Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
1540 conjugacy classes of subgroups.
The subgroup lattice has 686 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72223133 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72223132 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C5×#10602143 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72220908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72220903 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C5⋊D5×#498 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72220701 | C2 | 1 | 2 | yes | maximal |
| 8 | #72220687 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C4⋊Q8×C5⋊D5 | — | 2 | 1 | no | — |
| 10 | #13105775 | C22 | 1 | 1 | yes | characteristic |
| 11 | #13105760 | — | 2 | 1 | no | — |
| 12 | C52×#498 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #13102942 | — | 2 | 1 | no | — |
| 14 | #106×C5⋊D5 | — | 2 | 1 | no | — |
| 15 | #106×C5⋊D5 | C22 | 1 | 2 | yes | — |
| 16 | #13102717 | — | 2 | 1 | no | — |
| 17 | #13102717 | C22 | 1 | 2 | yes | complemented |
| 18 | C4×C8×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 19 | #13102543 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C5×#64989 | C22 | 1 | 2 | yes | — |
| 21 | #13101095 | — | 2 | 1 | no | — |
| 22 | #13101049 | C22 | 1 | 2 | yes | — |
| 23 | #13101043 | C22 | 1 | 1 | yes | characteristic |
| 24 | #13100806 | C22 | 1 | 2 | yes | — |
| 25 | #13100574 | — | 2 | 1 | no | — |
| 26 | #13100568 | — | 2 | 1 | no | — |
| 27 | C5×#64708 | C22 | 1 | 4 | yes | — |
| 28 | C5×#64707 | C22 | 1 | 4 | yes | complemented |
| 29 | C5×#64683 | C22 | 1 | 2 | yes | complemented |
| 30 | #13099307 | C22 | 1 | 4 | yes | complemented |
| 31 | #13099305 | C22 | 1 | 2 | yes | complemented |
| 32 | #13099294 | C22 | 1 | 4 | yes | — |
| 33 | D5×#2230 | — | 5 | 2 | no | maximal |
| 34 | C2×Q8×C5⋊D5 | — | 4 | 1 | no | — |
| 35 | #11717471 | — | 2 | 1 | no | — |
| 36 | C52×C4⋊Q8 | — | 2 | 1 | no | — |
| 37 | #11717264 | — | 4 | 1 | no | — |
| 38 | C2×C8×C5⋊D5 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×C8×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 40 | C4⋊C4×C5⋊D5 | — | 2 | 2 | no | — |
| 41 | C4⋊C4×C5⋊D5 | — | 4 | 1 | no | — |
| 42 | #11717208 | — | 2 | 2 | no | — |
| 43 | #11717208 | — | 4 | 1 | no | — |
| 44 | C42×C5⋊D5 | D4 | 1 | 1 | yes | characteristic |
| 45 | #11717189 | — | 2 | 1 | no | — |
| 46 | C5×#4050 | C23 | 1 | 2 | yes | — |
| 47 | C5×#4047 | — | 2 | 2 | no | — |
| 48 | #11716940 | — | 2 | 1 | no | — |
| 49 | #11716936 | — | 2 | 1 | no | — |
| 50 | #11716933 | — | 2 | 2 | no | — |
| 51 | #11716928 | Q8 | 1 | 2 | yes | complemented |
| 52 | #11716927 | — | 2 | 1 | no | — |
| 53 | #11716923 | — | 4 | 1 | no | — |
| 54 | #11716921 | — | 4 | 1 | no | — |
| 55 | #11716920 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 56 | #11716915 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 57 | #11716914 | — | 2 | 1 | no | — |
| 58 | #11716909 | — | 4 | 1 | no | — |
| 59 | C8×D52 | — | 4 | 1 | no | — |
| 60 | C52×#106 | — | 2 | 1 | no | — |
| 61 | C52×#106 | C23 | 1 | 2 | yes | — |
| 62 | C4×C52×C8 | C23 | 1 | 1 | yes | characteristic |
| 63 | #11716684 | — | 2 | 1 | no | — |
| 64 | #11716684 | C23 | 1 | 2 | yes | — |
| 65 | C8×#1039 | D4 | 1 | 1 | yes | characteristic |
| 66 | C8×#1039 | C23 | 1 | 1 | yes | characteristic |
| 67 | #11716675 | — | 2 | 2 | no | — |
| 68 | #11716675 | — | 2 | 2 | no | — |
| 69 | C4×#6029 | D4 | 1 | 1 | yes | characteristic |
| 70 | C5×#3951 | C23 | 1 | 2 | yes | — |
| 71 | C5×#3944 | C23 | 1 | 4 | yes | — |
| 72 | C5×#3937 | — | 2 | 2 | no | — |
| 73 | #11716619 | — | 2 | 1 | no | — |
| 74 | #11716609 | — | 2 | 2 | no | — |
| 75 | #11716585 | — | 2 | 2 | no | — |
| 76 | #11716583 | — | 2 | 2 | no | — |
| 77 | D5×#498 | — | 5 | 2 | no | — |
| 78 | D5×#498 | — | 10 | 2 | no | — |
| 79 | D5×#443 | — | 5 | 2 | no | — |
| 80 | C5×#2230 | — | 5 | 2 | no | — |
| 81 | #10602143 | D5 | 1 | 2 | yes | complemented |
| 82 | #10601712 | — | 5 | 2 | no | — |
| 83 | #10600108 | — | 5 | 4 | no | — |
| 84 | D5×#365 | — | 5 | 4 | no | — |
| 85 | #10600100 | — | 5 | 2 | no | — |
| 86 | D5×#364 | — | 5 | 2 | no | — |
| 87 | D5×#360 | — | 5 | 4 | no | — |
| 88 | #10600039 | — | 5 | 4 | no | — |
| 89 | C2×C52×Q8 | — | 4 | 1 | no | — |
| 90 | Q8×C5⋊D5 | — | 8 | 4 | no | — |
| 91 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 92 | C2×C4×C5⋊D5 | — | 4 | 2 | no | — |
| 93 | C2×C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | C2×#6045 | — | 4 | 2 | no | — |
| 95 | C2×#6045 | — | 4 | 1 | no | — |
| 96 | C5×#709 | — | 2 | 2 | no | — |
| 97 | #87886 | — | 4 | 1 | no | — |
| 98 | #87880 | — | 4 | 1 | no | — |
| 99 | #87877 | — | 2 | 1 | no | — |
| 100 | C4×D52 | — | 4 | 1 | no | — |
| 101 | #87873 | — | 4 | 1 | no | — |
| 102 | #87872 | — | 2 | 1 | no | — |
| 103 | #87871 | — | 2 | 2 | no | — |
| 104 | C2×C52×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C52×C8 | C24 | 1 | 1 | yes | characteristic |
| 106 | C52×C4⋊C4 | — | 2 | 2 | no | — |
| 107 | C52×C4⋊C4 | — | 4 | 1 | no | — |
| 108 | C42×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C4⋊#1039 | — | 2 | 2 | no | — |
| 110 | C4⋊#1039 | — | 4 | 1 | no | — |
| 111 | #87806 | — | 4 | 2 | no | — |
| 112 | #87806 | — | 4 | 2 | no | — |
| 113 | C4×#1039 | — | 2 | 1 | no | — |
| 114 | C4×#1039 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C2×#6029 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×#6029 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C8×C5⋊D5 | SD16 | 1 | 1 | yes | characteristic |
| 118 | C8×C5⋊D5 | SD16 | 1 | 1 | yes | characteristic |
| 119 | C8×C5⋊D5 | SD16 | 1 | 1 | yes | characteristic |
| 120 | C8×C5⋊D5 | SD16 | 1 | 1 | yes | characteristic |
| 121 | C8×C5⋊D5 | C2×Q8 | 1 | 1 | yes | characteristic |
| 122 | C8×C5⋊D5 | C2×Q8 | 1 | 1 | yes | characteristic |
| 123 | C8×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 124 | C8×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 125 | C5×#681 | — | 2 | 2 | no | — |
| 126 | C5×Dic20 | C2×Q8 | 1 | 2 | yes | complemented |
| 127 | C5×D40 | C2×Q8 | 1 | 2 | yes | complemented |
| 128 | C5×#677 | — | 2 | 2 | no | — |
| 129 | C5×#676 | — | 4 | 2 | no | — |
| 130 | C5×C8×D5 | — | 4 | 2 | no | — |
| 131 | #87775 | — | 2 | 1 | no | — |
| 132 | #87772 | — | 2 | 2 | no | — |
| 133 | #87770 | — | 2 | 1 | no | — |
| 134 | #87769 | — | 4 | 1 | no | — |
| 135 | #87768 | — | 4 | 2 | no | — |
| 136 | #87767 | — | 4 | 1 | no | — |
| 137 | D5×#168 | — | 4 | 2 | no | — |
| 138 | C5×#672 | — | 2 | 4 | no | — |
| 139 | D5×#135 | — | 5 | 2 | no | — |
| 140 | D5×#131 | — | 10 | 2 | no | — |
| 141 | D5×C4⋊Q8 | — | 10 | 2 | no | — |
| 142 | D5×C4⋊Q8 | — | 10 | 4 | no | — |
| 143 | C5×#498 | — | 2 | 2 | no | — |
| 144 | C5×#498 | C2×D5 | 1 | 2 | yes | complemented |
| 145 | C5×#443 | — | 5 | 2 | no | — |
| 146 | #65485 | — | 5 | 2 | no | — |
| 147 | #65433 | — | 10 | 2 | no | — |
| 148 | #65368 | — | 10 | 2 | no | — |
| 149 | #65368 | — | 10 | 4 | no | — |
| 150 | D5×M32 | — | 5 | 4 | no | — |
| 151 | #65184 | — | 5 | 2 | no | — |
| 152 | D5×#108 | — | 5 | 2 | no | — |
| 153 | D5×#106 | — | 5 | 4 | no | — |
| 154 | D5×#106 | — | 10 | 4 | no | — |
| 155 | D5×#106 | — | 10 | 2 | no | — |
| 156 | D5×#106 | — | 10 | 4 | no | — |
| 157 | #65144 | — | 5 | 4 | no | — |
| 158 | #65144 | — | 10 | 2 | no | — |
| 159 | #65144 | — | 10 | 4 | no | — |
| 160 | #65144 | — | 10 | 4 | no | — |
| 161 | #65113 | — | 10 | 2 | no | — |
| 162 | D5×#104 | — | 10 | 2 | no | — |
| 163 | #64989 | C2×D5 | 1 | 2 | yes | — |
| 164 | C4×C8×D5 | — | 5 | 2 | no | — |
| 165 | C4×C8×D5 | — | 10 | 2 | no | — |
| 166 | #64969 | — | 5 | 2 | no | — |
| 167 | #64969 | — | 10 | 2 | no | — |
| 168 | C5×#365 | — | 5 | 4 | no | — |
| 169 | C5×#364 | — | 5 | 2 | no | — |
| 170 | C5×#360 | — | 5 | 4 | no | — |
| 171 | #64786 | — | 5 | 4 | no | — |
| 172 | #64738 | — | 5 | 4 | no | — |
| 173 | #64733 | — | 5 | 4 | no | — |
| 174 | #64731 | — | 5 | 4 | no | — |
| 175 | #64714 | — | 5 | 4 | no | — |
| 176 | #64708 | C2×D5 | 1 | 4 | yes | — |
| 177 | #64707 | C2×D5 | 1 | 4 | yes | complemented |
| 178 | #64683 | C2×D5 | 1 | 2 | yes | complemented |
| 179 | C2×#2230 | — | 25 | 1 | no | Sylow |
| 180 | C22×C5⋊D5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 181 | C2×D52 | — | 4 | 1 | no | — |
| 182 | C52×Q8 | — | 8 | 2 | no | — |
| 183 | C2×C4×C52 | — | 2 | 1 | no | — |
| 184 | C2×C4×C52 | — | 4 | 2 | no | — |
| 185 | C2×C4×C52 | C22×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×#1039 | — | 2 | 1 | no | — |
| 187 | C2×#1039 | — | 4 | 2 | no | — |
| 188 | C2×#1039 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 189 | C4×C5⋊D5 | — | 2 | 4 | no | — |
| 190 | C4×C5⋊D5 | — | 8 | 4 | no | — |
| 191 | C4×C5⋊D5 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 192 | C4×C5⋊D5 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 193 | C4×C5⋊D5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 194 | C4×C5⋊D5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 195 | #6045 | — | 8 | 4 | no | — |
| 196 | #6045 | — | 8 | 2 | no | — |
| 197 | C5×C22⋊D5 | — | 4 | 2 | no | — |
| 198 | C5×D20 | — | 2 | 2 | no | — |
| 199 | C4×C5×D5 | — | 4 | 2 | no | — |
| 200 | C5×Dic10 | — | 2 | 2 | no | — |
| 201 | #6039 | — | 4 | 1 | no | — |
| 202 | #6038 | — | 4 | 2 | no | — |
| 203 | #6037 | — | 4 | 1 | no | — |
| 204 | #6036 | — | 4 | 1 | no | — |
| 205 | D5×Dic5 | — | 4 | 2 | no | — |
| 206 | C52×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 207 | C52×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 208 | C52×C8 | C22×Q8 | 1 | 1 | yes | characteristic |
| 209 | C52×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 210 | #6029 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 211 | #6029 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 212 | #6029 | C2×SD16 | 1 | 1 | yes | characteristic |
| 213 | #6029 | C2×SD16 | 1 | 1 | yes | characteristic |
| 214 | C5×#168 | — | 4 | 2 | no | — |
| 215 | D5×#41 | — | 10 | 2 | no | — |
| 216 | C2×Q8×D5 | — | 20 | 2 | no | — |
| 217 | C2×Q8×D5 | — | 20 | 4 | no | — |
| 218 | C5×#135 | — | 5 | 2 | no | — |
| 219 | C5×#131 | — | 10 | 2 | no | — |
| 220 | C5×C4⋊Q8 | — | 2 | 4 | no | — |
| 221 | C5×C4⋊Q8 | — | 2 | 2 | no | — |
| 222 | #4096 | — | 10 | 2 | no | — |
| 223 | #4094 | — | 10 | 2 | no | — |
| 224 | #4090 | — | 20 | 2 | no | — |
| 225 | #4090 | — | 20 | 4 | no | — |
| 226 | #4065 | — | 5 | 2 | no | — |
| 227 | D5×Q16 | — | 5 | 2 | no | — |
| 228 | #4062 | — | 10 | 2 | no | — |
| 229 | D5×SD16 | — | 10 | 2 | no | — |
| 230 | #4058 | — | 5 | 2 | no | — |
| 231 | D5×D8 | — | 5 | 2 | no | — |
| 232 | #4053 | — | 10 | 2 | no | — |
| 233 | #4053 | — | 20 | 2 | no | — |
| 234 | D5×M16 | — | 10 | 2 | no | — |
| 235 | D5×M16 | — | 20 | 2 | no | — |
| 236 | #4050 | C22×D5 | 1 | 2 | yes | — |
| 237 | #4047 | — | 2 | 2 | no | — |
| 238 | #4047 | — | 20 | 2 | no | — |
| 239 | C2×C8×D5 | — | 5 | 2 | no | — |
| 240 | C2×C8×D5 | — | 5 | 2 | no | — |
| 241 | C2×C8×D5 | — | 10 | 2 | no | — |
| 242 | C2×C8×D5 | — | 10 | 2 | no | — |
| 243 | C2×C8×D5 | — | 20 | 2 | no | — |
| 244 | D5×C4⋊C4 | — | 10 | 4 | no | — |
| 245 | D5×C4⋊C4 | — | 10 | 8 | no | — |
| 246 | D5×C4⋊C4 | — | 20 | 2 | no | — |
| 247 | D5×C4⋊C4 | — | 20 | 4 | no | — |
| 248 | #4034 | — | 10 | 4 | no | — |
| 249 | #4034 | — | 10 | 8 | no | — |
| 250 | #4034 | — | 20 | 2 | no | — |
| 251 | #4034 | — | 20 | 4 | no | — |
| 252 | C42×D5 | — | 5 | 2 | no | — |
| 253 | C42×D5 | — | 10 | 2 | no | — |
| 254 | #4015 | — | 10 | 4 | no | — |
| 255 | #4015 | — | 10 | 2 | no | — |
| 256 | C5×M32 | — | 5 | 4 | no | — |
| 257 | C5×#108 | — | 5 | 2 | no | — |
| 258 | C5×#106 | — | 2 | 4 | no | — |
| 259 | C5×#106 | — | 2 | 2 | no | — |
| 260 | C5×#106 | — | 2 | 4 | no | — |
| 261 | C5×#106 | C22×D5 | 1 | 4 | yes | — |
| 262 | C5×#104 | — | 10 | 2 | no | — |
| 263 | C4×C5×C8 | — | 2 | 2 | no | — |
| 264 | C4×C5×C8 | C22×D5 | 1 | 2 | yes | — |
| 265 | #3969 | — | 10 | 2 | no | — |
| 266 | #3957 | — | 10 | 2 | no | — |
| 267 | #3954 | — | 10 | 2 | no | — |
| 268 | #3951 | C22×D5 | 1 | 2 | yes | — |
| 269 | #3949 | — | 5 | 4 | no | — |
| 270 | #3949 | — | 10 | 4 | no | — |
| 271 | #3949 | — | 10 | 4 | no | — |
| 272 | #3949 | — | 10 | 2 | no | — |
| 273 | C8×Dic5 | — | 5 | 2 | no | — |
| 274 | C8×Dic5 | — | 5 | 2 | no | — |
| 275 | C8×Dic5 | — | 10 | 2 | no | — |
| 276 | C8×Dic5 | — | 10 | 2 | no | — |
| 277 | #3944 | C22×D5 | 1 | 4 | yes | — |
| 278 | #3940 | — | 10 | 4 | no | — |
| 279 | #3940 | — | 10 | 4 | no | — |
| 280 | #3940 | — | 10 | 8 | no | — |
| 281 | #3940 | — | 10 | 8 | no | — |
| 282 | #3937 | — | 2 | 2 | no | — |
| 283 | C4×#168 | — | 5 | 2 | no | — |
| 284 | C4×#168 | — | 10 | 2 | no | — |
| 285 | #3930 | — | 10 | 4 | no | — |
| 286 | D5×C16 | — | 10 | 4 | no | — |
| 287 | C2×#498 | — | 25 | 1 | no | — |
| 288 | C2×#443 | — | 25 | 1 | no | — |
| 289 | #2230 | — | 5 | 2 | no | — |
| 290 | #2230 | — | 25 | 4 | no | — |
| 291 | #2230 | — | 25 | 2 | no | — |
| 292 | C2×#365 | — | 25 | 2 | no | — |
| 293 | C2×#364 | — | 25 | 1 | no | — |
| 294 | C2×#360 | — | 25 | 2 | no | — |
| 295 | C22×C52 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 296 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 297 | C2×C5⋊D5 | #476 | 1 | 1 | yes | characteristic |
| 298 | C2×C5⋊D5 | #476 | 1 | 1 | yes | characteristic |
| 299 | C2×C5×D5 | — | 4 | 2 | no | — |
| 300 | D52 | — | 8 | 2 | no | — |
| 301 | C4×C52 | — | 2 | 2 | no | — |
| 302 | C4×C52 | — | 8 | 2 | no | — |
| 303 | C4×C52 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 304 | C4×C52 | C22×SD16 | 1 | 1 | yes | characteristic |
| 305 | #1039 | — | 2 | 2 | no | — |
| 306 | #1039 | — | 8 | 2 | no | — |
| 307 | #1039 | #476 | 1 | 1 | yes | characteristic |
| 308 | #1039 | #476 | 1 | 1 | yes | characteristic |
| 309 | C5×Dic5 | — | 4 | 2 | no | — |
| 310 | C5×#41 | — | 10 | 2 | no | — |
| 311 | C2×C5×Q8 | — | 4 | 4 | no | — |
| 312 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 313 | #713 | — | 10 | 2 | no | — |
| 314 | Q8×D5 | — | 10 | 2 | no | — |
| 315 | Q8×D5 | — | 40 | 8 | no | — |
| 316 | Q8×D5 | — | 40 | 16 | no | — |
| 317 | #711 | — | 10 | 2 | no | — |
| 318 | #711 | — | 20 | 2 | no | — |
| 319 | D4×D5 | — | 10 | 2 | no | — |
| 320 | D4×D5 | — | 20 | 2 | no | — |
| 321 | #709 | — | 2 | 2 | no | — |
| 322 | #709 | — | 20 | 2 | no | — |
| 323 | C2×C4×D5 | — | 5 | 2 | no | — |
| 324 | C2×C4×D5 | — | 10 | 2 | no | — |
| 325 | C2×C4×D5 | — | 10 | 2 | no | — |
| 326 | C2×C4×D5 | — | 10 | 4 | no | — |
| 327 | C2×C4×D5 | — | 20 | 2 | no | — |
| 328 | C2×C4×D5 | — | 20 | 4 | no | — |
| 329 | C2×C4×D5 | — | 20 | 8 | no | — |
| 330 | C2×Dic10 | — | 20 | 8 | no | — |
| 331 | C2×Dic10 | — | 20 | 4 | no | — |
| 332 | C2×Dic10 | — | 20 | 4 | no | — |
| 333 | C2×Dic10 | — | 20 | 2 | no | — |
| 334 | C5×Q16 | — | 5 | 2 | no | — |
| 335 | C5×SD16 | — | 10 | 2 | no | — |
| 336 | C5×D8 | — | 5 | 2 | no | — |
| 337 | C5×M16 | — | 10 | 2 | no | — |
| 338 | C5×M16 | — | 20 | 2 | no | — |
| 339 | C2×C5×C8 | — | 2 | 2 | no | — |
| 340 | C2×C5×C8 | — | 2 | 2 | no | — |
| 341 | C2×C5×C8 | — | 20 | 2 | no | — |
| 342 | C2×C5×C8 | D4×D5 | 1 | 2 | yes | — |
| 343 | C2×C5×C8 | C23×D5 | 1 | 2 | yes | — |
| 344 | C5×C4⋊C4 | — | 2 | 8 | no | — |
| 345 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 346 | C5×C4⋊C4 | — | 4 | 4 | no | — |
| 347 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 348 | C42×C5 | — | 2 | 2 | no | — |
| 349 | C42×C5 | D4×D5 | 1 | 2 | yes | — |
| 350 | #689 | — | 10 | 2 | no | — |
| 351 | #688 | — | 10 | 2 | no | — |
| 352 | #687 | — | 10 | 2 | no | — |
| 353 | #686 | — | 10 | 2 | no | — |
| 354 | C4⋊Dic5 | — | 10 | 8 | no | — |
| 355 | C4⋊Dic5 | — | 10 | 4 | no | — |
| 356 | C4⋊Dic5 | — | 20 | 4 | no | — |
| 357 | C4⋊Dic5 | — | 20 | 2 | no | — |
| 358 | #683 | — | 20 | 4 | no | — |
| 359 | #683 | — | 20 | 8 | no | — |
| 360 | #683 | — | 20 | 4 | no | — |
| 361 | #683 | — | 20 | 8 | no | — |
| 362 | C4×Dic5 | — | 5 | 2 | no | — |
| 363 | C4×Dic5 | — | 10 | 2 | no | — |
| 364 | C4×Dic5 | — | 10 | 2 | no | — |
| 365 | C4×Dic5 | — | 10 | 4 | no | — |
| 366 | #681 | — | 2 | 2 | no | — |
| 367 | #681 | — | 20 | 2 | no | — |
| 368 | C2×#168 | — | 5 | 2 | no | — |
| 369 | C2×#168 | — | 5 | 2 | no | — |
| 370 | C2×#168 | — | 10 | 2 | no | — |
| 371 | C2×#168 | — | 10 | 2 | no | — |
| 372 | C2×#168 | — | 20 | 2 | no | — |
| 373 | Dic20 | Q8×D5 | 1 | 2 | yes | complemented |
| 374 | D40 | Q8×D5 | 1 | 2 | yes | complemented |
| 375 | #677 | — | 2 | 2 | no | — |
| 376 | #676 | — | 4 | 2 | no | — |
| 377 | #676 | — | 20 | 2 | no | — |
| 378 | #676 | — | 20 | 2 | no | — |
| 379 | C8×D5 | — | 4 | 2 | no | — |
| 380 | C8×D5 | — | 5 | 2 | no | — |
| 381 | C8×D5 | — | 5 | 2 | no | — |
| 382 | C8×D5 | — | 5 | 2 | no | — |
| 383 | C8×D5 | — | 5 | 2 | no | — |
| 384 | C8×D5 | — | 5 | 2 | no | — |
| 385 | C8×D5 | — | 5 | 2 | no | — |
| 386 | C8×D5 | — | 5 | 2 | no | — |
| 387 | C8×D5 | — | 5 | 2 | no | — |
| 388 | C8×D5 | — | 10 | 2 | no | — |
| 389 | C8×D5 | — | 10 | 2 | no | — |
| 390 | C8×D5 | — | 10 | 2 | no | — |
| 391 | C8×D5 | — | 10 | 2 | no | — |
| 392 | C8×D5 | — | 10 | 2 | no | — |
| 393 | C8×D5 | — | 10 | 2 | no | — |
| 394 | C8×D5 | — | 10 | 2 | no | — |
| 395 | C8×D5 | — | 10 | 2 | no | — |
| 396 | C8×D5 | — | 20 | 2 | no | — |
| 397 | C8×D5 | — | 20 | 2 | no | — |
| 398 | C5×C16 | — | 10 | 4 | no | — |
| 399 | #672 | — | 2 | 4 | no | — |
| 400 | C2×#135 | — | 25 | 1 | no | — |
| 401 | C2×#131 | — | 50 | 1 | no | — |
| 402 | C2×C4⋊Q8 | — | 50 | 1 | no | — |
| 403 | C2×M32 | — | 25 | 2 | no | — |
| 404 | #498 | — | 25 | 2 | no | — |
| 405 | #498 | — | 25 | 1 | no | — |
| 406 | #498 | — | 50 | 1 | no | — |
| 407 | #498 | — | 50 | 1 | no | — |
| 408 | #498 | D52 | 1 | 1 | yes | characteristic, complemented |
| 409 | #443 | — | 5 | 2 | no | — |
| 410 | #443 | — | 25 | 2 | no | — |
| 411 | #443 | — | 50 | 1 | no | — |
| 412 | #443 | — | 50 | 1 | no | — |
| 413 | C2×#108 | — | 25 | 1 | no | — |
| 414 | C2×#106 | — | 25 | 2 | no | — |
| 415 | C2×#106 | — | 50 | 1 | no | — |
| 416 | C2×#104 | — | 50 | 1 | no | — |
| 417 | C2×C4×C8 | — | 25 | 1 | no | — |
| 418 | #365 | — | 5 | 4 | no | — |
| 419 | #365 | — | 25 | 4 | no | — |
| 420 | #364 | — | 5 | 2 | no | — |
| 421 | #364 | — | 25 | 2 | no | — |
| 422 | #360 | — | 5 | 4 | no | — |
| 423 | #360 | — | 25 | 4 | no | — |
| 424 | C2×C52 | — | 2 | 1 | no | — |
| 425 | C2×C52 | C2×#476 | 1 | 1 | yes | characteristic |
| 426 | C5⋊D5 | — | 2 | 1 | no | — |
| 427 | C5⋊D5 | #2230 | 1 | 2 | yes | complemented |
| 428 | C5×D5 | — | 8 | 2 | no | — |
| 429 | C22×D5 | — | 5 | 2 | no | — |
| 430 | C22×D5 | — | 10 | 2 | no | — |
| 431 | C22×D5 | — | 20 | 2 | no | — |
| 432 | C5×Q8 | — | 8 | 8 | no | — |
| 433 | C5×Q8 | — | 8 | 4 | no | — |
| 434 | C5×Q8 | — | 10 | 2 | no | — |
| 435 | C5×D4 | — | 10 | 2 | no | — |
| 436 | C5×D4 | — | 20 | 2 | no | — |
| 437 | C2×C4×C5 | — | 2 | 4 | no | — |
| 438 | C2×C4×C5 | — | 2 | 2 | no | — |
| 439 | C2×C4×C5 | — | 2 | 2 | no | — |
| 440 | C2×C4×C5 | — | 4 | 8 | no | — |
| 441 | C2×C4×C5 | — | 4 | 4 | no | — |
| 442 | C2×C4×C5 | — | 20 | 2 | no | — |
| 443 | C2×C4×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 444 | C22⋊D5 | — | 4 | 2 | no | — |
| 445 | C22⋊D5 | — | 20 | 2 | no | — |
| 446 | C22⋊D5 | — | 20 | 2 | no | — |
| 447 | C2×Dic5 | — | 5 | 2 | no | — |
| 448 | C2×Dic5 | — | 10 | 2 | no | — |
| 449 | C2×Dic5 | — | 10 | 4 | no | — |
| 450 | C2×Dic5 | — | 10 | 2 | no | — |
| 451 | C2×Dic5 | — | 20 | 2 | no | — |
| 452 | C2×Dic5 | — | 20 | 8 | no | — |
| 453 | C2×Dic5 | — | 20 | 4 | no | — |
| 454 | D20 | — | 2 | 2 | no | — |
| 455 | D20 | — | 20 | 2 | no | — |
| 456 | C4×D5 | — | 4 | 2 | no | — |
| 457 | C4×D5 | — | 5 | 2 | no | — |
| 458 | C4×D5 | — | 5 | 2 | no | — |
| 459 | C4×D5 | — | 5 | 2 | no | — |
| 460 | C4×D5 | — | 5 | 2 | no | — |
| 461 | C4×D5 | — | 10 | 2 | no | — |
| 462 | C4×D5 | — | 10 | 2 | no | — |
| 463 | C4×D5 | — | 10 | 2 | no | — |
| 464 | C4×D5 | — | 10 | 2 | no | — |
| 465 | C4×D5 | — | 10 | 8 | no | — |
| 466 | C4×D5 | — | 10 | 16 | no | — |
| 467 | C4×D5 | — | 20 | 2 | no | — |
| 468 | C4×D5 | — | 20 | 2 | no | — |
| 469 | C4×D5 | — | 40 | 8 | no | — |
| 470 | C4×D5 | — | 40 | 16 | no | — |
| 471 | Dic10 | — | 2 | 2 | no | — |
| 472 | Dic10 | — | 20 | 2 | no | — |
| 473 | Dic10 | — | 40 | 16 | no | — |
| 474 | Dic10 | — | 40 | 8 | no | — |
| 475 | Dic10 | — | 40 | 8 | no | — |
| 476 | Dic10 | — | 40 | 4 | no | — |
| 477 | C5×C8 | — | 2 | 2 | no | — |
| 478 | C5×C8 | — | 2 | 2 | no | — |
| 479 | C5×C8 | — | 2 | 2 | no | — |
| 480 | C5×C8 | — | 2 | 2 | no | — |
| 481 | C5×C8 | — | 20 | 2 | no | — |
| 482 | C5×C8 | D5×SD16 | 1 | 2 | yes | — |
| 483 | C5×C8 | D5×SD16 | 1 | 2 | yes | — |
| 484 | C5×C8 | C2×Q8×D5 | 1 | 2 | yes | — |
| 485 | C5×C8 | D5×#41 | 1 | 2 | yes | — |
| 486 | #168 | — | 4 | 2 | no | — |
| 487 | #168 | — | 5 | 2 | no | — |
| 488 | #168 | — | 5 | 2 | no | — |
| 489 | #168 | — | 5 | 2 | no | — |
| 490 | #168 | — | 5 | 2 | no | — |
| 491 | #168 | — | 10 | 2 | no | — |
| 492 | #168 | — | 10 | 2 | no | — |
| 493 | #168 | — | 10 | 2 | no | — |
| 494 | #168 | — | 10 | 2 | no | — |
| 495 | C2×#41 | — | 50 | 1 | no | — |
| 496 | C22×Q8 | — | 100 | 1 | no | — |
| 497 | #135 | — | 5 | 2 | no | — |
| 498 | #135 | — | 25 | 2 | no | — |
| 499 | #135 | — | 50 | 1 | no | — |
| 500 | #135 | — | 50 | 1 | no | — |
| 501 | C2×Q16 | — | 25 | 1 | no | — |
| 502 | C2×SD16 | — | 50 | 1 | no | — |
| 503 | C2×D8 | — | 25 | 1 | no | — |
| 504 | #131 | — | 10 | 2 | no | — |
| 505 | #131 | — | 50 | 2 | no | — |
| 506 | #131 | — | 100 | 1 | no | — |
| 507 | #131 | — | 100 | 1 | no | — |
| 508 | C2×M16 | — | 50 | 1 | no | — |
| 509 | C2×M16 | — | 100 | 1 | no | — |
| 510 | C22×C8 | — | 25 | 1 | no | — |
| 511 | C22×C8 | — | 25 | 1 | no | — |
| 512 | C22×C8 | — | 100 | 1 | no | — |
| 513 | C4⋊Q8 | — | 2 | 1 | no | — |
| 514 | C4⋊Q8 | — | 50 | 2 | no | — |
| 515 | C4⋊Q8 | — | 50 | 1 | no | — |
| 516 | C4⋊Q8 | — | 100 | 1 | no | — |
| 517 | C4⋊Q8 | — | 100 | 1 | no | — |
| 518 | C2×C4⋊C4 | — | 50 | 2 | no | — |
| 519 | C2×C4⋊C4 | — | 100 | 1 | no | — |
| 520 | C2×C42 | — | 25 | 1 | no | — |
| 521 | M32 | — | 5 | 4 | no | — |
| 522 | M32 | — | 50 | 2 | no | — |
| 523 | C2×C16 | — | 50 | 2 | no | — |
| 524 | #108 | — | 5 | 2 | no | — |
| 525 | #108 | — | 50 | 1 | no | — |
| 526 | #106 | — | 2 | 1 | no | — |
| 527 | #106 | — | 25 | 2 | no | — |
| 528 | #106 | — | 50 | 2 | no | — |
| 529 | #106 | — | 50 | 2 | no | — |
| 530 | #106 | — | 50 | 1 | no | — |
| 531 | #106 | C2×D52 | 1 | 2 | yes | — |
| 532 | #104 | — | 10 | 2 | no | — |
| 533 | #104 | — | 50 | 2 | no | — |
| 534 | C4×C8 | — | 25 | 1 | no | — |
| 535 | C4×C8 | — | 25 | 1 | no | — |
| 536 | C4×C8 | — | 25 | 1 | no | — |
| 537 | C4×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 538 | C52 | C2×#2230 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 539 | C22×C5 | — | 2 | 2 | no | — |
| 540 | C22×C5 | — | 20 | 2 | no | — |
| 541 | C22×C5 | D5×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 542 | C2×D5 | — | 4 | 2 | no | — |
| 543 | C2×D5 | — | 5 | 2 | no | — |
| 544 | C2×D5 | — | 5 | 2 | no | — |
| 545 | C2×D5 | — | 10 | 2 | no | — |
| 546 | C2×D5 | — | 10 | 2 | no | — |
| 547 | C2×D5 | — | 10 | 4 | no | — |
| 548 | C2×D5 | — | 10 | 8 | no | — |
| 549 | C2×D5 | — | 40 | 4 | no | — |
| 550 | C4×C5 | — | 2 | 8 | no | — |
| 551 | C4×C5 | — | 2 | 4 | no | — |
| 552 | C4×C5 | — | 2 | 2 | no | — |
| 553 | C4×C5 | — | 2 | 2 | no | — |
| 554 | C4×C5 | — | 8 | 8 | no | — |
| 555 | C4×C5 | — | 8 | 4 | no | — |
| 556 | C4×C5 | — | 20 | 2 | no | — |
| 557 | C4×C5 | D5×C22⋊Q8 | 1 | 2 | yes | — |
| 558 | C4×C5 | C2×D5×SD16 | 1 | 2 | yes | — |
| 559 | Dic5 | — | 4 | 2 | no | — |
| 560 | Dic5 | — | 5 | 2 | no | — |
| 561 | Dic5 | — | 5 | 2 | no | — |
| 562 | Dic5 | — | 10 | 2 | no | — |
| 563 | Dic5 | — | 10 | 2 | no | — |
| 564 | Dic5 | — | 10 | 8 | no | — |
| 565 | Dic5 | — | 10 | 4 | no | — |
| 566 | Dic5 | — | 40 | 8 | no | — |
| 567 | Dic5 | — | 40 | 4 | no | — |
| 568 | #41 | — | 10 | 2 | no | — |
| 569 | #41 | — | 50 | 2 | no | — |
| 570 | #41 | — | 100 | 1 | no | — |
| 571 | #41 | — | 100 | 1 | no | — |
| 572 | C2×Q8 | — | 4 | 1 | no | — |
| 573 | C2×Q8 | — | 50 | 1 | no | — |
| 574 | C2×Q8 | — | 100 | 1 | no | — |
| 575 | C2×Q8 | — | 100 | 2 | no | — |
| 576 | C2×Q8 | — | 200 | 4 | no | — |
| 577 | C2×D4 | — | 50 | 1 | no | — |
| 578 | C2×D4 | — | 100 | 1 | no | — |
| 579 | C22×C4 | — | 25 | 1 | no | — |
| 580 | C22×C4 | — | 50 | 1 | no | — |
| 581 | C22×C4 | — | 100 | 2 | no | — |
| 582 | C22×C4 | — | 100 | 1 | no | — |
| 583 | Q16 | — | 5 | 2 | no | — |
| 584 | Q16 | — | 50 | 1 | no | — |
| 585 | SD16 | — | 10 | 2 | no | — |
| 586 | SD16 | — | 50 | 2 | no | — |
| 587 | D8 | — | 5 | 2 | no | — |
| 588 | D8 | — | 50 | 1 | no | — |
| 589 | M16 | — | 10 | 2 | no | — |
| 590 | M16 | — | 20 | 2 | no | — |
| 591 | M16 | — | 100 | 1 | no | — |
| 592 | M16 | — | 100 | 2 | no | — |
| 593 | C2×C8 | — | 20 | 2 | no | — |
| 594 | C2×C8 | — | 25 | 1 | no | — |
| 595 | C2×C8 | — | 25 | 1 | no | — |
| 596 | C2×C8 | — | 25 | 1 | no | — |
| 597 | C2×C8 | — | 25 | 1 | no | — |
| 598 | C2×C8 | — | 25 | 1 | no | — |
| 599 | C2×C8 | — | 25 | 1 | no | — |
| 600 | C2×C8 | — | 25 | 1 | no | — |
| 601 | C2×C8 | — | 25 | 1 | no | — |
| 602 | C2×C8 | — | 25 | 1 | no | — |
| 603 | C2×C8 | — | 25 | 1 | no | — |
| 604 | C2×C8 | — | 100 | 1 | no | — |
| 605 | C2×C8 | — | 100 | 2 | no | — |
| 606 | C2×C8 | #87886 | 1 | 1 | yes | characteristic |
| 607 | C2×C8 | C22×D52 | 1 | 1 | yes | characteristic |
| 608 | C4⋊C4 | — | 2 | 2 | no | — |
| 609 | C4⋊C4 | — | 4 | 1 | no | — |
| 610 | C4⋊C4 | — | 50 | 2 | no | — |
| 611 | C4⋊C4 | — | 100 | 1 | no | — |
| 612 | C4⋊C4 | — | 100 | 2 | no | — |
| 613 | C4⋊C4 | — | 100 | 2 | no | — |
| 614 | C42 | — | 25 | 1 | no | — |
| 615 | C42 | — | 50 | 1 | no | — |
| 616 | C42 | #87886 | 1 | 1 | yes | characteristic |
| 617 | C16 | — | 10 | 4 | no | — |
| 618 | C2×C5 | — | 2 | 4 | no | — |
| 619 | C2×C5 | — | 2 | 2 | no | — |
| 620 | C2×C5 | — | 2 | 2 | no | — |
| 621 | C2×C5 | — | 40 | 2 | no | — |
| 622 | C2×C5 | D5×#476 | 1 | 2 | yes | — |
| 623 | D5 | — | 5 | 4 | no | — |
| 624 | D5 | — | 8 | 2 | no | — |
| 625 | D5 | — | 10 | 4 | no | — |
| 626 | D5 | — | 10 | 4 | no | — |
| 627 | D5 | — | 10 | 2 | no | — |
| 628 | C23 | — | 25 | 1 | no | — |
| 629 | C23 | — | 100 | 1 | no | — |
| 630 | Q8 | — | 8 | 2 | no | — |
| 631 | Q8 | — | 10 | 2 | no | — |
| 632 | Q8 | — | 100 | 1 | no | — |
| 633 | Q8 | — | 200 | 2 | no | — |
| 634 | Q8 | — | 200 | 4 | no | — |
| 635 | D4 | — | 10 | 2 | no | — |
| 636 | D4 | — | 20 | 2 | no | — |
| 637 | D4 | — | 100 | 2 | no | — |
| 638 | D4 | — | 100 | 1 | no | — |
| 639 | C2×C4 | — | 2 | 1 | no | — |
| 640 | C2×C4 | — | 4 | 2 | no | — |
| 641 | C2×C4 | — | 20 | 2 | no | — |
| 642 | C2×C4 | — | 25 | 1 | no | — |
| 643 | C2×C4 | — | 25 | 1 | no | — |
| 644 | C2×C4 | — | 25 | 1 | no | — |
| 645 | C2×C4 | — | 25 | 1 | no | — |
| 646 | C2×C4 | — | 25 | 1 | no | — |
| 647 | C2×C4 | — | 50 | 4 | no | — |
| 648 | C2×C4 | — | 50 | 1 | no | — |
| 649 | C2×C4 | — | 100 | 1 | no | — |
| 650 | C2×C4 | — | 100 | 2 | no | — |
| 651 | C2×C4 | — | 100 | 2 | no | — |
| 652 | C2×C4 | — | 200 | 4 | no | — |
| 653 | C2×C4 | C2×#87886 | 1 | 1 | yes | characteristic |
| 654 | C8 | — | 20 | 2 | no | — |
| 655 | C8 | — | 25 | 1 | no | — |
| 656 | C8 | — | 25 | 1 | no | — |
| 657 | C8 | — | 25 | 1 | no | — |
| 658 | C8 | — | 25 | 1 | no | — |
| 659 | C8 | #11717058 | 1 | 1 | yes | characteristic |
| 660 | C8 | #11717058 | 1 | 1 | yes | characteristic |
| 661 | C8 | Q8×D52 | 1 | 1 | yes | characteristic |
| 662 | C8 | #11717484 | 1 | 1 | yes | characteristic |
| 663 | C5 | — | 2 | 2 | no | — |
| 664 | C5 | D5×#2230 | 1 | 2 | yes | complemented |
| 665 | C22 | — | 20 | 2 | no | — |
| 666 | C22 | — | 25 | 1 | no | — |
| 667 | C22 | — | 25 | 1 | no | — |
| 668 | C22 | — | 50 | 2 | no | — |
| 669 | C22 | — | 200 | 2 | no | — |
| 670 | C22 | #13106298 | 1 | 1 | yes | characteristic |
| 671 | C4 | — | 2 | 2 | no | — |
| 672 | C4 | — | 8 | 2 | no | — |
| 673 | C4 | — | 20 | 2 | no | — |
| 674 | C4 | — | 25 | 1 | no | — |
| 675 | C4 | — | 25 | 1 | no | — |
| 676 | C4 | — | 50 | 2 | no | — |
| 677 | C4 | — | 200 | 2 | no | — |
| 678 | C4 | C2×#11717058 | 1 | 1 | yes | characteristic |
| 679 | C4 | #13106520 | 1 | 1 | yes | characteristic |
| 680 | C2 | — | 2 | 1 | no | — |
| 681 | C2 | — | 25 | 2 | no | — |
| 682 | C2 | — | 40 | 2 | no | — |
| 683 | C2 | — | 50 | 1 | no | — |
| 684 | C2 | #72223134 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72223133 | C2 | semidirect |
| 2. #72223132 | C2 | semidirect |
| 3. C5×#10602143 | C2 | semidirect |
| 4. #72220908 | C2 | semidirect |
| 6. C5⋊D5×#498 | C2 | semidirect |
| 8. #72220687 | C2 | semidirect |
| 12. C52×#498 | C22 | semidirect |
| 17. #13102717 | C22 | semidirect |
| 19. #13102543 | C22 | semidirect |
| 28. C5×#64707 | C22 | semidirect |
| 29. C5×#64683 | C22 | semidirect |
| 30. #13099307 | C22 | semidirect |
| 31. #13099305 | C22 | semidirect |
| 51. #11716928 | Q8 | semidirect |
| 55. #11716920 | Q8 | semidirect |
| 56. #11716915 | Q8 | semidirect |
| 81. #10602143 | D5 | semidirect |
| 126. C5×Dic20 | C2×Q8 | semidirect |
| 127. C5×D40 | C2×Q8 | semidirect |
| 144. C5×#498 | C2×D5 | semidirect |
| 177. #64707 | C2×D5 | semidirect |
| 178. #64683 | C2×D5 | semidirect |
| 373. Dic20 | Q8×D5 | semidirect |
| 374. D40 | Q8×D5 | semidirect |
| 408. #498 | D52 | semidirect |
| 427. C5⋊D5 | #2230 | semidirect |
| 538. C52 | C2×#2230 | semidirect |
| 664. C5 | D5×#2230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72223133 | 2 |
| #72223132 | 2 |
| C5×#10602143 | 2 |
| #72220908 | 2 |
| #72220903 | 2 |
| C5⋊D5×#498 | 2 |
| #72220701 | 2 |
| #72220687 | 2 |
| D5×#2230 | 5 |