Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
749 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 749 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #13107645 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13106581 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13104684 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#65798 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13103784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13099838 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13099837 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C23×C5×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#87879 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#87853 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#87853 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C5×#704 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C5×#704 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11717347 | — | 2 | 1 | no | — |
| 15 | #11717345 | — | 2 | 2 | no | — |
| 16 | D5×#704 | — | 2 | 1 | no | — |
| 17 | #11717343 | — | 2 | 2 | no | — |
| 18 | #11717273 | C4 | 1 | 1 | yes | characteristic |
| 19 | C5×#4099 | C4 | 1 | 1 | yes | characteristic |
| 20 | #11717096 | — | 2 | 1 | no | — |
| 21 | Dic5×C22⋊D5 | — | 2 | 1 | no | — |
| 22 | #11717084 | C4 | 1 | 1 | yes | characteristic |
| 23 | #11717082 | — | 2 | 1 | no | — |
| 24 | #11717079 | C4 | 1 | 1 | yes | characteristic |
| 25 | #11717073 | C22 | 1 | 1 | yes | characteristic |
| 26 | #11717070 | — | 2 | 1 | no | — |
| 27 | C22⋊#6032 | — | 2 | 2 | no | — |
| 28 | C5×C22⋊#170 | — | 2 | 2 | no | — |
| 29 | #11716758 | — | 2 | 1 | no | — |
| 30 | #11716757 | — | 2 | 1 | no | — |
| 31 | #10604463 | — | 5 | 1 | no | maximal |
| 32 | #10600785 | — | 5 | 1 | no | maximal |
| 33 | C24×C52 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 35 | C2×C22⋊(C5⋊D5) | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×C5×C22⋊D5 | — | 2 | 1 | no | — |
| 37 | C2×C5×C22⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C22×C5×Dic5 | — | 2 | 1 | no | — |
| 39 | C22×C5×Dic5 | — | 2 | 1 | no | — |
| 40 | C22×C5×Dic5 | — | 2 | 1 | no | — |
| 41 | C22×C5×Dic5 | — | 2 | 1 | no | — |
| 42 | C22×C5×Dic5 | — | 2 | 1 | no | — |
| 43 | C22×C5×Dic5 | — | 2 | 1 | no | — |
| 44 | C22×C5×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C22×C5×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×#6039 | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×#6038 | D4 | 1 | 1 | yes | characteristic |
| 48 | C2×#6036 | D4 | 1 | 1 | yes | characteristic |
| 49 | #87879 | — | 2 | 1 | no | — |
| 50 | #87879 | — | 2 | 1 | no | — |
| 51 | #87879 | — | 2 | 1 | no | — |
| 52 | #87879 | — | 2 | 1 | no | — |
| 53 | C2×D5×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 54 | #87853 | — | 2 | 1 | no | — |
| 55 | #87853 | — | 2 | 1 | no | — |
| 56 | #87853 | — | 2 | 1 | no | — |
| 57 | #87853 | — | 2 | 1 | no | — |
| 58 | C2×#6032 | — | 2 | 1 | no | — |
| 59 | C2×#6032 | D4 | 1 | 2 | yes | complemented |
| 60 | C5×#704 | — | 2 | 1 | no | — |
| 61 | C5×#704 | — | 2 | 1 | no | — |
| 62 | C5×#704 | — | 2 | 1 | no | — |
| 63 | C5×#704 | — | 2 | 1 | no | — |
| 64 | C2×C5×#170 | — | 2 | 1 | no | — |
| 65 | C2×C5×#170 | D4 | 1 | 2 | yes | complemented |
| 66 | #87829 | — | 2 | 2 | no | — |
| 67 | #87828 | — | 2 | 2 | no | — |
| 68 | #87827 | — | 2 | 2 | no | — |
| 69 | D5×#170 | — | 2 | 2 | no | — |
| 70 | C22⋊#1039 | — | 2 | 1 | no | — |
| 71 | C22⋊#1039 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | C5×C22⋊Dic5 | — | 2 | 1 | no | — |
| 73 | C5×C22⋊Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #87781 | — | 2 | 1 | no | — |
| 75 | #87780 | — | 2 | 1 | no | — |
| 76 | #87780 | — | 2 | 1 | no | — |
| 77 | #87779 | — | 2 | 1 | no | — |
| 78 | #87778 | — | 2 | 1 | no | — |
| 79 | Dic52 | — | 2 | 1 | no | — |
| 80 | #66256 | — | 5 | 1 | no | — |
| 81 | #66125 | — | 5 | 1 | no | — |
| 82 | #66079 | — | 5 | 1 | no | — |
| 83 | #65920 | — | 5 | 1 | no | — |
| 84 | #65798 | — | 5 | 1 | no | — |
| 85 | #65798 | D5 | 1 | 1 | yes | characteristic, complemented |
| 86 | #65777 | — | 5 | 1 | no | — |
| 87 | C5×#407 | — | 5 | 1 | no | — |
| 88 | #65496 | — | 5 | 1 | no | — |
| 89 | #65421 | — | 5 | 1 | no | — |
| 90 | #64867 | — | 5 | 1 | no | — |
| 91 | #64867 | — | 5 | 1 | no | — |
| 92 | #64779 | — | 5 | 1 | no | — |
| 93 | #64776 | — | 5 | 1 | no | — |
| 94 | C23×C52 | — | 2 | 1 | no | — |
| 95 | C23×C52 | — | 2 | 1 | no | — |
| 96 | C23×C52 | — | 2 | 1 | no | — |
| 97 | C23×C52 | — | 4 | 2 | no | — |
| 98 | C23×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 99 | C22×C5⋊D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 100 | C22×C5×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 101 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 102 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 103 | C22⋊(C5⋊D5) | — | 4 | 2 | no | — |
| 104 | C2×#1039 | — | 2 | 1 | no | — |
| 105 | C2×#1039 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 106 | C5×C22⋊D5 | — | 2 | 1 | no | — |
| 107 | C5×C22⋊D5 | — | 2 | 1 | no | — |
| 108 | C5×C22⋊D5 | — | 4 | 2 | no | — |
| 109 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 110 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 111 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 112 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 113 | C2×C5×Dic5 | — | 4 | 1 | no | — |
| 114 | C2×C5×Dic5 | — | 4 | 1 | no | — |
| 115 | C2×C5×Dic5 | — | 4 | 1 | no | — |
| 116 | C2×C5×Dic5 | — | 4 | 1 | no | — |
| 117 | C2×C5×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 118 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C5×Dic5 | #41 | 1 | 1 | yes | characteristic |
| 123 | C2×C5×Dic5 | #41 | 1 | 1 | yes | characteristic |
| 124 | #6039 | — | 2 | 1 | no | — |
| 125 | #6039 | — | 2 | 1 | no | — |
| 126 | #6038 | — | 2 | 1 | no | — |
| 127 | #6038 | — | 2 | 1 | no | — |
| 128 | #6036 | — | 2 | 1 | no | — |
| 129 | #6036 | — | 2 | 1 | no | — |
| 130 | D5×Dic5 | — | 2 | 1 | no | — |
| 131 | D5×Dic5 | — | 2 | 1 | no | — |
| 132 | #6032 | — | 2 | 2 | no | — |
| 133 | #6032 | — | 4 | 1 | no | — |
| 134 | C5×#170 | — | 2 | 2 | no | — |
| 135 | C5×#170 | — | 4 | 1 | no | — |
| 136 | C23×C4×C5 | — | 5 | 1 | no | — |
| 137 | C23×Dic5 | C2×D5 | 1 | 1 | yes | characteristic |
| 138 | C2×#711 | — | 5 | 1 | no | — |
| 139 | C2×#709 | — | 5 | 1 | no | — |
| 140 | C2×#704 | — | 5 | 1 | no | — |
| 141 | C2×#704 | — | 5 | 1 | no | — |
| 142 | C2×#704 | — | 10 | 1 | no | — |
| 143 | C2×#704 | C2×D5 | 1 | 1 | yes | characteristic |
| 144 | C2×#704 | C2×D5 | 1 | 1 | yes | characteristic |
| 145 | #4131 | — | 10 | 2 | no | — |
| 146 | #4131 | — | 10 | 2 | no | — |
| 147 | D5⋊M16 | — | 10 | 1 | no | — |
| 148 | C2×C5×M16 | — | 5 | 1 | no | — |
| 149 | C2×C5×M16 | — | 5 | 1 | no | — |
| 150 | C5×#120 | — | 5 | 1 | no | — |
| 151 | #4099 | — | 5 | 1 | no | — |
| 152 | #4099 | — | 5 | 1 | no | — |
| 153 | #4099 | — | 20 | 1 | no | — |
| 154 | #4099 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 155 | #4085 | — | 10 | 1 | no | — |
| 156 | #4081 | — | 5 | 1 | no | — |
| 157 | D4×Dic5 | — | 10 | 1 | no | — |
| 158 | #4076 | — | 10 | 1 | no | — |
| 159 | #4075 | — | 5 | 1 | no | — |
| 160 | #4075 | — | 5 | 1 | no | — |
| 161 | C4×C22⋊D5 | — | 10 | 1 | no | — |
| 162 | C4×C22⋊D5 | — | 10 | 1 | no | — |
| 163 | #4072 | — | 5 | 1 | no | — |
| 164 | #4070 | — | 10 | 1 | no | — |
| 165 | C2×#681 | — | 5 | 1 | no | — |
| 166 | C2×#681 | — | 5 | 1 | no | — |
| 167 | #4053 | — | 10 | 2 | no | — |
| 168 | D5×M16 | — | 10 | 1 | no | — |
| 169 | D5×M16 | — | 10 | 1 | no | — |
| 170 | #4047 | — | 10 | 2 | no | — |
| 171 | #4032 | — | 5 | 1 | no | — |
| 172 | #4027 | — | 10 | 1 | no | — |
| 173 | #4024 | — | 10 | 1 | no | — |
| 174 | #4023 | — | 5 | 1 | no | — |
| 175 | #4013 | — | 10 | 1 | no | — |
| 176 | C22⋊#170 | — | 2 | 2 | no | — |
| 177 | C22⋊#170 | — | 10 | 2 | no | — |
| 178 | #4005 | — | 10 | 1 | no | — |
| 179 | C5×C22⋊C8 | — | 10 | 2 | no | — |
| 180 | C22⋊#168 | — | 10 | 2 | no | — |
| 181 | #3956 | — | 10 | 1 | no | — |
| 182 | #3955 | — | 10 | 1 | no | — |
| 183 | #1891 | — | 25 | 1 | no | Sylow |
| 184 | C22×C52 | — | 2 | 2 | no | — |
| 185 | C22×C52 | — | 2 | 2 | no | — |
| 186 | C22×C52 | — | 2 | 2 | no | — |
| 187 | C22×C52 | — | 4 | 1 | no | — |
| 188 | C22×C52 | — | 4 | 1 | no | — |
| 189 | C22×C52 | — | 4 | 1 | no | — |
| 190 | C22×C52 | — | 4 | 1 | no | — |
| 191 | C22×C52 | — | 4 | 1 | no | — |
| 192 | C22×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 193 | C22×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 194 | C22×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 196 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 197 | C2×C5×D5 | — | 2 | 1 | no | — |
| 198 | C2×C5×D5 | — | 4 | 1 | no | — |
| 199 | #1039 | — | 2 | 1 | no | — |
| 200 | #1039 | — | 4 | 1 | no | — |
| 201 | C5×Dic5 | — | 2 | 1 | no | — |
| 202 | C5×Dic5 | — | 4 | 1 | no | — |
| 203 | C5×Dic5 | — | 4 | 1 | no | — |
| 204 | C5×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 205 | C5×Dic5 | #121 | 1 | 1 | yes | characteristic |
| 206 | C5×Dic5 | #121 | 1 | 1 | yes | characteristic |
| 207 | C5×Dic5 | #123 | 1 | 1 | yes | characteristic |
| 208 | C24×C5 | — | 4 | 1 | no | — |
| 209 | C24×C5 | C4×D5 | 1 | 1 | yes | characteristic |
| 210 | C24×C5 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 211 | C2×C5×D4 | — | 5 | 1 | no | — |
| 212 | C2×C5×D4 | — | 10 | 1 | no | — |
| 213 | C22×C4×C5 | — | 5 | 1 | no | — |
| 214 | C22×C4×C5 | — | 5 | 1 | no | — |
| 215 | C22×C4×C5 | — | 10 | 1 | no | — |
| 216 | C22×C4×C5 | — | 10 | 1 | no | — |
| 217 | C22×C4×C5 | — | 10 | 1 | no | — |
| 218 | C22×C4×C5 | — | 10 | 1 | no | — |
| 219 | C22×C4×C5 | — | 10 | 1 | no | — |
| 220 | C22×C4×C5 | — | 10 | 1 | no | — |
| 221 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 222 | C2×C22⋊D5 | — | 5 | 1 | no | — |
| 223 | C2×C22⋊D5 | — | 5 | 1 | no | — |
| 224 | C2×C22⋊D5 | — | 5 | 1 | no | — |
| 225 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 226 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 227 | C2×C22⋊D5 | — | 20 | 1 | no | — |
| 228 | C2×C22⋊D5 | — | 20 | 2 | no | — |
| 229 | C2×C22⋊D5 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 230 | C22×Dic5 | — | 2 | 1 | no | — |
| 231 | C22×Dic5 | — | 2 | 1 | no | — |
| 232 | C22×Dic5 | — | 2 | 1 | no | — |
| 233 | C22×Dic5 | — | 2 | 1 | no | — |
| 234 | C22×Dic5 | — | 2 | 1 | no | — |
| 235 | C22×Dic5 | — | 2 | 1 | no | — |
| 236 | C22×Dic5 | — | 5 | 1 | no | — |
| 237 | C22×Dic5 | C4×D5 | 1 | 1 | yes | characteristic |
| 238 | C22×Dic5 | C22×D5 | 1 | 1 | yes | characteristic |
| 239 | #711 | — | 10 | 1 | no | — |
| 240 | #711 | — | 10 | 1 | no | — |
| 241 | #711 | — | 10 | 1 | no | — |
| 242 | #711 | — | 10 | 1 | no | — |
| 243 | #709 | — | 10 | 1 | no | — |
| 244 | #709 | — | 10 | 1 | no | — |
| 245 | #709 | — | 10 | 1 | no | — |
| 246 | #709 | — | 10 | 1 | no | — |
| 247 | C2×D20 | — | 5 | 1 | no | — |
| 248 | C2×C4×D5 | — | 5 | 1 | no | — |
| 249 | C2×C4×D5 | — | 5 | 1 | no | — |
| 250 | C2×C4×D5 | — | 5 | 1 | no | — |
| 251 | C2×Dic10 | — | 5 | 1 | no | — |
| 252 | C2×Dic10 | — | 5 | 1 | no | — |
| 253 | #704 | — | 2 | 1 | no | — |
| 254 | #704 | — | 2 | 1 | no | — |
| 255 | #704 | — | 2 | 1 | no | — |
| 256 | #704 | — | 2 | 1 | no | — |
| 257 | #704 | — | 10 | 2 | no | — |
| 258 | #704 | — | 10 | 1 | no | — |
| 259 | #704 | — | 10 | 1 | no | — |
| 260 | #704 | — | 10 | 1 | no | — |
| 261 | #704 | — | 10 | 1 | no | — |
| 262 | C2×#170 | — | 2 | 1 | no | — |
| 263 | C2×#170 | — | 5 | 2 | no | — |
| 264 | C2×#170 | — | 10 | 2 | no | — |
| 265 | C2×#170 | — | 10 | 1 | no | — |
| 266 | C2×#170 | C22⋊D5 | 1 | 2 | yes | complemented |
| 267 | #700 | — | 10 | 2 | no | — |
| 268 | D5⋊C8 | — | 10 | 2 | no | — |
| 269 | C5×M16 | — | 10 | 1 | no | — |
| 270 | C5×M16 | — | 10 | 1 | no | — |
| 271 | C5×M16 | — | 10 | 1 | no | — |
| 272 | C5×M16 | — | 10 | 1 | no | — |
| 273 | C2×C5×C8 | — | 5 | 2 | no | — |
| 274 | C2×C5×C8 | — | 10 | 1 | no | — |
| 275 | C5×C22⋊C4 | — | 5 | 1 | no | — |
| 276 | C5×C22⋊C4 | — | 10 | 1 | no | — |
| 277 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 278 | C22⋊Dic5 | — | 5 | 1 | no | — |
| 279 | C22⋊Dic5 | — | 5 | 1 | no | — |
| 280 | C22⋊Dic5 | — | 10 | 1 | no | — |
| 281 | C22⋊Dic5 | — | 10 | 1 | no | — |
| 282 | C22⋊Dic5 | — | 10 | 1 | no | — |
| 283 | C22⋊Dic5 | — | 20 | 1 | no | — |
| 284 | C22⋊Dic5 | — | 20 | 2 | no | — |
| 285 | C22⋊Dic5 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 286 | #685 | — | 10 | 1 | no | — |
| 287 | #685 | — | 10 | 1 | no | — |
| 288 | #685 | — | 10 | 1 | no | — |
| 289 | C4⋊Dic5 | — | 10 | 1 | no | — |
| 290 | C4⋊Dic5 | — | 10 | 1 | no | — |
| 291 | #683 | — | 10 | 1 | no | — |
| 292 | #683 | — | 10 | 1 | no | — |
| 293 | #683 | — | 10 | 1 | no | — |
| 294 | #683 | — | 10 | 1 | no | — |
| 295 | C4×Dic5 | — | 10 | 1 | no | — |
| 296 | C4×Dic5 | — | 10 | 1 | no | — |
| 297 | #681 | — | 10 | 1 | no | — |
| 298 | #681 | — | 10 | 1 | no | — |
| 299 | #681 | — | 10 | 1 | no | — |
| 300 | #681 | — | 10 | 1 | no | — |
| 301 | C2×#168 | — | 5 | 2 | no | — |
| 302 | C2×#168 | — | 10 | 1 | no | — |
| 303 | #676 | — | 10 | 2 | no | — |
| 304 | #676 | — | 10 | 2 | no | — |
| 305 | C8×D5 | — | 10 | 2 | no | — |
| 306 | C8×D5 | — | 10 | 2 | no | — |
| 307 | #568 | — | 25 | 1 | no | — |
| 308 | #525 | — | 25 | 1 | no | — |
| 309 | #413 | — | 25 | 1 | no | — |
| 310 | #407 | — | 5 | 1 | no | — |
| 311 | #407 | — | 25 | 1 | no | — |
| 312 | #344 | — | 25 | 1 | no | — |
| 313 | #344 | — | 25 | 1 | no | — |
| 314 | C2×C52 | — | 2 | 1 | no | — |
| 315 | C2×C52 | — | 2 | 1 | no | — |
| 316 | C2×C52 | — | 2 | 1 | no | — |
| 317 | C2×C52 | — | 4 | 2 | no | — |
| 318 | C2×C52 | #386 | 1 | 1 | yes | characteristic |
| 319 | C5⋊D5 | — | 4 | 1 | no | — |
| 320 | C5×D5 | — | 4 | 1 | no | — |
| 321 | C23×C5 | — | 2 | 1 | no | — |
| 322 | C23×C5 | — | 2 | 1 | no | — |
| 323 | C23×C5 | — | 2 | 1 | no | — |
| 324 | C23×C5 | — | 2 | 1 | no | — |
| 325 | C23×C5 | — | 2 | 1 | no | — |
| 326 | C23×C5 | — | 2 | 1 | no | — |
| 327 | C23×C5 | — | 4 | 2 | no | — |
| 328 | C23×C5 | — | 4 | 2 | no | — |
| 329 | C23×C5 | — | 4 | 2 | no | — |
| 330 | C23×C5 | — | 4 | 1 | no | — |
| 331 | C23×C5 | — | 5 | 1 | no | — |
| 332 | C23×C5 | — | 8 | 1 | no | — |
| 333 | C23×C5 | — | 8 | 1 | no | — |
| 334 | C23×C5 | — | 8 | 4 | no | — |
| 335 | C23×C5 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 336 | C23×C5 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 337 | C22×D5 | — | 5 | 1 | no | — |
| 338 | C22×D5 | — | 5 | 1 | no | — |
| 339 | C22×D5 | — | 20 | 1 | no | — |
| 340 | C22×D5 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 341 | C5×D4 | — | 10 | 1 | no | — |
| 342 | C5×D4 | — | 10 | 1 | no | — |
| 343 | C5×D4 | — | 20 | 2 | no | — |
| 344 | C2×C4×C5 | — | 5 | 1 | no | — |
| 345 | C2×C4×C5 | — | 5 | 1 | no | — |
| 346 | C2×C4×C5 | — | 5 | 1 | no | — |
| 347 | C2×C4×C5 | — | 5 | 1 | no | — |
| 348 | C2×C4×C5 | — | 5 | 1 | no | — |
| 349 | C2×C4×C5 | — | 5 | 1 | no | — |
| 350 | C2×C4×C5 | — | 5 | 1 | no | — |
| 351 | C2×C4×C5 | — | 10 | 1 | no | — |
| 352 | C2×C4×C5 | — | 10 | 1 | no | — |
| 353 | C2×C4×C5 | — | 10 | 1 | no | — |
| 354 | C2×C4×C5 | — | 10 | 1 | no | — |
| 355 | C2×C4×C5 | — | 20 | 1 | no | — |
| 356 | C2×C4×C5 | — | 20 | 1 | no | — |
| 357 | C2×C4×C5 | — | 20 | 1 | no | — |
| 358 | C2×C4×C5 | — | 20 | 1 | no | — |
| 359 | C22⋊D5 | — | 2 | 1 | no | — |
| 360 | C22⋊D5 | — | 2 | 1 | no | — |
| 361 | C22⋊D5 | — | 4 | 2 | no | — |
| 362 | C22⋊D5 | — | 10 | 1 | no | — |
| 363 | C22⋊D5 | — | 10 | 1 | no | — |
| 364 | C22⋊D5 | — | 10 | 1 | no | — |
| 365 | C22⋊D5 | — | 10 | 1 | no | — |
| 366 | C22⋊D5 | — | 10 | 1 | no | — |
| 367 | C22⋊D5 | — | 10 | 1 | no | — |
| 368 | C22⋊D5 | — | 20 | 2 | no | — |
| 369 | C22⋊D5 | — | 20 | 2 | no | — |
| 370 | C22⋊D5 | — | 40 | 1 | no | — |
| 371 | C22⋊D5 | — | 40 | 1 | no | — |
| 372 | C22⋊D5 | — | 40 | 4 | no | — |
| 373 | C2×Dic5 | — | 2 | 1 | no | — |
| 374 | C2×Dic5 | — | 2 | 1 | no | — |
| 375 | C2×Dic5 | — | 2 | 1 | no | — |
| 376 | C2×Dic5 | — | 2 | 1 | no | — |
| 377 | C2×Dic5 | — | 4 | 1 | no | — |
| 378 | C2×Dic5 | — | 4 | 1 | no | — |
| 379 | C2×Dic5 | — | 4 | 1 | no | — |
| 380 | C2×Dic5 | — | 4 | 1 | no | — |
| 381 | C2×Dic5 | — | 5 | 1 | no | — |
| 382 | C2×Dic5 | — | 5 | 1 | no | — |
| 383 | C2×Dic5 | — | 10 | 1 | no | — |
| 384 | C2×Dic5 | — | 10 | 1 | no | — |
| 385 | C2×Dic5 | — | 10 | 1 | no | — |
| 386 | C2×Dic5 | — | 10 | 1 | no | — |
| 387 | C2×Dic5 | — | 20 | 1 | no | — |
| 388 | C2×Dic5 | — | 20 | 2 | no | — |
| 389 | C2×Dic5 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 390 | C2×Dic5 | #709 | 1 | 1 | yes | characteristic |
| 391 | C2×Dic5 | D4×D5 | 1 | 1 | yes | characteristic |
| 392 | C2×Dic5 | D4×D5 | 1 | 1 | yes | characteristic |
| 393 | C2×Dic5 | D4×D5 | 1 | 1 | yes | characteristic |
| 394 | C2×Dic5 | #711 | 1 | 1 | yes | characteristic |
| 395 | C2×Dic5 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 396 | D20 | — | 10 | 1 | no | — |
| 397 | D20 | — | 10 | 1 | no | — |
| 398 | C4×D5 | — | 10 | 1 | no | — |
| 399 | C4×D5 | — | 10 | 1 | no | — |
| 400 | C4×D5 | — | 10 | 1 | no | — |
| 401 | C4×D5 | — | 10 | 1 | no | — |
| 402 | C4×D5 | — | 10 | 1 | no | — |
| 403 | C4×D5 | — | 10 | 1 | no | — |
| 404 | Dic10 | — | 10 | 1 | no | — |
| 405 | Dic10 | — | 10 | 1 | no | — |
| 406 | Dic10 | — | 10 | 1 | no | — |
| 407 | Dic10 | — | 10 | 1 | no | — |
| 408 | #170 | — | 2 | 2 | no | — |
| 409 | #170 | — | 4 | 1 | no | — |
| 410 | #170 | — | 10 | 2 | no | — |
| 411 | #170 | — | 20 | 1 | no | — |
| 412 | C5×C8 | — | 10 | 2 | no | — |
| 413 | C5×C8 | — | 20 | 1 | no | — |
| 414 | #168 | — | 10 | 2 | no | — |
| 415 | #168 | — | 20 | 1 | no | — |
| 416 | C2×#41 | — | 25 | 1 | no | — |
| 417 | C23×C4 | — | 5 | 1 | no | — |
| 418 | #131 | — | 50 | 2 | no | — |
| 419 | #131 | — | 50 | 2 | no | — |
| 420 | C2×M16 | — | 5 | 1 | no | — |
| 421 | C2×M16 | — | 5 | 1 | no | — |
| 422 | C2×M16 | — | 25 | 1 | no | — |
| 423 | C2×M16 | — | 25 | 1 | no | — |
| 424 | C2×M16 | — | 50 | 1 | no | — |
| 425 | C2×M16 | — | 50 | 1 | no | — |
| 426 | #123 | — | 25 | 1 | no | — |
| 427 | #123 | — | 25 | 1 | no | — |
| 428 | C22⋊Q8 | — | 50 | 1 | no | — |
| 429 | #121 | — | 50 | 1 | no | — |
| 430 | #120 | — | 5 | 1 | no | — |
| 431 | #120 | — | 25 | 1 | no | — |
| 432 | C4×D4 | — | 50 | 1 | no | — |
| 433 | C4×D4 | — | 50 | 1 | no | — |
| 434 | #117 | — | 25 | 1 | no | — |
| 435 | #101 | — | 50 | 1 | no | — |
| 436 | #100 | — | 50 | 1 | no | — |
| 437 | C22⋊C8 | — | 10 | 2 | no | — |
| 438 | C22⋊C8 | — | 50 | 2 | no | — |
| 439 | C52 | #1891 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 440 | C22×C5 | — | 2 | 2 | no | — |
| 441 | C22×C5 | — | 2 | 2 | no | — |
| 442 | C22×C5 | — | 2 | 2 | no | — |
| 443 | C22×C5 | — | 2 | 2 | no | — |
| 444 | C22×C5 | — | 2 | 2 | no | — |
| 445 | C22×C5 | — | 2 | 2 | no | — |
| 446 | C22×C5 | — | 4 | 4 | no | — |
| 447 | C22×C5 | — | 4 | 1 | no | — |
| 448 | C22×C5 | — | 4 | 1 | no | — |
| 449 | C22×C5 | — | 4 | 1 | no | — |
| 450 | C22×C5 | — | 4 | 1 | no | — |
| 451 | C22×C5 | — | 4 | 1 | no | — |
| 452 | C22×C5 | — | 4 | 1 | no | — |
| 453 | C22×C5 | — | 4 | 1 | no | — |
| 454 | C22×C5 | — | 4 | 1 | no | — |
| 455 | C22×C5 | — | 4 | 1 | no | — |
| 456 | C22×C5 | — | 4 | 1 | no | — |
| 457 | C22×C5 | — | 4 | 1 | no | — |
| 458 | C22×C5 | — | 4 | 1 | no | — |
| 459 | C22×C5 | — | 4 | 1 | no | — |
| 460 | C22×C5 | — | 8 | 2 | no | — |
| 461 | C22×C5 | — | 8 | 2 | no | — |
| 462 | C22×C5 | — | 8 | 2 | no | — |
| 463 | C22×C5 | — | 8 | 2 | no | — |
| 464 | C22×C5 | — | 8 | 2 | no | — |
| 465 | C22×C5 | — | 8 | 2 | no | — |
| 466 | C22×C5 | — | 8 | 2 | no | — |
| 467 | C22×C5 | — | 10 | 1 | no | — |
| 468 | C22×C5 | — | 20 | 1 | no | — |
| 469 | C22×C5 | D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 470 | C22×C5 | #4027 | 1 | 1 | yes | characteristic |
| 471 | C22×C5 | C4×C22⋊D5 | 1 | 1 | yes | characteristic |
| 472 | C22×C5 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 473 | C22×C5 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 474 | C22×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 475 | C2×D5 | — | 2 | 1 | no | — |
| 476 | C2×D5 | — | 4 | 1 | no | — |
| 477 | C2×D5 | — | 10 | 1 | no | — |
| 478 | C2×D5 | — | 10 | 1 | no | — |
| 479 | C2×D5 | — | 20 | 1 | no | — |
| 480 | C2×D5 | — | 20 | 1 | no | — |
| 481 | C2×D5 | — | 40 | 1 | no | — |
| 482 | C2×D5 | — | 40 | 2 | no | — |
| 483 | C4×C5 | — | 5 | 1 | no | — |
| 484 | C4×C5 | — | 5 | 1 | no | — |
| 485 | C4×C5 | — | 5 | 1 | no | — |
| 486 | C4×C5 | — | 5 | 1 | no | — |
| 487 | C4×C5 | — | 10 | 1 | no | — |
| 488 | C4×C5 | — | 20 | 1 | no | — |
| 489 | C4×C5 | — | 20 | 1 | no | — |
| 490 | Dic5 | — | 2 | 1 | no | — |
| 491 | Dic5 | — | 4 | 1 | no | — |
| 492 | Dic5 | — | 4 | 1 | no | — |
| 493 | Dic5 | — | 10 | 1 | no | — |
| 494 | Dic5 | — | 10 | 1 | no | — |
| 495 | Dic5 | — | 20 | 1 | no | — |
| 496 | Dic5 | — | 20 | 1 | no | — |
| 497 | Dic5 | — | 40 | 1 | no | — |
| 498 | Dic5 | — | 40 | 2 | no | — |
| 499 | Dic5 | #4029 | 1 | 1 | yes | characteristic |
| 500 | Dic5 | #4030 | 1 | 1 | yes | characteristic |
| 501 | Dic5 | #4083 | 1 | 1 | yes | characteristic |
| 502 | Dic5 | #4084 | 1 | 1 | yes | characteristic |
| 503 | C24 | D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 504 | #41 | — | 50 | 1 | no | — |
| 505 | #41 | — | 50 | 1 | no | — |
| 506 | #41 | — | 50 | 1 | no | — |
| 507 | #41 | — | 50 | 1 | no | — |
| 508 | C2×Q8 | — | 25 | 1 | no | — |
| 509 | C2×D4 | — | 5 | 1 | no | — |
| 510 | C2×D4 | — | 10 | 1 | no | — |
| 511 | C2×D4 | — | 25 | 1 | no | — |
| 512 | C2×D4 | — | 25 | 1 | no | — |
| 513 | C2×D4 | — | 50 | 1 | no | — |
| 514 | C22×C4 | — | 5 | 1 | no | — |
| 515 | C22×C4 | — | 5 | 1 | no | — |
| 516 | C22×C4 | — | 10 | 1 | no | — |
| 517 | C22×C4 | — | 10 | 1 | no | — |
| 518 | C22×C4 | — | 10 | 1 | no | — |
| 519 | C22×C4 | — | 10 | 1 | no | — |
| 520 | C22×C4 | — | 10 | 1 | no | — |
| 521 | C22×C4 | — | 10 | 1 | no | — |
| 522 | C22×C4 | — | 25 | 1 | no | — |
| 523 | C22×C4 | — | 25 | 1 | no | — |
| 524 | M16 | — | 10 | 1 | no | — |
| 525 | M16 | — | 10 | 1 | no | — |
| 526 | M16 | — | 10 | 1 | no | — |
| 527 | M16 | — | 10 | 1 | no | — |
| 528 | M16 | — | 50 | 2 | no | — |
| 529 | M16 | — | 50 | 2 | no | — |
| 530 | M16 | — | 50 | 1 | no | — |
| 531 | M16 | — | 50 | 1 | no | — |
| 532 | M16 | — | 50 | 1 | no | — |
| 533 | M16 | — | 50 | 1 | no | — |
| 534 | C2×C8 | — | 5 | 2 | no | — |
| 535 | C2×C8 | — | 10 | 1 | no | — |
| 536 | C2×C8 | — | 25 | 2 | no | — |
| 537 | C2×C8 | — | 50 | 2 | no | — |
| 538 | C2×C8 | — | 50 | 2 | no | — |
| 539 | C2×C8 | — | 50 | 1 | no | — |
| 540 | C4⋊C4 | — | 50 | 1 | no | — |
| 541 | C4⋊C4 | — | 50 | 1 | no | — |
| 542 | C4⋊C4 | — | 50 | 1 | no | — |
| 543 | C22⋊C4 | — | 5 | 1 | no | — |
| 544 | C22⋊C4 | — | 10 | 1 | no | — |
| 545 | C22⋊C4 | — | 25 | 1 | no | — |
| 546 | C22⋊C4 | — | 50 | 1 | no | — |
| 547 | C22⋊C4 | — | 50 | 1 | no | — |
| 548 | C22⋊C4 | — | 50 | 1 | no | — |
| 549 | C42 | — | 50 | 1 | no | — |
| 550 | C2×C5 | — | 2 | 1 | no | — |
| 551 | C2×C5 | — | 2 | 1 | no | — |
| 552 | C2×C5 | — | 2 | 1 | no | — |
| 553 | C2×C5 | — | 2 | 1 | no | — |
| 554 | C2×C5 | — | 2 | 1 | no | — |
| 555 | C2×C5 | — | 2 | 1 | no | — |
| 556 | C2×C5 | — | 4 | 2 | no | — |
| 557 | C2×C5 | — | 4 | 2 | no | — |
| 558 | C2×C5 | — | 4 | 2 | no | — |
| 559 | C2×C5 | — | 4 | 1 | no | — |
| 560 | C2×C5 | — | 8 | 1 | no | — |
| 561 | C2×C5 | — | 8 | 1 | no | — |
| 562 | C2×C5 | — | 8 | 4 | no | — |
| 563 | C2×C5 | — | 20 | 1 | no | — |
| 564 | C2×C5 | #65245 | 1 | 1 | yes | characteristic |
| 565 | C2×C5 | #65779 | 1 | 1 | yes | characteristic |
| 566 | D5 | — | 4 | 1 | no | — |
| 567 | D5 | — | 20 | 1 | no | — |
| 568 | D5 | — | 20 | 1 | no | — |
| 569 | D5 | — | 80 | 1 | no | — |
| 570 | C23 | — | 2 | 1 | no | — |
| 571 | C23 | — | 2 | 1 | no | — |
| 572 | C23 | — | 2 | 1 | no | — |
| 573 | C23 | — | 4 | 2 | no | — |
| 574 | C23 | — | 5 | 1 | no | — |
| 575 | C23 | — | 25 | 1 | no | — |
| 576 | C23 | C2×D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 577 | Q8 | — | 50 | 1 | no | — |
| 578 | Q8 | — | 50 | 1 | no | — |
| 579 | D4 | — | 10 | 1 | no | — |
| 580 | D4 | — | 10 | 1 | no | — |
| 581 | D4 | — | 20 | 2 | no | — |
| 582 | D4 | — | 50 | 1 | no | — |
| 583 | D4 | — | 50 | 1 | no | — |
| 584 | D4 | — | 50 | 1 | no | — |
| 585 | D4 | — | 50 | 1 | no | — |
| 586 | D4 | — | 100 | 2 | no | — |
| 587 | C2×C4 | — | 5 | 1 | no | — |
| 588 | C2×C4 | — | 5 | 1 | no | — |
| 589 | C2×C4 | — | 5 | 1 | no | — |
| 590 | C2×C4 | — | 5 | 1 | no | — |
| 591 | C2×C4 | — | 5 | 1 | no | — |
| 592 | C2×C4 | — | 5 | 1 | no | — |
| 593 | C2×C4 | — | 5 | 1 | no | — |
| 594 | C2×C4 | — | 10 | 1 | no | — |
| 595 | C2×C4 | — | 10 | 1 | no | — |
| 596 | C2×C4 | — | 10 | 1 | no | — |
| 597 | C2×C4 | — | 10 | 1 | no | — |
| 598 | C2×C4 | — | 20 | 1 | no | — |
| 599 | C2×C4 | — | 20 | 1 | no | — |
| 600 | C2×C4 | — | 20 | 1 | no | — |
| 601 | C2×C4 | — | 20 | 1 | no | — |
| 602 | C2×C4 | — | 25 | 1 | no | — |
| 603 | C2×C4 | — | 50 | 1 | no | — |
| 604 | C2×C4 | — | 50 | 1 | no | — |
| 605 | C2×C4 | — | 50 | 1 | no | — |
| 606 | C2×C4 | — | 50 | 1 | no | — |
| 607 | C2×C4 | — | 50 | 1 | no | — |
| 608 | C8 | — | 10 | 2 | no | — |
| 609 | C8 | — | 20 | 1 | no | — |
| 610 | C8 | — | 50 | 2 | no | — |
| 611 | C8 | — | 100 | 1 | no | — |
| 612 | C5 | — | 4 | 1 | no | — |
| 613 | C5 | #10600785 | 1 | 1 | yes | characteristic, complemented |
| 614 | C5 | #10604463 | 1 | 1 | yes | characteristic, complemented |
| 615 | C22 | — | 2 | 2 | no | — |
| 616 | C22 | — | 2 | 2 | no | — |
| 617 | C22 | — | 2 | 2 | no | — |
| 618 | C22 | — | 4 | 1 | no | — |
| 619 | C22 | — | 4 | 1 | no | — |
| 620 | C22 | — | 4 | 1 | no | — |
| 621 | C22 | — | 4 | 1 | no | — |
| 622 | C22 | — | 4 | 1 | no | — |
| 623 | C22 | — | 10 | 1 | no | — |
| 624 | C22 | — | 20 | 1 | no | — |
| 625 | C22 | — | 50 | 1 | no | — |
| 626 | C22 | — | 100 | 1 | no | — |
| 627 | C22 | AGL(1,𝔽5)×C22⋊D5 | 1 | 1 | yes | characteristic |
| 628 | C22 | D5×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 629 | C22 | #11717352 | 1 | 1 | yes | characteristic |
| 630 | C4 | — | 5 | 1 | no | — |
| 631 | C4 | — | 5 | 1 | no | — |
| 632 | C4 | — | 5 | 1 | no | — |
| 633 | C4 | — | 5 | 1 | no | — |
| 634 | C4 | — | 10 | 1 | no | — |
| 635 | C4 | — | 20 | 1 | no | — |
| 636 | C4 | — | 20 | 1 | no | — |
| 637 | C4 | — | 50 | 1 | no | — |
| 638 | C4 | — | 100 | 1 | no | — |
| 639 | C2 | — | 2 | 1 | no | — |
| 640 | C2 | — | 2 | 1 | no | — |
| 641 | C2 | — | 2 | 1 | no | — |
| 642 | C2 | — | 4 | 2 | no | — |
| 643 | C2 | — | 20 | 1 | no | — |
| 644 | C2 | — | 100 | 1 | no | — |
| 645 | C2 | #13103835 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107645 | C2 | semidirect |
| 3. #13104684 | C2 | semidirect |
| 4. C5×#65798 | C2 | semidirect |
| 5. #13103784 | C2 | semidirect |
| 6. #13099838 | C2 | semidirect |
| 7. #13099837 | C2 | semidirect |
| 59. C2×#6032 | D4 | semidirect |
| 65. C2×C5×#170 | D4 | semidirect |
| 85. #65798 | D5 | semidirect |
| 266. C2×#170 | C22⋊D5 | semidirect |
| 439. C52 | #1891 | semidirect |
| 613. C5 | #10600785 | semidirect |
| 614. C5 | #10604463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107645 | 2 |
| #13106581 | 2 |
| #13104684 | 2 |
| C5×#65798 | 2 |
| #13103784 | 2 |
| #13099838 | 2 |
| #13099837 | 2 |
| #10604463 | 5 |
| #10600785 | 5 |