Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
2788 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 2788 conjugacy classes of subgroups — too many to draw. Only its 242 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 | #72221069 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #72220919 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72220906 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C5⋊D5×#493 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72213464 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13107767 | C22 | 1 | 4 | yes | — |
| 7 | C2×D8×C5⋊D5 | C22 | 1 | 4 | yes | — |
| 8 | #127×C5⋊D5 | C22 | 1 | 2 | yes | — |
| 9 | #13104916 | C22 | 1 | 4 | yes | — |
| 10 | #13104909 | C22 | 1 | 8 | yes | — |
| 11 | #13104869 | — | 2 | 8 | no | — |
| 12 | D8×#1044 | — | 2 | 8 | no | — |
| 13 | #13104862 | C22 | 1 | 2 | yes | — |
| 14 | #13104859 | C22 | 1 | 2 | yes | — |
| 15 | #13104856 | C22 | 1 | 4 | yes | — |
| 16 | C52×#493 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #13103011 | C4 | 1 | 4 | yes | complemented |
| 18 | #13102935 | C4 | 1 | 2 | yes | complemented |
| 19 | #13102558 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | C4×C8×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 21 | #13100332 | C22 | 1 | 4 | yes | — |
| 22 | #13042040 | — | 5 | 2 | no | maximal |
| 23 | C2×D4×C5⋊D5 | — | 4 | 2 | no | — |
| 24 | C2×D4×C5⋊D5 | C23 | 1 | 4 | yes | — |
| 25 | C2×C22⋊#1044 | — | 4 | 4 | no | — |
| 26 | D4×#1044 | — | 2 | 16 | no | — |
| 27 | #11717451 | C23 | 1 | 4 | yes | — |
| 28 | #11717448 | C23 | 1 | 4 | yes | — |
| 29 | C2×C52×D8 | C2×C4 | 1 | 4 | yes | complemented |
| 30 | C52×#127 | C2×C4 | 1 | 2 | yes | complemented |
| 31 | #11717260 | — | 4 | 2 | no | — |
| 32 | #11717260 | C2×C4 | 1 | 4 | yes | complemented |
| 33 | C2×#87809 | C2×C4 | 1 | 8 | yes | complemented |
| 34 | D8×C5⋊D5 | — | 2 | 4 | no | — |
| 35 | D8×C5⋊D5 | — | 2 | 4 | no | — |
| 36 | D8×C5⋊D5 | — | 2 | 4 | no | — |
| 37 | D8×C5⋊D5 | — | 2 | 4 | no | — |
| 38 | C2×#87801 | C2×C4 | 1 | 4 | yes | complemented |
| 39 | C2×C8×C5⋊D5 | C23 | 1 | 2 | yes | — |
| 40 | #11717194 | C2×C4 | 1 | 2 | yes | complemented |
| 41 | C42×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 42 | #11716906 | — | 4 | 4 | no | — |
| 43 | #11716900 | — | 2 | 16 | no | — |
| 44 | #11716889 | — | 2 | 2 | no | — |
| 45 | #11716888 | — | 2 | 2 | no | — |
| 46 | #11716887 | D4 | 1 | 4 | yes | complemented |
| 47 | #11716886 | D4 | 1 | 4 | yes | complemented |
| 48 | #11716885 | — | 2 | 4 | no | — |
| 49 | C8×#1044 | — | 2 | 4 | no | — |
| 50 | C4×C52×C8 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 51 | C8×#1039 | C2×C4 | 1 | 2 | yes | complemented |
| 52 | C4×#6029 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 53 | #10617422 | — | 5 | 8 | no | — |
| 54 | D5×#493 | — | 5 | 2 | no | — |
| 55 | D5×#493 | — | 10 | 2 | no | — |
| 56 | #10604806 | — | 5 | 8 | no | — |
| 57 | #10604614 | — | 5 | 8 | no | — |
| 58 | #10603851 | — | 5 | 4 | no | — |
| 59 | C23×C5⋊D5 | — | 2 | 4 | no | — |
| 60 | C22×#1044 | — | 4 | 8 | no | — |
| 61 | C2×C52×D4 | — | 4 | 2 | no | — |
| 62 | C2×C52×D4 | C22×C4 | 1 | 4 | yes | — |
| 63 | C2×C22⋊(C5⋊D5) | — | 2 | 4 | no | — |
| 64 | C2×C22⋊(C5⋊D5) | — | 4 | 4 | no | — |
| 65 | D4×C5⋊D5 | — | 2 | 8 | no | — |
| 66 | D4×C5⋊D5 | — | 2 | 8 | no | — |
| 67 | D4×C5⋊D5 | — | 8 | 8 | no | — |
| 68 | C2×C4⋊(C5⋊D5) | — | 4 | 2 | no | — |
| 69 | C2×C4⋊(C5⋊D5) | C22×C4 | 1 | 4 | yes | — |
| 70 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 71 | C2×C4×C5⋊D5 | C24 | 1 | 1 | yes | characteristic |
| 72 | C22⋊#1044 | — | 2 | 4 | no | — |
| 73 | C22⋊#1044 | — | 4 | 8 | no | — |
| 74 | #87867 | — | 2 | 4 | no | — |
| 75 | C4⋊#1044 | C2×D4 | 1 | 8 | yes | — |
| 76 | C4×#1044 | — | 2 | 4 | no | — |
| 77 | #87863 | — | 2 | 4 | no | — |
| 78 | #87862 | — | 2 | 4 | no | — |
| 79 | C52×D8 | — | 2 | 4 | no | — |
| 80 | C52×D8 | — | 2 | 4 | no | — |
| 81 | C2×C52×C8 | C22×C4 | 1 | 2 | yes | — |
| 82 | C42×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 83 | #87809 | — | 2 | 8 | no | — |
| 84 | #87809 | — | 2 | 8 | no | — |
| 85 | C4×#1039 | — | 2 | 1 | no | — |
| 86 | C4×#1039 | C22×C4 | 1 | 1 | yes | characteristic |
| 87 | C2×#6029 | C22×C4 | 1 | 2 | yes | — |
| 88 | #87801 | — | 2 | 4 | no | — |
| 89 | #87801 | — | 2 | 4 | no | — |
| 90 | C8×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 91 | C8×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 92 | C8×C5⋊D5 | #41 | 1 | 2 | yes | — |
| 93 | C8×C5⋊D5 | #41 | 1 | 2 | yes | — |
| 94 | #66258 | — | 5 | 8 | no | — |
| 95 | C2×D5×D8 | — | 5 | 8 | no | — |
| 96 | C2×D5×D8 | — | 10 | 8 | no | — |
| 97 | D5×#127 | — | 5 | 4 | no | — |
| 98 | D5×#127 | — | 10 | 4 | no | — |
| 99 | D5⋊#100 | — | 5 | 8 | no | — |
| 100 | #65767 | — | 5 | 16 | no | — |
| 101 | #65731 | — | 10 | 16 | no | — |
| 102 | D8×AGL(1,𝔽5) | — | 10 | 16 | no | — |
| 103 | D5⋊#108 | — | 5 | 4 | no | — |
| 104 | #65721 | — | 5 | 4 | no | — |
| 105 | #65718 | — | 5 | 8 | no | — |
| 106 | C5×#493 | — | 2 | 2 | no | — |
| 107 | C5×#493 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 108 | #65440 | — | 5 | 8 | no | — |
| 109 | #65440 | — | 10 | 8 | no | — |
| 110 | #65362 | — | 5 | 4 | no | — |
| 111 | #65362 | — | 10 | 4 | no | — |
| 112 | #64984 | — | 5 | 2 | no | — |
| 113 | #64984 | — | 10 | 2 | no | — |
| 114 | C4×C8×D5 | — | 5 | 2 | no | — |
| 115 | C4×C8×D5 | — | 10 | 2 | no | — |
| 116 | #64862 | — | 5 | 8 | no | — |
| 117 | #23201 | — | 25 | 1 | no | Sylow |
| 118 | C23×C52 | — | 2 | 4 | no | — |
| 119 | C22×C5⋊D5 | — | 2 | 4 | no | — |
| 120 | C22×C5⋊D5 | — | 4 | 4 | no | — |
| 121 | C22×C5⋊D5 | — | 4 | 4 | no | — |
| 122 | C22×C5⋊D5 | — | 8 | 8 | no | — |
| 123 | C22×C5⋊D5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 124 | C2×#1044 | — | 2 | 8 | no | — |
| 125 | C2×#1044 | — | 16 | 8 | no | — |
| 126 | C52×D4 | — | 2 | 8 | no | — |
| 127 | C52×D4 | — | 8 | 4 | no | — |
| 128 | C2×C4×C52 | — | 2 | 1 | no | — |
| 129 | C2×C4×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 130 | C22⋊(C5⋊D5) | — | 4 | 8 | no | — |
| 131 | C22⋊(C5⋊D5) | — | 8 | 8 | no | — |
| 132 | C2×#1039 | — | 2 | 1 | no | — |
| 133 | C2×#1039 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 134 | C4⋊(C5⋊D5) | — | 2 | 8 | no | — |
| 135 | C4⋊(C5⋊D5) | — | 8 | 4 | no | — |
| 136 | C4×C5⋊D5 | — | 2 | 4 | no | — |
| 137 | C4×C5⋊D5 | C22×D4 | 1 | 2 | yes | — |
| 138 | C4×C5⋊D5 | C2×#41 | 1 | 2 | yes | — |
| 139 | #6034 | — | 4 | 4 | no | — |
| 140 | C52×C8 | C4×D4 | 1 | 2 | yes | — |
| 141 | C52×C8 | C4×D4 | 1 | 2 | yes | — |
| 142 | #6029 | C4×D4 | 1 | 2 | yes | — |
| 143 | #6029 | C4×D4 | 1 | 2 | yes | — |
| 144 | C2×D4×D5 | — | 5 | 8 | no | — |
| 145 | C2×D4×D5 | — | 10 | 8 | no | — |
| 146 | C2×D4×D5 | — | 20 | 4 | no | — |
| 147 | C2×D4×D5 | — | 20 | 8 | no | — |
| 148 | C2×C22⋊AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 149 | D4×AGL(1,𝔽5) | — | 10 | 32 | no | — |
| 150 | #4130 | — | 5 | 8 | no | — |
| 151 | D5⋊M16 | — | 5 | 8 | no | — |
| 152 | C2×C5×D8 | — | 2 | 8 | no | — |
| 153 | C2×C5×D8 | C2×AGL(1,𝔽5) | 1 | 8 | yes | complemented |
| 154 | C5×#127 | — | 2 | 4 | no | — |
| 155 | C5×#127 | C2×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 156 | #4086 | — | 5 | 8 | no | — |
| 157 | #4086 | — | 10 | 8 | no | — |
| 158 | #4086 | — | 20 | 4 | no | — |
| 159 | #4086 | — | 20 | 8 | no | — |
| 160 | C2×#686 | — | 5 | 16 | no | — |
| 161 | C2×#686 | — | 10 | 16 | no | — |
| 162 | D5×D8 | — | 10 | 8 | no | — |
| 163 | D5×D8 | — | 10 | 8 | no | — |
| 164 | D5×D8 | — | 10 | 8 | no | — |
| 165 | D5×D8 | — | 10 | 8 | no | — |
| 166 | D5×D8 | — | 20 | 8 | no | — |
| 167 | D5×D8 | — | 20 | 8 | no | — |
| 168 | D5×D8 | — | 20 | 8 | no | — |
| 169 | D5×D8 | — | 20 | 8 | no | — |
| 170 | C2×D40 | — | 5 | 8 | no | — |
| 171 | C2×D40 | — | 10 | 8 | no | — |
| 172 | C2×C8×D5 | — | 5 | 4 | no | — |
| 173 | C2×C8×D5 | — | 10 | 4 | no | — |
| 174 | #4020 | — | 5 | 4 | no | — |
| 175 | #4020 | — | 10 | 4 | no | — |
| 176 | C42×D5 | — | 5 | 2 | no | — |
| 177 | C42×D5 | — | 10 | 2 | no | — |
| 178 | #4013 | — | 20 | 8 | no | — |
| 179 | #4007 | — | 10 | 32 | no | — |
| 180 | #3996 | — | 10 | 4 | no | — |
| 181 | #3995 | — | 10 | 4 | no | — |
| 182 | #3994 | — | 5 | 8 | no | — |
| 183 | #3993 | — | 5 | 8 | no | — |
| 184 | #3992 | — | 10 | 8 | no | — |
| 185 | C8×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 186 | C4×C5×C8 | — | 2 | 2 | no | — |
| 187 | C4×C5×C8 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 188 | C8×Dic5 | — | 5 | 4 | no | — |
| 189 | C8×Dic5 | — | 10 | 4 | no | — |
| 190 | C4×#168 | — | 5 | 2 | no | — |
| 191 | C4×#168 | — | 10 | 2 | no | — |
| 192 | C2×#493 | — | 25 | 1 | no | — |
| 193 | #2948 | — | 25 | 4 | no | — |
| 194 | #1978 | — | 25 | 4 | no | — |
| 195 | #1887 | — | 25 | 4 | no | — |
| 196 | #1772 | — | 25 | 2 | no | — |
| 197 | C22×C52 | — | 4 | 4 | no | — |
| 198 | C22×C52 | — | 8 | 4 | no | — |
| 199 | C22×C52 | #518 | 1 | 1 | yes | characteristic |
| 200 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 201 | C2×C5⋊D5 | — | 4 | 4 | no | — |
| 202 | C2×C5⋊D5 | — | 8 | 8 | no | — |
| 203 | C2×C5⋊D5 | — | 8 | 4 | no | — |
| 204 | C2×C5⋊D5 | — | 16 | 4 | no | — |
| 205 | C2×C5⋊D5 | D42 | 1 | 1 | yes | characteristic |
| 206 | C2×C5⋊D5 | #559 | 1 | 1 | yes | characteristic |
| 207 | #1044 | — | 4 | 8 | no | — |
| 208 | C4×C52 | — | 2 | 2 | no | — |
| 209 | C4×C52 | C2×C4×D4 | 1 | 2 | yes | — |
| 210 | #1039 | — | 2 | 2 | no | — |
| 211 | #1039 | #550 | 1 | 2 | yes | — |
| 212 | C23×D5 | — | 10 | 8 | no | — |
| 213 | C23×D5 | — | 20 | 8 | no | — |
| 214 | C22×AGL(1,𝔽5) | — | 20 | 16 | no | — |
| 215 | C2×C5×D4 | — | 2 | 8 | no | — |
| 216 | C2×C5×D4 | — | 4 | 4 | no | — |
| 217 | C2×C5×D4 | — | 4 | 8 | no | — |
| 218 | C2×C5×D4 | C22×AGL(1,𝔽5) | 1 | 8 | yes | — |
| 219 | C2×C22⋊D5 | — | 10 | 8 | no | — |
| 220 | C2×C22⋊D5 | — | 20 | 8 | no | — |
| 221 | C2×C22⋊D5 | — | 20 | 8 | no | — |
| 222 | C2×C22⋊D5 | — | 20 | 16 | no | — |
| 223 | D4×D5 | — | 10 | 16 | no | — |
| 224 | D4×D5 | — | 10 | 16 | no | — |
| 225 | D4×D5 | — | 20 | 16 | no | — |
| 226 | D4×D5 | — | 20 | 16 | no | — |
| 227 | D4×D5 | — | 40 | 16 | no | — |
| 228 | D4×D5 | — | 40 | 32 | no | — |
| 229 | C2×D20 | — | 5 | 8 | no | — |
| 230 | C2×D20 | — | 10 | 8 | no | — |
| 231 | C2×D20 | — | 20 | 4 | no | — |
| 232 | C2×D20 | — | 20 | 8 | no | — |
| 233 | C2×C4×D5 | — | 5 | 2 | no | — |
| 234 | C2×C4×D5 | — | 10 | 2 | no | — |
| 235 | C2×C4×D5 | — | 10 | 2 | no | — |
| 236 | C2×C4×D5 | — | 10 | 4 | no | — |
| 237 | C22⋊AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 238 | C22⋊AGL(1,𝔽5) | — | 20 | 16 | no | — |
| 239 | #704 | — | 10 | 8 | no | — |
| 240 | C4⋊AGL(1,𝔽5) | — | 5 | 16 | no | — |
| 241 | C4×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 242 | #700 | — | 10 | 8 | no | — |
| 243 | D5⋊C8 | — | 10 | 8 | no | — |
| 244 | C5×D8 | — | 2 | 8 | no | — |
| 245 | C5×D8 | — | 2 | 8 | no | — |
| 246 | C5×D8 | — | 4 | 8 | no | — |
| 247 | C5×D8 | — | 4 | 8 | no | — |
| 248 | C2×C5×C8 | — | 2 | 4 | no | — |
| 249 | C2×C5×C8 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 250 | C42×C5 | — | 2 | 2 | no | — |
| 251 | C42×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 252 | #686 | — | 10 | 16 | no | — |
| 253 | #686 | — | 10 | 16 | no | — |
| 254 | #686 | — | 20 | 16 | no | — |
| 255 | #686 | — | 20 | 16 | no | — |
| 256 | C4×Dic5 | — | 5 | 2 | no | — |
| 257 | C4×Dic5 | — | 10 | 2 | no | — |
| 258 | C4×Dic5 | — | 10 | 2 | no | — |
| 259 | C4×Dic5 | — | 10 | 4 | no | — |
| 260 | C2×#168 | — | 5 | 4 | no | — |
| 261 | C2×#168 | — | 10 | 4 | no | — |
| 262 | D40 | — | 10 | 8 | no | — |
| 263 | D40 | — | 10 | 8 | no | — |
| 264 | D40 | — | 20 | 8 | no | — |
| 265 | D40 | — | 20 | 8 | no | — |
| 266 | C8×D5 | — | 5 | 4 | no | — |
| 267 | C8×D5 | — | 5 | 4 | no | — |
| 268 | C8×D5 | — | 5 | 4 | no | — |
| 269 | C8×D5 | — | 5 | 4 | no | — |
| 270 | C8×D5 | — | 10 | 4 | no | — |
| 271 | C8×D5 | — | 10 | 4 | no | — |
| 272 | C8×D5 | — | 10 | 4 | no | — |
| 273 | C8×D5 | — | 10 | 4 | no | — |
| 274 | C22×D8 | — | 25 | 4 | no | — |
| 275 | C2×#127 | — | 25 | 2 | no | — |
| 276 | #518 | — | 25 | 4 | no | — |
| 277 | #493 | — | 25 | 4 | no | — |
| 278 | #493 | — | 25 | 2 | no | — |
| 279 | #493 | — | 25 | 1 | no | — |
| 280 | #493 | #1044 | 1 | 1 | yes | characteristic, complemented |
| 281 | #442 | — | 50 | 8 | no | — |
| 282 | C4×D8 | — | 50 | 8 | no | — |
| 283 | C2×#108 | — | 25 | 2 | no | — |
| 284 | #427 | — | 25 | 2 | no | — |
| 285 | #418 | — | 25 | 8 | no | — |
| 286 | C2×#100 | — | 25 | 4 | no | — |
| 287 | #405 | — | 25 | 4 | no | — |
| 288 | C2×C4×C8 | — | 25 | 1 | no | — |
| 289 | #339 | — | 25 | 4 | no | — |
| 290 | C2×C52 | — | 2 | 1 | no | — |
| 291 | C2×C52 | — | 8 | 4 | no | — |
| 292 | C2×C52 | #2366 | 1 | 1 | yes | characteristic |
| 293 | C5⋊D5 | — | 2 | 1 | no | — |
| 294 | C5⋊D5 | — | 8 | 4 | no | — |
| 295 | C5⋊D5 | #3292 | 1 | 2 | yes | — |
| 296 | C23×C5 | — | 2 | 8 | no | — |
| 297 | C23×C5 | — | 4 | 8 | no | — |
| 298 | C22×D5 | — | 5 | 2 | no | — |
| 299 | C22×D5 | — | 10 | 2 | no | — |
| 300 | C22×D5 | — | 10 | 8 | no | — |
| 301 | C22×D5 | — | 20 | 8 | no | — |
| 302 | C22×D5 | — | 20 | 8 | no | — |
| 303 | C22×D5 | — | 20 | 8 | no | — |
| 304 | C22×D5 | — | 40 | 8 | no | — |
| 305 | C22×D5 | — | 40 | 8 | no | — |
| 306 | C22×D5 | — | 40 | 16 | no | — |
| 307 | C22×D5 | — | 40 | 32 | no | — |
| 308 | C2×AGL(1,𝔽5) | — | 10 | 16 | no | — |
| 309 | C2×AGL(1,𝔽5) | — | 80 | 16 | no | — |
| 310 | C5×D4 | — | 2 | 16 | no | — |
| 311 | C5×D4 | — | 4 | 16 | no | — |
| 312 | C5×D4 | — | 8 | 8 | no | — |
| 313 | C5×D4 | — | 8 | 16 | no | — |
| 314 | C2×C4×C5 | — | 2 | 4 | no | — |
| 315 | C2×C4×C5 | — | 2 | 2 | no | — |
| 316 | C2×C4×C5 | — | 2 | 2 | no | — |
| 317 | C2×C4×C5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 318 | C22⋊D5 | — | 20 | 16 | no | — |
| 319 | C22⋊D5 | — | 40 | 16 | no | — |
| 320 | C22⋊D5 | — | 40 | 16 | no | — |
| 321 | C22⋊D5 | — | 40 | 32 | no | — |
| 322 | C2×Dic5 | — | 5 | 2 | no | — |
| 323 | C2×Dic5 | — | 10 | 2 | no | — |
| 324 | C2×Dic5 | — | 10 | 4 | no | — |
| 325 | C2×Dic5 | — | 10 | 2 | no | — |
| 326 | D20 | — | 10 | 16 | no | — |
| 327 | D20 | — | 20 | 16 | no | — |
| 328 | D20 | — | 40 | 8 | no | — |
| 329 | D20 | — | 40 | 16 | no | — |
| 330 | C4×D5 | — | 5 | 4 | no | — |
| 331 | C4×D5 | — | 5 | 4 | no | — |
| 332 | C4×D5 | — | 10 | 4 | no | — |
| 333 | C4×D5 | — | 10 | 4 | no | — |
| 334 | C4×D5 | — | 10 | 8 | no | — |
| 335 | C4×D5 | — | 10 | 16 | no | — |
| 336 | #170 | — | 20 | 8 | no | — |
| 337 | C5×C8 | — | 2 | 4 | no | — |
| 338 | C5×C8 | — | 2 | 4 | no | — |
| 339 | C5×C8 | D4×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 340 | C5×C8 | D4×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 341 | #168 | — | 5 | 4 | no | — |
| 342 | #168 | — | 5 | 4 | no | — |
| 343 | #168 | — | 10 | 4 | no | — |
| 344 | #168 | — | 10 | 4 | no | — |
| 345 | C22×D4 | — | 25 | 4 | no | — |
| 346 | C22×D4 | — | 100 | 2 | no | — |
| 347 | C2×D8 | — | 25 | 8 | no | — |
| 348 | C2×D8 | — | 25 | 4 | no | — |
| 349 | C2×D8 | — | 50 | 4 | no | — |
| 350 | C2×D8 | — | 50 | 4 | no | — |
| 351 | C2×D8 | — | 50 | 4 | no | — |
| 352 | C2×D8 | — | 50 | 4 | no | — |
| 353 | C2×D8 | C2×#1044 | 1 | 4 | yes | complemented |
| 354 | C2×M16 | — | 25 | 4 | no | — |
| 355 | C22×C8 | — | 25 | 2 | no | — |
| 356 | #127 | — | 25 | 4 | no | — |
| 357 | #127 | — | 25 | 2 | no | — |
| 358 | #127 | — | 100 | 2 | no | — |
| 359 | #127 | C2×#1044 | 1 | 2 | yes | complemented |
| 360 | C4×D4 | — | 50 | 16 | no | — |
| 361 | #117 | — | 25 | 4 | no | — |
| 362 | C2×C22⋊C4 | — | 100 | 4 | no | — |
| 363 | C2×C42 | — | 25 | 1 | no | — |
| 364 | #108 | — | 50 | 2 | no | — |
| 365 | #108 | — | 50 | 2 | no | — |
| 366 | #107 | — | 25 | 4 | no | — |
| 367 | #106 | — | 25 | 4 | no | — |
| 368 | #102 | — | 50 | 16 | no | — |
| 369 | #100 | — | 100 | 4 | no | — |
| 370 | #97 | — | 50 | 4 | no | — |
| 371 | C4×C8 | — | 25 | 2 | no | — |
| 372 | C4×C8 | — | 25 | 1 | no | — |
| 373 | C4×C8 | — | 50 | 4 | no | — |
| 374 | C4×C8 | C2×#1044 | 1 | 1 | yes | characteristic, complemented |
| 375 | C52 | #23201 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 376 | C22×C5 | — | 2 | 2 | no | — |
| 377 | C22×C5 | — | 4 | 8 | no | — |
| 378 | C22×C5 | — | 8 | 8 | no | — |
| 379 | C22×C5 | — | 8 | 8 | no | — |
| 380 | C22×C5 | — | 8 | 16 | no | — |
| 381 | C22×C5 | #66258 | 1 | 2 | yes | — |
| 382 | C2×D5 | — | 5 | 2 | no | — |
| 383 | C2×D5 | — | 5 | 2 | no | — |
| 384 | C2×D5 | — | 10 | 2 | no | — |
| 385 | C2×D5 | — | 10 | 2 | no | — |
| 386 | C2×D5 | — | 10 | 4 | no | — |
| 387 | C2×D5 | — | 10 | 8 | no | — |
| 388 | C2×D5 | — | 20 | 8 | no | — |
| 389 | C2×D5 | — | 40 | 8 | no | — |
| 390 | C2×D5 | — | 40 | 16 | no | — |
| 391 | C2×D5 | — | 40 | 8 | no | — |
| 392 | C2×D5 | — | 40 | 16 | no | — |
| 393 | C2×D5 | — | 80 | 8 | no | — |
| 394 | C2×D5 | — | 80 | 16 | no | — |
| 395 | C2×D5 | — | 80 | 16 | no | — |
| 396 | AGL(1,𝔽5) | — | 20 | 16 | no | — |
| 397 | C4×C5 | — | 2 | 8 | no | — |
| 398 | C4×C5 | — | 2 | 4 | no | — |
| 399 | C4×C5 | — | 2 | 4 | no | — |
| 400 | C4×C5 | C2×D4×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 401 | Dic5 | — | 5 | 4 | no | — |
| 402 | Dic5 | — | 10 | 4 | no | — |
| 403 | Dic5 | — | 10 | 8 | no | — |
| 404 | Dic5 | — | 10 | 4 | no | — |
| 405 | C24 | — | 50 | 4 | no | — |
| 406 | C2×D4 | — | 4 | 2 | no | — |
| 407 | C2×D4 | — | 25 | 4 | no | — |
| 408 | C2×D4 | — | 50 | 8 | no | — |
| 409 | C2×D4 | — | 50 | 8 | no | — |
| 410 | C2×D4 | — | 50 | 4 | no | — |
| 411 | C2×D4 | — | 100 | 2 | no | — |
| 412 | C2×D4 | — | 100 | 4 | no | — |
| 413 | C2×D4 | — | 200 | 8 | no | — |
| 414 | C2×D4 | C22×#1044 | 1 | 4 | yes | — |
| 415 | C22×C4 | — | 25 | 1 | no | — |
| 416 | C22×C4 | — | 50 | 1 | no | — |
| 417 | C22×C4 | — | 100 | 8 | no | — |
| 418 | D8 | — | 2 | 4 | no | — |
| 419 | D8 | — | 2 | 4 | no | — |
| 420 | D8 | — | 50 | 8 | no | — |
| 421 | D8 | — | 50 | 8 | no | — |
| 422 | D8 | — | 50 | 4 | no | — |
| 423 | D8 | — | 50 | 4 | no | — |
| 424 | M16 | — | 50 | 4 | no | — |
| 425 | M16 | — | 50 | 4 | no | — |
| 426 | C2×C8 | — | 25 | 2 | no | — |
| 427 | C2×C8 | — | 25 | 2 | no | — |
| 428 | C2×C8 | — | 25 | 2 | no | — |
| 429 | C2×C8 | — | 25 | 2 | no | — |
| 430 | C2×C8 | — | 25 | 2 | no | — |
| 431 | C2×C8 | — | 50 | 4 | no | — |
| 432 | C2×C8 | C22×#1044 | 1 | 2 | yes | — |
| 433 | C4⋊C4 | — | 25 | 8 | no | — |
| 434 | C22⋊C4 | — | 50 | 4 | no | — |
| 435 | C22⋊C4 | — | 100 | 8 | no | — |
| 436 | C42 | — | 25 | 1 | no | — |
| 437 | C42 | — | 50 | 1 | no | — |
| 438 | C42 | — | 50 | 4 | no | — |
| 439 | C42 | C22×#1044 | 1 | 1 | yes | characteristic |
| 440 | C2×C5 | — | 2 | 4 | no | — |
| 441 | C2×C5 | — | 2 | 2 | no | — |
| 442 | C2×C5 | — | 2 | 2 | no | — |
| 443 | C2×C5 | — | 8 | 8 | no | — |
| 444 | C2×C5 | — | 16 | 8 | no | — |
| 445 | C2×C5 | #10617369 | 1 | 2 | yes | — |
| 446 | D5 | — | 5 | 4 | no | — |
| 447 | D5 | — | 10 | 4 | no | — |
| 448 | D5 | — | 10 | 4 | no | — |
| 449 | D5 | — | 10 | 2 | no | — |
| 450 | D5 | — | 40 | 8 | no | — |
| 451 | D5 | — | 80 | 8 | no | — |
| 452 | C23 | — | 2 | 4 | no | — |
| 453 | C23 | — | 25 | 1 | no | — |
| 454 | C23 | — | 50 | 4 | no | — |
| 455 | C23 | — | 100 | 4 | no | — |
| 456 | C23 | — | 100 | 4 | no | — |
| 457 | C23 | — | 200 | 8 | no | — |
| 458 | D4 | — | 2 | 8 | no | — |
| 459 | D4 | — | 8 | 4 | no | — |
| 460 | D4 | — | 50 | 8 | no | — |
| 461 | D4 | — | 100 | 8 | no | — |
| 462 | D4 | — | 200 | 4 | no | — |
| 463 | D4 | — | 200 | 8 | no | — |
| 464 | C2×C4 | — | 2 | 1 | no | — |
| 465 | C2×C4 | — | 25 | 1 | no | — |
| 466 | C2×C4 | — | 25 | 2 | no | — |
| 467 | C2×C4 | — | 25 | 2 | no | — |
| 468 | C2×C4 | — | 50 | 4 | no | — |
| 469 | C2×C4 | — | 50 | 1 | no | — |
| 470 | C2×C4 | — | 50 | 8 | no | — |
| 471 | C2×C4 | — | 400 | 8 | no | — |
| 472 | C2×C4 | C23×#1044 | 1 | 1 | yes | characteristic |
| 473 | C8 | — | 25 | 2 | no | — |
| 474 | C8 | — | 25 | 2 | no | — |
| 475 | C8 | — | 100 | 4 | no | — |
| 476 | C8 | D4×#1044 | 1 | 2 | yes | — |
| 477 | C8 | D4×#1044 | 1 | 2 | yes | — |
| 478 | C5 | — | 2 | 2 | no | — |
| 479 | C5 | #13042040 | 1 | 2 | yes | complemented |
| 480 | C22 | — | 4 | 4 | no | — |
| 481 | C22 | — | 8 | 4 | no | — |
| 482 | C22 | — | 25 | 1 | no | — |
| 483 | C22 | — | 25 | 1 | no | — |
| 484 | C22 | — | 50 | 2 | no | — |
| 485 | C22 | — | 100 | 4 | no | — |
| 486 | C22 | — | 400 | 4 | no | — |
| 487 | C22 | — | 200 | 4 | no | — |
| 488 | C22 | — | 200 | 8 | no | — |
| 489 | C22 | #13107767 | 1 | 1 | yes | characteristic |
| 490 | C4 | — | 2 | 2 | no | — |
| 491 | C4 | — | 25 | 2 | no | — |
| 492 | C4 | — | 50 | 2 | no | — |
| 493 | C4 | — | 100 | 8 | no | — |
| 494 | C4 | C2×D4×#1044 | 1 | 2 | yes | — |
| 495 | C2 | — | 2 | 1 | no | — |
| 496 | C2 | — | 8 | 4 | no | — |
| 497 | C2 | — | 25 | 2 | no | — |
| 498 | C2 | — | 50 | 1 | no | — |
| 499 | C2 | — | 200 | 4 | no | — |
| 500 | C2 | #72223143 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72221069 | C2 | semidirect |
| 2. #72220919 | C2 | semidirect |
| 3. #72220906 | C2 | semidirect |
| 5. #72213464 | C2 | semidirect |
| 16. C52×#493 | C4 | semidirect |
| 17. #13103011 | C4 | semidirect |
| 18. #13102935 | C4 | semidirect |
| 19. #13102558 | C4 | semidirect |
| 29. C2×C52×D8 | C2×C4 | semidirect |
| 30. C52×#127 | C2×C4 | semidirect |
| 32. #11717260 | C2×C4 | semidirect |
| 33. C2×#87809 | C2×C4 | semidirect |
| 38. C2×#87801 | C2×C4 | semidirect |
| 40. #11717194 | C2×C4 | semidirect |
| 46. #11716887 | D4 | semidirect |
| 47. #11716886 | D4 | semidirect |
| 50. C4×C52×C8 | C2×C4 | semidirect |
| 51. C8×#1039 | C2×C4 | semidirect |
| 52. C4×#6029 | C2×C4 | semidirect |
| 107. C5×#493 | AGL(1,𝔽5) | semidirect |
| 153. C2×C5×D8 | C2×AGL(1,𝔽5) | semidirect |
| 155. C5×#127 | C2×AGL(1,𝔽5) | semidirect |
| 187. C4×C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 280. #493 | #1044 | semidirect |
| 353. C2×D8 | C2×#1044 | semidirect |
| 359. #127 | C2×#1044 | semidirect |
| 374. C4×C8 | C2×#1044 | semidirect |
| 375. C52 | #23201 | semidirect |
| 479. C5 | #13042040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72221069 | 2 |
| #72220919 | 2 |
| #72220906 | 2 |
| C5⋊D5×#493 | 2 |
| #72213464 | 2 |
| #13042040 | 5 |