Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1072 conjugacy classes of subgroups.
The subgroup lattice has 578 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13106458 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13106286 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13102921 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#65351 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#65350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13101825 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13101699 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13100579 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13100569 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C5×#4147 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×#4144 | C22 | 1 | 1 | yes | characteristic |
| 12 | #11717473 | C22 | 1 | 2 | yes | complemented |
| 13 | C52×#124 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×#87811 | C22 | 1 | 2 | yes | complemented |
| 15 | C2×#87809 | C22 | 1 | 2 | yes | complemented |
| 16 | #11717194 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C5×#4088 | C22 | 1 | 2 | yes | complemented |
| 18 | C5×#4078 | C22 | 1 | 2 | yes | complemented |
| 19 | #11717067 | — | 2 | 2 | no | — |
| 20 | #11717066 | — | 2 | 2 | no | — |
| 21 | #11717057 | — | 2 | 2 | no | — |
| 22 | D5×#688 | — | 2 | 2 | no | — |
| 23 | #11717053 | — | 2 | 2 | no | — |
| 24 | #11717052 | — | 2 | 2 | no | — |
| 25 | #11717043 | — | 2 | 2 | no | — |
| 26 | D5×#686 | — | 2 | 2 | no | — |
| 27 | #11716943 | C22 | 1 | 2 | yes | — |
| 28 | #11716943 | C22 | 1 | 2 | yes | complemented |
| 29 | #11716940 | C22 | 1 | 2 | yes | — |
| 30 | #11716933 | C22 | 1 | 2 | yes | complemented |
| 31 | #11716933 | C22 | 1 | 2 | yes | complemented |
| 32 | #11716670 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | C5×#3968 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C5×#3965 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C5×#3937 | C22 | 1 | 2 | yes | complemented |
| 36 | C5×#3937 | C22 | 1 | 2 | yes | complemented |
| 37 | #11716619 | C22 | 1 | 2 | yes | complemented |
| 38 | #11716600 | C22 | 1 | 2 | yes | complemented |
| 39 | #10612025 | — | 5 | 1 | no | maximal |
| 40 | #10612018 | — | 5 | 1 | no | maximal |
| 41 | C2×C52×Q8 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×C52×D4 | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×C4⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 44 | C2×C4⋊(C5⋊D5) | C23 | 1 | 2 | yes | — |
| 45 | C2×C5×C22⋊D5 | — | 4 | 1 | no | — |
| 46 | C5×#713 | — | 2 | 2 | no | — |
| 47 | C5×Q8×D5 | — | 2 | 2 | no | — |
| 48 | C5×#711 | — | 2 | 2 | no | — |
| 49 | C5×D4×D5 | — | 2 | 2 | no | — |
| 50 | C5×#709 | — | 4 | 1 | no | — |
| 51 | C5×#709 | C23 | 1 | 2 | yes | — |
| 52 | C5×#709 | C23 | 1 | 2 | yes | — |
| 53 | #87886 | — | 4 | 2 | no | — |
| 54 | D5×D20 | — | 2 | 2 | no | — |
| 55 | D5×D20 | — | 2 | 2 | no | — |
| 56 | #87874 | — | 2 | 2 | no | — |
| 57 | #87874 | — | 2 | 2 | no | — |
| 58 | C52×C22⋊C4 | — | 4 | 1 | no | — |
| 59 | C42×C52 | C23 | 1 | 1 | yes | characteristic |
| 60 | #87811 | — | 2 | 2 | no | — |
| 61 | #87811 | — | 2 | 2 | no | — |
| 62 | #87809 | — | 2 | 2 | no | — |
| 63 | #87809 | — | 2 | 2 | no | — |
| 64 | C2×#6029 | C23 | 1 | 2 | yes | — |
| 65 | C5×#689 | — | 2 | 2 | no | — |
| 66 | C5×#688 | — | 2 | 2 | no | — |
| 67 | C5×#687 | — | 2 | 2 | no | — |
| 68 | C5×#686 | — | 2 | 2 | no | — |
| 69 | C5×#681 | C23 | 1 | 2 | yes | — |
| 70 | C5×#681 | C23 | 1 | 2 | yes | — |
| 71 | #87775 | D4 | 1 | 2 | yes | complemented |
| 72 | #87774 | — | 2 | 2 | no | — |
| 73 | #87774 | — | 2 | 2 | no | — |
| 74 | #87772 | D4 | 1 | 2 | yes | complemented |
| 75 | #87772 | D4 | 1 | 2 | yes | complemented |
| 76 | #87771 | — | 2 | 2 | no | — |
| 77 | #87771 | — | 2 | 2 | no | — |
| 78 | #87770 | D4 | 1 | 2 | yes | complemented |
| 79 | #87768 | — | 2 | 2 | no | — |
| 80 | #87768 | — | 2 | 2 | no | — |
| 81 | D5×#168 | — | 2 | 2 | no | — |
| 82 | D5×#168 | — | 2 | 2 | no | — |
| 83 | #66171 | — | 5 | 2 | no | — |
| 84 | #66169 | — | 5 | 2 | no | — |
| 85 | #66112 | — | 5 | 2 | no | — |
| 86 | #66108 | — | 5 | 2 | no | — |
| 87 | C5×#455 | — | 5 | 1 | no | — |
| 88 | C5×#454 | — | 5 | 1 | no | — |
| 89 | #65492 | — | 5 | 2 | no | — |
| 90 | #65488 | — | 5 | 2 | no | — |
| 91 | #65351 | D5 | 1 | 1 | yes | characteristic, complemented |
| 92 | #65350 | D5 | 1 | 1 | yes | characteristic, complemented |
| 93 | #65347 | — | 5 | 1 | no | — |
| 94 | #65347 | — | 5 | 1 | no | — |
| 95 | #65347 | — | 10 | 2 | no | — |
| 96 | #65112 | — | 5 | 2 | no | — |
| 97 | #65112 | — | 5 | 2 | no | — |
| 98 | #65111 | — | 5 | 2 | no | — |
| 99 | #65111 | — | 5 | 2 | no | — |
| 100 | #65043 | — | 5 | 2 | no | — |
| 101 | #65038 | — | 5 | 2 | no | — |
| 102 | C23×C52 | — | 2 | 1 | no | — |
| 103 | C22×C5⋊D5 | — | 2 | 2 | no | — |
| 104 | C22×C5×D5 | — | 4 | 1 | no | — |
| 105 | C2×D52 | — | 4 | 2 | no | — |
| 106 | C52×Q8 | — | 2 | 2 | no | — |
| 107 | C52×D4 | — | 2 | 2 | no | — |
| 108 | C2×C4×C52 | — | 2 | 1 | no | — |
| 109 | C2×C4×C52 | — | 2 | 1 | no | — |
| 110 | C2×C4×C52 | C24 | 1 | 1 | yes | characteristic |
| 111 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 112 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 113 | C4⋊(C5⋊D5) | — | 8 | 2 | no | — |
| 114 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 115 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 116 | C5×C22⋊D5 | — | 4 | 2 | no | — |
| 117 | C2×C5×Dic5 | — | 4 | 1 | no | — |
| 118 | C5×D20 | — | 4 | 1 | no | — |
| 119 | C5×D20 | C2×D4 | 1 | 2 | yes | — |
| 120 | C5×D20 | C2×D4 | 1 | 2 | yes | — |
| 121 | C4×C5×D5 | — | 2 | 2 | no | — |
| 122 | C4×C5×D5 | — | 2 | 2 | no | — |
| 123 | C4×C5×D5 | — | 4 | 2 | no | — |
| 124 | C5×Dic10 | — | 4 | 1 | no | — |
| 125 | C5×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 126 | C5×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 127 | #6038 | — | 4 | 2 | no | — |
| 128 | #6038 | — | 4 | 2 | no | — |
| 129 | #6036 | — | 4 | 2 | no | — |
| 130 | #6029 | C2×D4 | 1 | 2 | yes | — |
| 131 | #6029 | C2×D4 | 1 | 2 | yes | — |
| 132 | C5×#168 | — | 2 | 2 | no | — |
| 133 | C5×#168 | — | 2 | 2 | no | — |
| 134 | C5×2−1+4 | — | 5 | 1 | no | — |
| 135 | C5×H(5,𝔽2) | — | 5 | 1 | no | — |
| 136 | #4149 | — | 5 | 2 | no | — |
| 137 | #4149 | — | 5 | 2 | no | — |
| 138 | #4147 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 139 | #4144 | C2×D5 | 1 | 1 | yes | characteristic |
| 140 | C5×#137 | — | 5 | 2 | no | — |
| 141 | C5×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 142 | C5×#124 | — | 2 | 2 | no | — |
| 143 | C5×#124 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 144 | C5×#124 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 145 | #4096 | — | 5 | 2 | no | — |
| 146 | #4096 | — | 5 | 2 | no | — |
| 147 | #4096 | — | 10 | 2 | no | — |
| 148 | #4096 | — | 10 | 2 | no | — |
| 149 | #4095 | — | 5 | 2 | no | — |
| 150 | #4095 | — | 5 | 2 | no | — |
| 151 | #4095 | — | 10 | 2 | no | — |
| 152 | #4095 | — | 10 | 2 | no | — |
| 153 | #4094 | — | 5 | 2 | no | — |
| 154 | #4094 | — | 5 | 2 | no | — |
| 155 | #4088 | — | 10 | 2 | no | — |
| 156 | #4088 | C2×D5 | 1 | 2 | yes | complemented |
| 157 | C2×#688 | — | 5 | 2 | no | — |
| 158 | C2×#688 | — | 5 | 2 | no | — |
| 159 | C2×#688 | — | 10 | 4 | no | — |
| 160 | C2×#688 | — | 10 | 2 | no | — |
| 161 | #4078 | — | 10 | 2 | no | — |
| 162 | #4078 | C2×D5 | 1 | 2 | yes | complemented |
| 163 | C2×#686 | — | 5 | 2 | no | — |
| 164 | C2×#686 | — | 5 | 2 | no | — |
| 165 | C2×#686 | — | 10 | 4 | no | — |
| 166 | C2×#686 | — | 10 | 2 | no | — |
| 167 | #4065 | — | 10 | 2 | no | — |
| 168 | #4064 | — | 10 | 2 | no | — |
| 169 | #4062 | — | 10 | 2 | no | — |
| 170 | #4060 | — | 10 | 2 | no | — |
| 171 | #4060 | — | 10 | 2 | no | — |
| 172 | D5×SD16 | — | 10 | 2 | no | — |
| 173 | #4057 | — | 10 | 2 | no | — |
| 174 | D5×D8 | — | 10 | 2 | no | — |
| 175 | #4054 | — | 5 | 2 | no | — |
| 176 | #4054 | — | 5 | 2 | no | — |
| 177 | #4053 | — | 5 | 2 | no | — |
| 178 | #4053 | — | 5 | 2 | no | — |
| 179 | #4020 | — | 5 | 1 | no | — |
| 180 | #4020 | — | 5 | 1 | no | — |
| 181 | #4020 | — | 10 | 2 | no | — |
| 182 | C5×#104 | — | 5 | 2 | no | — |
| 183 | C5×#104 | — | 5 | 2 | no | — |
| 184 | C5×#101 | — | 5 | 1 | no | — |
| 185 | C5×#100 | — | 5 | 1 | no | — |
| 186 | #3968 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 187 | #3965 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 188 | #3955 | — | 5 | 2 | no | — |
| 189 | #3955 | — | 5 | 2 | no | — |
| 190 | #3954 | — | 5 | 2 | no | — |
| 191 | #3954 | — | 5 | 2 | no | — |
| 192 | #3937 | C2×D5 | 1 | 2 | yes | complemented |
| 193 | #3937 | C2×D5 | 1 | 2 | yes | complemented |
| 194 | #3935 | — | 5 | 1 | no | — |
| 195 | #3935 | — | 5 | 1 | no | — |
| 196 | #3935 | — | 10 | 2 | no | — |
| 197 | #3288 | — | 25 | 1 | no | Sylow |
| 198 | C22×C52 | — | 4 | 1 | no | — |
| 199 | C22×C52 | — | 8 | 1 | no | — |
| 200 | C22×C52 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 201 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 202 | C2×C5⋊D5 | — | 8 | 2 | no | — |
| 203 | C2×C5×D5 | — | 2 | 2 | no | — |
| 204 | C2×C5×D5 | — | 2 | 2 | no | — |
| 205 | C2×C5×D5 | — | 16 | 1 | no | — |
| 206 | D52 | — | 16 | 2 | no | — |
| 207 | C4×C52 | — | 4 | 1 | no | — |
| 208 | C4×C52 | — | 4 | 1 | no | — |
| 209 | C4×C52 | C22×D4 | 1 | 2 | yes | — |
| 210 | C5×Dic5 | — | 2 | 2 | no | — |
| 211 | C5×Dic5 | — | 2 | 2 | no | — |
| 212 | C5×#41 | — | 5 | 2 | no | — |
| 213 | C5×#41 | — | 5 | 2 | no | — |
| 214 | C5×#41 | — | 10 | 2 | no | — |
| 215 | C5×#41 | — | 10 | 2 | no | — |
| 216 | C5×#41 | — | 20 | 1 | no | — |
| 217 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 218 | C2×C5×Q8 | — | 10 | 2 | no | — |
| 219 | C2×C5×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 220 | C2×C5×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 221 | C2×C5×D4 | — | 2 | 2 | no | — |
| 222 | C2×C5×D4 | — | 10 | 2 | no | — |
| 223 | C2×C5×D4 | — | 20 | 1 | no | — |
| 224 | C2×C5×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 225 | C2×C5×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 226 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 227 | #713 | — | 2 | 2 | no | — |
| 228 | #713 | — | 10 | 2 | no | — |
| 229 | #713 | — | 10 | 2 | no | — |
| 230 | Q8×D5 | — | 2 | 2 | no | — |
| 231 | #711 | — | 2 | 2 | no | — |
| 232 | D4×D5 | — | 2 | 2 | no | — |
| 233 | D4×D5 | — | 10 | 2 | no | — |
| 234 | D4×D5 | — | 10 | 2 | no | — |
| 235 | D4×D5 | — | 20 | 2 | no | — |
| 236 | D4×D5 | — | 20 | 2 | no | — |
| 237 | #709 | — | 4 | 1 | no | — |
| 238 | #709 | — | 10 | 2 | no | — |
| 239 | #709 | — | 10 | 2 | no | — |
| 240 | #709 | C22×D5 | 1 | 2 | yes | — |
| 241 | #709 | C22×D5 | 1 | 2 | yes | — |
| 242 | C2×D20 | — | 5 | 2 | no | — |
| 243 | C2×D20 | — | 5 | 2 | no | — |
| 244 | C2×D20 | — | 10 | 4 | no | — |
| 245 | C2×D20 | — | 10 | 2 | no | — |
| 246 | C2×D20 | — | 10 | 2 | no | — |
| 247 | C2×D20 | — | 20 | 1 | no | — |
| 248 | C2×D20 | — | 20 | 1 | no | — |
| 249 | C2×D20 | — | 20 | 4 | no | — |
| 250 | C5×Q16 | — | 10 | 2 | no | — |
| 251 | C5×SD16 | — | 10 | 2 | no | — |
| 252 | C5×SD16 | — | 10 | 2 | no | — |
| 253 | C5×D8 | — | 10 | 2 | no | — |
| 254 | C5×M16 | — | 5 | 2 | no | — |
| 255 | C5×M16 | — | 5 | 2 | no | — |
| 256 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 257 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 258 | C5×C22⋊C4 | — | 4 | 4 | no | — |
| 259 | C42×C5 | — | 2 | 2 | no | — |
| 260 | C42×C5 | C22×D5 | 1 | 1 | yes | characteristic |
| 261 | C42×C5 | C22×D5 | 1 | 1 | yes | characteristic |
| 262 | #689 | — | 2 | 2 | no | — |
| 263 | #689 | — | 5 | 2 | no | — |
| 264 | #689 | — | 5 | 2 | no | — |
| 265 | #688 | — | 2 | 2 | no | — |
| 266 | #688 | — | 5 | 2 | no | — |
| 267 | #688 | — | 5 | 2 | no | — |
| 268 | #688 | — | 10 | 2 | no | — |
| 269 | #688 | — | 10 | 2 | no | — |
| 270 | #688 | — | 10 | 2 | no | — |
| 271 | #688 | — | 10 | 2 | no | — |
| 272 | #688 | — | 10 | 2 | no | — |
| 273 | #688 | — | 10 | 2 | no | — |
| 274 | #688 | — | 20 | 4 | no | — |
| 275 | #688 | — | 20 | 4 | no | — |
| 276 | #687 | — | 2 | 2 | no | — |
| 277 | #687 | — | 5 | 2 | no | — |
| 278 | #687 | — | 5 | 2 | no | — |
| 279 | #686 | — | 2 | 2 | no | — |
| 280 | #686 | — | 5 | 2 | no | — |
| 281 | #686 | — | 5 | 2 | no | — |
| 282 | #686 | — | 10 | 2 | no | — |
| 283 | #686 | — | 10 | 2 | no | — |
| 284 | #686 | — | 10 | 2 | no | — |
| 285 | #686 | — | 10 | 2 | no | — |
| 286 | #686 | — | 10 | 2 | no | — |
| 287 | #686 | — | 10 | 2 | no | — |
| 288 | #686 | — | 20 | 4 | no | — |
| 289 | #686 | — | 20 | 4 | no | — |
| 290 | #681 | — | 10 | 2 | no | — |
| 291 | #681 | — | 10 | 2 | no | — |
| 292 | #681 | C22×D5 | 1 | 2 | yes | — |
| 293 | #681 | C22×D5 | 1 | 2 | yes | — |
| 294 | C2×#168 | — | 5 | 2 | no | — |
| 295 | C2×#168 | — | 5 | 2 | no | — |
| 296 | C2×#168 | — | 10 | 4 | no | — |
| 297 | C2×#168 | — | 10 | 2 | no | — |
| 298 | C2×#168 | — | 10 | 2 | no | — |
| 299 | D40 | — | 10 | 2 | no | — |
| 300 | D40 | — | 10 | 2 | no | — |
| 301 | #677 | — | 10 | 2 | no | — |
| 302 | #677 | — | 10 | 2 | no | — |
| 303 | #676 | — | 10 | 2 | no | — |
| 304 | #676 | — | 10 | 2 | no | — |
| 305 | C8×D5 | — | 10 | 2 | no | — |
| 306 | C8×D5 | — | 10 | 2 | no | — |
| 307 | #577 | — | 25 | 2 | no | — |
| 308 | #576 | — | 25 | 2 | no | — |
| 309 | #496 | — | 25 | 1 | no | — |
| 310 | #472 | — | 25 | 2 | no | — |
| 311 | #471 | — | 25 | 2 | no | — |
| 312 | #455 | — | 5 | 1 | no | — |
| 313 | #454 | — | 5 | 1 | no | — |
| 314 | #453 | — | 25 | 2 | no | — |
| 315 | #444 | — | 25 | 2 | no | — |
| 316 | C2×C52 | — | 2 | 1 | no | — |
| 317 | C2×C52 | — | 8 | 1 | no | — |
| 318 | C2×C52 | D42 | 1 | 1 | yes | characteristic |
| 319 | C5⋊D5 | — | 8 | 2 | no | — |
| 320 | C5×D5 | — | 4 | 2 | no | — |
| 321 | C5×D5 | — | 4 | 2 | no | — |
| 322 | C23×C5 | — | 2 | 1 | no | — |
| 323 | C23×C5 | — | 2 | 1 | no | — |
| 324 | C23×C5 | — | 4 | 2 | no | — |
| 325 | C23×C5 | — | 20 | 1 | no | — |
| 326 | C22×D5 | — | 4 | 1 | no | — |
| 327 | C22×D5 | — | 10 | 2 | no | — |
| 328 | C22×D5 | — | 10 | 2 | no | — |
| 329 | C22×D5 | — | 20 | 4 | no | — |
| 330 | C22×D5 | — | 20 | 2 | no | — |
| 331 | C22×D5 | — | 20 | 2 | no | — |
| 332 | C5×Q8 | — | 2 | 2 | no | — |
| 333 | C5×Q8 | — | 2 | 2 | no | — |
| 334 | C5×Q8 | — | 4 | 4 | no | — |
| 335 | C5×Q8 | — | 5 | 2 | no | — |
| 336 | C5×Q8 | — | 5 | 2 | no | — |
| 337 | C5×Q8 | — | 20 | 1 | no | — |
| 338 | C5×D4 | — | 2 | 2 | no | — |
| 339 | C5×D4 | — | 2 | 2 | no | — |
| 340 | C5×D4 | — | 4 | 4 | no | — |
| 341 | C5×D4 | — | 5 | 2 | no | — |
| 342 | C5×D4 | — | 5 | 2 | no | — |
| 343 | C5×D4 | — | 10 | 2 | no | — |
| 344 | C5×D4 | — | 10 | 2 | no | — |
| 345 | C5×D4 | — | 20 | 1 | no | — |
| 346 | C5×D4 | — | 20 | 2 | no | — |
| 347 | C2×C4×C5 | — | 2 | 4 | no | — |
| 348 | C2×C4×C5 | — | 2 | 1 | no | — |
| 349 | C2×C4×C5 | — | 2 | 1 | no | — |
| 350 | C2×C4×C5 | — | 2 | 1 | no | — |
| 351 | C2×C4×C5 | — | 2 | 1 | no | — |
| 352 | C2×C4×C5 | — | 2 | 2 | no | — |
| 353 | C2×C4×C5 | — | 4 | 2 | no | — |
| 354 | C2×C4×C5 | — | 10 | 2 | no | — |
| 355 | C2×C4×C5 | — | 10 | 2 | no | — |
| 356 | C2×C4×C5 | — | 20 | 2 | no | — |
| 357 | C2×C4×C5 | — | 20 | 1 | no | — |
| 358 | C2×C4×C5 | C23×D5 | 1 | 1 | yes | characteristic |
| 359 | C2×C4×C5 | C23×D5 | 1 | 1 | yes | characteristic |
| 360 | C22⋊D5 | — | 2 | 2 | no | — |
| 361 | C22⋊D5 | — | 2 | 2 | no | — |
| 362 | C22⋊D5 | — | 4 | 2 | no | — |
| 363 | C22⋊D5 | — | 20 | 2 | no | — |
| 364 | C22⋊D5 | — | 20 | 2 | no | — |
| 365 | C2×Dic5 | — | 4 | 1 | no | — |
| 366 | D20 | — | 4 | 1 | no | — |
| 367 | D20 | — | 10 | 2 | no | — |
| 368 | D20 | — | 10 | 2 | no | — |
| 369 | D20 | — | 10 | 2 | no | — |
| 370 | D20 | — | 10 | 2 | no | — |
| 371 | D20 | — | 20 | 4 | no | — |
| 372 | D20 | — | 20 | 4 | no | — |
| 373 | D20 | — | 20 | 2 | no | — |
| 374 | D20 | — | 20 | 2 | no | — |
| 375 | D20 | — | 40 | 2 | no | — |
| 376 | D20 | — | 40 | 2 | no | — |
| 377 | D20 | — | 40 | 8 | no | — |
| 378 | D20 | D4×D5 | 1 | 2 | yes | — |
| 379 | D20 | D4×D5 | 1 | 2 | yes | — |
| 380 | C4×D5 | — | 2 | 2 | no | — |
| 381 | C4×D5 | — | 2 | 2 | no | — |
| 382 | C4×D5 | — | 4 | 2 | no | — |
| 383 | C4×D5 | — | 20 | 2 | no | — |
| 384 | C4×D5 | — | 20 | 2 | no | — |
| 385 | Dic10 | — | 4 | 1 | no | — |
| 386 | Dic10 | D4×D5 | 1 | 2 | yes | — |
| 387 | Dic10 | D4×D5 | 1 | 2 | yes | — |
| 388 | C5×C8 | — | 10 | 2 | no | — |
| 389 | C5×C8 | — | 10 | 2 | no | — |
| 390 | #168 | — | 2 | 2 | no | — |
| 391 | #168 | — | 2 | 2 | no | — |
| 392 | #168 | — | 5 | 2 | no | — |
| 393 | #168 | — | 5 | 2 | no | — |
| 394 | #168 | — | 5 | 2 | no | — |
| 395 | #168 | — | 5 | 2 | no | — |
| 396 | #168 | — | 10 | 4 | no | — |
| 397 | #168 | — | 10 | 4 | no | — |
| 398 | 2−1+4 | — | 5 | 1 | no | — |
| 399 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 400 | H(5,𝔽2) | — | 25 | 2 | no | — |
| 401 | #137 | — | 5 | 2 | no | — |
| 402 | #137 | — | 50 | 2 | no | — |
| 403 | AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 404 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 405 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 406 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 407 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 408 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 409 | #135 | — | 25 | 2 | no | — |
| 410 | #135 | — | 50 | 2 | no | — |
| 411 | #135 | — | 50 | 2 | no | — |
| 412 | C2×SD16 | — | 25 | 2 | no | — |
| 413 | C2×SD16 | — | 50 | 2 | no | — |
| 414 | C2×D8 | — | 25 | 2 | no | — |
| 415 | C2×D8 | — | 50 | 2 | no | — |
| 416 | #131 | — | 25 | 2 | no | — |
| 417 | #131 | — | 25 | 2 | no | — |
| 418 | #127 | — | 25 | 1 | no | — |
| 419 | #124 | D52 | 1 | 1 | yes | characteristic, complemented |
| 420 | #108 | — | 25 | 2 | no | — |
| 421 | #104 | — | 5 | 2 | no | — |
| 422 | #104 | — | 5 | 2 | no | — |
| 423 | #101 | — | 5 | 1 | no | — |
| 424 | #100 | — | 5 | 1 | no | — |
| 425 | #100 | — | 25 | 2 | no | — |
| 426 | #97 | — | 25 | 1 | no | — |
| 427 | C52 | #3288 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 428 | C22×C5 | — | 2 | 2 | no | — |
| 429 | C22×C5 | — | 4 | 1 | no | — |
| 430 | C22×C5 | — | 4 | 1 | no | — |
| 431 | C22×C5 | — | 8 | 2 | no | — |
| 432 | C22×C5 | — | 8 | 1 | no | — |
| 433 | C22×C5 | — | 8 | 1 | no | — |
| 434 | C22×C5 | — | 8 | 4 | no | — |
| 435 | C22×C5 | — | 10 | 2 | no | — |
| 436 | C22×C5 | — | 10 | 2 | no | — |
| 437 | C22×C5 | — | 80 | 1 | no | — |
| 438 | C22×C5 | #4144 | 1 | 1 | yes | characteristic |
| 439 | C22×C5 | #4144 | 1 | 1 | yes | characteristic |
| 440 | C2×D5 | — | 2 | 2 | no | — |
| 441 | C2×D5 | — | 2 | 2 | no | — |
| 442 | C2×D5 | — | 16 | 1 | no | — |
| 443 | C2×D5 | — | 20 | 2 | no | — |
| 444 | C2×D5 | — | 20 | 2 | no | — |
| 445 | C2×D5 | — | 40 | 4 | no | — |
| 446 | C2×D5 | — | 40 | 2 | no | — |
| 447 | C2×D5 | — | 40 | 2 | no | — |
| 448 | C2×D5 | — | 40 | 8 | no | — |
| 449 | C2×D5 | — | 80 | 2 | no | — |
| 450 | C2×D5 | — | 80 | 2 | no | — |
| 451 | C4×C5 | — | 2 | 4 | no | — |
| 452 | C4×C5 | — | 4 | 4 | no | — |
| 453 | C4×C5 | — | 4 | 1 | no | — |
| 454 | C4×C5 | — | 4 | 1 | no | — |
| 455 | C4×C5 | — | 4 | 1 | no | — |
| 456 | C4×C5 | — | 4 | 1 | no | — |
| 457 | C4×C5 | — | 8 | 2 | no | — |
| 458 | C4×C5 | — | 10 | 2 | no | — |
| 459 | C4×C5 | — | 10 | 2 | no | — |
| 460 | C4×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 461 | C4×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 462 | Dic5 | — | 2 | 2 | no | — |
| 463 | Dic5 | — | 2 | 2 | no | — |
| 464 | #41 | — | 5 | 2 | no | — |
| 465 | #41 | — | 5 | 2 | no | — |
| 466 | #41 | — | 10 | 2 | no | — |
| 467 | #41 | — | 10 | 2 | no | — |
| 468 | #41 | — | 20 | 1 | no | — |
| 469 | #41 | — | 50 | 2 | no | — |
| 470 | #41 | — | 50 | 2 | no | — |
| 471 | C2×Q8 | — | 10 | 2 | no | — |
| 472 | C2×Q8 | C2×D52 | 1 | 1 | yes | characteristic |
| 473 | C2×D4 | — | 10 | 2 | no | — |
| 474 | C2×D4 | — | 20 | 1 | no | — |
| 475 | C2×D4 | — | 25 | 2 | no | — |
| 476 | C2×D4 | — | 50 | 2 | no | — |
| 477 | C2×D4 | — | 50 | 2 | no | — |
| 478 | C2×D4 | — | 100 | 1 | no | — |
| 479 | C2×D4 | — | 100 | 2 | no | — |
| 480 | C2×D4 | C2×D52 | 1 | 1 | yes | characteristic |
| 481 | Q16 | — | 10 | 2 | no | — |
| 482 | Q16 | — | 25 | 2 | no | — |
| 483 | SD16 | — | 10 | 2 | no | — |
| 484 | SD16 | — | 10 | 2 | no | — |
| 485 | SD16 | — | 25 | 2 | no | — |
| 486 | SD16 | — | 25 | 2 | no | — |
| 487 | SD16 | — | 50 | 2 | no | — |
| 488 | SD16 | — | 50 | 2 | no | — |
| 489 | SD16 | — | 50 | 2 | no | — |
| 490 | SD16 | — | 50 | 2 | no | — |
| 491 | D8 | — | 10 | 2 | no | — |
| 492 | D8 | — | 25 | 2 | no | — |
| 493 | D8 | — | 50 | 2 | no | — |
| 494 | D8 | — | 50 | 2 | no | — |
| 495 | D8 | — | 50 | 2 | no | — |
| 496 | D8 | — | 50 | 2 | no | — |
| 497 | M16 | — | 5 | 2 | no | — |
| 498 | M16 | — | 5 | 2 | no | — |
| 499 | M16 | — | 50 | 2 | no | — |
| 500 | M16 | — | 50 | 2 | no | — |
| 501 | C2×C8 | — | 25 | 2 | no | — |
| 502 | C2×C8 | — | 50 | 2 | no | — |
| 503 | C2×C8 | — | 50 | 2 | no | — |
| 504 | C22⋊C4 | — | 4 | 1 | no | — |
| 505 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 506 | C2×C5 | — | 2 | 4 | no | — |
| 507 | C2×C5 | — | 2 | 1 | no | — |
| 508 | C2×C5 | — | 2 | 1 | no | — |
| 509 | C2×C5 | — | 2 | 2 | no | — |
| 510 | C2×C5 | — | 8 | 1 | no | — |
| 511 | C2×C5 | — | 8 | 1 | no | — |
| 512 | C2×C5 | — | 16 | 2 | no | — |
| 513 | C2×C5 | — | 20 | 2 | no | — |
| 514 | C2×C5 | — | 20 | 2 | no | — |
| 515 | C2×C5 | #65924 | 1 | 1 | yes | characteristic |
| 516 | C2×C5 | #65924 | 1 | 1 | yes | characteristic |
| 517 | D5 | — | 4 | 2 | no | — |
| 518 | D5 | — | 4 | 2 | no | — |
| 519 | D5 | — | 40 | 2 | no | — |
| 520 | D5 | — | 40 | 2 | no | — |
| 521 | D5 | — | 80 | 4 | no | — |
| 522 | C23 | — | 2 | 1 | no | — |
| 523 | C23 | — | 20 | 1 | no | — |
| 524 | C23 | — | 50 | 2 | no | — |
| 525 | C23 | — | 100 | 2 | no | — |
| 526 | Q8 | — | 2 | 2 | no | — |
| 527 | Q8 | — | 5 | 2 | no | — |
| 528 | Q8 | — | 5 | 2 | no | — |
| 529 | Q8 | — | 20 | 1 | no | — |
| 530 | D4 | — | 2 | 2 | no | — |
| 531 | D4 | — | 5 | 2 | no | — |
| 532 | D4 | — | 5 | 2 | no | — |
| 533 | D4 | — | 10 | 2 | no | — |
| 534 | D4 | — | 10 | 2 | no | — |
| 535 | D4 | — | 20 | 1 | no | — |
| 536 | D4 | — | 20 | 2 | no | — |
| 537 | D4 | — | 50 | 2 | no | — |
| 538 | D4 | — | 50 | 2 | no | — |
| 539 | D4 | — | 100 | 2 | no | — |
| 540 | D4 | — | 100 | 2 | no | — |
| 541 | D4 | — | 200 | 2 | no | — |
| 542 | C2×C4 | — | 2 | 1 | no | — |
| 543 | C2×C4 | — | 2 | 1 | no | — |
| 544 | C2×C4 | — | 10 | 2 | no | — |
| 545 | C2×C4 | — | 10 | 2 | no | — |
| 546 | C2×C4 | — | 20 | 2 | no | — |
| 547 | C2×C4 | — | 20 | 1 | no | — |
| 548 | C2×C4 | — | 100 | 2 | no | — |
| 549 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 550 | C8 | — | 10 | 2 | no | — |
| 551 | C8 | — | 10 | 2 | no | — |
| 552 | C8 | — | 25 | 2 | no | — |
| 553 | C8 | — | 25 | 2 | no | — |
| 554 | C5 | — | 2 | 2 | no | — |
| 555 | C5 | #10612018 | 1 | 1 | yes | characteristic, complemented |
| 556 | C5 | #10612025 | 1 | 1 | yes | characteristic, complemented |
| 557 | C22 | — | 4 | 1 | no | — |
| 558 | C22 | — | 8 | 1 | no | — |
| 559 | C22 | — | 10 | 2 | no | — |
| 560 | C22 | — | 10 | 2 | no | — |
| 561 | C22 | — | 80 | 1 | no | — |
| 562 | C22 | — | 100 | 2 | no | — |
| 563 | C22 | — | 400 | 2 | no | — |
| 564 | C22 | — | 200 | 2 | no | — |
| 565 | C22 | #11717495 | 1 | 1 | yes | characteristic |
| 566 | C4 | — | 4 | 1 | no | — |
| 567 | C4 | — | 4 | 1 | no | — |
| 568 | C4 | — | 10 | 2 | no | — |
| 569 | C4 | — | 10 | 2 | no | — |
| 570 | C4 | D4×D52 | 1 | 2 | yes | — |
| 571 | C2 | — | 2 | 1 | no | — |
| 572 | C2 | — | 8 | 1 | no | — |
| 573 | C2 | — | 20 | 2 | no | — |
| 574 | C2 | — | 20 | 2 | no | — |
| 575 | C2 | — | 200 | 2 | no | — |
| 576 | C2 | #13106268 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13106458 | C2 | semidirect |
| 2. #13106286 | C2 | semidirect |
| 3. #13102921 | C2 | semidirect |
| 4. C5×#65351 | C2 | semidirect |
| 5. C5×#65350 | C2 | semidirect |
| 6. #13101825 | C2 | semidirect |
| 7. #13101699 | C2 | semidirect |
| 8. #13100579 | C2 | semidirect |
| 9. #13100569 | C2 | semidirect |
| 10. C5×#4147 | C22 | semidirect |
| 12. #11717473 | C22 | semidirect |
| 13. C52×#124 | C22 | semidirect |
| 14. C2×#87811 | C22 | semidirect |
| 15. C2×#87809 | C22 | semidirect |
| 16. #11717194 | C22 | semidirect |
| 17. C5×#4088 | C22 | semidirect |
| 18. C5×#4078 | C22 | semidirect |
| 28. #11716943 | C22 | semidirect |
| 30. #11716933 | C22 | semidirect |
| 31. #11716933 | C22 | semidirect |
| 32. #11716670 | C22 | semidirect |
| 33. C5×#3968 | C22 | semidirect |
| 34. C5×#3965 | C22 | semidirect |
| 35. C5×#3937 | C22 | semidirect |
| 36. C5×#3937 | C22 | semidirect |
| 37. #11716619 | C22 | semidirect |
| 38. #11716600 | C22 | semidirect |
| 71. #87775 | D4 | semidirect |
| 74. #87772 | D4 | semidirect |
| 75. #87772 | D4 | semidirect |
| 78. #87770 | D4 | semidirect |
| 91. #65351 | D5 | semidirect |
| 92. #65350 | D5 | semidirect |
| 138. #4147 | C2×D5 | semidirect |
| 143. C5×#124 | C2×D5 | semidirect |
| 144. C5×#124 | C2×D5 | semidirect |
| 156. #4088 | C2×D5 | semidirect |
| 162. #4078 | C2×D5 | semidirect |
| 186. #3968 | C2×D5 | semidirect |
| 187. #3965 | C2×D5 | semidirect |
| 192. #3937 | C2×D5 | semidirect |
| 193. #3937 | C2×D5 | semidirect |
| 419. #124 | D52 | semidirect |
| 427. C52 | #3288 | semidirect |
| 555. C5 | #10612018 | semidirect |
| 556. C5 | #10612025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13106458 | 2 |
| #13106286 | 2 |
| #13102921 | 2 |
| C5×#65351 | 2 |
| C5×#65350 | 2 |
| #13101825 | 2 |
| #13101699 | 2 |
| #13100579 | 2 |
| #13100569 | 2 |
| #10612025 | 5 |
| #10612018 | 5 |