Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1806 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13107815 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13107056 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#11716943 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C5×#65294 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13101272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13100582 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #13100579 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | C2×#87900 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×C4⋊(C5⋊D5) | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×C5×#709 | C22 | 1 | 2 | yes | — |
| 11 | #11717495 | — | 2 | 2 | no | — |
| 12 | #11717473 | C22 | 1 | 2 | yes | complemented |
| 13 | #11717472 | — | 2 | 2 | no | — |
| 14 | #11717471 | — | 2 | 2 | no | — |
| 15 | D5×#709 | — | 2 | 4 | no | — |
| 16 | #11717463 | C22 | 1 | 2 | yes | complemented |
| 17 | #11717462 | — | 2 | 2 | no | — |
| 18 | C52×#117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #11717215 | — | 2 | 2 | no | — |
| 20 | #11717202 | — | 2 | 2 | no | — |
| 21 | #11717195 | C22 | 1 | 2 | yes | complemented |
| 22 | #11717194 | C22 | 1 | 2 | yes | complemented |
| 23 | C2×C5×#681 | C22 | 1 | 2 | yes | complemented |
| 24 | C2×#87774 | — | 2 | 2 | no | — |
| 25 | #11716943 | — | 2 | 4 | no | — |
| 26 | #11716943 | C22 | 1 | 8 | yes | complemented |
| 27 | C2×#87771 | — | 2 | 2 | no | — |
| 28 | C5×#3937 | C22 | 1 | 8 | yes | complemented |
| 29 | #11716602 | C22 | 1 | 2 | yes | complemented |
| 30 | #11716600 | C22 | 1 | 2 | yes | complemented |
| 31 | #10610725 | — | 5 | 2 | no | maximal |
| 32 | C23×C5⋊D5 | — | 2 | 1 | no | — |
| 33 | C22×C4×C52 | C23 | 1 | 1 | yes | characteristic |
| 34 | C2×C22⋊(C5⋊D5) | D4 | 1 | 2 | yes | — |
| 35 | #87900 | — | 2 | 2 | no | — |
| 36 | #87900 | — | 2 | 2 | no | — |
| 37 | C2×C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 38 | C2×C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 39 | C2×C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 40 | C2×C4⋊(C5⋊D5) | — | 2 | 4 | no | — |
| 41 | C2×C4⋊(C5⋊D5) | C23 | 1 | 2 | yes | — |
| 42 | C2×C4⋊(C5⋊D5) | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×C4×C5⋊D5 | D4 | 1 | 2 | yes | — |
| 44 | C2×#6045 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×C5×C22⋊D5 | — | 2 | 2 | no | — |
| 46 | C5×#709 | — | 2 | 2 | no | — |
| 47 | C5×#709 | — | 2 | 2 | no | — |
| 48 | C5×#709 | D4 | 1 | 4 | yes | complemented |
| 49 | C5×#709 | C23 | 1 | 4 | yes | — |
| 50 | C2×C5×D20 | D4 | 1 | 2 | yes | complemented |
| 51 | C2×C4×C5×D5 | — | 2 | 2 | no | — |
| 52 | C2×C5×Dic10 | D4 | 1 | 2 | yes | complemented |
| 53 | #87886 | — | 2 | 4 | no | — |
| 54 | D5×C22⋊D5 | — | 2 | 8 | no | — |
| 55 | #87880 | — | 2 | 4 | no | — |
| 56 | #87879 | — | 2 | 8 | no | — |
| 57 | #87877 | — | 2 | 2 | no | — |
| 58 | D5×D20 | — | 2 | 4 | no | — |
| 59 | C4×D52 | — | 2 | 4 | no | — |
| 60 | #87874 | — | 2 | 4 | no | — |
| 61 | #87873 | — | 2 | 4 | no | — |
| 62 | #87872 | — | 2 | 2 | no | — |
| 63 | #87871 | — | 2 | 4 | no | — |
| 64 | #87870 | — | 2 | 4 | no | — |
| 65 | D5×Dic10 | — | 2 | 4 | no | — |
| 66 | C52×C4⋊C4 | — | 2 | 1 | no | — |
| 67 | C52×C22⋊C4 | — | 2 | 1 | no | — |
| 68 | C42×C52 | C23 | 1 | 2 | yes | — |
| 69 | #87808 | — | 2 | 4 | no | — |
| 70 | C5×#681 | — | 2 | 2 | no | — |
| 71 | C5×#681 | C23 | 1 | 4 | yes | — |
| 72 | C2×C5×#168 | — | 2 | 2 | no | — |
| 73 | #87774 | — | 2 | 8 | no | — |
| 74 | #87771 | — | 2 | 8 | no | — |
| 75 | #66283 | — | 5 | 2 | no | — |
| 76 | C2×#4095 | — | 5 | 2 | no | — |
| 77 | C2×#4054 | — | 5 | 2 | no | — |
| 78 | #65859 | — | 5 | 2 | no | — |
| 79 | #65859 | — | 10 | 2 | no | — |
| 80 | C5×#421 | — | 5 | 2 | no | — |
| 81 | #65421 | — | 5 | 2 | no | — |
| 82 | #65294 | D5 | 1 | 2 | yes | complemented |
| 83 | #65116 | — | 5 | 8 | no | — |
| 84 | #65111 | — | 5 | 8 | no | — |
| 85 | C23×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C22×C5⋊D5 | — | 2 | 2 | no | — |
| 87 | C22×C5⋊D5 | — | 4 | 2 | no | — |
| 88 | C22×C5⋊D5 | — | 8 | 2 | no | — |
| 89 | C22×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 90 | C22×C5×D5 | — | 2 | 2 | no | — |
| 91 | C2×D52 | — | 2 | 4 | no | — |
| 92 | C2×C4×C52 | — | 2 | 2 | no | — |
| 93 | C2×C4×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | C2×C4×C52 | C2×D4 | 1 | 2 | yes | — |
| 95 | C2×C4×C52 | C2×D4 | 1 | 2 | yes | — |
| 96 | C2×C4×C52 | C24 | 1 | 1 | yes | characteristic |
| 97 | C22⋊(C5⋊D5) | — | 2 | 4 | no | — |
| 98 | C2×#1039 | C2×D4 | 1 | 2 | yes | — |
| 99 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 100 | C4⋊(C5⋊D5) | — | 2 | 4 | no | — |
| 101 | C4⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 102 | C4⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 103 | C4⋊(C5⋊D5) | — | 8 | 4 | no | — |
| 104 | C4×C5⋊D5 | — | 2 | 2 | no | — |
| 105 | C4×C5⋊D5 | — | 2 | 2 | no | — |
| 106 | #6045 | — | 2 | 2 | no | — |
| 107 | C5×C22⋊D5 | — | 2 | 4 | no | — |
| 108 | C5×C22⋊D5 | — | 2 | 4 | no | — |
| 109 | C2×C5×Dic5 | — | 2 | 2 | no | — |
| 110 | C5×D20 | — | 2 | 2 | no | — |
| 111 | C5×D20 | C2×D4 | 1 | 4 | yes | — |
| 112 | C4×C5×D5 | — | 2 | 4 | no | — |
| 113 | C4×C5×D5 | — | 2 | 4 | no | — |
| 114 | C5×Dic10 | — | 2 | 2 | no | — |
| 115 | C5×Dic10 | C2×D4 | 1 | 4 | yes | — |
| 116 | #6039 | — | 2 | 4 | no | — |
| 117 | #6038 | — | 2 | 8 | no | — |
| 118 | #6037 | — | 2 | 4 | no | — |
| 119 | #6036 | — | 2 | 4 | no | — |
| 120 | D5×Dic5 | — | 2 | 8 | no | — |
| 121 | C5×#168 | — | 2 | 4 | no | — |
| 122 | C2×C5×#41 | — | 5 | 2 | no | — |
| 123 | #4150 | — | 5 | 4 | no | — |
| 124 | #4150 | — | 10 | 2 | no | — |
| 125 | #4149 | — | 5 | 4 | no | — |
| 126 | #4149 | — | 10 | 2 | no | — |
| 127 | D5×#41 | — | 10 | 4 | no | — |
| 128 | D5×#41 | — | 10 | 4 | no | — |
| 129 | #4147 | — | 10 | 2 | no | — |
| 130 | #4144 | — | 10 | 2 | no | — |
| 131 | #4144 | — | 10 | 4 | no | — |
| 132 | C2×#709 | — | 5 | 2 | no | — |
| 133 | C2×#709 | — | 10 | 2 | no | — |
| 134 | C2×#709 | — | 10 | 4 | no | — |
| 135 | C2×#709 | C2×D5 | 1 | 2 | yes | — |
| 136 | C22×D20 | — | 5 | 2 | no | — |
| 137 | C22×D20 | — | 10 | 2 | no | — |
| 138 | C2×C5×M16 | — | 5 | 2 | no | — |
| 139 | C5×#117 | — | 2 | 2 | no | — |
| 140 | C5×#117 | C2×D5 | 1 | 2 | yes | complemented |
| 141 | #4095 | — | 5 | 8 | no | — |
| 142 | #4095 | — | 10 | 4 | no | — |
| 143 | C2×#688 | — | 10 | 2 | no | — |
| 144 | C2×#686 | — | 10 | 2 | no | — |
| 145 | C2×#681 | C2×D5 | 1 | 2 | yes | complemented |
| 146 | #4054 | — | 5 | 8 | no | — |
| 147 | #4054 | — | 10 | 4 | no | — |
| 148 | C2×D40 | — | 10 | 2 | no | — |
| 149 | C2×#677 | — | 10 | 2 | no | — |
| 150 | #4041 | — | 10 | 4 | no | — |
| 151 | #4041 | — | 10 | 8 | no | — |
| 152 | #4028 | — | 10 | 4 | no | — |
| 153 | #4028 | — | 10 | 8 | no | — |
| 154 | #4021 | — | 5 | 4 | no | — |
| 155 | #4021 | — | 10 | 4 | no | — |
| 156 | #4020 | — | 5 | 4 | no | — |
| 157 | #4020 | — | 10 | 4 | no | — |
| 158 | C5×#104 | — | 5 | 8 | no | — |
| 159 | #3956 | — | 5 | 4 | no | — |
| 160 | #3955 | — | 5 | 4 | no | — |
| 161 | #3937 | C2×D5 | 1 | 8 | yes | complemented |
| 162 | #3021 | — | 25 | 1 | no | Sylow |
| 163 | C22×C52 | — | 4 | 1 | no | — |
| 164 | C22×C52 | #120 | 1 | 2 | yes | — |
| 165 | C22×C52 | C22×D4 | 1 | 1 | yes | characteristic |
| 166 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 167 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 168 | C2×C5⋊D5 | — | 4 | 4 | no | — |
| 169 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 170 | C2×C5⋊D5 | — | 8 | 4 | no | — |
| 171 | C2×C5×D5 | — | 2 | 4 | no | — |
| 172 | C2×C5×D5 | — | 8 | 2 | no | — |
| 173 | D52 | — | 8 | 4 | no | — |
| 174 | C4×C52 | — | 4 | 2 | no | — |
| 175 | C4×C52 | #120 | 1 | 1 | yes | characteristic |
| 176 | C4×C52 | #120 | 1 | 1 | yes | characteristic |
| 177 | C4×C52 | C22×D4 | 1 | 2 | yes | — |
| 178 | #1039 | — | 2 | 2 | no | — |
| 179 | C5×Dic5 | — | 2 | 4 | no | — |
| 180 | C23×D5 | — | 10 | 4 | no | — |
| 181 | C23×D5 | — | 10 | 2 | no | — |
| 182 | C5×#41 | — | 5 | 4 | no | — |
| 183 | C5×#41 | — | 5 | 4 | no | — |
| 184 | C5×#41 | — | 10 | 2 | no | — |
| 185 | C5×#41 | — | 10 | 2 | no | — |
| 186 | C2×C5×Q8 | — | 5 | 2 | no | — |
| 187 | C2×C5×D4 | — | 5 | 2 | no | — |
| 188 | C2×C5×D4 | — | 10 | 2 | no | — |
| 189 | C22×C4×C5 | — | 2 | 2 | no | — |
| 190 | C22×C4×C5 | — | 10 | 2 | no | — |
| 191 | C22×C4×C5 | C22×D5 | 1 | 2 | yes | — |
| 192 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 193 | C2×C22⋊D5 | — | 5 | 4 | no | — |
| 194 | C2×C22⋊D5 | — | 10 | 4 | no | — |
| 195 | C2×C22⋊D5 | — | 10 | 8 | no | — |
| 196 | #713 | — | 10 | 4 | no | — |
| 197 | #713 | — | 10 | 4 | no | — |
| 198 | Q8×D5 | — | 10 | 4 | no | — |
| 199 | Q8×D5 | — | 10 | 4 | no | — |
| 200 | #711 | — | 10 | 4 | no | — |
| 201 | #711 | — | 10 | 4 | no | — |
| 202 | #711 | — | 10 | 8 | no | — |
| 203 | #711 | — | 10 | 8 | no | — |
| 204 | D4×D5 | — | 10 | 4 | no | — |
| 205 | D4×D5 | — | 10 | 4 | no | — |
| 206 | D4×D5 | — | 10 | 8 | no | — |
| 207 | D4×D5 | — | 10 | 8 | no | — |
| 208 | #709 | — | 2 | 2 | no | — |
| 209 | #709 | — | 2 | 2 | no | — |
| 210 | #709 | — | 10 | 8 | no | — |
| 211 | #709 | — | 10 | 8 | no | — |
| 212 | #709 | — | 10 | 2 | no | — |
| 213 | #709 | — | 10 | 2 | no | — |
| 214 | #709 | — | 10 | 2 | no | — |
| 215 | #709 | — | 10 | 2 | no | — |
| 216 | #709 | — | 10 | 4 | no | — |
| 217 | #709 | — | 10 | 4 | no | — |
| 218 | #709 | — | 20 | 4 | no | — |
| 219 | #709 | — | 20 | 4 | no | — |
| 220 | #709 | D20 | 1 | 4 | yes | complemented |
| 221 | #709 | C22×D5 | 1 | 4 | yes | — |
| 222 | C2×D20 | — | 5 | 2 | no | — |
| 223 | C2×D20 | — | 5 | 4 | no | — |
| 224 | C2×D20 | — | 10 | 4 | no | — |
| 225 | C2×D20 | — | 10 | 2 | no | — |
| 226 | C2×D20 | — | 10 | 4 | no | — |
| 227 | C2×D20 | — | 10 | 2 | no | — |
| 228 | C2×D20 | — | 10 | 2 | no | — |
| 229 | C2×D20 | — | 10 | 2 | no | — |
| 230 | C2×D20 | — | 10 | 2 | no | — |
| 231 | C2×D20 | — | 10 | 4 | no | — |
| 232 | C2×D20 | — | 10 | 2 | no | — |
| 233 | C2×D20 | — | 10 | 8 | no | — |
| 234 | C2×D20 | — | 10 | 16 | no | — |
| 235 | C2×D20 | — | 20 | 4 | no | — |
| 236 | C2×D20 | — | 20 | 4 | no | — |
| 237 | C2×D20 | D20 | 1 | 2 | yes | complemented |
| 238 | C2×C4×D5 | — | 2 | 2 | no | — |
| 239 | C2×C4×D5 | — | 5 | 4 | no | — |
| 240 | C2×C4×D5 | — | 10 | 4 | no | — |
| 241 | C2×C4×D5 | — | 10 | 8 | no | — |
| 242 | C2×Dic10 | — | 5 | 2 | no | — |
| 243 | C2×Dic10 | — | 10 | 2 | no | — |
| 244 | C2×Dic10 | — | 10 | 4 | no | — |
| 245 | C2×Dic10 | D20 | 1 | 2 | yes | complemented |
| 246 | C5×M16 | — | 5 | 4 | no | — |
| 247 | C5×M16 | — | 10 | 2 | no | — |
| 248 | C2×C5×C8 | — | 10 | 2 | no | — |
| 249 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 250 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 251 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 252 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 253 | C42×C5 | — | 2 | 4 | no | — |
| 254 | C42×C5 | C22×D5 | 1 | 4 | yes | — |
| 255 | #688 | — | 10 | 8 | no | — |
| 256 | #686 | — | 10 | 8 | no | — |
| 257 | #685 | — | 10 | 8 | no | — |
| 258 | #685 | — | 10 | 16 | no | — |
| 259 | #681 | — | 2 | 2 | no | — |
| 260 | #681 | C22×D5 | 1 | 4 | yes | — |
| 261 | C2×#168 | — | 2 | 2 | no | — |
| 262 | D40 | — | 10 | 8 | no | — |
| 263 | #677 | — | 10 | 8 | no | — |
| 264 | #585 | — | 25 | 1 | no | — |
| 265 | C2×AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 266 | #535 | — | 25 | 1 | no | — |
| 267 | #454 | — | 25 | 4 | no | — |
| 268 | #453 | — | 25 | 4 | no | — |
| 269 | #421 | — | 5 | 2 | no | — |
| 270 | #413 | — | 25 | 1 | no | — |
| 271 | C2×C52 | — | 2 | 1 | no | — |
| 272 | C2×C52 | — | 2 | 2 | no | — |
| 273 | C2×C52 | C2×#120 | 1 | 1 | yes | characteristic |
| 274 | C5⋊D5 | — | 4 | 2 | no | — |
| 275 | C5⋊D5 | — | 8 | 2 | no | — |
| 276 | C5×D5 | — | 4 | 4 | no | — |
| 277 | C23×C5 | — | 2 | 2 | no | — |
| 278 | C23×C5 | — | 10 | 2 | no | — |
| 279 | C23×C5 | D4×D5 | 1 | 2 | yes | — |
| 280 | C22×D5 | — | 2 | 2 | no | — |
| 281 | C22×D5 | — | 5 | 4 | no | — |
| 282 | C22×D5 | — | 10 | 4 | no | — |
| 283 | C22×D5 | — | 10 | 8 | no | — |
| 284 | C22×D5 | — | 10 | 8 | no | — |
| 285 | C22×D5 | — | 10 | 4 | no | — |
| 286 | C22×D5 | — | 20 | 8 | no | — |
| 287 | C22×D5 | — | 20 | 2 | no | — |
| 288 | C22×D5 | — | 20 | 2 | no | — |
| 289 | C22×D5 | — | 40 | 4 | no | — |
| 290 | C22×D5 | — | 40 | 8 | no | — |
| 291 | C5×Q8 | — | 5 | 4 | no | — |
| 292 | C5×Q8 | — | 10 | 2 | no | — |
| 293 | C5×D4 | — | 5 | 4 | no | — |
| 294 | C5×D4 | — | 10 | 4 | no | — |
| 295 | C5×D4 | — | 10 | 4 | no | — |
| 296 | C5×D4 | — | 10 | 2 | no | — |
| 297 | C2×C4×C5 | — | 2 | 8 | no | — |
| 298 | C2×C4×C5 | — | 2 | 4 | no | — |
| 299 | C2×C4×C5 | — | 2 | 4 | no | — |
| 300 | C2×C4×C5 | — | 2 | 4 | no | — |
| 301 | C2×C4×C5 | — | 2 | 2 | no | — |
| 302 | C2×C4×C5 | — | 2 | 2 | no | — |
| 303 | C2×C4×C5 | — | 10 | 2 | no | — |
| 304 | C2×C4×C5 | — | 10 | 4 | no | — |
| 305 | C2×C4×C5 | — | 10 | 4 | no | — |
| 306 | C2×C4×C5 | C2×D20 | 1 | 2 | yes | — |
| 307 | C2×C4×C5 | C2×D20 | 1 | 2 | yes | — |
| 308 | C2×C4×C5 | D4×D5 | 1 | 2 | yes | — |
| 309 | C2×C4×C5 | D4×D5 | 1 | 2 | yes | — |
| 310 | C2×C4×C5 | D4×D5 | 1 | 2 | yes | — |
| 311 | C2×C4×C5 | C23×D5 | 1 | 2 | yes | — |
| 312 | C22⋊D5 | — | 2 | 4 | no | — |
| 313 | C22⋊D5 | — | 2 | 4 | no | — |
| 314 | C22⋊D5 | — | 10 | 8 | no | — |
| 315 | C22⋊D5 | — | 10 | 8 | no | — |
| 316 | C22⋊D5 | — | 10 | 4 | no | — |
| 317 | C22⋊D5 | — | 10 | 4 | no | — |
| 318 | C22⋊D5 | — | 20 | 8 | no | — |
| 319 | C2×Dic5 | — | 2 | 2 | no | — |
| 320 | C2×Dic5 | — | 5 | 4 | no | — |
| 321 | C2×Dic5 | — | 10 | 4 | no | — |
| 322 | C2×Dic5 | — | 10 | 8 | no | — |
| 323 | D20 | — | 2 | 2 | no | — |
| 324 | D20 | — | 10 | 8 | no | — |
| 325 | D20 | — | 10 | 2 | no | — |
| 326 | D20 | — | 10 | 4 | no | — |
| 327 | D20 | — | 10 | 2 | no | — |
| 328 | D20 | — | 10 | 4 | no | — |
| 329 | D20 | — | 20 | 8 | no | — |
| 330 | D20 | — | 20 | 4 | no | — |
| 331 | D20 | — | 20 | 4 | no | — |
| 332 | D20 | — | 20 | 4 | no | — |
| 333 | D20 | — | 20 | 2 | no | — |
| 334 | D20 | — | 20 | 2 | no | — |
| 335 | D20 | — | 40 | 8 | no | — |
| 336 | D20 | — | 40 | 16 | no | — |
| 337 | D20 | C2×D20 | 1 | 4 | yes | — |
| 338 | C4×D5 | — | 2 | 4 | no | — |
| 339 | C4×D5 | — | 2 | 4 | no | — |
| 340 | C4×D5 | — | 10 | 8 | no | — |
| 341 | C4×D5 | — | 10 | 8 | no | — |
| 342 | C4×D5 | — | 10 | 4 | no | — |
| 343 | C4×D5 | — | 10 | 4 | no | — |
| 344 | C4×D5 | — | 20 | 4 | no | — |
| 345 | C4×D5 | — | 20 | 4 | no | — |
| 346 | Dic10 | — | 2 | 2 | no | — |
| 347 | Dic10 | — | 10 | 8 | no | — |
| 348 | Dic10 | — | 10 | 2 | no | — |
| 349 | Dic10 | — | 10 | 2 | no | — |
| 350 | Dic10 | — | 20 | 4 | no | — |
| 351 | Dic10 | C2×D20 | 1 | 4 | yes | — |
| 352 | C5×C8 | — | 10 | 4 | no | — |
| 353 | #168 | — | 2 | 4 | no | — |
| 354 | 2−1+4 | — | 25 | 2 | no | — |
| 355 | 2−1+4 | — | 50 | 2 | no | — |
| 356 | H(5,𝔽2) | — | 25 | 2 | no | — |
| 357 | H(5,𝔽2) | — | 50 | 2 | no | — |
| 358 | H(5,𝔽2) | — | 50 | 2 | no | — |
| 359 | C2×#41 | — | 5 | 2 | no | — |
| 360 | C2×#41 | — | 25 | 1 | no | — |
| 361 | C2×#41 | — | 50 | 4 | no | — |
| 362 | C2×#41 | — | 50 | 2 | no | — |
| 363 | C22×D4 | — | 25 | 1 | no | — |
| 364 | AGL(1,ℤ/8) | — | 25 | 8 | no | — |
| 365 | AGL(1,ℤ/8) | — | 50 | 4 | no | — |
| 366 | C2×SD16 | — | 50 | 2 | no | — |
| 367 | C2×D8 | — | 50 | 2 | no | — |
| 368 | C2×M16 | — | 5 | 2 | no | — |
| 369 | #127 | — | 25 | 2 | no | — |
| 370 | #124 | — | 25 | 2 | no | — |
| 371 | #121 | — | 50 | 2 | no | — |
| 372 | #120 | — | 50 | 2 | no | — |
| 373 | #117 | D52 | 1 | 1 | yes | characteristic, complemented |
| 374 | #104 | — | 5 | 8 | no | — |
| 375 | #101 | — | 25 | 2 | no | — |
| 376 | #100 | — | 25 | 2 | no | — |
| 377 | C52 | #3021 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 378 | C22×C5 | — | 2 | 2 | no | — |
| 379 | C22×C5 | — | 2 | 4 | no | — |
| 380 | C22×C5 | — | 4 | 2 | no | — |
| 381 | C22×C5 | — | 4 | 4 | no | — |
| 382 | C22×C5 | — | 10 | 4 | no | — |
| 383 | C22×C5 | — | 40 | 2 | no | — |
| 384 | C22×C5 | #4028 | 1 | 2 | yes | — |
| 385 | C22×C5 | #4028 | 1 | 2 | yes | — |
| 386 | C22×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 387 | C2×D5 | — | 2 | 4 | no | — |
| 388 | C2×D5 | — | 8 | 2 | no | — |
| 389 | C2×D5 | — | 10 | 4 | no | — |
| 390 | C2×D5 | — | 20 | 4 | no | — |
| 391 | C2×D5 | — | 20 | 4 | no | — |
| 392 | C2×D5 | — | 20 | 8 | no | — |
| 393 | C2×D5 | — | 20 | 8 | no | — |
| 394 | C2×D5 | — | 20 | 16 | no | — |
| 395 | C2×D5 | — | 20 | 8 | no | — |
| 396 | C2×D5 | — | 20 | 4 | no | — |
| 397 | C2×D5 | — | 40 | 8 | no | — |
| 398 | C2×D5 | — | 40 | 4 | no | — |
| 399 | C2×D5 | — | 40 | 4 | no | — |
| 400 | C2×D5 | — | 40 | 16 | no | — |
| 401 | C4×C5 | — | 2 | 4 | no | — |
| 402 | C4×C5 | — | 2 | 2 | no | — |
| 403 | C4×C5 | — | 2 | 2 | no | — |
| 404 | C4×C5 | — | 4 | 8 | no | — |
| 405 | C4×C5 | — | 4 | 4 | no | — |
| 406 | C4×C5 | — | 10 | 4 | no | — |
| 407 | C4×C5 | #4028 | 1 | 2 | yes | — |
| 408 | C4×C5 | #4028 | 1 | 2 | yes | — |
| 409 | C4×C5 | C22×D20 | 1 | 2 | yes | — |
| 410 | C4×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 411 | Dic5 | — | 2 | 4 | no | — |
| 412 | Dic5 | — | 10 | 4 | no | — |
| 413 | Dic5 | — | 20 | 4 | no | — |
| 414 | C24 | — | 50 | 1 | no | — |
| 415 | #41 | — | 5 | 4 | no | — |
| 416 | #41 | — | 5 | 4 | no | — |
| 417 | #41 | — | 10 | 2 | no | — |
| 418 | #41 | — | 10 | 2 | no | — |
| 419 | #41 | — | 50 | 4 | no | — |
| 420 | #41 | — | 50 | 4 | no | — |
| 421 | #41 | — | 50 | 8 | no | — |
| 422 | #41 | — | 50 | 4 | no | — |
| 423 | #41 | — | 50 | 4 | no | — |
| 424 | #41 | — | 50 | 4 | no | — |
| 425 | #41 | — | 50 | 2 | no | — |
| 426 | #41 | — | 50 | 2 | no | — |
| 427 | C2×Q8 | — | 5 | 2 | no | — |
| 428 | C2×Q8 | — | 25 | 1 | no | — |
| 429 | C2×Q8 | — | 50 | 4 | no | — |
| 430 | C2×Q8 | — | 50 | 2 | no | — |
| 431 | C2×D4 | — | 5 | 2 | no | — |
| 432 | C2×D4 | — | 10 | 2 | no | — |
| 433 | C2×D4 | — | 25 | 2 | no | — |
| 434 | C2×D4 | — | 25 | 1 | no | — |
| 435 | C2×D4 | — | 25 | 2 | no | — |
| 436 | C2×D4 | — | 50 | 4 | no | — |
| 437 | C2×D4 | — | 50 | 4 | no | — |
| 438 | C2×D4 | — | 50 | 4 | no | — |
| 439 | C2×D4 | — | 50 | 2 | no | — |
| 440 | C2×D4 | — | 50 | 8 | no | — |
| 441 | C2×D4 | — | 50 | 2 | no | — |
| 442 | C2×D4 | — | 50 | 2 | no | — |
| 443 | C2×D4 | — | 50 | 1 | no | — |
| 444 | C22×C4 | — | 10 | 2 | no | — |
| 445 | C22×C4 | — | 25 | 2 | no | — |
| 446 | C22×C4 | — | 50 | 4 | no | — |
| 447 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 448 | SD16 | — | 50 | 8 | no | — |
| 449 | D8 | — | 50 | 8 | no | — |
| 450 | M16 | — | 5 | 4 | no | — |
| 451 | M16 | — | 10 | 2 | no | — |
| 452 | C2×C8 | — | 10 | 2 | no | — |
| 453 | C4⋊C4 | — | 2 | 1 | no | — |
| 454 | C22⋊C4 | — | 2 | 1 | no | — |
| 455 | C22⋊C4 | — | 50 | 4 | no | — |
| 456 | C42 | C2×D52 | 1 | 2 | yes | — |
| 457 | C2×C5 | — | 2 | 4 | no | — |
| 458 | C2×C5 | — | 2 | 2 | no | — |
| 459 | C2×C5 | — | 2 | 2 | no | — |
| 460 | C2×C5 | — | 2 | 2 | no | — |
| 461 | C2×C5 | — | 2 | 2 | no | — |
| 462 | C2×C5 | — | 4 | 4 | no | — |
| 463 | C2×C5 | — | 20 | 4 | no | — |
| 464 | C2×C5 | C2×#4028 | 1 | 2 | yes | — |
| 465 | D5 | — | 4 | 4 | no | — |
| 466 | D5 | — | 20 | 4 | no | — |
| 467 | D5 | — | 40 | 4 | no | — |
| 468 | D5 | — | 40 | 8 | no | — |
| 469 | D5 | — | 40 | 4 | no | — |
| 470 | C23 | — | 10 | 2 | no | — |
| 471 | C23 | — | 25 | 2 | no | — |
| 472 | C23 | — | 50 | 4 | no | — |
| 473 | C23 | — | 50 | 2 | no | — |
| 474 | C23 | — | 100 | 2 | no | — |
| 475 | C23 | — | 200 | 2 | no | — |
| 476 | C23 | #87886 | 1 | 1 | yes | characteristic |
| 477 | Q8 | — | 5 | 4 | no | — |
| 478 | Q8 | — | 10 | 2 | no | — |
| 479 | Q8 | — | 50 | 4 | no | — |
| 480 | Q8 | — | 50 | 2 | no | — |
| 481 | D4 | — | 5 | 4 | no | — |
| 482 | D4 | — | 10 | 4 | no | — |
| 483 | D4 | — | 10 | 4 | no | — |
| 484 | D4 | — | 10 | 2 | no | — |
| 485 | D4 | — | 50 | 8 | no | — |
| 486 | D4 | — | 50 | 4 | no | — |
| 487 | D4 | — | 50 | 4 | no | — |
| 488 | D4 | — | 50 | 2 | no | — |
| 489 | D4 | — | 50 | 4 | no | — |
| 490 | D4 | — | 100 | 1 | no | — |
| 491 | D4 | — | 100 | 1 | no | — |
| 492 | D4 | — | 200 | 4 | no | — |
| 493 | C2×C4 | — | 2 | 2 | no | — |
| 494 | C2×C4 | — | 10 | 2 | no | — |
| 495 | C2×C4 | — | 10 | 4 | no | — |
| 496 | C2×C4 | — | 10 | 4 | no | — |
| 497 | C2×C4 | — | 25 | 2 | no | — |
| 498 | C2×C4 | — | 50 | 4 | no | — |
| 499 | C2×C4 | — | 50 | 8 | no | — |
| 500 | C2×C4 | — | 50 | 2 | no | — |
| 501 | C2×C4 | — | 50 | 2 | no | — |
| 502 | C2×C4 | D5×D20 | 1 | 2 | yes | — |
| 503 | C2×C4 | D5×D20 | 1 | 2 | yes | — |
| 504 | C2×C4 | #87886 | 1 | 1 | yes | characteristic |
| 505 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 506 | C8 | — | 10 | 4 | no | — |
| 507 | C5 | — | 2 | 2 | no | — |
| 508 | C5 | #10610725 | 1 | 2 | yes | complemented |
| 509 | C22 | — | 4 | 1 | no | — |
| 510 | C22 | — | 10 | 4 | no | — |
| 511 | C22 | — | 40 | 2 | no | — |
| 512 | C22 | — | 50 | 2 | no | — |
| 513 | C22 | — | 100 | 2 | no | — |
| 514 | C22 | — | 100 | 4 | no | — |
| 515 | C22 | — | 100 | 2 | no | — |
| 516 | C22 | — | 200 | 4 | no | — |
| 517 | C22 | — | 200 | 4 | no | — |
| 518 | C22 | #11717041 | 1 | 2 | yes | — |
| 519 | C22 | C2×#87886 | 1 | 1 | yes | characteristic |
| 520 | C4 | — | 4 | 2 | no | — |
| 521 | C4 | — | 10 | 4 | no | — |
| 522 | C4 | — | 50 | 2 | no | — |
| 523 | C4 | #11717041 | 1 | 1 | yes | characteristic |
| 524 | C4 | #11717041 | 1 | 1 | yes | characteristic |
| 525 | C4 | C2×D5×D20 | 1 | 2 | yes | — |
| 526 | C2 | — | 2 | 1 | no | — |
| 527 | C2 | — | 2 | 2 | no | — |
| 528 | C2 | — | 20 | 4 | no | — |
| 529 | C2 | — | 100 | 2 | no | — |
| 530 | C2 | — | 200 | 2 | no | — |
| 531 | C2 | C2×#11717041 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107815 | C2 | semidirect |
| 2. #13107056 | C2 | semidirect |
| 3. C2×#11716943 | C2 | semidirect |
| 4. C5×#65294 | C2 | semidirect |
| 5. #13101272 | C2 | semidirect |
| 6. #13100582 | C2 | semidirect |
| 7. #13100579 | C2 | semidirect |
| 9. C22×C4⋊(C5⋊D5) | C22 | semidirect |
| 12. #11717473 | C22 | semidirect |
| 16. #11717463 | C22 | semidirect |
| 18. C52×#117 | C22 | semidirect |
| 21. #11717195 | C22 | semidirect |
| 22. #11717194 | C22 | semidirect |
| 23. C2×C5×#681 | C22 | semidirect |
| 26. #11716943 | C22 | semidirect |
| 28. C5×#3937 | C22 | semidirect |
| 29. #11716602 | C22 | semidirect |
| 30. #11716600 | C22 | semidirect |
| 48. C5×#709 | D4 | semidirect |
| 50. C2×C5×D20 | D4 | semidirect |
| 52. C2×C5×Dic10 | D4 | semidirect |
| 82. #65294 | D5 | semidirect |
| 140. C5×#117 | C2×D5 | semidirect |
| 145. C2×#681 | C2×D5 | semidirect |
| 161. #3937 | C2×D5 | semidirect |
| 220. #709 | D20 | semidirect |
| 237. C2×D20 | D20 | semidirect |
| 245. C2×Dic10 | D20 | semidirect |
| 373. #117 | D52 | semidirect |
| 377. C52 | #3021 | semidirect |
| 508. C5 | #10610725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107815 | 2 |
| #13107056 | 2 |
| C2×#11716943 | 2 |
| C5×#65294 | 2 |
| #13101272 | 2 |
| #13100582 | 2 |
| #13100579 | 2 |
| #10610725 | 5 |