Q8 | — | 106 | 2 | no | — |
| 674 | C2×Q8 | — | 106 | 2 | no | — |
| 675 | C2×Q8 | — | 106 | 1 | no | — |
| 676 | C2×Q8 | — | 106 | 1 | no | — |
| 677 | C2×Q8 | — | 106 | 1 | no | — |
| 678 | C2×Q8 | — | 106 | 1 | no | — |
| 679 | C2×Q8 | — | 106 | 1 | no | — |
| 680 | C2×Q8 | — | 212 | 1 | no | — |
| 681 | C2×Q8 | — | 212 | 1 | no | — |
| 682 | C2×Q8 | — | 212 | 1 | no | — |
| 683 | C2×Q8 | — | 212 | 1 | no | — |
| 684 | C2×Q8 | — | 212 | 1 | no | — |
| 685 | C2×Q8 | — | 212 | 1 | no | — |
| 686 | C2×Q8 | — | 212 | 1 | no | — |
| 687 | C2×Q8 | — | 212 | 1 | no | — |
| 688 | C2×Q8 | — | 212 | 1 | no | — |
| 689 | C2×Q8 | — | 212 | 1 | no | — |
| 690 | C2×Q8 | — | 212 | 1 | no | — |
| 691 | C2×Q8 | — | 212 | 1 | no | — |
| 692 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 693 | C2×Q8 | C22×#6157 | 1 | 2 | yes | — |
| 694 | C2×D4 | — | 2 | 1 | no | — |
| 695 | C2×D4 | — | 53 | 2 | no | — |
| 696 | C2×D4 | — | 53 | 2 | no | — |
| 697 | C2×D4 | — | 53 | 1 | no | — |
| 698 | C2×D4 | — | 106 | 1 | no | — |
| 699 | C2×D4 | — | 106 | 1 | no | — |
| 700 | C2×D4 | — | 106 | 1 | no | — |
| 701 | C2×D4 | — | 106 | 1 | no | — |
| 702 | C2×D4 | — | 106 | 2 | no | — |
| 703 | C2×D4 | — | 106 | 2 | no | — |
| 704 | C2×D4 | — | 106 | 2 | no | — |
| 705 | C2×D4 | — | 106 | 2 | no | — |
| 706 | C2×D4 | — | 106 | 1 | no | — |
| 707 | C2×D4 | — | 106 | 1 | no | — |
| 708 | C2×D4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 709 | C22×C4 | — | 2 | 1 | no | — |
| 710 | C22×C4 | — | 2 | 1 | no | — |
| 711 | C22×C4 | — | 53 | 1 | no | — |
| 712 | C22×C4 | — | 53 | 1 | no | — |
| 713 | C22×C4 | — | 53 | 1 | no | — |
| 714 | C22×C4 | — | 53 | 1 | no | — |
| 715 | C22×C4 | — | 53 | 1 | no | — |
| 716 | C22×C4 | — | 53 | 1 | no | — |
| 717 | C22×C4 | — | 53 | 1 | no | — |
| 718 | C22×C4 | — | 53 | 1 | no | — |
| 719 | C22×C4 | — | 53 | 1 | no | — |
| 720 | C22×C4 | — | 53 | 1 | no | — |
| 721 | C22×C4 | — | 53 | 1 | no | — |
| 722 | C22×C4 | — | 53 | 1 | no | — |
| 723 | C22×C4 | — | 53 | 1 | no | — |
| 724 | C22×C4 | — | 106 | 2 | no | — |
| 725 | C22×C4 | — | 106 | 1 | no | — |
| 726 | C22×C4 | — | 106 | 2 | no | — |
| 727 | C22×C4 | — | 106 | 2 | no | — |
| 728 | C22×C4 | — | 106 | 2 | no | — |
| 729 | C22×C4 | — | 106 | 1 | no | — |
| 730 | C22×C4 | — | 106 | 2 | no | — |
| 731 | C22×C4 | — | 106 | 2 | no | — |
| 732 | C22×C4 | — | 106 | 1 | no | — |
| 733 | C22×C4 | — | 106 | 1 | no | — |
| 734 | C22×C4 | — | 106 | 1 | no | — |
| 735 | C22×C4 | — | 106 | 2 | no | — |
| 736 | C22×C4 | — | 212 | 1 | no | — |
| 737 | C22×C4 | — | 212 | 1 | no | — |
| 738 | C22×C4 | — | 212 | 1 | no | — |
| 739 | C22×C4 | — | 212 | 1 | no | — |
| 740 | C22×C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 741 | Q16 | — | 2 | 4 | no | — |
| 742 | Q16 | — | 106 | 4 | no | — |
| 743 | Q16 | — | 106 | 4 | no | — |
| 744 | Q16 | — | 106 | 4 | no | — |
| 745 | SD16 | — | 2 | 4 | no | — |
| 746 | SD16 | — | 106 | 4 | no | — |
| 747 | SD16 | — | 106 | 4 | no | — |
| 748 | SD16 | — | 106 | 4 | no | — |
| 749 | M16 | — | 2 | 1 | no | — |
| 750 | M16 | — | 53 | 4 | no | — |
| 751 | M16 | — | 53 | 2 | no | — |
| 752 | M16 | — | 106 | 2 | no | — |
| 753 | M16 | — | 106 | 2 | no | — |
| 754 | M16 | — | 106 | 2 | no | — |
| 755 | M16 | — | 106 | 2 | no | — |
| 756 | M16 | — | 106 | 2 | no | — |
| 757 | M16 | — | 106 | 2 | no | — |
| 758 | M16 | — | 106 | 2 | no | — |
| 759 | M16 | — | 106 | 2 | no | — |
| 760 | M16 | — | 106 | 2 | no | — |
| 761 | M16 | — | 106 | 8 | no | — |
| 762 | M16 | — | 106 | 8 | no | — |
| 763 | M16 | — | 106 | 1 | no | — |
| 764 | M16 | — | 106 | 2 | no | — |
| 765 | M16 | — | 106 | 2 | no | — |
| 766 | M16 | — | 212 | 1 | no | — |
| 767 | M16 | — | 212 | 1 | no | — |
| 768 | M16 | C22×#6157 | 1 | 2 | yes | — |
| 769 | C2×C8 | — | 2 | 1 | no | — |
| 770 | C2×C8 | — | 53 | 4 | no | — |
| 771 | C2×C8 | — | 106 | 2 | no | — |
| 772 | C2×C8 | — | 106 | 2 | no | — |
| 773 | C2×C8 | — | 106 | 2 | no | — |
| 774 | C2×C8 | — | 106 | 2 | no | — |
| 775 | C2×C8 | — | 106 | 2 | no | — |
| 776 | C2×C8 | — | 106 | 2 | no | — |
| 777 | C2×C8 | — | 106 | 2 | no | — |
| 778 | C2×C8 | — | 106 | 8 | no | — |
| 779 | C2×C8 | — | 106 | 8 | no | — |
| 780 | C2×C8 | — | 106 | 1 | no | — |
| 781 | C2×C8 | — | 106 | 2 | no | — |
| 782 | C2×C8 | — | 212 | 1 | no | — |
| 783 | C2×C8 | — | 212 | 1 | no | — |
| 784 | C4⋊C4 | — | 106 | 2 | no | — |
| 785 | C4⋊C4 | — | 106 | 2 | no | — |
| 786 | C22⋊C4 | — | 212 | 1 | no | — |
| 787 | C22⋊C4 | — | 212 | 1 | no | — |
| 788 | C42 | — | 212 | 1 | no | — |
| 789 | C42 | — | 212 | 1 | no | — |
| 790 | C23 | — | 2 | 1 | no | — |
| 791 | C23 | — | 53 | 1 | no | — |
| 792 | C23 | — | 53 | 1 | no | — |
| 793 | C23 | — | 53 | 1 | no | — |
| 794 | C23 | — | 53 | 1 | no | — |
| 795 | C23 | — | 53 | 1 | no | — |
| 796 | C23 | — | 53 | 1 | no | — |
| 797 | C23 | — | 106 | 2 | no | — |
| 798 | C23 | — | 106 | 2 | no | — |
| 799 | C23 | — | 106 | 1 | no | — |
| 800 | C23 | — | 424 | 2 | no | — |
| 801 | C23 | — | 212 | 2 | no | — |
| 802 | C23 | D4×#6157 | 1 | 1 | yes | characteristic |
| 803 | Q8 | — | 2 | 1 | no | — |
| 804 | Q8 | — | 2 | 2 | no | — |
| 805 | Q8 | — | 2 | 2 | no | — |
| 806 | Q8 | — | 4 | 1 | no | — |
| 807 | Q8 | — | 4 | 1 | no | — |
| 808 | Q8 | — | 53 | 2 | no | — |
| 809 | Q8 | — | 106 | 2 | no | — |
| 810 | Q8 | — | 106 | 2 | no | — |
| 811 | Q8 | — | 106 | 1 | no | — |
| 812 | Q8 | — | 106 | 2 | no | — |
| 813 | Q8 | — | 106 | 2 | no | — |
| 814 | Q8 | — | 212 | 2 | no | — |
| 815 | Q8 | — | 212 | 2 | no | — |
| 816 | Q8 | — | 212 | 2 | no | — |
| 817 | Q8 | — | 212 | 2 | no | — |
| 818 | Q8 | — | 212 | 1 | no | — |
| 819 | Q8 | — | 212 | 1 | no | — |
| 820 | Q8 | C2×C22⋊#6157 | 1 | 2 | yes | — |
| 821 | D4 | — | 2 | 2 | no | — |
| 822 | D4 | — | 2 | 2 | no | — |
| 823 | D4 | — | 2 | 1 | no | — |
| 824 | D4 | — | 53 | 2 | no | — |
| 825 | D4 | — | 106 | 2 | no | — |
| 826 | D4 | — | 106 | 2 | no | — |
| 827 | D4 | — | 106 | 2 | no | — |
| 828 | D4 | — | 106 | 2 | no | — |
| 829 | D4 | — | 106 | 2 | no | — |
| 830 | D4 | — | 106 | 2 | no | — |
| 831 | D4 | — | 106 | 2 | no | — |
| 832 | D4 | — | 106 | 2 | no | — |
| 833 | D4 | — | 106 | 1 | no | — |
| 834 | D4 | C2×C22⋊#6157 | 1 | 2 | yes | — |
| 835 | C2×C4 | — | 2 | 1 | no | — |
| 836 | C2×C4 | — | 2 | 2 | no | — |
| 837 | C2×C4 | — | 2 | 2 | no | — |
| 838 | C2×C4 | — | 2 | 2 | no | — |
| 839 | C2×C4 | — | 4 | 1 | no | — |
| 840 | C2×C4 | — | 4 | 1 | no | — |
| 841 | C2×C4 | — | 53 | 1 | no | — |
| 842 | C2×C4 | — | 53 | 1 | no | — |
| 843 | C2×C4 | — | 53 | 1 | no | — |
| 844 | C2×C4 | — | 53 | 1 | no | — |
| 845 | C2×C4 | — | 53 | 1 | no | — |
| 846 | C2×C4 | — | 53 | 1 | no | — |
| 847 | C2×C4 | — | 53 | 1 | no | — |
| 848 | C2×C4 | — | 53 | 1 | no | — |
| 849 | C2×C4 | — | 53 | 1 | no | — |
| 850 | C2×C4 | — | 53 | 1 | no | — |
| 851 | C2×C4 | — | 53 | 1 | no | — |
| 852 | C2×C4 | — | 53 | 1 | no | — |
| 853 | C2×C4 | — | 53 | 1 | no | — |
| 854 | C2×C4 | — | 53 | 1 | no | — |
| 855 | C2×C4 | — | 53 | 1 | no | — |
| 856 | C2×C4 | — | 53 | 1 | no | — |
| 857 | C2×C4 | — | 53 | 1 | no | — |
| 858 | C2×C4 | — | 53 | 1 | no | — |
| 859 | C2×C4 | — | 53 | 1 | no | — |
| 860 | C2×C4 | — | 53 | 1 | no | — |
| 861 | C2×C4 | — | 53 | 1 | no | — |
| 862 | C2×C4 | — | 53 | 1 | no | — |
| 863 | C2×C4 | — | 106 | 2 | no | — |
| 864 | C2×C4 | — | 106 | 2 | no | — |
| 865 | C2×C4 | — | 106 | 2 | no | — |
| 866 | C2×C4 | — | 106 | 2 | no | — |
| 867 | C2×C4 | — | 106 | 2 | no | — |
| 868 | C2×C4 | — | 106 | 2 | no | — |
| 869 | C2×C4 | — | 106 | 1 | no | — |
| 870 | C2×C4 | — | 106 | 2 | no | — |
| 871 | C2×C4 | — | 106 | 2 | no | — |
| 872 | C2×C4 | — | 106 | 2 | no | — |
| 873 | C2×C4 | — | 424 | 2 | no | — |
| 874 | C2×C4 | — | 212 | 2 | no | — |
| 875 | C2×C4 | — | 212 | 2 | no | — |
| 876 | C2×C4 | — | 212 | 2 | no | — |
| 877 | C2×C4 | — | 212 | 2 | no | — |
| 878 | C2×C4 | — | 212 | 2 | no | — |
| 879 | C2×C4 | — | 212 | 1 | no | — |
| 880 | C2×C4 | — | 212 | 1 | no | — |
| 881 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 882 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 883 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 884 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 885 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 886 | C2×C4 | C23×#6157 | 1 | 1 | yes | characteristic |
| 887 | C8 | — | 2 | 2 | no | — |
| 888 | C8 | — | 106 | 4 | no | — |
| 889 | C8 | — | 106 | 4 | no | — |
| 890 | C8 | — | 106 | 2 | no | — |
| 891 | C8 | — | 212 | 2 | no | — |
| 892 | C22 | — | 2 | 2 | no | — |
| 893 | C22 | — | 4 | 1 | no | — |
| 894 | C22 | — | 8 | 1 | no | — |
| 895 | C22 | — | 53 | 1 | no | — |
| 896 | C22 | — | 53 | 1 | no | — |
| 897 | C22 | — | 53 | 1 | no | — |
| 898 | C22 | — | 53 | 1 | no | — |
| 899 | C22 | — | 106 | 2 | no | — |
| 900 | C22 | — | 106 | 2 | no | — |
| 901 | C22 | — | 106 | 2 | no | — |
| 902 | C22 | — | 106 | 2 | no | — |
| 903 | C22 | — | 424 | 1 | no | — |
| 904 | C22 | — | 424 | 2 | no | — |
| 905 | C22 | — | 212 | 1 | no | — |
| 906 | C22 | — | 212 | 1 | no | — |
| 907 | C22 | — | 212 | 1 | no | — |
| 908 | C22 | — | 212 | 4 | no | — |
| 909 | C22 | #16811571 | 1 | 1 | yes | characteristic |
| 910 | C22 | #16811571 | 1 | 1 | yes | characteristic |
| 911 | C22 | C2×D4×#6157 | 1 | 1 | yes | characteristic |
| 912 | C4 | — | 2 | 2 | no | — |
| 913 | C4 | — | 4 | 2 | no | — |
| 914 | C4 | — | 53 | 1 | no | — |
| 915 | C4 | — | 53 | 1 | no | — |
| 916 | C4 | — | 53 | 1 | no | — |
| 917 | C4 | — | 53 | 1 | no | — |
| 918 | C4 | — | 106 | 2 | no | — |
| 919 | C4 | — | 424 | 2 | no | — |
| 920 | C4 | — | 212 | 2 | no | — |
| 921 | C4 | #16811571 | 1 | 1 | yes | characteristic |
| 922 | C4 | #16811571 | 1 | 1 | yes | characteristic |
| 923 | C4 | C22×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 924 | C4 | C2×D4×#6157 | 1 | 1 | yes | characteristic |
| 925 | C2 | — | 2 | 1 | no | — |
| 926 | C2 | — | 2 | 1 | no | — |
| 927 | C2 | — | 2 | 1 | no | — |
| 928 | C2 | — | 4 | 2 | no | — |
| 929 | C2 | — | 53 | 2 | no | — |
| 930 | C2 | — | 106 | 1 | no | — |
| 931 | C2 | — | 106 | 1 | no | — |
| 932 | C2 | — | 106 | 1 | no | — |
| 933 | C2 | — | 212 | 2 | no | — |
| 934 | C2 | C2×#16811571 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#16811616 | C2 | semidirect |
| 4. C2×D53⋊#101 | C2 | semidirect |
| 5. #20290755 | C2 | semidirect |
| 6. #20290419 | C2 | semidirect |
| 7. #20290408 | C2 | semidirect |
| 27. C2×#13133280 | C22 | semidirect |
| 29. D53⋊#101 | C22 | semidirect |
| 31. #16811502 | C22 | semidirect |
| 32. #16811498 | C22 | semidirect |
| 35. C2×#13133250 | C4 | semidirect |
| 37. C2×#13133248 | C4 | semidirect |
| 38. C2×#13133247 | C4 | semidirect |
| 42. #137×D53 | C4 | semidirect |
| 47. C2×#137×C53 | C4 | semidirect |
| 487. C2×#137 | #6157 | semidirect |
| 515. C53 | #21006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#568 | 2 |
| #20291335 | 2 |
| C2×#16811616 | 2 |
| C2×D53⋊#101 | 2 |
| #20290755 | 2 |
| #20290419 | 2 |
| #20290408 | 2 |
| C2×#137×D53 | 2 |
| #21006 | 53 |