Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
942 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 110 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 | #13107788 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D5×#4086 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C5×D5⋊#100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13103546 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13099788 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×C5×D4×D5 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×D5×C22⋊D5 | — | 2 | 2 | no | — |
| 8 | C2×D5×D20 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×C22⋊#1042 | — | 2 | 2 | no | — |
| 10 | D4×#1042 | — | 2 | 4 | no | — |
| 11 | #11717425 | C22 | 1 | 2 | yes | — |
| 12 | C5×D5⋊M16 | C22 | 1 | 2 | yes | — |
| 13 | #11717260 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | C5×#4086 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | #11717097 | — | 2 | 2 | no | — |
| 16 | #11717032 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #11717029 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | C4×D5×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 19 | C5×#4013 | — | 2 | 2 | no | — |
| 20 | #11716735 | — | 2 | 4 | no | — |
| 21 | #10604614 | — | 5 | 1 | no | maximal |
| 22 | #10600863 | — | 5 | 1 | no | maximal |
| 23 | C23×C5×D5 | D4 | 1 | 2 | yes | — |
| 24 | C22×D52 | — | 2 | 1 | no | — |
| 25 | C22×#1042 | — | 2 | 4 | no | — |
| 26 | C2×C52×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C2×C22⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 28 | C2×C4⋊(C5⋊D5) | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×C5×C22⋊D5 | — | 2 | 2 | no | — |
| 30 | C2×C5×C22⋊D5 | D4 | 1 | 2 | yes | — |
| 31 | C5×D4×D5 | — | 2 | 2 | no | — |
| 32 | C5×D4×D5 | — | 2 | 2 | no | — |
| 33 | C2×C5×D20 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×C5×D20 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×C4×C5×D5 | C23 | 1 | 1 | yes | characteristic |
| 36 | D5×C22⋊D5 | — | 4 | 8 | no | — |
| 37 | C2×#6038 | — | 2 | 2 | no | — |
| 38 | C2×#6038 | — | 2 | 1 | no | — |
| 39 | C2×#6037 | — | 2 | 2 | no | — |
| 40 | C2×D5×Dic5 | — | 2 | 1 | no | — |
| 41 | D5×D20 | — | 2 | 2 | no | — |
| 42 | D5×D20 | — | 2 | 2 | no | — |
| 43 | C22⋊#1042 | — | 2 | 4 | no | — |
| 44 | C22⋊#1042 | — | 2 | 2 | no | — |
| 45 | C4⋊#1042 | D4 | 1 | 4 | yes | complemented |
| 46 | C4×#1042 | — | 2 | 2 | no | — |
| 47 | C5×#704 | — | 2 | 2 | no | — |
| 48 | C5×#700 | — | 2 | 2 | no | — |
| 49 | C5×D5⋊C8 | — | 2 | 2 | no | — |
| 50 | C4×#1039 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 51 | C4×C5×Dic5 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 52 | Dic52 | — | 2 | 1 | no | — |
| 53 | #66258 | — | 5 | 1 | no | — |
| 54 | C2×#4086 | — | 5 | 1 | no | — |
| 55 | #66132 | — | 5 | 1 | no | — |
| 56 | D5×#127 | — | 5 | 1 | no | — |
| 57 | D5⋊#100 | D5 | 1 | 1 | yes | characteristic, complemented |
| 58 | #65767 | — | 5 | 2 | no | — |
| 59 | C2×C5×#100 | — | 5 | 1 | no | — |
| 60 | #65420 | — | 5 | 2 | no | — |
| 61 | #64862 | — | 5 | 2 | no | — |
| 62 | #64775 | — | 5 | 2 | no | — |
| 63 | C23×C52 | C22⋊C4 | 1 | 2 | yes | — |
| 64 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 65 | C22×C5×D5 | — | 2 | 2 | no | — |
| 66 | C22×C5×D5 | — | 2 | 2 | no | — |
| 67 | C22×C5×D5 | — | 2 | 1 | no | — |
| 68 | C22×C5×D5 | — | 4 | 4 | no | — |
| 69 | C22×C5×D5 | C22⋊C4 | 1 | 2 | yes | — |
| 70 | C22×C5×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C2×D52 | — | 4 | 4 | no | — |
| 72 | C2×D52 | — | 4 | 1 | no | — |
| 73 | C2×D52 | — | 4 | 1 | no | — |
| 74 | C2×#1042 | — | 2 | 4 | no | — |
| 75 | C2×#1042 | — | 8 | 4 | no | — |
| 76 | C52×D4 | — | 2 | 2 | no | — |
| 77 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 78 | C22⋊(C5⋊D5) | — | 4 | 4 | no | — |
| 79 | C2×#1039 | — | 2 | 1 | no | — |
| 80 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 81 | C5×C22⋊D5 | — | 2 | 4 | no | — |
| 82 | C5×C22⋊D5 | — | 4 | 4 | no | — |
| 83 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 84 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C5×D20 | — | 2 | 2 | no | — |
| 86 | C5×D20 | — | 2 | 2 | no | — |
| 87 | C4×C5×D5 | C2×D4 | 1 | 2 | yes | — |
| 88 | C4×C5×D5 | #41 | 1 | 2 | yes | — |
| 89 | #6038 | — | 4 | 4 | no | — |
| 90 | #6038 | — | 4 | 2 | no | — |
| 91 | #6037 | — | 4 | 4 | no | — |
| 92 | D5×Dic5 | — | 2 | 4 | no | — |
| 93 | C5×#170 | — | 4 | 2 | no | — |
| 94 | C22×C5×D4 | — | 5 | 1 | no | — |
| 95 | C22×C22⋊D5 | — | 10 | 2 | no | — |
| 96 | C2×D4×D5 | — | 5 | 1 | no | — |
| 97 | C2×D4×D5 | — | 10 | 2 | no | — |
| 98 | C2×D4×D5 | C2×D5 | 1 | 1 | yes | characteristic |
| 99 | C22×D20 | — | 5 | 1 | no | — |
| 100 | C2×C22⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 101 | D4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 102 | #4130 | — | 5 | 2 | no | — |
| 103 | D5⋊M16 | C2×D5 | 1 | 2 | yes | — |
| 104 | C2×C5×M16 | — | 5 | 2 | no | — |
| 105 | C5×#127 | — | 5 | 1 | no | — |
| 106 | C2×C22⋊Dic5 | — | 10 | 2 | no | — |
| 107 | #4086 | — | 5 | 1 | no | — |
| 108 | #4086 | — | 5 | 1 | no | — |
| 109 | #4086 | — | 5 | 1 | no | — |
| 110 | #4086 | — | 5 | 1 | no | — |
| 111 | #4086 | — | 5 | 1 | no | — |
| 112 | #4086 | — | 10 | 2 | no | — |
| 113 | #4086 | — | 10 | 2 | no | — |
| 114 | #4086 | — | 20 | 1 | no | — |
| 115 | #4086 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 116 | D4×Dic5 | — | 10 | 4 | no | — |
| 117 | #4072 | — | 5 | 2 | no | — |
| 118 | C2×C4×Dic5 | — | 5 | 1 | no | — |
| 119 | #4020 | — | 5 | 1 | no | — |
| 120 | C42×D5 | — | 5 | 1 | no | — |
| 121 | #4013 | — | 2 | 2 | no | — |
| 122 | #4007 | — | 10 | 4 | no | — |
| 123 | C5×#100 | — | 10 | 2 | no | — |
| 124 | #3953 | — | 10 | 4 | no | — |
| 125 | #1887 | — | 25 | 1 | no | Sylow |
| 126 | C22×C52 | — | 2 | 2 | no | — |
| 127 | C22×C52 | — | 4 | 2 | no | — |
| 128 | C22×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 129 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 130 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 131 | C2×C5×D5 | — | 2 | 2 | no | — |
| 132 | C2×C5×D5 | — | 2 | 2 | no | — |
| 133 | C2×C5×D5 | — | 4 | 2 | no | — |
| 134 | C2×C5×D5 | — | 4 | 2 | no | — |
| 135 | C2×C5×D5 | — | 4 | 4 | no | — |
| 136 | C2×C5×D5 | — | 4 | 1 | no | — |
| 137 | C2×C5×D5 | — | 8 | 2 | no | — |
| 138 | C2×C5×D5 | #120 | 1 | 1 | yes | characteristic |
| 139 | C2×C5×D5 | #123 | 1 | 1 | yes | characteristic |
| 140 | D52 | — | 8 | 2 | no | — |
| 141 | D52 | — | 8 | 2 | no | — |
| 142 | #1042 | — | 4 | 4 | no | — |
| 143 | C4×C52 | C4×D4 | 1 | 2 | yes | — |
| 144 | #1039 | — | 2 | 2 | no | — |
| 145 | C5×Dic5 | — | 2 | 2 | no | — |
| 146 | C5×Dic5 | #121 | 1 | 2 | yes | — |
| 147 | C24×C5 | — | 5 | 2 | no | — |
| 148 | C23×D5 | — | 10 | 1 | no | — |
| 149 | C23×D5 | — | 10 | 1 | no | — |
| 150 | C23×D5 | D20 | 1 | 2 | yes | — |
| 151 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 152 | C2×C5×D4 | — | 4 | 1 | no | — |
| 153 | C2×C5×D4 | — | 5 | 2 | no | — |
| 154 | C2×C5×D4 | — | 5 | 1 | no | — |
| 155 | C2×C5×D4 | — | 5 | 1 | no | — |
| 156 | C2×C5×D4 | — | 10 | 2 | no | — |
| 157 | C2×C5×D4 | — | 10 | 2 | no | — |
| 158 | C2×C5×D4 | — | 10 | 2 | no | — |
| 159 | C2×C5×D4 | C4×D5 | 1 | 1 | yes | characteristic |
| 160 | C2×C5×D4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 161 | C22×C4×C5 | — | 5 | 1 | no | — |
| 162 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 163 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 164 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 165 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 166 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 167 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 168 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 169 | C2×C22⋊D5 | — | 20 | 4 | no | — |
| 170 | C2×C22⋊D5 | — | 20 | 8 | no | — |
| 171 | C2×C22⋊D5 | C22⋊D5 | 1 | 2 | yes | — |
| 172 | C22×Dic5 | — | 10 | 1 | no | — |
| 173 | C22×Dic5 | — | 10 | 4 | no | — |
| 174 | D4×D5 | — | 2 | 2 | no | — |
| 175 | D4×D5 | — | 2 | 2 | no | — |
| 176 | D4×D5 | — | 10 | 2 | no | — |
| 177 | D4×D5 | — | 10 | 2 | no | — |
| 178 | D4×D5 | — | 20 | 8 | no | — |
| 179 | C2×D20 | — | 5 | 1 | no | — |
| 180 | C2×D20 | — | 5 | 1 | no | — |
| 181 | C2×D20 | — | 10 | 2 | no | — |
| 182 | C2×D20 | — | 10 | 2 | no | — |
| 183 | C2×D20 | — | 10 | 1 | no | — |
| 184 | C2×D20 | — | 10 | 2 | no | — |
| 185 | C2×D20 | — | 20 | 1 | no | — |
| 186 | C2×D20 | C4×D5 | 1 | 1 | yes | characteristic |
| 187 | C2×D20 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 188 | C2×C4×D5 | — | 10 | 1 | no | — |
| 189 | C2×C4×D5 | C22×D5 | 1 | 1 | yes | characteristic |
| 190 | C22⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 191 | C22⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 192 | #704 | — | 2 | 2 | no | — |
| 193 | C4⋊AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 194 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 195 | #700 | — | 2 | 2 | no | — |
| 196 | D5⋊C8 | — | 2 | 2 | no | — |
| 197 | C5×M16 | — | 10 | 2 | no | — |
| 198 | C5×M16 | — | 10 | 2 | no | — |
| 199 | C2×C5×C8 | — | 10 | 2 | no | — |
| 200 | C42×C5 | — | 5 | 1 | no | — |
| 201 | C22⋊Dic5 | — | 10 | 2 | no | — |
| 202 | C22⋊Dic5 | — | 10 | 4 | no | — |
| 203 | C4⋊Dic5 | — | 5 | 4 | no | — |
| 204 | C4×Dic5 | — | 5 | 1 | no | — |
| 205 | C4×Dic5 | — | 5 | 1 | no | — |
| 206 | C4×Dic5 | — | 10 | 1 | no | — |
| 207 | C4×Dic5 | — | 10 | 2 | no | — |
| 208 | C4×Dic5 | — | 10 | 1 | no | — |
| 209 | C4×Dic5 | — | 20 | 1 | no | — |
| 210 | C4×Dic5 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 211 | C2×#127 | — | 25 | 1 | no | — |
| 212 | #518 | — | 25 | 1 | no | — |
| 213 | #418 | — | 25 | 2 | no | — |
| 214 | C2×#100 | — | 5 | 1 | no | — |
| 215 | #339 | — | 25 | 2 | no | — |
| 216 | C2×C52 | — | 2 | 1 | no | — |
| 217 | C2×C52 | — | 4 | 2 | no | — |
| 218 | C2×C52 | #386 | 1 | 1 | yes | characteristic |
| 219 | C5⋊D5 | — | 8 | 1 | no | — |
| 220 | C5×D5 | — | 2 | 1 | no | — |
| 221 | C5×D5 | — | 4 | 2 | no | — |
| 222 | C5×D5 | — | 8 | 1 | no | — |
| 223 | C5×D5 | #453 | 1 | 2 | yes | — |
| 224 | C23×C5 | — | 4 | 2 | no | — |
| 225 | C23×C5 | — | 5 | 1 | no | — |
| 226 | C23×C5 | — | 5 | 2 | no | — |
| 227 | C23×C5 | — | 10 | 2 | no | — |
| 228 | C23×C5 | — | 10 | 2 | no | — |
| 229 | C23×C5 | — | 10 | 1 | no | — |
| 230 | C23×C5 | — | 20 | 4 | no | — |
| 231 | C23×C5 | #685 | 1 | 2 | yes | — |
| 232 | C23×C5 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 233 | C22×D5 | — | 2 | 2 | no | — |
| 234 | C22×D5 | — | 2 | 2 | no | — |
| 235 | C22×D5 | — | 2 | 1 | no | — |
| 236 | C22×D5 | — | 4 | 4 | no | — |
| 237 | C22×D5 | — | 10 | 1 | no | — |
| 238 | C22×D5 | — | 10 | 1 | no | — |
| 239 | C22×D5 | — | 20 | 2 | no | — |
| 240 | C22×D5 | — | 20 | 4 | no | — |
| 241 | C22×D5 | — | 20 | 1 | no | — |
| 242 | C22×D5 | — | 20 | 1 | no | — |
| 243 | C22×D5 | — | 20 | 4 | no | — |
| 244 | C22×D5 | — | 20 | 1 | no | — |
| 245 | C22×D5 | — | 20 | 1 | no | — |
| 246 | C22×D5 | #685 | 1 | 2 | yes | — |
| 247 | C22×D5 | C2×D20 | 1 | 1 | yes | characteristic |
| 248 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 249 | C2×AGL(1,𝔽5) | — | 40 | 4 | no | — |
| 250 | C5×D4 | — | 2 | 2 | no | — |
| 251 | C5×D4 | — | 2 | 2 | no | — |
| 252 | C5×D4 | — | 8 | 2 | no | — |
| 253 | C5×D4 | — | 10 | 4 | no | — |
| 254 | C5×D4 | — | 10 | 2 | no | — |
| 255 | C5×D4 | — | 10 | 2 | no | — |
| 256 | C5×D4 | — | 20 | 4 | no | — |
| 257 | C2×C4×C5 | — | 4 | 1 | no | — |
| 258 | C2×C4×C5 | — | 5 | 1 | no | — |
| 259 | C2×C4×C5 | — | 5 | 2 | no | — |
| 260 | C2×C4×C5 | — | 5 | 2 | no | — |
| 261 | C2×C4×C5 | — | 10 | 1 | no | — |
| 262 | C2×C4×C5 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 264 | C22⋊D5 | — | 2 | 4 | no | — |
| 265 | C22⋊D5 | — | 4 | 4 | no | — |
| 266 | C22⋊D5 | — | 20 | 4 | no | — |
| 267 | C22⋊D5 | — | 20 | 4 | no | — |
| 268 | C22⋊D5 | — | 20 | 4 | no | — |
| 269 | C22⋊D5 | — | 20 | 4 | no | — |
| 270 | C22⋊D5 | — | 20 | 4 | no | — |
| 271 | C22⋊D5 | — | 20 | 2 | no | — |
| 272 | C22⋊D5 | — | 40 | 8 | no | — |
| 273 | C2×Dic5 | — | 2 | 1 | no | — |
| 274 | C2×Dic5 | — | 10 | 4 | no | — |
| 275 | C2×Dic5 | — | 10 | 1 | no | — |
| 276 | C2×Dic5 | — | 10 | 1 | no | — |
| 277 | C2×Dic5 | — | 10 | 4 | no | — |
| 278 | C2×Dic5 | — | 20 | 2 | no | — |
| 279 | C2×Dic5 | — | 40 | 4 | no | — |
| 280 | C2×Dic5 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 281 | D20 | — | 2 | 2 | no | — |
| 282 | D20 | — | 2 | 2 | no | — |
| 283 | D20 | — | 10 | 2 | no | — |
| 284 | D20 | — | 10 | 2 | no | — |
| 285 | D20 | — | 20 | 2 | no | — |
| 286 | D20 | — | 20 | 4 | no | — |
| 287 | D20 | — | 40 | 2 | no | — |
| 288 | C4×D5 | — | 10 | 4 | no | — |
| 289 | C4×D5 | D4×D5 | 1 | 2 | yes | — |
| 290 | C4×D5 | #711 | 1 | 2 | yes | — |
| 291 | #170 | — | 4 | 2 | no | — |
| 292 | C5×C8 | — | 20 | 2 | no | — |
| 293 | C22×D4 | — | 5 | 1 | no | — |
| 294 | C22×D4 | — | 25 | 1 | no | — |
| 295 | C22×D4 | — | 50 | 2 | no | — |
| 296 | C2×M16 | — | 5 | 2 | no | — |
| 297 | #127 | — | 5 | 1 | no | — |
| 298 | #127 | — | 25 | 1 | no | — |
| 299 | #127 | — | 25 | 1 | no | — |
| 300 | #127 | — | 25 | 1 | no | — |
| 301 | #127 | — | 50 | 2 | no | — |
| 302 | C4×D4 | — | 50 | 4 | no | — |
| 303 | #117 | — | 25 | 2 | no | — |
| 304 | C2×C22⋊C4 | — | 50 | 2 | no | — |
| 305 | C2×C42 | — | 25 | 1 | no | — |
| 306 | #102 | — | 50 | 4 | no | — |
| 307 | #100 | — | 10 | 2 | no | — |
| 308 | C52 | #1887 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 309 | C22×C5 | — | 2 | 2 | no | — |
| 310 | C22×C5 | — | 2 | 2 | no | — |
| 311 | C22×C5 | — | 4 | 2 | no | — |
| 312 | C22×C5 | — | 4 | 2 | no | — |
| 313 | C22×C5 | — | 4 | 1 | no | — |
| 314 | C22×C5 | — | 5 | 1 | no | — |
| 315 | C22×C5 | — | 5 | 1 | no | — |
| 316 | C22×C5 | — | 8 | 2 | no | — |
| 317 | C22×C5 | — | 8 | 4 | no | — |
| 318 | C22×C5 | — | 10 | 2 | no | — |
| 319 | C22×C5 | — | 10 | 2 | no | — |
| 320 | C22×C5 | — | 20 | 2 | no | — |
| 321 | C22×C5 | — | 20 | 2 | no | — |
| 322 | C22×C5 | — | 20 | 4 | no | — |
| 323 | C22×C5 | — | 20 | 1 | no | — |
| 324 | C22×C5 | — | 40 | 2 | no | — |
| 325 | C22×C5 | C2×#685 | 1 | 1 | yes | characteristic |
| 326 | C22×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 327 | C2×D5 | — | 2 | 2 | no | — |
| 328 | C2×D5 | — | 2 | 2 | no | — |
| 329 | C2×D5 | — | 4 | 4 | no | — |
| 330 | C2×D5 | — | 4 | 2 | no | — |
| 331 | C2×D5 | — | 4 | 2 | no | — |
| 332 | C2×D5 | — | 4 | 1 | no | — |
| 333 | C2×D5 | — | 8 | 2 | no | — |
| 334 | C2×D5 | — | 20 | 2 | no | — |
| 335 | C2×D5 | — | 20 | 2 | no | — |
| 336 | C2×D5 | — | 20 | 1 | no | — |
| 337 | C2×D5 | — | 20 | 1 | no | — |
| 338 | C2×D5 | — | 40 | 2 | no | — |
| 339 | C2×D5 | — | 40 | 4 | no | — |
| 340 | C2×D5 | — | 40 | 2 | no | — |
| 341 | C2×D5 | — | 40 | 2 | no | — |
| 342 | C2×D5 | — | 40 | 2 | no | — |
| 343 | C2×D5 | — | 40 | 2 | no | — |
| 344 | C2×D5 | #4028 | 1 | 1 | yes | characteristic |
| 345 | C2×D5 | #4032 | 1 | 1 | yes | characteristic |
| 346 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 347 | C4×C5 | — | 4 | 2 | no | — |
| 348 | C4×C5 | — | 5 | 2 | no | — |
| 349 | C4×C5 | — | 10 | 2 | no | — |
| 350 | C4×C5 | #4027 | 1 | 2 | yes | — |
| 351 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 352 | Dic5 | — | 2 | 2 | no | — |
| 353 | Dic5 | — | 10 | 2 | no | — |
| 354 | Dic5 | — | 10 | 2 | no | — |
| 355 | Dic5 | — | 20 | 4 | no | — |
| 356 | Dic5 | — | 20 | 4 | no | — |
| 357 | Dic5 | #4085 | 1 | 2 | yes | — |
| 358 | C24 | — | 5 | 2 | no | — |
| 359 | C24 | — | 50 | 1 | no | — |
| 360 | C2×D4 | — | 5 | 2 | no | — |
| 361 | C2×D4 | — | 5 | 1 | no | — |
| 362 | C2×D4 | — | 5 | 1 | no | — |
| 363 | C2×D4 | — | 10 | 2 | no | — |
| 364 | C2×D4 | — | 10 | 2 | no | — |
| 365 | C2×D4 | — | 10 | 2 | no | — |
| 366 | C2×D4 | — | 25 | 1 | no | — |
| 367 | C2×D4 | — | 50 | 2 | no | — |
| 368 | C2×D4 | — | 50 | 2 | no | — |
| 369 | C2×D4 | — | 50 | 1 | no | — |
| 370 | C2×D4 | — | 50 | 2 | no | — |
| 371 | C2×D4 | — | 50 | 2 | no | — |
| 372 | C2×D4 | — | 50 | 2 | no | — |
| 373 | C2×D4 | — | 100 | 8 | no | — |
| 374 | C2×D4 | D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 375 | C22×C4 | — | 5 | 1 | no | — |
| 376 | C22×C4 | — | 50 | 1 | no | — |
| 377 | C22×C4 | — | 50 | 4 | no | — |
| 378 | M16 | — | 10 | 2 | no | — |
| 379 | M16 | — | 10 | 2 | no | — |
| 380 | C2×C8 | — | 10 | 2 | no | — |
| 381 | C4⋊C4 | — | 25 | 4 | no | — |
| 382 | C22⋊C4 | — | 50 | 2 | no | — |
| 383 | C22⋊C4 | — | 50 | 4 | no | — |
| 384 | C42 | — | 5 | 1 | no | — |
| 385 | C42 | — | 25 | 1 | no | — |
| 386 | C42 | — | 50 | 1 | no | — |
| 387 | C42 | — | 50 | 2 | no | — |
| 388 | C2×C5 | — | 2 | 1 | no | — |
| 389 | C2×C5 | — | 2 | 1 | no | — |
| 390 | C2×C5 | — | 4 | 2 | no | — |
| 391 | C2×C5 | — | 4 | 2 | no | — |
| 392 | C2×C5 | — | 4 | 2 | no | — |
| 393 | C2×C5 | — | 4 | 1 | no | — |
| 394 | C2×C5 | — | 5 | 2 | no | — |
| 395 | C2×C5 | — | 10 | 1 | no | — |
| 396 | C2×C5 | — | 16 | 2 | no | — |
| 397 | C2×C5 | — | 20 | 2 | no | — |
| 398 | C2×C5 | — | 40 | 1 | no | — |
| 399 | C2×C5 | #65247 | 1 | 1 | yes | characteristic |
| 400 | C2×C5 | #65779 | 1 | 1 | yes | characteristic |
| 401 | D5 | — | 2 | 1 | no | — |
| 402 | D5 | — | 4 | 2 | no | — |
| 403 | D5 | — | 8 | 1 | no | — |
| 404 | D5 | — | 40 | 1 | no | — |
| 405 | D5 | — | 40 | 1 | no | — |
| 406 | D5 | — | 80 | 2 | no | — |
| 407 | D5 | #65036 | 1 | 2 | yes | — |
| 408 | C23 | — | 5 | 1 | no | — |
| 409 | C23 | — | 5 | 2 | no | — |
| 410 | C23 | — | 10 | 2 | no | — |
| 411 | C23 | — | 10 | 2 | no | — |
| 412 | C23 | — | 10 | 1 | no | — |
| 413 | C23 | — | 20 | 4 | no | — |
| 414 | C23 | — | 50 | 1 | no | — |
| 415 | C23 | — | 100 | 1 | no | — |
| 416 | C23 | — | 100 | 1 | no | — |
| 417 | C23 | — | 100 | 4 | no | — |
| 418 | C23 | (C2×AGL(1,𝔽5))⋊D5 | 1 | 2 | yes | — |
| 419 | D4 | — | 2 | 2 | no | — |
| 420 | D4 | — | 10 | 4 | no | — |
| 421 | D4 | — | 10 | 2 | no | — |
| 422 | D4 | — | 10 | 2 | no | — |
| 423 | D4 | — | 20 | 4 | no | — |
| 424 | D4 | — | 50 | 2 | no | — |
| 425 | D4 | — | 100 | 2 | no | — |
| 426 | D4 | — | 100 | 4 | no | — |
| 427 | D4 | — | 100 | 4 | no | — |
| 428 | D4 | — | 100 | 4 | no | — |
| 429 | C2×C4 | — | 5 | 1 | no | — |
| 430 | C2×C4 | — | 5 | 2 | no | — |
| 431 | C2×C4 | — | 5 | 2 | no | — |
| 432 | C2×C4 | — | 10 | 1 | no | — |
| 433 | C2×C4 | — | 50 | 4 | no | — |
| 434 | C2×C4 | — | 50 | 1 | no | — |
| 435 | C2×C4 | — | 50 | 4 | no | — |
| 436 | C2×C4 | — | 200 | 4 | no | — |
| 437 | C2×C4 | C2×D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 438 | C8 | — | 20 | 2 | no | — |
| 439 | C5 | — | 4 | 1 | no | — |
| 440 | C5 | #10600863 | 1 | 1 | yes | characteristic, complemented |
| 441 | C5 | #10604614 | 1 | 1 | yes | characteristic, complemented |
| 442 | C22 | — | 2 | 2 | no | — |
| 443 | C22 | — | 4 | 2 | no | — |
| 444 | C22 | — | 5 | 1 | no | — |
| 445 | C22 | — | 5 | 1 | no | — |
| 446 | C22 | — | 10 | 2 | no | — |
| 447 | C22 | — | 10 | 2 | no | — |
| 448 | C22 | — | 20 | 2 | no | — |
| 449 | C22 | — | 20 | 2 | no | — |
| 450 | C22 | — | 20 | 4 | no | — |
| 451 | C22 | — | 20 | 1 | no | — |
| 452 | C22 | — | 40 | 2 | no | — |
| 453 | C22 | — | 100 | 2 | no | — |
| 454 | C22 | — | 100 | 1 | no | — |
| 455 | C22 | — | 200 | 2 | no | — |
| 456 | C22 | — | 200 | 2 | no | — |
| 457 | C22 | C2×(C2×AGL(1,𝔽5))⋊D5 | 1 | 1 | yes | characteristic |
| 458 | C4 | — | 5 | 2 | no | — |
| 459 | C4 | — | 10 | 2 | no | — |
| 460 | C4 | — | 50 | 2 | no | — |
| 461 | C4 | — | 100 | 4 | no | — |
| 462 | C4 | #11717352 | 1 | 2 | yes | — |
| 463 | C2 | — | 2 | 1 | no | — |
| 464 | C2 | — | 4 | 2 | no | — |
| 465 | C2 | — | 5 | 2 | no | — |
| 466 | C2 | — | 10 | 1 | no | — |
| 467 | C2 | — | 20 | 2 | no | — |
| 468 | C2 | — | 40 | 1 | no | — |
| 469 | C2 | — | 200 | 1 | no | — |
| 470 | C2 | #13103802 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107788 | C2 | semidirect |
| 3. C5×D5⋊#100 | C2 | semidirect |
| 4. #13103546 | C2 | semidirect |
| 5. #13099788 | C2 | semidirect |
| 13. #11717260 | C4 | semidirect |
| 14. C5×#4086 | C4 | semidirect |
| 16. #11717032 | C4 | semidirect |
| 17. #11717029 | C4 | semidirect |
| 28. C2×C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 34. C2×C5×D20 | C2×C4 | semidirect |
| 45. C4⋊#1042 | D4 | semidirect |
| 50. C4×#1039 | C2×C4 | semidirect |
| 51. C4×C5×Dic5 | C2×C4 | semidirect |
| 57. D5⋊#100 | D5 | semidirect |
| 115. #4086 | AGL(1,𝔽5) | semidirect |
| 187. C2×D20 | C2×AGL(1,𝔽5) | semidirect |
| 210. C4×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 308. C52 | #1887 | semidirect |
| 440. C5 | #10600863 | semidirect |
| 441. C5 | #10604614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107788 | 2 |
| D5×#4086 | 2 |
| C5×D5⋊#100 | 2 |
| #13103546 | 2 |
| #13099788 | 2 |
| #10604614 | 5 |
| #10600863 | 5 |