Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4874 conjugacy classes of subgroups.
The subgroup lattice has 712 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×D53⋊#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20291695 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20291337 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #20291336 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #20291335 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×#16811613 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #585×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#13133305 | — | 2 | 1 | no | — |
| 9 | D53⋊#131 | — | 2 | 4 | no | — |
| 10 | D53⋊#131 | C22 | 1 | 8 | yes | complemented |
| 11 | C2×#13133304 | — | 2 | 3 | no | — |
| 12 | C2×D53⋊M16 | C22 | 1 | 3 | yes | complemented |
| 13 | C22×D53⋊C8 | C22 | 1 | 3 | yes | complemented |
| 14 | #16811692 | C22 | 1 | 8 | yes | complemented |
| 15 | #16811691 | — | 2 | 1 | no | — |
| 16 | #16811690 | — | 2 | 3 | no | — |
| 17 | #41×#6157 | — | 2 | 4 | no | — |
| 18 | C2×#13133296 | C22 | 1 | 6 | yes | complemented |
| 19 | #16811616 | C22 | 1 | 12 | yes | complemented |
| 20 | #16811615 | C22 | 1 | 12 | yes | complemented |
| 21 | #16811614 | C22 | 1 | 24 | yes | complemented |
| 22 | #16811613 | C22 | 1 | 4 | yes | complemented |
| 23 | #16811613 | C22 | 1 | 12 | yes | complemented |
| 24 | #16811613 | C22 | 1 | 24 | yes | complemented |
| 25 | C2×#13133280 | C22 | 1 | 12 | yes | complemented |
| 26 | C2×#13133279 | C22 | 1 | 12 | yes | complemented |
| 27 | #16811460 | — | 2 | 1 | no | — |
| 28 | #16811460 | C4 | 1 | 4 | yes | complemented |
| 29 | #16811459 | — | 2 | 4 | no | — |
| 30 | #16811459 | C4 | 1 | 1 | yes | characteristic, complemented |
| 31 | #16811459 | C4 | 1 | 6 | yes | complemented |
| 32 | #16811458 | — | 2 | 3 | no | — |
| 33 | #16811458 | C4 | 1 | 4 | yes | complemented |
| 34 | 2−1+4×D53 | — | 2 | 1 | no | — |
| 35 | 2−1+4×D53 | C22 | 1 | 4 | yes | — |
| 36 | H(5,𝔽2)×D53 | — | 2 | 3 | no | — |
| 37 | H(5,𝔽2)×D53 | C22 | 1 | 4 | yes | — |
| 38 | C2×#41×D53 | — | 2 | 4 | no | — |
| 39 | C2×#41×D53 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#41×D53 | C22 | 1 | 6 | yes | — |
| 41 | C53×#585 | C4 | 1 | 1 | yes | characteristic, complemented |
| 42 | #13133305 | — | 2 | 8 | no | — |
| 43 | #13133304 | — | 2 | 24 | no | — |
| 44 | C2×#11719936 | — | 2 | 3 | no | — |
| 45 | D53⋊M16 | — | 2 | 6 | no | — |
| 46 | D53⋊M16 | C23 | 1 | 12 | yes | — |
| 47 | C2×#11719940 | — | 2 | 3 | no | — |
| 48 | C2×D53⋊C8 | — | 2 | 3 | no | — |
| 49 | C2×D53⋊C8 | — | 2 | 6 | no | — |
| 50 | C2×D53⋊C8 | C23 | 1 | 12 | yes | — |
| 51 | C2×D53⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×D53⋊C8 | C23 | 1 | 3 | yes | — |
| 53 | C22×#88324 | — | 2 | 3 | no | — |
| 54 | Q8×#6157 | — | 2 | 8 | no | — |
| 55 | D4×#6157 | — | 2 | 24 | no | — |
| 56 | #13133296 | — | 2 | 6 | no | — |
| 57 | #13133296 | — | 2 | 6 | no | — |
| 58 | #13133296 | C23 | 1 | 4 | yes | — |
| 59 | #13133296 | C23 | 1 | 12 | yes | — |
| 60 | C2×C4⋊#6157 | C23 | 1 | 12 | yes | — |
| 61 | C2×C22⋊#6157 | — | 2 | 6 | no | — |
| 62 | C2×C4×#6157 | — | 2 | 6 | no | — |
| 63 | #13133280 | C23 | 1 | 8 | yes | — |
| 64 | #13133280 | C23 | 1 | 24 | yes | — |
| 65 | #13133279 | C23 | 1 | 8 | yes | — |
| 66 | #13133279 | C23 | 1 | 24 | yes | — |
| 67 | #13133265 | — | 2 | 1 | no | — |
| 68 | #13133265 | — | 2 | 4 | no | — |
| 69 | #13133265 | — | 2 | 4 | no | — |
| 70 | #13133265 | C2×C4 | 1 | 12 | yes | complemented |
| 71 | #13133264 | — | 2 | 4 | no | — |
| 72 | #13133264 | — | 2 | 12 | no | — |
| 73 | #13133264 | — | 2 | 6 | no | — |
| 74 | #13133264 | C2×C4 | 1 | 12 | yes | complemented |
| 75 | #13133264 | C2×C4 | 1 | 4 | yes | complemented |
| 76 | #13133263 | — | 2 | 4 | no | — |
| 77 | #13133263 | — | 2 | 12 | no | — |
| 78 | #13133263 | — | 2 | 6 | no | — |
| 79 | #13133263 | C2×C4 | 1 | 12 | yes | complemented |
| 80 | #13133263 | C2×C4 | 1 | 4 | yes | complemented |
| 81 | #13133262 | — | 2 | 3 | no | — |
| 82 | #13133262 | — | 2 | 12 | no | — |
| 83 | #13133262 | — | 2 | 12 | no | — |
| 84 | #13133262 | — | 2 | 12 | no | — |
| 85 | #13133262 | C2×C4 | 1 | 12 | yes | complemented |
| 86 | C2×#11719949 | — | 2 | 4 | no | — |
| 87 | C2×#11719949 | C2×C4 | 1 | 6 | yes | complemented |
| 88 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 89 | C2×#11719945 | — | 2 | 12 | no | — |
| 90 | C2×#11719945 | — | 2 | 6 | no | — |
| 91 | C2×#11719945 | C2×C4 | 1 | 3 | yes | — |
| 92 | C2×#11719945 | C2×C4 | 1 | 6 | yes | complemented |
| 93 | C2×#11719947 | — | 2 | 6 | no | — |
| 94 | C2×#11719947 | — | 2 | 12 | no | — |
| 95 | C2×#11719947 | C2×C4 | 1 | 6 | yes | complemented |
| 96 | C2×#11719947 | D4 | 1 | 3 | yes | — |
| 97 | #41×D53 | — | 2 | 4 | no | — |
| 98 | #41×D53 | — | 2 | 4 | no | — |
| 99 | #41×D53 | — | 2 | 4 | no | — |
| 100 | #41×D53 | — | 2 | 12 | no | — |
| 101 | #41×D53 | — | 2 | 12 | no | — |
| 102 | #41×D53 | — | 2 | 12 | no | — |
| 103 | #41×D53 | — | 2 | 6 | no | — |
| 104 | #41×D53 | — | 2 | 6 | no | — |
| 105 | #41×D53 | — | 2 | 6 | no | — |
| 106 | #41×D53 | — | 2 | 6 | no | — |
| 107 | #41×D53 | C2×C4 | 1 | 4 | yes | — |
| 108 | #41×D53 | C2×C4 | 1 | 12 | yes | complemented |
| 109 | #41×D53 | C2×C4 | 1 | 12 | yes | complemented |
| 110 | #41×D53 | D4 | 1 | 4 | yes | — |
| 111 | #41×D53 | D4 | 1 | 4 | yes | — |
| 112 | #41×D53 | C23 | 1 | 4 | yes | — |
| 113 | #41×D53 | C23 | 1 | 12 | yes | — |
| 114 | #41×D53 | C23 | 1 | 4 | yes | — |
| 115 | C2×Q8×D53 | — | 2 | 4 | no | — |
| 116 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 117 | C2×Q8×D53 | C23 | 1 | 6 | yes | — |
| 118 | C2×D4×D53 | — | 2 | 6 | no | — |
| 119 | C2×D4×D53 | — | 2 | 12 | no | — |
| 120 | C2×D4×D53 | D4 | 1 | 3 | yes | — |
| 121 | C2×D4×D53 | C23 | 1 | 6 | yes | — |
| 122 | C22×C4×D53 | — | 2 | 6 | no | — |
| 123 | C22×C4×D53 | C23 | 1 | 3 | yes | — |
| 124 | 2−1+4×C53 | — | 2 | 1 | no | — |
| 125 | 2−1+4×C53 | C2×C4 | 1 | 4 | yes | complemented |
| 126 | H(5,𝔽2)×C53 | — | 2 | 3 | no | — |
| 127 | H(5,𝔽2)×C53 | C2×C4 | 1 | 4 | yes | complemented |
| 128 | C2×#41×C53 | — | 2 | 4 | no | — |
| 129 | C2×#41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 130 | C2×#41×C53 | C2×C4 | 1 | 6 | yes | complemented |
| 131 | C23×D53 | — | 2 | 6 | no | — |
| 132 | C23×D53 | C2×D4 | 1 | 3 | yes | — |
| 133 | C22×#6157 | — | 2 | 12 | no | — |
| 134 | #41×C53 | — | 2 | 4 | no | — |
| 135 | #41×C53 | — | 2 | 12 | no | — |
| 136 | #41×C53 | — | 2 | 6 | no | — |
| 137 | #41×C53 | — | 2 | 6 | no | — |
| 138 | #41×C53 | C22⋊C4 | 1 | 4 | yes | — |
| 139 | #41×C53 | C22×C4 | 1 | 4 | yes | — |
| 140 | #41×C53 | C22×C4 | 1 | 12 | yes | — |
| 141 | #41×C53 | C22×C4 | 1 | 4 | yes | — |
| 142 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 143 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 144 | C2×Q8×C53 | C22×C4 | 1 | 6 | yes | — |
| 145 | C2×D4×C53 | — | 2 | 6 | no | — |
| 146 | C2×D4×C53 | — | 2 | 12 | no | — |
| 147 | C2×D4×C53 | C22⋊C4 | 1 | 3 | yes | — |
| 148 | C2×D4×C53 | C22×C4 | 1 | 6 | yes | — |
| 149 | C22×C4×C53 | — | 2 | 6 | no | — |
| 150 | C22×C4×C53 | C22×C4 | 1 | 3 | yes | — |
| 151 | C2×C22⋊D53 | — | 2 | 6 | no | — |
| 152 | C2×C22⋊D53 | — | 2 | 6 | no | — |
| 153 | C2×C22⋊D53 | — | 2 | 24 | no | — |
| 154 | C2×C22⋊D53 | — | 2 | 6 | no | — |
| 155 | C2×C22⋊D53 | C22⋊C4 | 1 | 6 | yes | — |
| 156 | C22×Dic53 | — | 2 | 6 | no | — |
| 157 | C22×Dic53 | C2×D4 | 1 | 3 | yes | — |
| 158 | #11719949 | — | 2 | 4 | no | — |
| 159 | #11719949 | — | 2 | 12 | no | — |
| 160 | #11719949 | — | 2 | 6 | no | — |
| 161 | #11719949 | — | 2 | 6 | no | — |
| 162 | #11719949 | C22⋊C4 | 1 | 4 | yes | — |
| 163 | #11719949 | C22×C4 | 1 | 4 | yes | — |
| 164 | #11719949 | C22×C4 | 1 | 12 | yes | — |
| 165 | #11719949 | C2×D4 | 1 | 4 | yes | — |
| 166 | Q8×D53 | — | 2 | 4 | no | — |
| 167 | Q8×D53 | — | 2 | 6 | no | — |
| 168 | Q8×D53 | — | 2 | 6 | no | — |
| 169 | Q8×D53 | — | 2 | 12 | no | — |
| 170 | Q8×D53 | C22⋊C4 | 1 | 4 | yes | — |
| 171 | Q8×D53 | C22×C4 | 1 | 12 | yes | — |
| 172 | Q8×D53 | C2×D4 | 1 | 4 | yes | — |
| 173 | Q8×D53 | C24 | 1 | 4 | yes | — |
| 174 | #11719947 | — | 2 | 12 | no | — |
| 175 | #11719947 | — | 2 | 24 | no | — |
| 176 | #11719947 | — | 2 | 12 | no | — |
| 177 | #11719947 | — | 2 | 12 | no | — |
| 178 | #11719947 | — | 2 | 4 | no | — |
| 179 | #11719947 | — | 2 | 12 | no | — |
| 180 | #11719947 | — | 2 | 6 | no | — |
| 181 | #11719947 | — | 2 | 6 | no | — |
| 182 | #11719947 | — | 2 | 12 | no | — |
| 183 | #11719947 | C22⋊C4 | 1 | 12 | yes | — |
| 184 | #11719947 | C22×C4 | 1 | 4 | yes | — |
| 185 | #11719947 | C22×C4 | 1 | 12 | yes | — |
| 186 | #11719947 | C2×D4 | 1 | 12 | yes | — |
| 187 | D4×D53 | — | 2 | 12 | no | — |
| 188 | D4×D53 | — | 2 | 12 | no | — |
| 189 | D4×D53 | — | 2 | 4 | no | — |
| 190 | D4×D53 | — | 2 | 12 | no | — |
| 191 | D4×D53 | — | 2 | 12 | no | — |
| 192 | D4×D53 | — | 2 | 24 | no | — |
| 193 | D4×D53 | — | 2 | 12 | no | — |
| 194 | D4×D53 | — | 2 | 6 | no | — |
| 195 | D4×D53 | — | 2 | 6 | no | — |
| 196 | D4×D53 | C22⋊C4 | 1 | 12 | yes | — |
| 197 | D4×D53 | C22×C4 | 1 | 12 | yes | — |
| 198 | D4×D53 | C2×D4 | 1 | 12 | yes | — |
| 199 | D4×D53 | C24 | 1 | 4 | yes | — |
| 200 | #11719945 | — | 2 | 6 | no | — |
| 201 | #11719945 | — | 2 | 6 | no | — |
| 202 | #11719945 | — | 2 | 24 | no | — |
| 203 | #11719945 | — | 2 | 12 | no | — |
| 204 | #11719945 | — | 2 | 12 | no | — |
| 205 | #11719945 | — | 2 | 12 | no | — |
| 206 | #11719945 | — | 2 | 4 | no | — |
| 207 | #11719945 | — | 2 | 12 | no | — |
| 208 | #11719945 | — | 2 | 12 | no | — |
| 209 | #11719945 | C22⋊C4 | 1 | 12 | yes | — |
| 210 | #11719945 | C22×C4 | 1 | 12 | yes | — |
| 211 | #11719945 | C22×C4 | 1 | 4 | yes | — |
| 212 | #11719945 | C22×C4 | 1 | 12 | yes | — |
| 213 | C2×D212 | — | 2 | 6 | no | — |
| 214 | C2×D212 | — | 2 | 12 | no | — |
| 215 | C2×D212 | C22⋊C4 | 1 | 3 | yes | — |
| 216 | C2×D212 | C22×C4 | 1 | 6 | yes | — |
| 217 | C2×C4×D53 | — | 2 | 6 | no | — |
| 218 | C2×C4×D53 | — | 2 | 6 | no | — |
| 219 | C2×C4×D53 | — | 2 | 6 | no | — |
| 220 | C2×C4×D53 | — | 2 | 12 | no | — |
| 221 | C2×C4×D53 | — | 2 | 12 | no | — |
| 222 | C2×C4×D53 | — | 2 | 4 | no | — |
| 223 | C2×C4×D53 | — | 2 | 12 | no | — |
| 224 | C2×C4×D53 | C22×C4 | 1 | 6 | yes | — |
| 225 | C2×C4×D53 | C22×C4 | 1 | 3 | yes | — |
| 226 | C2×C4×D53 | C2×D4 | 1 | 6 | yes | — |
| 227 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 228 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 229 | C2×C4×D53 | C2×D4 | 1 | 6 | yes | — |
| 230 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 231 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 232 | C2×Dic106 | — | 2 | 6 | no | — |
| 233 | C2×Dic106 | — | 2 | 12 | no | — |
| 234 | C2×Dic106 | C22⋊C4 | 1 | 3 | yes | — |
| 235 | C2×Dic106 | C22×C4 | 1 | 6 | yes | — |
| 236 | C22⋊#6157 | — | 2 | 4 | no | — |
| 237 | C22⋊#6157 | — | 2 | 12 | no | — |
| 238 | #11719940 | — | 2 | 12 | no | — |
| 239 | C2×#88324 | — | 2 | 1 | no | — |
| 240 | C2×#88324 | — | 2 | 3 | no | — |
| 241 | C2×#88324 | — | 2 | 12 | no | — |
| 242 | C4⋊#6157 | — | 2 | 12 | no | — |
| 243 | C4⋊#6157 | C24 | 1 | 8 | yes | — |
| 244 | C4×#6157 | — | 2 | 4 | no | — |
| 245 | C4×#6157 | — | 2 | 12 | no | — |
| 246 | #11719936 | — | 2 | 12 | no | — |
| 247 | D53⋊C8 | — | 2 | 1 | no | — |
| 248 | D53⋊C8 | — | 2 | 3 | no | — |
| 249 | D53⋊C8 | — | 2 | 12 | no | — |
| 250 | D53⋊C8 | C24 | 1 | 2 | yes | — |
| 251 | D53⋊C8 | C24 | 1 | 6 | yes | — |
| 252 | C23×C53 | — | 2 | 6 | no | — |
| 253 | C23×C53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 254 | C22×D53 | — | 2 | 6 | no | — |
| 255 | C22×D53 | — | 2 | 4 | no | — |
| 256 | C22×D53 | — | 2 | 12 | no | — |
| 257 | C22×D53 | — | 4 | 6 | no | — |
| 258 | C22×D53 | — | 8 | 12 | no | — |
| 259 | C22×D53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 260 | C22×D53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 261 | C22×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 262 | C22×D53 | C22×D4 | 1 | 6 | yes | — |
| 263 | C2×#6157 | — | 2 | 8 | no | — |
| 264 | C2×#6157 | — | 8 | 12 | no | — |
| 265 | Q8×C53 | — | 2 | 6 | no | — |
| 266 | Q8×C53 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 267 | Q8×C53 | C23×C4 | 1 | 4 | yes | — |
| 268 | D4×C53 | — | 2 | 12 | no | — |
| 269 | D4×C53 | — | 2 | 4 | no | — |
| 270 | D4×C53 | — | 2 | 6 | no | — |
| 271 | D4×C53 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 272 | D4×C53 | C23×C4 | 1 | 4 | yes | — |
| 273 | C2×C4×C53 | — | 2 | 6 | no | — |
| 274 | C2×C4×C53 | — | 2 | 12 | no | — |
| 275 | C2×C4×C53 | — | 2 | 4 | no | — |
| 276 | C2×C4×C53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 277 | C2×C4×C53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 278 | C2×C4×C53 | C23×C4 | 1 | 6 | yes | — |
| 279 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 280 | C22⋊D53 | — | 2 | 12 | no | — |
| 281 | C22⋊D53 | — | 2 | 4 | no | — |
| 282 | C22⋊D53 | — | 2 | 12 | no | — |
| 283 | C22⋊D53 | — | 2 | 4 | no | — |
| 284 | C22⋊D53 | — | 2 | 12 | no | — |
| 285 | C22⋊D53 | — | 2 | 4 | no | — |
| 286 | C22⋊D53 | C2×C22⋊C4 | 1 | 24 | yes | — |
| 287 | C2×Dic53 | — | 2 | 6 | no | — |
| 288 | C2×Dic53 | — | 2 | 12 | no | — |
| 289 | C2×Dic53 | — | 2 | 4 | no | — |
| 290 | C2×Dic53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 291 | C2×Dic53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 292 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×Dic53 | C22×D4 | 1 | 6 | yes | — |
| 294 | D212 | — | 2 | 12 | no | — |
| 295 | D212 | — | 2 | 4 | no | — |
| 296 | D212 | — | 2 | 6 | no | — |
| 297 | D212 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 298 | D212 | C23×C4 | 1 | 4 | yes | — |
| 299 | C4×D53 | — | 2 | 12 | no | — |
| 300 | C4×D53 | — | 2 | 4 | no | — |
| 301 | C4×D53 | — | 2 | 4 | no | — |
| 302 | C4×D53 | — | 2 | 12 | no | — |
| 303 | C4×D53 | — | 2 | 4 | no | — |
| 304 | C4×D53 | — | 2 | 12 | no | — |
| 305 | C4×D53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 306 | C4×D53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 307 | C4×D53 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 308 | C4×D53 | C23×C4 | 1 | 1 | yes | characteristic |
| 309 | C4×D53 | C23×C4 | 1 | 6 | yes | — |
| 310 | C4×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 311 | C4×D53 | C22×D4 | 1 | 6 | yes | — |
| 312 | C4×D53 | C22×D4 | 1 | 6 | yes | — |
| 313 | C4×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 314 | C4×D53 | C25 | 1 | 1 | yes | characteristic |
| 315 | Dic106 | — | 2 | 6 | no | — |
| 316 | Dic106 | — | 2 | 12 | no | — |
| 317 | Dic106 | — | 2 | 4 | no | — |
| 318 | Dic106 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 319 | Dic106 | C23×C4 | 1 | 4 | yes | — |
| 320 | #88324 | — | 2 | 6 | no | — |
| 321 | #88324 | — | 2 | 2 | no | — |
| 322 | #60086 | — | 53 | 1 | no | maximal, Sylow |
| 323 | C22×C53 | — | 2 | 4 | no | — |
| 324 | C22×C53 | — | 4 | 3 | no | — |
| 325 | C22×C53 | — | 8 | 6 | no | — |
| 326 | C22×C53 | C22×C22⋊C4 | 1 | 6 | yes | — |
| 327 | C22×C53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 328 | C2×D53 | — | 2 | 12 | no | — |
| 329 | C2×D53 | — | 2 | 2 | no | — |
| 330 | C2×D53 | — | 2 | 4 | no | — |
| 331 | C2×D53 | — | 4 | 6 | no | — |
| 332 | C2×D53 | — | 4 | 3 | no | — |
| 333 | C2×D53 | — | 4 | 8 | no | — |
| 334 | C2×D53 | — | 8 | 12 | no | — |
| 335 | C2×D53 | — | 8 | 6 | no | — |
| 336 | C2×D53 | C22×C22⋊C4 | 1 | 6 | yes | — |
| 337 | C2×D53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 338 | C2×D53 | C23×D4 | 1 | 1 | yes | characteristic |
| 339 | #6157 | — | 4 | 8 | no | — |
| 340 | C4×C53 | — | 2 | 4 | no | — |
| 341 | C4×C53 | C22×C22⋊C4 | 1 | 6 | yes | — |
| 342 | C4×C53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 343 | C4×C53 | C24×C4 | 1 | 1 | yes | characteristic |
| 344 | Dic53 | — | 2 | 4 | no | — |
| 345 | Dic53 | C22×C22⋊C4 | 1 | 6 | yes | — |
| 346 | Dic53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 347 | Dic53 | C23×D4 | 1 | 1 | yes | characteristic |
| 348 | C2×#585 | — | 53 | 1 | no | — |
| 349 | C22×#131 | — | 53 | 1 | no | — |
| 350 | #3428 | — | 53 | 1 | no | — |
| 351 | #2898 | — | 53 | 8 | no | — |
| 352 | #2897 | — | 53 | 8 | no | — |
| 353 | #2896 | — | 53 | 6 | no | — |
| 354 | C2×#416 | — | 53 | 6 | no | — |
| 355 | C2×C53 | — | 2 | 1 | no | — |
| 356 | C2×C53 | — | 2 | 6 | no | — |
| 357 | C2×C53 | — | 4 | 4 | no | — |
| 358 | C2×C53 | C23×C22⋊C4 | 1 | 1 | yes | characteristic |
| 359 | D53 | — | 2 | 1 | no | — |
| 360 | D53 | — | 2 | 6 | no | — |
| 361 | D53 | — | 4 | 4 | no | — |
| 362 | D53 | #3584 | 1 | 2 | yes | — |
| 363 | #585 | — | 53 | 4 | no | — |
| 364 | #585 | — | 53 | 4 | no | — |
| 365 | #585 | — | 53 | 1 | no | — |
| 366 | #585 | — | 53 | 6 | no | — |
| 367 | #585 | — | 106 | 4 | no | — |
| 368 | #585 | — | 106 | 3 | no | — |
| 369 | #585 | — | 106 | 1 | no | — |
| 370 | #585 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 371 | C2×2−1+4 | — | 53 | 4 | no | — |
| 372 | C2×2−1+4 | — | 106 | 1 | no | — |
| 373 | C2×H(5,𝔽2) | — | 53 | 4 | no | — |
| 374 | C2×H(5,𝔽2) | — | 106 | 3 | no | — |
| 375 | C22×#41 | — | 53 | 1 | no | — |
| 376 | C22×#41 | — | 53 | 6 | no | — |
| 377 | C22×#41 | — | 106 | 4 | no | — |
| 378 | C2×#131 | — | 53 | 8 | no | — |
| 379 | C2×#131 | — | 106 | 3 | no | — |
| 380 | C2×#131 | — | 106 | 4 | no | — |
| 381 | C2×#131 | — | 106 | 1 | no | — |
| 382 | C22×M16 | — | 53 | 3 | no | — |
| 383 | C23×C8 | — | 53 | 3 | no | — |
| 384 | #520 | — | 53 | 8 | no | — |
| 385 | #519 | — | 106 | 1 | no | — |
| 386 | #518 | — | 106 | 3 | no | — |
| 387 | C4×#41 | — | 106 | 4 | no | — |
| 388 | C2×#117 | — | 53 | 6 | no | — |
| 389 | #419 | — | 53 | 12 | no | — |
| 390 | #418 | — | 53 | 12 | no | — |
| 391 | #417 | — | 53 | 24 | no | — |
| 392 | #416 | — | 53 | 4 | no | — |
| 393 | #416 | — | 53 | 12 | no | — |
| 394 | #416 | — | 53 | 24 | no | — |
| 395 | C2×#103 | — | 53 | 12 | no | — |
| 396 | C2×#102 | — | 53 | 12 | no | — |
| 397 | C53 | #60086 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 398 | 2−1+4 | — | 2 | 1 | no | — |
| 399 | 2−1+4 | — | 53 | 12 | no | — |
| 400 | 2−1+4 | — | 53 | 4 | no | — |
| 401 | 2−1+4 | — | 53 | 12 | no | — |
| 402 | 2−1+4 | — | 106 | 4 | no | — |
| 403 | 2−1+4 | — | 106 | 4 | no | — |
| 404 | 2−1+4 | — | 106 | 4 | no | — |
| 405 | 2−1+4 | — | 106 | 6 | no | — |
| 406 | 2−1+4 | — | 106 | 12 | no | — |
| 407 | 2−1+4 | — | 106 | 1 | no | — |
| 408 | 2−1+4 | C2×#6157 | 1 | 4 | yes | complemented |
| 409 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 410 | H(5,𝔽2) | — | 53 | 12 | no | — |
| 411 | H(5,𝔽2) | — | 53 | 4 | no | — |
| 412 | H(5,𝔽2) | — | 53 | 12 | no | — |
| 413 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 414 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 415 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 416 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 417 | H(5,𝔽2) | — | 106 | 6 | no | — |
| 418 | H(5,𝔽2) | — | 106 | 4 | no | — |
| 419 | H(5,𝔽2) | — | 106 | 3 | no | — |
| 420 | H(5,𝔽2) | C2×#6157 | 1 | 4 | yes | complemented |
| 421 | C2×#41 | — | 2 | 4 | no | — |
| 422 | C2×#41 | — | 53 | 4 | no | — |
| 423 | C2×#41 | — | 53 | 4 | no | — |
| 424 | C2×#41 | — | 53 | 4 | no | — |
| 425 | C2×#41 | — | 53 | 4 | no | — |
| 426 | C2×#41 | — | 53 | 1 | no | — |
| 427 | C2×#41 | — | 53 | 3 | no | — |
| 428 | C2×#41 | — | 53 | 3 | no | — |
| 429 | C2×#41 | — | 53 | 4 | no | — |
| 430 | C2×#41 | — | 53 | 12 | no | — |
| 431 | C2×#41 | — | 53 | 12 | no | — |
| 432 | C2×#41 | — | 53 | 12 | no | — |
| 433 | C2×#41 | — | 53 | 6 | no | — |
| 434 | C2×#41 | — | 53 | 6 | no | — |
| 435 | C2×#41 | — | 53 | 6 | no | — |
| 436 | C2×#41 | — | 106 | 6 | no | — |
| 437 | C2×#41 | — | 106 | 12 | no | — |
| 438 | C2×#41 | — | 106 | 6 | no | — |
| 439 | C2×#41 | — | 106 | 6 | no | — |
| 440 | C2×#41 | — | 106 | 6 | no | — |
| 441 | C2×#41 | — | 106 | 6 | no | — |
| 442 | C2×#41 | — | 106 | 6 | no | — |
| 443 | C2×#41 | — | 106 | 12 | no | — |
| 444 | C2×#41 | — | 106 | 12 | no | — |
| 445 | C2×#41 | — | 106 | 4 | no | — |
| 446 | C2×#41 | — | 106 | 4 | no | — |
| 447 | C2×#41 | — | 106 | 4 | no | — |
| 448 | C2×#41 | — | 106 | 12 | no | — |
| 449 | C2×#41 | — | 106 | 12 | no | — |
| 450 | C2×#41 | — | 106 | 4 | no | — |
| 451 | C2×#41 | C2×#6157 | 1 | 1 | yes | characteristic |
| 452 | C2×#41 | C2×#6157 | 1 | 6 | yes | complemented |
| 453 | C22×Q8 | — | 53 | 1 | no | — |
| 454 | C22×Q8 | — | 53 | 6 | no | — |
| 455 | C22×Q8 | — | 106 | 4 | no | — |
| 456 | C22×D4 | — | 53 | 3 | no | — |
| 457 | C22×D4 | — | 53 | 6 | no | — |
| 458 | C22×D4 | — | 106 | 12 | no | — |
| 459 | C22×D4 | — | 106 | 6 | no | — |
| 460 | C23×C4 | — | 53 | 3 | no | — |
| 461 | C23×C4 | — | 106 | 6 | no | — |
| 462 | #131 | — | 106 | 24 | no | — |
| 463 | #131 | — | 106 | 8 | no | — |
| 464 | C2×M16 | — | 53 | 12 | no | — |
| 465 | C2×M16 | — | 106 | 3 | no | — |
| 466 | C2×M16 | — | 106 | 6 | no | — |
| 467 | C2×M16 | — | 106 | 3 | no | — |
| 468 | C22×C8 | — | 53 | 1 | no | — |
| 469 | C22×C8 | — | 53 | 3 | no | — |
| 470 | C22×C8 | — | 53 | 12 | no | — |
| 471 | C22×C8 | — | 106 | 3 | no | — |
| 472 | C22×C8 | — | 106 | 3 | no | — |
| 473 | C22×C8 | — | 106 | 6 | no | — |
| 474 | C4×Q8 | — | 106 | 8 | no | — |
| 475 | C4×D4 | — | 106 | 24 | no | — |
| 476 | #117 | — | 53 | 4 | no | — |
| 477 | #117 | — | 53 | 12 | no | — |
| 478 | #117 | — | 106 | 6 | no | — |
| 479 | #117 | — | 106 | 6 | no | — |
| 480 | C2×C4⋊C4 | — | 53 | 12 | no | — |
| 481 | C2×C22⋊C4 | — | 106 | 6 | no | — |
| 482 | C2×C42 | — | 106 | 6 | no | — |
| 483 | #103 | — | 53 | 8 | no | — |
| 484 | #103 | — | 53 | 24 | no | — |
| 485 | #102 | — | 53 | 8 | no | — |
| 486 | #102 | — | 53 | 24 | no | — |
| 487 | C24 | — | 53 | 3 | no | — |
| 488 | C24 | — | 106 | 6 | no | — |
| 489 | #41 | — | 2 | 4 | no | — |
| 490 | #41 | — | 2 | 12 | no | — |
| 491 | #41 | — | 2 | 6 | no | — |
| 492 | #41 | — | 2 | 6 | no | — |
| 493 | #41 | — | 53 | 4 | no | — |
| 494 | #41 | — | 53 | 4 | no | — |
| 495 | #41 | — | 53 | 12 | no | — |
| 496 | #41 | — | 53 | 12 | no | — |
| 497 | #41 | — | 53 | 12 | no | — |
| 498 | #41 | — | 53 | 12 | no | — |
| 499 | #41 | — | 53 | 4 | no | — |
| 500 | #41 | — | 53 | 12 | no | — |
| 501 | #41 | — | 53 | 4 | no | — |
| 502 | #41 | — | 53 | 12 | no | — |
| 503 | #41 | — | 53 | 4 | no | — |
| 504 | #41 | — | 53 | 12 | no | — |
| 505 | #41 | — | 106 | 12 | no | — |
| 506 | #41 | — | 106 | 4 | no | — |
| 507 | #41 | — | 106 | 12 | no | — |
| 508 | #41 | — | 106 | 12 | no | — |
| 509 | #41 | — | 106 | 24 | no | — |
| 510 | #41 | — | 106 | 12 | no | — |
| 511 | #41 | — | 106 | 12 | no | — |
| 512 | #41 | — | 106 | 12 | no | — |
| 513 | #41 | — | 106 | 4 | no | — |
| 514 | #41 | — | 106 | 6 | no | — |
| 515 | #41 | — | 106 | 12 | no | — |
| 516 | #41 | — | 106 | 12 | no | — |
| 517 | #41 | — | 106 | 6 | no | — |
| 518 | #41 | — | 106 | 6 | no | — |
| 519 | #41 | — | 106 | 6 | no | — |
| 520 | #41 | — | 106 | 24 | no | — |
| 521 | #41 | — | 106 | 12 | no | — |
| 522 | #41 | — | 106 | 12 | no | — |
| 523 | #41 | — | 106 | 4 | no | — |
| 524 | #41 | — | 106 | 12 | no | — |
| 525 | #41 | — | 106 | 6 | no | — |
| 526 | #41 | — | 106 | 6 | no | — |
| 527 | #41 | C22⋊#6157 | 1 | 4 | yes | — |
| 528 | #41 | C22×#6157 | 1 | 4 | yes | — |
| 529 | #41 | C22×#6157 | 1 | 12 | yes | — |
| 530 | #41 | C22×#6157 | 1 | 4 | yes | — |
| 531 | C2×Q8 | — | 2 | 4 | no | — |
| 532 | C2×Q8 | — | 53 | 4 | no | — |
| 533 | C2×Q8 | — | 53 | 4 | no | — |
| 534 | C2×Q8 | — | 53 | 3 | no | — |
| 535 | C2×Q8 | — | 53 | 12 | no | — |
| 536 | C2×Q8 | — | 53 | 4 | no | — |
| 537 | C2×Q8 | — | 53 | 6 | no | — |
| 538 | C2×Q8 | — | 106 | 6 | no | — |
| 539 | C2×Q8 | — | 106 | 12 | no | — |
| 540 | C2×Q8 | — | 106 | 6 | no | — |
| 541 | C2×Q8 | — | 106 | 6 | no | — |
| 542 | C2×Q8 | — | 106 | 12 | no | — |
| 543 | C2×Q8 | — | 106 | 4 | no | — |
| 544 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 545 | C2×Q8 | C22×#6157 | 1 | 6 | yes | — |
| 546 | C2×D4 | — | 2 | 6 | no | — |
| 547 | C2×D4 | — | 2 | 12 | no | — |
| 548 | C2×D4 | — | 53 | 6 | no | — |
| 549 | C2×D4 | — | 53 | 12 | no | — |
| 550 | C2×D4 | — | 53 | 12 | no | — |
| 551 | C2×D4 | — | 53 | 12 | no | — |
| 552 | C2×D4 | — | 53 | 4 | no | — |
| 553 | C2×D4 | — | 53 | 3 | no | — |
| 554 | C2×D4 | — | 53 | 6 | no | — |
| 555 | C2×D4 | — | 106 | 12 | no | — |
| 556 | C2×D4 | — | 106 | 6 | no | — |
| 557 | C2×D4 | — | 106 | 6 | no | — |
| 558 | C2×D4 | — | 106 | 6 | no | — |
| 559 | C2×D4 | — | 106 | 6 | no | — |
| 560 | C2×D4 | — | 106 | 24 | no | — |
| 561 | C2×D4 | — | 106 | 12 | no | — |
| 562 | C2×D4 | — | 106 | 4 | no | — |
| 563 | C2×D4 | — | 106 | 12 | no | — |
| 564 | C2×D4 | — | 106 | 12 | no | — |
| 565 | C2×D4 | — | 106 | 12 | no | — |
| 566 | C2×D4 | — | 106 | 24 | no | — |
| 567 | C2×D4 | — | 106 | 6 | no | — |
| 568 | C2×D4 | — | 106 | 6 | no | — |
| 569 | C2×D4 | — | 106 | 12 | no | — |
| 570 | C2×D4 | C22⋊#6157 | 1 | 3 | yes | — |
| 571 | C2×D4 | C22×#6157 | 1 | 6 | yes | — |
| 572 | C22×C4 | — | 2 | 6 | no | — |
| 573 | C22×C4 | — | 53 | 3 | no | — |
| 574 | C22×C4 | — | 53 | 6 | no | — |
| 575 | C22×C4 | — | 53 | 3 | no | — |
| 576 | C22×C4 | — | 53 | 3 | no | — |
| 577 | C22×C4 | — | 53 | 6 | no | — |
| 578 | C22×C4 | — | 53 | 6 | no | — |
| 579 | C22×C4 | — | 53 | 3 | no | — |
| 580 | C22×C4 | — | 53 | 6 | no | — |
| 581 | C22×C4 | — | 53 | 1 | no | — |
| 582 | C22×C4 | — | 106 | 4 | no | — |
| 583 | C22×C4 | — | 106 | 12 | no | — |
| 584 | C22×C4 | — | 106 | 6 | no | — |
| 585 | C22×C4 | — | 106 | 12 | no | — |
| 586 | C22×C4 | — | 106 | 12 | no | — |
| 587 | C22×C4 | — | 106 | 6 | no | — |
| 588 | C22×C4 | — | 106 | 6 | no | — |
| 589 | C22×C4 | — | 106 | 6 | no | — |
| 590 | C22×C4 | — | 106 | 12 | no | — |
| 591 | C22×C4 | C22×#6157 | 1 | 3 | yes | — |
| 592 | M16 | — | 106 | 12 | no | — |
| 593 | M16 | — | 106 | 12 | no | — |
| 594 | C2×C8 | — | 53 | 2 | no | — |
| 595 | C2×C8 | — | 53 | 6 | no | — |
| 596 | C2×C8 | — | 106 | 1 | no | — |
| 597 | C2×C8 | — | 106 | 3 | no | — |
| 598 | C2×C8 | — | 106 | 12 | no | — |
| 599 | C2×C8 | — | 106 | 1 | no | — |
| 600 | C2×C8 | — | 106 | 3 | no | — |
| 601 | C2×C8 | — | 106 | 12 | no | — |
| 602 | C4⋊C4 | — | 53 | 8 | no | — |
| 603 | C4⋊C4 | — | 106 | 12 | no | — |
| 604 | C22⋊C4 | — | 106 | 4 | no | — |
| 605 | C22⋊C4 | — | 106 | 12 | no | — |
| 606 | C42 | — | 106 | 4 | no | — |
| 607 | C42 | — | 106 | 12 | no | — |
| 608 | C23 | — | 2 | 6 | no | — |
| 609 | C23 | — | 53 | 1 | no | — |
| 610 | C23 | — | 53 | 6 | no | — |
| 611 | C23 | — | 53 | 6 | no | — |
| 612 | C23 | — | 53 | 3 | no | — |
| 613 | C23 | — | 106 | 12 | no | — |
| 614 | C23 | — | 106 | 4 | no | — |
| 615 | C23 | — | 106 | 6 | no | — |
| 616 | C23 | — | 424 | 12 | no | — |
| 617 | C23 | — | 212 | 6 | no | — |
| 618 | C23 | C2×C22⋊#6157 | 1 | 3 | yes | — |
| 619 | Q8 | — | 2 | 6 | no | — |
| 620 | Q8 | — | 53 | 12 | no | — |
| 621 | Q8 | — | 53 | 4 | no | — |
| 622 | Q8 | — | 106 | 4 | no | — |
| 623 | Q8 | — | 106 | 12 | no | — |
| 624 | Q8 | — | 106 | 6 | no | — |
| 625 | Q8 | C2×C22⋊#6157 | 1 | 4 | yes | — |
| 626 | Q8 | C23×#6157 | 1 | 4 | yes | — |
| 627 | D4 | — | 2 | 12 | no | — |
| 628 | D4 | — | 2 | 4 | no | — |
| 629 | D4 | — | 2 | 6 | no | — |
| 630 | D4 | — | 53 | 24 | no | — |
| 631 | D4 | — | 53 | 12 | no | — |
| 632 | D4 | — | 53 | 4 | no | — |
| 633 | D4 | — | 106 | 4 | no | — |
| 634 | D4 | — | 106 | 12 | no | — |
| 635 | D4 | — | 106 | 4 | no | — |
| 636 | D4 | — | 106 | 12 | no | — |
| 637 | D4 | — | 106 | 4 | no | — |
| 638 | D4 | — | 106 | 12 | no | — |
| 639 | D4 | — | 106 | 12 | no | — |
| 640 | D4 | — | 106 | 4 | no | — |
| 641 | D4 | — | 106 | 6 | no | — |
| 642 | D4 | C2×C22⋊#6157 | 1 | 12 | yes | — |
| 643 | D4 | C23×#6157 | 1 | 4 | yes | — |
| 644 | C2×C4 | — | 2 | 6 | no | — |
| 645 | C2×C4 | — | 2 | 12 | no | — |
| 646 | C2×C4 | — | 2 | 4 | no | — |
| 647 | C2×C4 | — | 53 | 6 | no | — |
| 648 | C2×C4 | — | 53 | 3 | no | — |
| 649 | C2×C4 | — | 53 | 1 | no | — |
| 650 | C2×C4 | — | 53 | 6 | no | — |
| 651 | C2×C4 | — | 53 | 6 | no | — |
| 652 | C2×C4 | — | 53 | 6 | no | — |
| 653 | C2×C4 | — | 53 | 6 | no | — |
| 654 | C2×C4 | — | 53 | 6 | no | — |
| 655 | C2×C4 | — | 53 | 6 | no | — |
| 656 | C2×C4 | — | 53 | 1 | no | — |
| 657 | C2×C4 | — | 53 | 1 | no | — |
| 658 | C2×C4 | — | 53 | 1 | no | — |
| 659 | C2×C4 | — | 53 | 6 | no | — |
| 660 | C2×C4 | — | 53 | 1 | no | — |
| 661 | C2×C4 | — | 106 | 4 | no | — |
| 662 | C2×C4 | — | 106 | 12 | no | — |
| 663 | C2×C4 | — | 106 | 4 | no | — |
| 664 | C2×C4 | — | 106 | 12 | no | — |
| 665 | C2×C4 | — | 106 | 4 | no | — |
| 666 | C2×C4 | — | 106 | 12 | no | — |
| 667 | C2×C4 | — | 106 | 6 | no | — |
| 668 | C2×C4 | — | 106 | 12 | no | — |
| 669 | C2×C4 | — | 106 | 4 | no | — |
| 670 | C2×C4 | — | 106 | 8 | no | — |
| 671 | C2×C4 | — | 424 | 12 | no | — |
| 672 | C2×C4 | C2×C22⋊#6157 | 1 | 3 | yes | — |
| 673 | C2×C4 | C2×C22⋊#6157 | 1 | 6 | yes | — |
| 674 | C2×C4 | C23×#6157 | 1 | 6 | yes | — |
| 675 | C2×C4 | C23×#6157 | 1 | 1 | yes | characteristic |
| 676 | C8 | — | 106 | 2 | no | — |
| 677 | C8 | — | 106 | 6 | no | — |
| 678 | C22 | — | 2 | 4 | no | — |
| 679 | C22 | — | 4 | 3 | no | — |
| 680 | C22 | — | 8 | 6 | no | — |
| 681 | C22 | — | 53 | 1 | no | — |
| 682 | C22 | — | 53 | 1 | no | — |
| 683 | C22 | — | 53 | 6 | no | — |
| 684 | C22 | — | 106 | 12 | no | — |
| 685 | C22 | — | 106 | 2 | no | — |
| 686 | C22 | — | 106 | 4 | no | — |
| 687 | C22 | — | 424 | 6 | no | — |
| 688 | C22 | — | 424 | 12 | no | — |
| 689 | C22 | — | 212 | 3 | no | — |
| 690 | C22 | — | 212 | 6 | no | — |
| 691 | C22 | — | 212 | 8 | no | — |
| 692 | C22 | C22×C22⋊#6157 | 1 | 6 | yes | — |
| 693 | C22 | C22×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 694 | C4 | — | 2 | 4 | no | — |
| 695 | C4 | — | 53 | 1 | no | — |
| 696 | C4 | — | 53 | 1 | no | — |
| 697 | C4 | — | 53 | 6 | no | — |
| 698 | C4 | — | 106 | 4 | no | — |
| 699 | C4 | — | 212 | 8 | no | — |
| 700 | C4 | C22×C22⋊#6157 | 1 | 6 | yes | — |
| 701 | C4 | C22×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 702 | C4 | C24×#6157 | 1 | 1 | yes | characteristic |
| 703 | C2 | — | 2 | 1 | no | — |
| 704 | C2 | — | 2 | 6 | no | — |
| 705 | C2 | — | 4 | 4 | no | — |
| 706 | C2 | — | 53 | 2 | no | — |
| 707 | C2 | — | 106 | 6 | no | — |
| 708 | C2 | — | 106 | 1 | no | — |
| 709 | C2 | — | 212 | 4 | no | — |
| 710 | C2 | C23×C22⋊#6157 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D53⋊#131 | C2 | semidirect |
| 2. #20291695 | C2 | semidirect |
| 3. #20291337 | C2 | semidirect |
| 4. #20291336 | C2 | semidirect |
| 5. #20291335 | C2 | semidirect |
| 6. C2×#16811613 | C2 | semidirect |
| 10. D53⋊#131 | C22 | semidirect |
| 12. C2×D53⋊M16 | C22 | semidirect |
| 13. C22×D53⋊C8 | C22 | semidirect |
| 14. #16811692 | C22 | semidirect |
| 18. C2×#13133296 | C22 | semidirect |
| 19. #16811616 | C22 | semidirect |
| 20. #16811615 | C22 | semidirect |
| 21. #16811614 | C22 | semidirect |
| 22. #16811613 | C22 | semidirect |
| 23. #16811613 | C22 | semidirect |
| 24. #16811613 | C22 | semidirect |
| 25. C2×#13133280 | C22 | semidirect |
| 26. C2×#13133279 | C22 | semidirect |
| 28. #16811460 | C4 | semidirect |
| 30. #16811459 | C4 | semidirect |
| 31. #16811459 | C4 | semidirect |
| 33. #16811458 | C4 | semidirect |
| 41. C53×#585 | C4 | semidirect |
| 70. #13133265 | C2×C4 | semidirect |
| 74. #13133264 | C2×C4 | semidirect |
| 75. #13133264 | C2×C4 | semidirect |
| 79. #13133263 | C2×C4 | semidirect |
| 80. #13133263 | C2×C4 | semidirect |
| 85. #13133262 | C2×C4 | semidirect |
| 87. C2×#11719949 | C2×C4 | semidirect |
| 92. C2×#11719945 | C2×C4 | semidirect |
| 95. C2×#11719947 | C2×C4 | semidirect |
| 108. #41×D53 | C2×C4 | semidirect |
| 109. #41×D53 | C2×C4 | semidirect |
| 125. 2−1+4×C53 | C2×C4 | semidirect |
| 127. H(5,𝔽2)×C53 | C2×C4 | semidirect |
| 130. C2×#41×C53 | C2×C4 | semidirect |
| 370. #585 | #6157 | semidirect |
| 397. C53 | #60086 | semidirect |
| 408. 2−1+4 | C2×#6157 | semidirect |
| 420. H(5,𝔽2) | C2×#6157 | semidirect |
| 452. C2×#41 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊#131 | 2 |
| #20291695 | 2 |
| #20291337 | 2 |
| #20291336 | 2 |
| #20291335 | 2 |
| C2×#16811613 | 2 |
| #585×D53 | 2 |
| #60086 | 53 |