Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1230 conjugacy classes of subgroups.
The subgroup lattice has 662 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#11717234 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13106468 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13106298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13105761 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#65466 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13101825 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13101809 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13101699 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13101682 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13101101 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #13101044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#87904 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×D4×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11717471 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C52×SD16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×#87811 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#87809 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #11717234 | — | 2 | 2 | no | — |
| 19 | #11717234 | — | 2 | 2 | no | — |
| 20 | C2×#87801 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#87799 | C22 | 1 | 1 | yes | characteristic |
| 22 | C5×#4088 | C22 | 1 | 2 | yes | complemented |
| 23 | C5×#4078 | C22 | 1 | 2 | yes | — |
| 24 | C5×#4047 | C22 | 1 | 2 | yes | complemented |
| 25 | #11717068 | — | 2 | 2 | no | — |
| 26 | #11717063 | — | 2 | 1 | no | — |
| 27 | #11717059 | — | 2 | 1 | no | — |
| 28 | #11717055 | — | 2 | 2 | no | — |
| 29 | #11717048 | — | 2 | 1 | no | — |
| 30 | #11717044 | — | 2 | 1 | no | — |
| 31 | #11716943 | C22 | 1 | 2 | yes | — |
| 32 | #11716943 | C22 | 1 | 2 | yes | complemented |
| 33 | #11716936 | C22 | 1 | 1 | yes | characteristic |
| 34 | #11716936 | C22 | 1 | 1 | yes | characteristic |
| 35 | #11716936 | C22 | 1 | 1 | yes | characteristic |
| 36 | #11716933 | C22 | 1 | 2 | yes | complemented |
| 37 | #11716922 | — | 2 | 2 | no | — |
| 38 | D5×#676 | — | 2 | 2 | no | — |
| 39 | C5×#3968 | C22 | 1 | 2 | yes | complemented |
| 40 | C5×#3965 | C22 | 1 | 2 | yes | complemented |
| 41 | C5×#3951 | C22 | 1 | 2 | yes | complemented |
| 42 | #11716619 | C22 | 1 | 2 | yes | complemented |
| 43 | #11716600 | C22 | 1 | 2 | yes | complemented |
| 44 | #11716600 | C22 | 1 | 2 | yes | complemented |
| 45 | #10612661 | — | 5 | 2 | no | maximal |
| 46 | C23×C5⋊D5 | — | 2 | 1 | no | — |
| 47 | C2×C52×Q8 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×C52×D4 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 50 | #87904 | — | 2 | 1 | no | — |
| 51 | #87904 | — | 2 | 1 | no | — |
| 52 | #87904 | — | 2 | 1 | no | — |
| 53 | #87904 | — | 2 | 1 | no | — |
| 54 | D4×C5⋊D5 | — | 2 | 1 | no | — |
| 55 | D4×C5⋊D5 | — | 2 | 1 | no | — |
| 56 | D4×C5⋊D5 | — | 2 | 1 | no | — |
| 57 | D4×C5⋊D5 | — | 2 | 1 | no | — |
| 58 | C2×C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 59 | C2×C4⋊(C5⋊D5) | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C4⋊(C5⋊D5) | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 62 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 63 | C5×#709 | C23 | 1 | 2 | yes | — |
| 64 | #87886 | — | 2 | 1 | no | — |
| 65 | #87880 | — | 2 | 1 | no | — |
| 66 | #87877 | D4 | 1 | 1 | yes | characteristic |
| 67 | C4×D52 | — | 2 | 1 | no | — |
| 68 | #87873 | — | 2 | 1 | no | — |
| 69 | #87872 | D4 | 1 | 1 | yes | characteristic |
| 70 | #87871 | D4 | 1 | 2 | yes | — |
| 71 | C52×SD16 | — | 2 | 2 | no | — |
| 72 | C2×C52×C8 | C23 | 1 | 1 | yes | characteristic |
| 73 | #87811 | — | 2 | 2 | no | — |
| 74 | #87809 | — | 2 | 2 | no | — |
| 75 | C2×#6029 | C23 | 1 | 1 | yes | characteristic |
| 76 | #87801 | — | 2 | 2 | no | — |
| 77 | #87799 | D4 | 1 | 2 | yes | — |
| 78 | #87799 | D4 | 1 | 2 | yes | — |
| 79 | C5×#689 | — | 2 | 2 | no | — |
| 80 | C5×#688 | — | 2 | 2 | no | — |
| 81 | C5×#687 | — | 2 | 2 | no | — |
| 82 | C5×#686 | — | 2 | 2 | no | — |
| 83 | C5×#681 | C23 | 1 | 2 | yes | — |
| 84 | C5×#681 | C23 | 1 | 2 | yes | — |
| 85 | C5×#681 | C23 | 1 | 2 | yes | — |
| 86 | C5×#676 | — | 2 | 2 | no | — |
| 87 | C5×C8×D5 | — | 2 | 2 | no | — |
| 88 | #87774 | — | 2 | 2 | no | — |
| 89 | #87774 | — | 2 | 2 | no | — |
| 90 | #87771 | — | 2 | 2 | no | — |
| 91 | #87771 | — | 2 | 2 | no | — |
| 92 | #87769 | — | 2 | 1 | no | — |
| 93 | #87769 | — | 2 | 1 | no | — |
| 94 | #87769 | — | 2 | 1 | no | — |
| 95 | #87768 | — | 2 | 2 | no | — |
| 96 | #87767 | — | 2 | 1 | no | — |
| 97 | #87767 | — | 2 | 1 | no | — |
| 98 | #87767 | — | 2 | 1 | no | — |
| 99 | D5×#168 | — | 2 | 2 | no | — |
| 100 | #66111 | — | 5 | 2 | no | — |
| 101 | D5×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 102 | C2×#4060 | — | 5 | 2 | no | — |
| 103 | C2×#4060 | — | 10 | 2 | no | — |
| 104 | #66084 | — | 5 | 2 | no | — |
| 105 | C5×#471 | — | 5 | 2 | no | — |
| 106 | #65492 | — | 5 | 2 | no | — |
| 107 | #65488 | — | 5 | 2 | no | — |
| 108 | #65466 | D5 | 1 | 2 | yes | complemented |
| 109 | #65431 | — | 5 | 2 | no | — |
| 110 | #65186 | — | 5 | 2 | no | — |
| 111 | #65182 | — | 5 | 2 | no | — |
| 112 | #65043 | — | 5 | 2 | no | — |
| 113 | #65040 | — | 5 | 2 | no | — |
| 114 | #65038 | — | 5 | 2 | no | — |
| 115 | D5×#100 | — | 5 | 2 | no | — |
| 116 | C23×C52 | — | 2 | 1 | no | — |
| 117 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 118 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 119 | C22×C5⋊D5 | — | 4 | 1 | no | — |
| 120 | C22×C5⋊D5 | — | 4 | 1 | no | — |
| 121 | C22×C5⋊D5 | — | 8 | 2 | no | — |
| 122 | C22×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 123 | C2×D52 | — | 2 | 1 | no | — |
| 124 | C52×Q8 | — | 2 | 1 | no | — |
| 125 | C52×Q8 | — | 2 | 1 | no | — |
| 126 | C52×D4 | — | 2 | 1 | no | — |
| 127 | C52×D4 | — | 2 | 1 | no | — |
| 128 | C2×C4×C52 | — | 2 | 1 | no | — |
| 129 | C2×C4×C52 | C24 | 1 | 1 | yes | characteristic |
| 130 | C22⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 131 | C22⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 132 | C2×#1039 | #41 | 1 | 1 | yes | characteristic |
| 133 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 134 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 135 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 136 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 137 | C4⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 138 | C4⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 139 | C4×C5⋊D5 | — | 4 | 1 | no | — |
| 140 | C4×C5⋊D5 | — | 4 | 1 | no | — |
| 141 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 146 | C5×D20 | C2×D4 | 1 | 2 | yes | — |
| 147 | C4×C5×D5 | — | 2 | 2 | no | — |
| 148 | C5×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 149 | #6039 | — | 2 | 1 | no | — |
| 150 | #6038 | — | 2 | 2 | no | — |
| 151 | #6037 | — | 2 | 1 | no | — |
| 152 | #6036 | — | 2 | 1 | no | — |
| 153 | D5×Dic5 | — | 2 | 2 | no | — |
| 154 | C52×C8 | C2×D4 | 1 | 2 | yes | — |
| 155 | #6029 | C2×D4 | 1 | 2 | yes | — |
| 156 | C5×#168 | — | 2 | 2 | no | — |
| 157 | C5×#168 | — | 2 | 2 | no | — |
| 158 | C5×#168 | — | 2 | 2 | no | — |
| 159 | D5×#41 | — | 5 | 2 | no | — |
| 160 | C2×#713 | — | 5 | 2 | no | — |
| 161 | C2×#713 | — | 10 | 2 | no | — |
| 162 | C2×D4×D5 | — | 5 | 2 | no | — |
| 163 | C2×D4×D5 | — | 10 | 2 | no | — |
| 164 | C5×#137 | — | 5 | 2 | no | — |
| 165 | C5×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 166 | C2×C5×SD16 | — | 2 | 2 | no | — |
| 167 | C2×C5×SD16 | C2×D5 | 1 | 2 | yes | complemented |
| 168 | C5×#131 | — | 5 | 2 | no | — |
| 169 | #4095 | — | 5 | 2 | no | — |
| 170 | #4095 | — | 5 | 2 | no | — |
| 171 | #4094 | — | 5 | 2 | no | — |
| 172 | #4088 | C2×D5 | 1 | 2 | yes | complemented |
| 173 | C2×#688 | — | 5 | 2 | no | — |
| 174 | C2×#688 | — | 10 | 2 | no | — |
| 175 | #4078 | C2×D5 | 1 | 2 | yes | — |
| 176 | C2×#686 | — | 5 | 2 | no | — |
| 177 | C2×#686 | — | 10 | 2 | no | — |
| 178 | #4065 | — | 10 | 2 | no | — |
| 179 | #4064 | — | 10 | 2 | no | — |
| 180 | #4062 | — | 10 | 2 | no | — |
| 181 | #4060 | — | 10 | 2 | no | — |
| 182 | #4060 | — | 10 | 2 | no | — |
| 183 | #4060 | — | 10 | 2 | no | — |
| 184 | #4060 | — | 10 | 2 | no | — |
| 185 | #4060 | — | 10 | 2 | no | — |
| 186 | #4060 | — | 10 | 2 | no | — |
| 187 | #4060 | — | 10 | 8 | no | — |
| 188 | #4060 | — | 10 | 8 | no | — |
| 189 | D5×SD16 | — | 10 | 2 | no | — |
| 190 | #4057 | — | 10 | 2 | no | — |
| 191 | D5×D8 | — | 10 | 2 | no | — |
| 192 | #4054 | — | 5 | 2 | no | — |
| 193 | #4054 | — | 5 | 2 | no | — |
| 194 | #4053 | — | 5 | 2 | no | — |
| 195 | #4053 | — | 10 | 2 | no | — |
| 196 | D5×M16 | — | 5 | 2 | no | — |
| 197 | D5×M16 | — | 5 | 2 | no | — |
| 198 | D5×M16 | — | 5 | 2 | no | — |
| 199 | D5×M16 | — | 10 | 2 | no | — |
| 200 | C2×D40 | — | 5 | 2 | no | — |
| 201 | C2×D40 | — | 10 | 2 | no | — |
| 202 | #4047 | — | 10 | 2 | no | — |
| 203 | #4047 | C2×D5 | 1 | 2 | yes | complemented |
| 204 | C2×#676 | — | 5 | 2 | no | — |
| 205 | C2×#676 | — | 10 | 2 | no | — |
| 206 | C2×#676 | — | 10 | 2 | no | — |
| 207 | C5×#108 | — | 5 | 2 | no | — |
| 208 | C5×#101 | — | 5 | 2 | no | — |
| 209 | C5×#100 | — | 5 | 2 | no | — |
| 210 | #3968 | C2×D5 | 1 | 2 | yes | complemented |
| 211 | #3965 | C2×D5 | 1 | 2 | yes | complemented |
| 212 | #3955 | — | 5 | 2 | no | — |
| 213 | #3955 | — | 5 | 2 | no | — |
| 214 | #3955 | — | 5 | 2 | no | — |
| 215 | #3955 | — | 5 | 2 | no | — |
| 216 | #3954 | — | 5 | 2 | no | — |
| 217 | #3954 | — | 5 | 2 | no | — |
| 218 | #3951 | C2×D5 | 1 | 2 | yes | complemented |
| 219 | #3068 | — | 25 | 1 | no | Sylow |
| 220 | C22×C52 | — | 4 | 1 | no | — |
| 221 | C22×C52 | — | 8 | 1 | no | — |
| 222 | C22×C52 | C2×#41 | 1 | 1 | yes | characteristic |
| 223 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 224 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 225 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 226 | C2×C5⋊D5 | — | 8 | 2 | no | — |
| 227 | C2×C5⋊D5 | — | 8 | 2 | no | — |
| 228 | C2×C5⋊D5 | — | 8 | 1 | no | — |
| 229 | C2×C5⋊D5 | — | 8 | 1 | no | — |
| 230 | C2×C5⋊D5 | #121 | 1 | 1 | yes | characteristic |
| 231 | C2×C5⋊D5 | #121 | 1 | 1 | yes | characteristic |
| 232 | C2×C5×D5 | — | 2 | 2 | no | — |
| 233 | D52 | — | 8 | 1 | no | — |
| 234 | C4×C52 | — | 4 | 1 | no | — |
| 235 | C4×C52 | C22×D4 | 1 | 1 | yes | characteristic |
| 236 | C4×C52 | C22×D4 | 1 | 1 | yes | characteristic |
| 237 | #1039 | #121 | 1 | 1 | yes | characteristic |
| 238 | #1039 | #121 | 1 | 1 | yes | characteristic |
| 239 | C5×Dic5 | — | 2 | 2 | no | — |
| 240 | C23×D5 | — | 10 | 2 | no | — |
| 241 | C23×D5 | — | 20 | 2 | no | — |
| 242 | C5×#41 | — | 5 | 2 | no | — |
| 243 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 244 | C2×C5×Q8 | C22×D5 | 1 | 2 | yes | — |
| 245 | C2×C5×D4 | — | 2 | 2 | no | — |
| 246 | C2×C5×D4 | C22×D5 | 1 | 2 | yes | — |
| 247 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 248 | C2×C22⋊D5 | — | 20 | 2 | no | — |
| 249 | #713 | — | 5 | 2 | no | — |
| 250 | #713 | — | 10 | 2 | no | — |
| 251 | #713 | — | 10 | 2 | no | — |
| 252 | #713 | — | 10 | 2 | no | — |
| 253 | #713 | — | 10 | 2 | no | — |
| 254 | #713 | — | 10 | 4 | no | — |
| 255 | #713 | — | 10 | 4 | no | — |
| 256 | #713 | — | 20 | 2 | no | — |
| 257 | #713 | — | 20 | 2 | no | — |
| 258 | Q8×D5 | — | 5 | 2 | no | — |
| 259 | #711 | — | 5 | 2 | no | — |
| 260 | #711 | — | 10 | 2 | no | — |
| 261 | D4×D5 | — | 5 | 2 | no | — |
| 262 | D4×D5 | — | 10 | 2 | no | — |
| 263 | D4×D5 | — | 10 | 2 | no | — |
| 264 | D4×D5 | — | 10 | 2 | no | — |
| 265 | D4×D5 | — | 10 | 2 | no | — |
| 266 | D4×D5 | — | 10 | 2 | no | — |
| 267 | D4×D5 | — | 10 | 4 | no | — |
| 268 | D4×D5 | — | 10 | 4 | no | — |
| 269 | D4×D5 | — | 20 | 2 | no | — |
| 270 | D4×D5 | — | 20 | 2 | no | — |
| 271 | #709 | — | 10 | 2 | no | — |
| 272 | #709 | C22×D5 | 1 | 2 | yes | — |
| 273 | C2×D20 | — | 5 | 2 | no | — |
| 274 | C2×D20 | — | 5 | 2 | no | — |
| 275 | C2×D20 | — | 10 | 2 | no | — |
| 276 | C2×D20 | — | 10 | 2 | no | — |
| 277 | C2×D20 | — | 10 | 2 | no | — |
| 278 | C2×D20 | — | 20 | 2 | no | — |
| 279 | C2×C4×D5 | — | 5 | 2 | no | — |
| 280 | C2×C4×D5 | — | 10 | 2 | no | — |
| 281 | C2×C4×D5 | — | 10 | 2 | no | — |
| 282 | C2×C4×D5 | — | 10 | 2 | no | — |
| 283 | C2×C4×D5 | — | 20 | 2 | no | — |
| 284 | C5×Q16 | — | 10 | 2 | no | — |
| 285 | C5×SD16 | — | 2 | 8 | no | — |
| 286 | C5×SD16 | — | 2 | 2 | no | — |
| 287 | C5×SD16 | — | 2 | 2 | no | — |
| 288 | C5×SD16 | — | 10 | 2 | no | — |
| 289 | C5×SD16 | — | 10 | 2 | no | — |
| 290 | C5×D8 | — | 10 | 2 | no | — |
| 291 | C5×M16 | — | 5 | 2 | no | — |
| 292 | C5×M16 | — | 5 | 2 | no | — |
| 293 | C5×M16 | — | 5 | 2 | no | — |
| 294 | C5×M16 | — | 10 | 2 | no | — |
| 295 | C2×C5×C8 | — | 2 | 2 | no | — |
| 296 | C2×C5×C8 | — | 10 | 2 | no | — |
| 297 | C2×C5×C8 | C22×D5 | 1 | 2 | yes | — |
| 298 | #689 | — | 2 | 2 | no | — |
| 299 | #688 | — | 2 | 2 | no | — |
| 300 | #688 | — | 10 | 2 | no | — |
| 301 | #688 | — | 10 | 2 | no | — |
| 302 | #688 | — | 10 | 2 | no | — |
| 303 | #688 | — | 10 | 2 | no | — |
| 304 | #688 | — | 10 | 8 | no | — |
| 305 | #687 | — | 2 | 2 | no | — |
| 306 | #686 | — | 2 | 2 | no | — |
| 307 | #686 | — | 10 | 2 | no | — |
| 308 | #686 | — | 10 | 2 | no | — |
| 309 | #686 | — | 10 | 2 | no | — |
| 310 | #686 | — | 10 | 2 | no | — |
| 311 | #686 | — | 10 | 8 | no | — |
| 312 | #681 | — | 10 | 2 | no | — |
| 313 | #681 | C22×D5 | 1 | 2 | yes | — |
| 314 | #681 | C22×D5 | 1 | 2 | yes | — |
| 315 | #681 | C22×D5 | 1 | 2 | yes | — |
| 316 | C2×#168 | — | 5 | 2 | no | — |
| 317 | C2×#168 | — | 10 | 2 | no | — |
| 318 | C2×#168 | — | 10 | 2 | no | — |
| 319 | D40 | — | 10 | 8 | no | — |
| 320 | D40 | — | 10 | 2 | no | — |
| 321 | D40 | — | 10 | 2 | no | — |
| 322 | D40 | — | 10 | 2 | no | — |
| 323 | D40 | — | 10 | 2 | no | — |
| 324 | #677 | — | 10 | 2 | no | — |
| 325 | #677 | — | 10 | 2 | no | — |
| 326 | #676 | — | 2 | 2 | no | — |
| 327 | #676 | — | 5 | 2 | no | — |
| 328 | #676 | — | 5 | 2 | no | — |
| 329 | #676 | — | 5 | 2 | no | — |
| 330 | #676 | — | 5 | 2 | no | — |
| 331 | #676 | — | 10 | 4 | no | — |
| 332 | #676 | — | 10 | 4 | no | — |
| 333 | #676 | — | 10 | 2 | no | — |
| 334 | #676 | — | 10 | 2 | no | — |
| 335 | #676 | — | 10 | 2 | no | — |
| 336 | #676 | — | 10 | 2 | no | — |
| 337 | C8×D5 | — | 2 | 2 | no | — |
| 338 | C8×D5 | — | 10 | 2 | no | — |
| 339 | C8×D5 | — | 10 | 2 | no | — |
| 340 | C8×D5 | — | 10 | 2 | no | — |
| 341 | C8×D5 | — | 10 | 2 | no | — |
| 342 | #575 | — | 25 | 1 | no | — |
| 343 | C2×AGL(1,ℤ/8) | — | 25 | 1 | no | — |
| 344 | C2×AGL(1,ℤ/8) | — | 25 | 1 | no | — |
| 345 | #568 | — | 25 | 1 | no | — |
| 346 | #472 | — | 25 | 2 | no | — |
| 347 | #472 | — | 25 | 2 | no | — |
| 348 | #471 | — | 5 | 2 | no | — |
| 349 | #471 | — | 25 | 2 | no | — |
| 350 | #430 | — | 25 | 1 | no | — |
| 351 | #413 | — | 25 | 1 | no | — |
| 352 | C2×#100 | — | 25 | 1 | no | — |
| 353 | C2×C52 | — | 2 | 1 | no | — |
| 354 | C2×C52 | — | 8 | 1 | no | — |
| 355 | C2×C52 | C2×#121 | 1 | 1 | yes | characteristic |
| 356 | C5⋊D5 | — | 2 | 1 | no | — |
| 357 | C5⋊D5 | — | 2 | 1 | no | — |
| 358 | C5⋊D5 | — | 8 | 1 | no | — |
| 359 | C5⋊D5 | — | 8 | 1 | no | — |
| 360 | C5×D5 | — | 4 | 2 | no | — |
| 361 | C23×C5 | — | 2 | 2 | no | — |
| 362 | C23×C5 | — | 4 | 2 | no | — |
| 363 | C22×D5 | — | 5 | 2 | no | — |
| 364 | C22×D5 | — | 10 | 2 | no | — |
| 365 | C22×D5 | — | 10 | 2 | no | — |
| 366 | C22×D5 | — | 10 | 2 | no | — |
| 367 | C22×D5 | — | 10 | 2 | no | — |
| 368 | C22×D5 | — | 20 | 2 | no | — |
| 369 | C22×D5 | — | 20 | 2 | no | — |
| 370 | C22×D5 | — | 20 | 2 | no | — |
| 371 | C22×D5 | — | 20 | 2 | no | — |
| 372 | C22×D5 | — | 20 | 4 | no | — |
| 373 | C22×D5 | — | 20 | 4 | no | — |
| 374 | C22×D5 | — | 40 | 8 | no | — |
| 375 | C22×D5 | — | 40 | 4 | no | — |
| 376 | C5×Q8 | — | 2 | 4 | no | — |
| 377 | C5×Q8 | — | 2 | 2 | no | — |
| 378 | C5×Q8 | — | 2 | 2 | no | — |
| 379 | C5×Q8 | — | 4 | 2 | no | — |
| 380 | C5×Q8 | — | 5 | 2 | no | — |
| 381 | C5×D4 | — | 2 | 4 | no | — |
| 382 | C5×D4 | — | 2 | 2 | no | — |
| 383 | C5×D4 | — | 2 | 2 | no | — |
| 384 | C5×D4 | — | 4 | 2 | no | — |
| 385 | C5×D4 | — | 5 | 2 | no | — |
| 386 | C5×D4 | — | 10 | 2 | no | — |
| 387 | C2×C4×C5 | — | 2 | 2 | no | — |
| 388 | C2×C4×C5 | — | 2 | 2 | no | — |
| 389 | C2×C4×C5 | — | 4 | 2 | no | — |
| 390 | C2×C4×C5 | — | 10 | 2 | no | — |
| 391 | C2×C4×C5 | C23×D5 | 1 | 2 | yes | — |
| 392 | C22⋊D5 | — | 2 | 2 | no | — |
| 393 | C22⋊D5 | — | 10 | 2 | no | — |
| 394 | C22⋊D5 | — | 10 | 2 | no | — |
| 395 | C22⋊D5 | — | 20 | 2 | no | — |
| 396 | C22⋊D5 | — | 20 | 2 | no | — |
| 397 | C22⋊D5 | — | 20 | 4 | no | — |
| 398 | C22⋊D5 | — | 20 | 4 | no | — |
| 399 | C2×Dic5 | — | 5 | 2 | no | — |
| 400 | C2×Dic5 | — | 10 | 2 | no | — |
| 401 | C2×Dic5 | — | 10 | 2 | no | — |
| 402 | D20 | — | 10 | 4 | no | — |
| 403 | D20 | — | 10 | 4 | no | — |
| 404 | D20 | — | 10 | 2 | no | — |
| 405 | D20 | — | 10 | 2 | no | — |
| 406 | D20 | — | 10 | 2 | no | — |
| 407 | D20 | — | 10 | 2 | no | — |
| 408 | D20 | — | 10 | 2 | no | — |
| 409 | D20 | — | 20 | 2 | no | — |
| 410 | D20 | — | 20 | 2 | no | — |
| 411 | D20 | — | 20 | 2 | no | — |
| 412 | D20 | — | 20 | 2 | no | — |
| 413 | D20 | — | 20 | 4 | no | — |
| 414 | D20 | — | 20 | 4 | no | — |
| 415 | D20 | D4×D5 | 1 | 2 | yes | — |
| 416 | C4×D5 | — | 2 | 2 | no | — |
| 417 | C4×D5 | — | 5 | 2 | no | — |
| 418 | C4×D5 | — | 5 | 2 | no | — |
| 419 | C4×D5 | — | 5 | 2 | no | — |
| 420 | C4×D5 | — | 5 | 2 | no | — |
| 421 | C4×D5 | — | 10 | 2 | no | — |
| 422 | C4×D5 | — | 10 | 2 | no | — |
| 423 | C4×D5 | — | 10 | 2 | no | — |
| 424 | C4×D5 | — | 10 | 2 | no | — |
| 425 | C4×D5 | — | 10 | 2 | no | — |
| 426 | C4×D5 | — | 10 | 2 | no | — |
| 427 | C4×D5 | — | 20 | 2 | no | — |
| 428 | C4×D5 | — | 20 | 2 | no | — |
| 429 | C4×D5 | — | 20 | 4 | no | — |
| 430 | C4×D5 | — | 20 | 4 | no | — |
| 431 | Dic10 | — | 10 | 2 | no | — |
| 432 | Dic10 | D4×D5 | 1 | 2 | yes | — |
| 433 | C5×C8 | — | 2 | 4 | no | — |
| 434 | C5×C8 | — | 10 | 2 | no | — |
| 435 | C5×C8 | — | 10 | 2 | no | — |
| 436 | C5×C8 | — | 10 | 2 | no | — |
| 437 | C5×C8 | D4×D5 | 1 | 2 | yes | — |
| 438 | C5×C8 | D4×D5 | 1 | 2 | yes | — |
| 439 | #168 | — | 2 | 2 | no | — |
| 440 | #168 | — | 2 | 2 | no | — |
| 441 | #168 | — | 2 | 2 | no | — |
| 442 | #168 | — | 5 | 2 | no | — |
| 443 | #168 | — | 5 | 2 | no | — |
| 444 | #168 | — | 10 | 4 | no | — |
| 445 | C2×#41 | — | 25 | 1 | no | — |
| 446 | C2×#41 | — | 25 | 1 | no | — |
| 447 | C22×D4 | — | 25 | 1 | no | — |
| 448 | #137 | — | 5 | 2 | no | — |
| 449 | #137 | — | 50 | 1 | no | — |
| 450 | AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 451 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 452 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 453 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 454 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 455 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 456 | AGL(1,ℤ/8) | — | 50 | 1 | no | — |
| 457 | #135 | — | 50 | 2 | no | — |
| 458 | C2×SD16 | — | 25 | 1 | no | — |
| 459 | C2×SD16 | — | 50 | 1 | no | — |
| 460 | C2×SD16 | D52 | 1 | 1 | yes | characteristic, complemented |
| 461 | C2×D8 | — | 25 | 1 | no | — |
| 462 | C2×D8 | — | 25 | 1 | no | — |
| 463 | C2×D8 | — | 50 | 1 | no | — |
| 464 | #131 | — | 5 | 2 | no | — |
| 465 | #131 | — | 25 | 2 | no | — |
| 466 | #131 | — | 50 | 2 | no | — |
| 467 | C2×M16 | — | 25 | 1 | no | — |
| 468 | C2×M16 | — | 25 | 1 | no | — |
| 469 | C2×M16 | — | 25 | 1 | no | — |
| 470 | C2×M16 | — | 25 | 1 | no | — |
| 471 | C2×M16 | — | 50 | 2 | no | — |
| 472 | #108 | — | 5 | 2 | no | — |
| 473 | #108 | — | 25 | 2 | no | — |
| 474 | #101 | — | 5 | 2 | no | — |
| 475 | #100 | — | 5 | 2 | no | — |
| 476 | #100 | — | 25 | 2 | no | — |
| 477 | #100 | — | 25 | 2 | no | — |
| 478 | C52 | #3068 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 479 | C22×C5 | — | 2 | 2 | no | — |
| 480 | C22×C5 | — | 4 | 4 | no | — |
| 481 | C22×C5 | — | 4 | 2 | no | — |
| 482 | C22×C5 | — | 8 | 2 | no | — |
| 483 | C22×C5 | — | 8 | 4 | no | — |
| 484 | C22×C5 | — | 10 | 2 | no | — |
| 485 | C22×C5 | D5×#41 | 1 | 2 | yes | — |
| 486 | C2×D5 | — | 2 | 2 | no | — |
| 487 | C2×D5 | — | 5 | 2 | no | — |
| 488 | C2×D5 | — | 5 | 2 | no | — |
| 489 | C2×D5 | — | 10 | 2 | no | — |
| 490 | C2×D5 | — | 10 | 2 | no | — |
| 491 | C2×D5 | — | 20 | 2 | no | — |
| 492 | C2×D5 | — | 20 | 4 | no | — |
| 493 | C2×D5 | — | 20 | 4 | no | — |
| 494 | C2×D5 | — | 20 | 4 | no | — |
| 495 | C2×D5 | — | 20 | 2 | no | — |
| 496 | C2×D5 | — | 20 | 2 | no | — |
| 497 | C2×D5 | — | 40 | 2 | no | — |
| 498 | C2×D5 | — | 40 | 4 | no | — |
| 499 | C2×D5 | — | 40 | 4 | no | — |
| 500 | C2×D5 | — | 40 | 8 | no | — |
| 501 | C2×D5 | — | 40 | 8 | no | — |
| 502 | C2×D5 | — | 40 | 4 | no | — |
| 503 | C2×D5 | — | 40 | 4 | no | — |
| 504 | C2×D5 | — | 40 | 2 | no | — |
| 505 | C2×D5 | — | 40 | 2 | no | — |
| 506 | C4×C5 | — | 2 | 2 | no | — |
| 507 | C4×C5 | — | 2 | 2 | no | — |
| 508 | C4×C5 | — | 4 | 4 | no | — |
| 509 | C4×C5 | — | 4 | 2 | no | — |
| 510 | C4×C5 | — | 10 | 2 | no | — |
| 511 | C4×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 512 | C4×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 513 | Dic5 | — | 2 | 2 | no | — |
| 514 | Dic5 | — | 5 | 2 | no | — |
| 515 | Dic5 | — | 5 | 2 | no | — |
| 516 | Dic5 | — | 10 | 2 | no | — |
| 517 | Dic5 | — | 10 | 2 | no | — |
| 518 | C24 | — | 50 | 1 | no | — |
| 519 | #41 | — | 5 | 2 | no | — |
| 520 | #41 | — | 25 | 2 | no | — |
| 521 | #41 | — | 50 | 1 | no | — |
| 522 | #41 | — | 50 | 1 | no | — |
| 523 | #41 | — | 50 | 1 | no | — |
| 524 | #41 | — | 50 | 1 | no | — |
| 525 | #41 | — | 50 | 1 | no | — |
| 526 | #41 | — | 50 | 1 | no | — |
| 527 | C2×Q8 | — | 25 | 1 | no | — |
| 528 | C2×Q8 | C2×D52 | 1 | 1 | yes | characteristic |
| 529 | C2×D4 | — | 25 | 1 | no | — |
| 530 | C2×D4 | — | 25 | 1 | no | — |
| 531 | C2×D4 | — | 25 | 1 | no | — |
| 532 | C2×D4 | — | 50 | 1 | no | — |
| 533 | C2×D4 | — | 50 | 1 | no | — |
| 534 | C2×D4 | — | 50 | 1 | no | — |
| 535 | C2×D4 | — | 50 | 1 | no | — |
| 536 | C2×D4 | — | 50 | 1 | no | — |
| 537 | C2×D4 | — | 50 | 1 | no | — |
| 538 | C2×D4 | — | 50 | 1 | no | — |
| 539 | C2×D4 | C2×D52 | 1 | 1 | yes | characteristic |
| 540 | C22×C4 | — | 25 | 1 | no | — |
| 541 | C22×C4 | — | 50 | 1 | no | — |
| 542 | C22×C4 | — | 50 | 1 | no | — |
| 543 | Q16 | — | 10 | 2 | no | — |
| 544 | SD16 | — | 2 | 2 | no | — |
| 545 | SD16 | — | 10 | 2 | no | — |
| 546 | SD16 | — | 10 | 2 | no | — |
| 547 | SD16 | — | 50 | 2 | no | — |
| 548 | SD16 | — | 50 | 2 | no | — |
| 549 | SD16 | — | 50 | 2 | no | — |
| 550 | D8 | — | 10 | 2 | no | — |
| 551 | D8 | — | 50 | 2 | no | — |
| 552 | D8 | — | 50 | 2 | no | — |
| 553 | D8 | — | 50 | 2 | no | — |
| 554 | D8 | — | 50 | 2 | no | — |
| 555 | M16 | — | 5 | 2 | no | — |
| 556 | M16 | — | 5 | 2 | no | — |
| 557 | M16 | — | 5 | 2 | no | — |
| 558 | M16 | — | 10 | 2 | no | — |
| 559 | M16 | — | 25 | 2 | no | — |
| 560 | M16 | — | 25 | 2 | no | — |
| 561 | M16 | — | 50 | 1 | no | — |
| 562 | M16 | — | 50 | 1 | no | — |
| 563 | M16 | — | 50 | 1 | no | — |
| 564 | M16 | — | 50 | 2 | no | — |
| 565 | C2×C8 | — | 10 | 2 | no | — |
| 566 | C2×C8 | — | 25 | 1 | no | — |
| 567 | C2×C8 | — | 50 | 1 | no | — |
| 568 | C2×C8 | — | 50 | 1 | no | — |
| 569 | C2×C8 | — | 50 | 1 | no | — |
| 570 | C2×C8 | — | 50 | 2 | no | — |
| 571 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 572 | C2×C5 | — | 2 | 4 | no | — |
| 573 | C2×C5 | — | 2 | 2 | no | — |
| 574 | C2×C5 | — | 2 | 2 | no | — |
| 575 | C2×C5 | — | 8 | 4 | no | — |
| 576 | C2×C5 | — | 8 | 2 | no | — |
| 577 | C2×C5 | — | 20 | 2 | no | — |
| 578 | C2×C5 | D5×#121 | 1 | 2 | yes | — |
| 579 | D5 | — | 4 | 2 | no | — |
| 580 | D5 | — | 10 | 2 | no | — |
| 581 | D5 | — | 10 | 2 | no | — |
| 582 | D5 | — | 20 | 2 | no | — |
| 583 | D5 | — | 20 | 2 | no | — |
| 584 | D5 | — | 40 | 4 | no | — |
| 585 | D5 | — | 40 | 4 | no | — |
| 586 | D5 | — | 40 | 2 | no | — |
| 587 | D5 | — | 40 | 2 | no | — |
| 588 | C23 | — | 2 | 1 | no | — |
| 589 | C23 | — | 25 | 1 | no | — |
| 590 | C23 | — | 50 | 1 | no | — |
| 591 | C23 | — | 50 | 1 | no | — |
| 592 | C23 | — | 50 | 1 | no | — |
| 593 | C23 | — | 100 | 1 | no | — |
| 594 | C23 | — | 100 | 1 | no | — |
| 595 | C23 | — | 200 | 2 | no | — |
| 596 | Q8 | — | 2 | 1 | no | — |
| 597 | Q8 | — | 2 | 1 | no | — |
| 598 | Q8 | — | 5 | 2 | no | — |
| 599 | Q8 | — | 50 | 1 | no | — |
| 600 | D4 | — | 2 | 1 | no | — |
| 601 | D4 | — | 2 | 1 | no | — |
| 602 | D4 | — | 5 | 2 | no | — |
| 603 | D4 | — | 10 | 2 | no | — |
| 604 | D4 | — | 50 | 2 | no | — |
| 605 | D4 | — | 50 | 1 | no | — |
| 606 | D4 | — | 50 | 1 | no | — |
| 607 | D4 | — | 50 | 1 | no | — |
| 608 | D4 | — | 50 | 1 | no | — |
| 609 | D4 | — | 50 | 1 | no | — |
| 610 | D4 | — | 100 | 1 | no | — |
| 611 | D4 | — | 100 | 1 | no | — |
| 612 | D4 | — | 100 | 1 | no | — |
| 613 | D4 | — | 100 | 1 | no | — |
| 614 | C2×C4 | — | 2 | 1 | no | — |
| 615 | C2×C4 | — | 10 | 2 | no | — |
| 616 | C2×C4 | — | 25 | 1 | no | — |
| 617 | C2×C4 | — | 25 | 1 | no | — |
| 618 | C2×C4 | — | 25 | 1 | no | — |
| 619 | C2×C4 | — | 25 | 1 | no | — |
| 620 | C2×C4 | — | 25 | 1 | no | — |
| 621 | C2×C4 | — | 50 | 1 | no | — |
| 622 | C2×C4 | — | 50 | 2 | no | — |
| 623 | C2×C4 | — | 100 | 1 | no | — |
| 624 | C2×C4 | — | 100 | 1 | no | — |
| 625 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 626 | C8 | — | 10 | 2 | no | — |
| 627 | C8 | — | 10 | 2 | no | — |
| 628 | C8 | — | 10 | 2 | no | — |
| 629 | C8 | — | 25 | 2 | no | — |
| 630 | C8 | #87886 | 1 | 2 | yes | — |
| 631 | C5 | — | 2 | 2 | no | — |
| 632 | C5 | #10612661 | 1 | 2 | yes | complemented |
| 633 | C22 | — | 4 | 1 | no | — |
| 634 | C22 | — | 8 | 1 | no | — |
| 635 | C22 | — | 10 | 2 | no | — |
| 636 | C22 | — | 25 | 1 | no | — |
| 637 | C22 | — | 25 | 1 | no | — |
| 638 | C22 | — | 100 | 1 | no | — |
| 639 | C22 | — | 100 | 1 | no | — |
| 640 | C22 | — | 100 | 1 | no | — |
| 641 | C22 | — | 200 | 1 | no | — |
| 642 | C22 | — | 200 | 1 | no | — |
| 643 | C22 | — | 200 | 2 | no | — |
| 644 | C22 | — | 200 | 2 | no | — |
| 645 | C22 | — | 200 | 1 | no | — |
| 646 | C22 | #11717477 | 1 | 1 | yes | characteristic |
| 647 | C4 | — | 4 | 1 | no | — |
| 648 | C4 | — | 10 | 2 | no | — |
| 649 | C4 | — | 25 | 1 | no | — |
| 650 | C4 | — | 25 | 1 | no | — |
| 651 | C4 | D4×D52 | 1 | 1 | yes | characteristic |
| 652 | C4 | C2×#87886 | 1 | 1 | yes | characteristic |
| 653 | C2 | — | 2 | 1 | no | — |
| 654 | C2 | — | 8 | 1 | no | — |
| 655 | C2 | — | 20 | 2 | no | — |
| 656 | C2 | — | 50 | 1 | no | — |
| 657 | C2 | — | 50 | 1 | no | — |
| 658 | C2 | — | 200 | 1 | no | — |
| 659 | C2 | — | 200 | 1 | no | — |
| 660 | C2 | #13106391 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11717234 | C2 | semidirect |
| 2. #13106468 | C2 | semidirect |
| 3. #13106298 | C2 | semidirect |
| 4. #13105761 | C2 | semidirect |
| 5. C5×#65466 | C2 | semidirect |
| 6. #13101825 | C2 | semidirect |
| 7. #13101809 | C2 | semidirect |
| 8. #13101699 | C2 | semidirect |
| 9. #13101682 | C2 | semidirect |
| 10. #13101101 | C2 | semidirect |
| 11. #13101044 | C2 | semidirect |
| 15. C2×C52×SD16 | C22 | semidirect |
| 16. C2×#87811 | C22 | semidirect |
| 17. C2×#87809 | C22 | semidirect |
| 20. C2×#87801 | C22 | semidirect |
| 22. C5×#4088 | C22 | semidirect |
| 24. C5×#4047 | C22 | semidirect |
| 32. #11716943 | C22 | semidirect |
| 36. #11716933 | C22 | semidirect |
| 39. C5×#3968 | C22 | semidirect |
| 40. C5×#3965 | C22 | semidirect |
| 41. C5×#3951 | C22 | semidirect |
| 42. #11716619 | C22 | semidirect |
| 43. #11716600 | C22 | semidirect |
| 44. #11716600 | C22 | semidirect |
| 108. #65466 | D5 | semidirect |
| 167. C2×C5×SD16 | C2×D5 | semidirect |
| 172. #4088 | C2×D5 | semidirect |
| 203. #4047 | C2×D5 | semidirect |
| 210. #3968 | C2×D5 | semidirect |
| 211. #3965 | C2×D5 | semidirect |
| 218. #3951 | C2×D5 | semidirect |
| 460. C2×SD16 | D52 | semidirect |
| 478. C52 | #3068 | semidirect |
| 632. C5 | #10612661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717234 | 2 |
| #13106468 | 2 |
| #13106298 | 2 |
| #13105761 | 2 |
| C5×#65466 | 2 |
| #13101825 | 2 |
| #13101809 | 2 |
| #13101699 | 2 |
| #13101682 | 2 |
| #13101101 | 2 |
| #13101044 | 2 |
| #10612661 | 5 |