Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
745 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 745 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 | #13105146 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13103784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#11716757 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#11716757 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13100151 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C5×#64867 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#6038 | 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 | #11717202 | C4 | 1 | 1 | yes | characteristic |
| 19 | C5×#4028 | C4 | 1 | 1 | yes | characteristic |
| 20 | C5×#4023 | C22 | 1 | 1 | yes | characteristic |
| 21 | #11717099 | C4 | 1 | 1 | yes | characteristic |
| 22 | #11717095 | C4 | 1 | 1 | yes | characteristic |
| 23 | #11717029 | — | 2 | 1 | no | — |
| 24 | #11717028 | — | 2 | 1 | no | — |
| 25 | #11717005 | — | 2 | 1 | no | — |
| 26 | #11716970 | — | 2 | 1 | no | — |
| 27 | #11716758 | — | 2 | 1 | no | — |
| 28 | #11716757 | — | 2 | 1 | no | — |
| 29 | #11716757 | — | 2 | 2 | no | — |
| 30 | #11716757 | — | 2 | 2 | no | — |
| 31 | #10604464 | — | 5 | 1 | no | maximal |
| 32 | #10599833 | — | 5 | 1 | no | maximal |
| 33 | C23×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C23×C5×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×C22⋊(C5⋊D5) | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 37 | C2×C5×C22⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C22×C5×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×C5×D20 | — | 2 | 1 | no | — |
| 40 | C2×#6039 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×#6038 | — | 2 | 1 | no | — |
| 42 | C2×#6038 | — | 2 | 1 | no | — |
| 43 | C2×#6038 | — | 2 | 1 | no | — |
| 44 | C2×#6038 | — | 2 | 1 | no | — |
| 45 | C2×#6038 | — | 2 | 1 | no | — |
| 46 | C2×#6038 | — | 2 | 1 | no | — |
| 47 | C2×#6038 | — | 2 | 1 | no | — |
| 48 | C2×#6038 | — | 2 | 1 | no | — |
| 49 | C2×#6038 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×#6036 | D4 | 1 | 1 | yes | characteristic |
| 51 | #87879 | — | 2 | 1 | no | — |
| 52 | #87879 | — | 2 | 1 | no | — |
| 53 | #87879 | — | 2 | 1 | no | — |
| 54 | #87879 | — | 2 | 1 | no | — |
| 55 | C2×D5×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 56 | #87853 | — | 2 | 1 | no | — |
| 57 | #87853 | — | 2 | 1 | no | — |
| 58 | #87853 | — | 2 | 1 | no | — |
| 59 | #87853 | D4 | 1 | 2 | yes | complemented |
| 60 | C2×#6032 | — | 2 | 1 | no | — |
| 61 | C2×#6032 | — | 2 | 1 | no | — |
| 62 | C5×#704 | — | 2 | 1 | no | — |
| 63 | C5×#704 | — | 2 | 1 | no | — |
| 64 | C5×#704 | — | 2 | 1 | no | — |
| 65 | C5×#704 | D4 | 1 | 2 | yes | complemented |
| 66 | C2×C5×#170 | — | 2 | 1 | no | — |
| 67 | C2×C5×#170 | — | 2 | 1 | no | — |
| 68 | #87829 | — | 2 | 2 | no | — |
| 69 | #87828 | — | 2 | 2 | no | — |
| 70 | #87827 | — | 2 | 2 | no | — |
| 71 | D5×#170 | — | 2 | 2 | no | — |
| 72 | C52×C22⋊C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | #87808 | — | 2 | 1 | no | — |
| 74 | C5×C22⋊Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | C5×#685 | — | 2 | 1 | no | — |
| 76 | C5×#683 | — | 2 | 1 | no | — |
| 77 | C4×C5×Dic5 | — | 2 | 1 | no | — |
| 78 | #87779 | — | 2 | 1 | no | — |
| 79 | #87778 | — | 2 | 1 | no | — |
| 80 | #66256 | — | 5 | 1 | no | — |
| 81 | #66079 | — | 5 | 1 | no | — |
| 82 | #65926 | — | 5 | 1 | no | — |
| 83 | #65859 | — | 5 | 1 | no | — |
| 84 | C2×#4013 | — | 5 | 1 | no | — |
| 85 | C2×#4013 | — | 5 | 1 | no | — |
| 86 | #65777 | — | 5 | 1 | no | — |
| 87 | #65421 | — | 5 | 1 | no | — |
| 88 | C2×#3955 | — | 5 | 1 | no | — |
| 89 | C2×#3955 | — | 5 | 1 | no | — |
| 90 | #64867 | — | 5 | 1 | no | — |
| 91 | #64867 | D5 | 1 | 1 | yes | characteristic, complemented |
| 92 | C5×#344 | — | 5 | 1 | no | — |
| 93 | #64753 | — | 5 | 1 | no | — |
| 94 | C23×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 96 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 97 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 98 | C22×C5⋊D5 | — | 8 | 1 | no | — |
| 99 | C22×C5⋊D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 100 | C22×C5×D5 | — | 2 | 1 | no | — |
| 101 | C22×C5×D5 | — | 2 | 1 | no | — |
| 102 | C22×C5×D5 | — | 2 | 1 | no | — |
| 103 | C22×C5×D5 | — | 8 | 1 | no | — |
| 104 | C22×C5×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C52 | — | 2 | 1 | no | — |
| 106 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 107 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 108 | C2×#1039 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 109 | C4⋊(C5⋊D5) | — | 8 | 1 | no | — |
| 110 | C5×C22⋊D5 | — | 2 | 1 | no | — |
| 111 | C5×C22⋊D5 | — | 2 | 1 | no | — |
| 112 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 113 | C2×C5×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 114 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×C5×Dic5 | #41 | 1 | 1 | yes | characteristic |
| 119 | C2×C5×Dic5 | #41 | 1 | 1 | yes | characteristic |
| 120 | C5×D20 | — | 8 | 1 | no | — |
| 121 | #6039 | — | 2 | 1 | no | — |
| 122 | #6039 | — | 2 | 1 | no | — |
| 123 | #6038 | — | 2 | 1 | no | — |
| 124 | #6038 | — | 2 | 1 | no | — |
| 125 | #6038 | — | 4 | 1 | no | — |
| 126 | #6038 | — | 4 | 1 | no | — |
| 127 | #6038 | — | 4 | 1 | no | — |
| 128 | #6038 | — | 4 | 1 | no | — |
| 129 | #6038 | — | 8 | 1 | no | — |
| 130 | #6038 | — | 8 | 1 | no | — |
| 131 | #6036 | — | 2 | 1 | no | — |
| 132 | #6036 | — | 2 | 1 | no | — |
| 133 | D5×Dic5 | — | 2 | 1 | no | — |
| 134 | D5×Dic5 | — | 2 | 1 | no | — |
| 135 | #6032 | — | 2 | 2 | no | — |
| 136 | #6032 | — | 4 | 1 | no | — |
| 137 | C5×#170 | — | 2 | 2 | no | — |
| 138 | C5×#170 | — | 4 | 1 | no | — |
| 139 | C22×C22⋊D5 | — | 5 | 1 | no | — |
| 140 | C2×#711 | — | 5 | 1 | no | — |
| 141 | C2×#709 | — | 5 | 1 | no | — |
| 142 | C22×D20 | — | 5 | 1 | no | — |
| 143 | C2×#704 | — | 5 | 1 | no | — |
| 144 | C2×#704 | — | 5 | 1 | no | — |
| 145 | C2×#704 | — | 10 | 1 | no | — |
| 146 | C2×#704 | C2×D5 | 1 | 1 | yes | characteristic |
| 147 | C2×#704 | C2×D5 | 1 | 1 | yes | characteristic |
| 148 | #4131 | — | 10 | 2 | no | — |
| 149 | #4131 | — | 10 | 2 | no | — |
| 150 | D5⋊M16 | — | 10 | 1 | no | — |
| 151 | C2×C5×M16 | — | 5 | 1 | no | — |
| 152 | C2×C5×M16 | — | 5 | 1 | no | — |
| 153 | C5×#120 | — | 5 | 1 | no | — |
| 154 | C5×#117 | — | 5 | 1 | no | — |
| 155 | #4099 | — | 5 | 1 | no | — |
| 156 | #4086 | — | 10 | 1 | no | — |
| 157 | #4085 | — | 10 | 1 | no | — |
| 158 | #4083 | — | 5 | 1 | no | — |
| 159 | C2×#681 | — | 5 | 1 | no | — |
| 160 | C2×#681 | — | 5 | 1 | no | — |
| 161 | #4053 | — | 10 | 2 | no | — |
| 162 | D5×M16 | — | 10 | 1 | no | — |
| 163 | D5×M16 | — | 10 | 1 | no | — |
| 164 | #4047 | — | 10 | 2 | no | — |
| 165 | #4041 | — | 10 | 1 | no | — |
| 166 | #4041 | — | 10 | 1 | no | — |
| 167 | #4031 | — | 10 | 1 | no | — |
| 168 | #4030 | — | 10 | 1 | no | — |
| 169 | #4028 | — | 5 | 1 | no | — |
| 170 | #4028 | — | 5 | 1 | no | — |
| 171 | #4028 | — | 5 | 1 | no | — |
| 172 | #4028 | — | 5 | 1 | no | — |
| 173 | #4028 | — | 20 | 1 | no | — |
| 174 | #4028 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 175 | #4023 | C2×D5 | 1 | 1 | yes | characteristic |
| 176 | #4021 | — | 10 | 1 | no | — |
| 177 | #4020 | — | 10 | 1 | no | — |
| 178 | #4013 | — | 10 | 2 | no | — |
| 179 | #4013 | — | 10 | 1 | no | — |
| 180 | #4013 | — | 10 | 2 | no | — |
| 181 | #4005 | — | 10 | 1 | no | — |
| 182 | #3956 | — | 10 | 1 | no | — |
| 183 | #3955 | — | 10 | 2 | no | — |
| 184 | #3955 | — | 10 | 2 | no | — |
| 185 | #3955 | — | 10 | 1 | no | — |
| 186 | #1914 | — | 25 | 1 | no | Sylow |
| 187 | C22×C52 | — | 4 | 1 | no | — |
| 188 | C22×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 189 | C22×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 190 | C22×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 192 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 193 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 194 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 195 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 196 | C2×C5⋊D5 | — | 8 | 1 | no | — |
| 197 | C2×C5⋊D5 | — | 8 | 1 | no | — |
| 198 | C2×C5×D5 | — | 2 | 1 | no | — |
| 199 | C2×C5×D5 | — | 4 | 1 | no | — |
| 200 | C2×C5×D5 | — | 4 | 1 | no | — |
| 201 | C2×C5×D5 | — | 4 | 1 | no | — |
| 202 | C2×C5×D5 | — | 4 | 1 | no | — |
| 203 | C2×C5×D5 | — | 8 | 1 | no | — |
| 204 | C2×C5×D5 | — | 8 | 1 | no | — |
| 205 | C4×C52 | — | 4 | 1 | no | — |
| 206 | #1039 | — | 2 | 1 | no | — |
| 207 | C5×Dic5 | — | 2 | 1 | no | — |
| 208 | C5×Dic5 | — | 4 | 1 | no | — |
| 209 | C5×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 210 | C5×Dic5 | #121 | 1 | 1 | yes | characteristic |
| 211 | C5×Dic5 | #121 | 1 | 1 | yes | characteristic |
| 212 | C5×Dic5 | #123 | 1 | 1 | yes | characteristic |
| 213 | C24×C5 | — | 5 | 1 | no | — |
| 214 | C23×D5 | — | 5 | 1 | no | — |
| 215 | C23×D5 | — | 5 | 1 | no | — |
| 216 | C23×D5 | — | 20 | 1 | no | — |
| 217 | C23×D5 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 218 | C2×C5×D4 | — | 5 | 1 | no | — |
| 219 | C2×C5×D4 | — | 10 | 1 | no | — |
| 220 | C22×C4×C5 | — | 5 | 1 | no | — |
| 221 | C2×C22⋊D5 | — | 5 | 1 | no | — |
| 222 | C2×C22⋊D5 | — | 5 | 1 | no | — |
| 223 | C2×C22⋊D5 | — | 5 | 1 | no | — |
| 224 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 225 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 226 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 227 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 228 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 229 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 230 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 231 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 232 | C2×C22⋊D5 | — | 20 | 1 | no | — |
| 233 | C2×C22⋊D5 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 234 | C22×Dic5 | — | 5 | 1 | no | — |
| 235 | C22×Dic5 | C22×D5 | 1 | 1 | yes | characteristic |
| 236 | #711 | — | 10 | 1 | no | — |
| 237 | #711 | — | 10 | 1 | no | — |
| 238 | #711 | — | 10 | 1 | no | — |
| 239 | #711 | — | 10 | 1 | no | — |
| 240 | #709 | — | 10 | 1 | no | — |
| 241 | #709 | — | 10 | 1 | no | — |
| 242 | #709 | — | 10 | 1 | no | — |
| 243 | #709 | — | 10 | 1 | no | — |
| 244 | C2×D20 | — | 2 | 1 | no | — |
| 245 | C2×D20 | — | 5 | 1 | no | — |
| 246 | C2×D20 | — | 10 | 1 | no | — |
| 247 | C2×D20 | — | 10 | 1 | no | — |
| 248 | C2×D20 | — | 10 | 1 | no | — |
| 249 | C2×D20 | — | 10 | 1 | no | — |
| 250 | C2×D20 | — | 10 | 1 | no | — |
| 251 | C2×D20 | — | 10 | 1 | no | — |
| 252 | C2×D20 | — | 10 | 1 | no | — |
| 253 | C2×D20 | — | 10 | 1 | no | — |
| 254 | C2×D20 | — | 10 | 1 | no | — |
| 255 | C2×D20 | — | 10 | 1 | no | — |
| 256 | C2×D20 | — | 20 | 2 | no | — |
| 257 | C2×C4×D5 | — | 5 | 1 | no | — |
| 258 | C2×C4×D5 | — | 5 | 1 | no | — |
| 259 | C2×C4×D5 | — | 5 | 1 | no | — |
| 260 | C2×Dic10 | — | 5 | 1 | no | — |
| 261 | C2×Dic10 | — | 5 | 1 | no | — |
| 262 | #704 | — | 2 | 1 | no | — |
| 263 | #704 | — | 2 | 1 | no | — |
| 264 | #704 | — | 2 | 1 | no | — |
| 265 | #704 | — | 5 | 2 | no | — |
| 266 | #704 | — | 10 | 2 | no | — |
| 267 | #704 | — | 10 | 1 | no | — |
| 268 | #704 | — | 10 | 1 | no | — |
| 269 | #704 | — | 10 | 1 | no | — |
| 270 | #704 | D20 | 1 | 2 | yes | complemented |
| 271 | C2×#170 | — | 2 | 1 | no | — |
| 272 | C2×#170 | — | 2 | 1 | no | — |
| 273 | C2×#170 | — | 10 | 2 | no | — |
| 274 | C2×#170 | — | 10 | 1 | no | — |
| 275 | C2×#170 | — | 10 | 1 | no | — |
| 276 | #700 | — | 10 | 2 | no | — |
| 277 | D5⋊C8 | — | 10 | 2 | no | — |
| 278 | C5×M16 | — | 5 | 2 | no | — |
| 279 | C5×M16 | — | 10 | 1 | no | — |
| 280 | C5×M16 | — | 10 | 1 | no | — |
| 281 | C5×M16 | — | 10 | 1 | no | — |
| 282 | C2×C5×C8 | — | 10 | 1 | no | — |
| 283 | C2×C5×C8 | — | 10 | 1 | no | — |
| 284 | C5×C4⋊C4 | — | 10 | 1 | no | — |
| 285 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 286 | C5×C22⋊C4 | — | 5 | 1 | no | — |
| 287 | C5×C22⋊C4 | — | 10 | 1 | no | — |
| 288 | C5×C22⋊C4 | C4×D5 | 1 | 1 | yes | characteristic |
| 289 | C5×C22⋊C4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 290 | C42×C5 | — | 10 | 1 | no | — |
| 291 | C22⋊Dic5 | — | 10 | 1 | no | — |
| 292 | C22⋊Dic5 | C4×D5 | 1 | 1 | yes | characteristic |
| 293 | #685 | — | 2 | 1 | no | — |
| 294 | #685 | — | 10 | 1 | no | — |
| 295 | #685 | — | 10 | 1 | no | — |
| 296 | #685 | — | 10 | 1 | no | — |
| 297 | #685 | — | 10 | 1 | no | — |
| 298 | #685 | — | 10 | 1 | no | — |
| 299 | #685 | — | 20 | 2 | no | — |
| 300 | #683 | — | 2 | 1 | no | — |
| 301 | C4×Dic5 | — | 2 | 1 | no | — |
| 302 | #681 | — | 5 | 2 | no | — |
| 303 | #681 | — | 10 | 1 | no | — |
| 304 | #681 | — | 10 | 1 | no | — |
| 305 | #681 | — | 10 | 1 | no | — |
| 306 | C2×#168 | — | 10 | 1 | no | — |
| 307 | C2×#168 | — | 10 | 1 | no | — |
| 308 | #676 | — | 10 | 2 | no | — |
| 309 | #676 | — | 10 | 2 | no | — |
| 310 | C8×D5 | — | 10 | 2 | no | — |
| 311 | C8×D5 | — | 10 | 2 | no | — |
| 312 | #568 | — | 25 | 1 | no | — |
| 313 | #535 | — | 25 | 1 | no | — |
| 314 | #413 | — | 25 | 1 | no | — |
| 315 | C2×#100 | — | 25 | 1 | no | — |
| 316 | C2×#100 | — | 25 | 1 | no | — |
| 317 | #344 | — | 5 | 1 | no | — |
| 318 | #344 | — | 25 | 1 | no | — |
| 319 | C2×C52 | — | 2 | 1 | no | — |
| 320 | C2×C52 | — | 2 | 1 | no | — |
| 321 | C2×C52 | — | 2 | 1 | no | — |
| 322 | C2×C52 | #386 | 1 | 1 | yes | characteristic |
| 323 | C5⋊D5 | — | 4 | 1 | no | — |
| 324 | C5⋊D5 | — | 8 | 1 | no | — |
| 325 | C5×D5 | — | 4 | 1 | no | — |
| 326 | C5×D5 | — | 8 | 1 | no | — |
| 327 | C23×C5 | — | 4 | 1 | no | — |
| 328 | C23×C5 | — | 5 | 1 | no | — |
| 329 | C23×C5 | — | 10 | 1 | no | — |
| 330 | C23×C5 | — | 10 | 1 | no | — |
| 331 | C23×C5 | — | 10 | 1 | no | — |
| 332 | C23×C5 | — | 40 | 1 | no | — |
| 333 | C23×C5 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 334 | C23×C5 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 335 | C22×D5 | — | 2 | 1 | no | — |
| 336 | C22×D5 | — | 2 | 1 | no | — |
| 337 | C22×D5 | — | 2 | 1 | no | — |
| 338 | C22×D5 | — | 5 | 1 | no | — |
| 339 | C22×D5 | — | 5 | 1 | no | — |
| 340 | C22×D5 | — | 8 | 1 | no | — |
| 341 | C22×D5 | — | 10 | 1 | no | — |
| 342 | C22×D5 | — | 10 | 1 | no | — |
| 343 | C22×D5 | — | 10 | 1 | no | — |
| 344 | C22×D5 | — | 10 | 1 | no | — |
| 345 | C22×D5 | — | 10 | 1 | no | — |
| 346 | C22×D5 | — | 10 | 1 | no | — |
| 347 | C22×D5 | — | 20 | 1 | no | — |
| 348 | C22×D5 | — | 20 | 2 | no | — |
| 349 | C22×D5 | — | 40 | 1 | no | — |
| 350 | C22×D5 | — | 40 | 1 | no | — |
| 351 | C22×D5 | — | 40 | 1 | no | — |
| 352 | C22×D5 | — | 40 | 1 | no | — |
| 353 | C22×D5 | — | 40 | 4 | no | — |
| 354 | C22×D5 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 355 | C5×D4 | — | 10 | 1 | no | — |
| 356 | C5×D4 | — | 10 | 1 | no | — |
| 357 | C5×D4 | — | 40 | 1 | no | — |
| 358 | C2×C4×C5 | — | 2 | 1 | no | — |
| 359 | C2×C4×C5 | — | 2 | 1 | no | — |
| 360 | C2×C4×C5 | — | 4 | 2 | no | — |
| 361 | C2×C4×C5 | — | 5 | 1 | no | — |
| 362 | C2×C4×C5 | — | 5 | 1 | no | — |
| 363 | C2×C4×C5 | — | 5 | 1 | no | — |
| 364 | C2×C4×C5 | — | 5 | 1 | no | — |
| 365 | C2×C4×C5 | — | 5 | 1 | no | — |
| 366 | C2×C4×C5 | — | 5 | 1 | no | — |
| 367 | C2×C4×C5 | — | 5 | 1 | no | — |
| 368 | C2×C4×C5 | — | 10 | 1 | no | — |
| 369 | C22⋊D5 | — | 2 | 1 | no | — |
| 370 | C22⋊D5 | — | 2 | 1 | no | — |
| 371 | C22⋊D5 | — | 10 | 1 | no | — |
| 372 | C22⋊D5 | — | 10 | 1 | no | — |
| 373 | C22⋊D5 | — | 10 | 1 | no | — |
| 374 | C22⋊D5 | — | 10 | 1 | no | — |
| 375 | C22⋊D5 | — | 10 | 1 | no | — |
| 376 | C22⋊D5 | — | 10 | 1 | no | — |
| 377 | C22⋊D5 | — | 20 | 1 | no | — |
| 378 | C22⋊D5 | — | 20 | 1 | no | — |
| 379 | C22⋊D5 | — | 20 | 1 | no | — |
| 380 | C22⋊D5 | — | 20 | 1 | no | — |
| 381 | C22⋊D5 | — | 40 | 1 | no | — |
| 382 | C22⋊D5 | — | 40 | 1 | no | — |
| 383 | C22⋊D5 | — | 40 | 1 | no | — |
| 384 | C22⋊D5 | — | 40 | 1 | no | — |
| 385 | C2×Dic5 | — | 2 | 1 | no | — |
| 386 | C2×Dic5 | — | 5 | 1 | no | — |
| 387 | C2×Dic5 | — | 5 | 1 | no | — |
| 388 | C2×Dic5 | — | 10 | 1 | no | — |
| 389 | C2×Dic5 | — | 10 | 1 | no | — |
| 390 | C2×Dic5 | — | 20 | 1 | no | — |
| 391 | C2×Dic5 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 392 | C2×Dic5 | C2×D20 | 1 | 1 | yes | characteristic |
| 393 | C2×Dic5 | #709 | 1 | 1 | yes | characteristic |
| 394 | C2×Dic5 | D4×D5 | 1 | 1 | yes | characteristic |
| 395 | C2×Dic5 | D4×D5 | 1 | 1 | yes | characteristic |
| 396 | C2×Dic5 | D4×D5 | 1 | 1 | yes | characteristic |
| 397 | C2×Dic5 | #713 | 1 | 1 | yes | characteristic |
| 398 | D20 | — | 8 | 1 | no | — |
| 399 | D20 | — | 10 | 1 | no | — |
| 400 | D20 | — | 10 | 1 | no | — |
| 401 | D20 | — | 20 | 1 | no | — |
| 402 | D20 | — | 20 | 1 | no | — |
| 403 | D20 | — | 20 | 1 | no | — |
| 404 | D20 | — | 20 | 1 | no | — |
| 405 | D20 | — | 40 | 1 | no | — |
| 406 | D20 | — | 40 | 1 | no | — |
| 407 | D20 | — | 40 | 4 | no | — |
| 408 | D20 | — | 40 | 1 | no | — |
| 409 | D20 | — | 40 | 1 | no | — |
| 410 | C4×D5 | — | 10 | 1 | no | — |
| 411 | C4×D5 | — | 10 | 1 | no | — |
| 412 | C4×D5 | — | 10 | 1 | no | — |
| 413 | C4×D5 | — | 10 | 1 | no | — |
| 414 | C4×D5 | — | 10 | 1 | no | — |
| 415 | C4×D5 | — | 10 | 1 | no | — |
| 416 | Dic10 | — | 10 | 1 | no | — |
| 417 | Dic10 | — | 10 | 1 | no | — |
| 418 | Dic10 | — | 10 | 1 | no | — |
| 419 | Dic10 | — | 10 | 1 | no | — |
| 420 | #170 | — | 2 | 2 | no | — |
| 421 | #170 | — | 4 | 1 | no | — |
| 422 | #170 | — | 10 | 2 | no | — |
| 423 | #170 | — | 20 | 1 | no | — |
| 424 | C5×C8 | — | 10 | 2 | no | — |
| 425 | C5×C8 | — | 20 | 1 | no | — |
| 426 | #168 | — | 10 | 2 | no | — |
| 427 | #168 | — | 20 | 1 | no | — |
| 428 | C2×#41 | — | 25 | 1 | no | — |
| 429 | C22×D4 | — | 25 | 1 | no | — |
| 430 | #131 | — | 50 | 2 | no | — |
| 431 | #131 | — | 50 | 2 | no | — |
| 432 | C2×M16 | — | 5 | 1 | no | — |
| 433 | C2×M16 | — | 5 | 1 | no | — |
| 434 | C2×M16 | — | 25 | 1 | no | — |
| 435 | C2×M16 | — | 25 | 1 | no | — |
| 436 | C2×M16 | — | 50 | 1 | no | — |
| 437 | C2×M16 | — | 50 | 1 | no | — |
| 438 | #127 | — | 50 | 1 | no | — |
| 439 | #124 | — | 50 | 1 | no | — |
| 440 | #121 | — | 50 | 1 | no | — |
| 441 | #121 | — | 50 | 1 | no | — |
| 442 | #120 | — | 5 | 1 | no | — |
| 443 | #120 | — | 25 | 1 | no | — |
| 444 | #120 | — | 25 | 1 | no | — |
| 445 | #120 | — | 25 | 1 | no | — |
| 446 | #117 | — | 5 | 1 | no | — |
| 447 | #101 | — | 50 | 1 | no | — |
| 448 | #100 | — | 50 | 2 | no | — |
| 449 | #100 | — | 50 | 2 | no | — |
| 450 | #100 | — | 50 | 1 | no | — |
| 451 | C52 | #1914 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 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 | — | 8 | 2 | no | — |
| 458 | C22×C5 | — | 10 | 1 | no | — |
| 459 | C22×C5 | — | 20 | 1 | no | — |
| 460 | C22×C5 | — | 20 | 1 | no | — |
| 461 | C22×C5 | — | 20 | 1 | no | — |
| 462 | C22×C5 | — | 20 | 1 | no | — |
| 463 | C22×C5 | — | 40 | 1 | no | — |
| 464 | C22×C5 | — | 40 | 1 | no | — |
| 465 | C22×C5 | C4×D20 | 1 | 1 | yes | characteristic |
| 466 | C22×C5 | D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 467 | C22×C5 | #4039 | 1 | 1 | yes | characteristic |
| 468 | C22×C5 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 469 | C22×C5 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 470 | C22×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 471 | C2×D5 | — | 2 | 1 | no | — |
| 472 | C2×D5 | — | 4 | 1 | no | — |
| 473 | C2×D5 | — | 4 | 1 | no | — |
| 474 | C2×D5 | — | 4 | 1 | no | — |
| 475 | C2×D5 | — | 4 | 1 | no | — |
| 476 | C2×D5 | — | 8 | 1 | no | — |
| 477 | C2×D5 | — | 8 | 1 | no | — |
| 478 | C2×D5 | — | 10 | 1 | no | — |
| 479 | C2×D5 | — | 10 | 1 | no | — |
| 480 | C2×D5 | — | 20 | 1 | no | — |
| 481 | C2×D5 | — | 20 | 1 | no | — |
| 482 | C2×D5 | — | 20 | 1 | no | — |
| 483 | C2×D5 | — | 20 | 1 | no | — |
| 484 | C2×D5 | — | 20 | 1 | no | — |
| 485 | C2×D5 | — | 20 | 1 | no | — |
| 486 | C2×D5 | — | 20 | 4 | no | — |
| 487 | C2×D5 | — | 20 | 1 | no | — |
| 488 | C2×D5 | — | 20 | 1 | no | — |
| 489 | C2×D5 | — | 40 | 1 | no | — |
| 490 | C2×D5 | — | 40 | 2 | no | — |
| 491 | C2×D5 | — | 40 | 2 | no | — |
| 492 | C2×D5 | — | 40 | 2 | no | — |
| 493 | C2×D5 | — | 40 | 4 | no | — |
| 494 | C2×D5 | — | 40 | 4 | no | — |
| 495 | C2×D5 | — | 40 | 1 | no | — |
| 496 | C2×D5 | — | 40 | 1 | no | — |
| 497 | C2×D5 | — | 40 | 1 | no | — |
| 498 | C2×D5 | — | 40 | 1 | no | — |
| 499 | C4×C5 | — | 4 | 1 | no | — |
| 500 | C4×C5 | — | 4 | 1 | no | — |
| 501 | C4×C5 | — | 5 | 1 | no | — |
| 502 | C4×C5 | — | 5 | 1 | no | — |
| 503 | C4×C5 | — | 5 | 1 | no | — |
| 504 | C4×C5 | — | 5 | 1 | no | — |
| 505 | C4×C5 | — | 8 | 2 | no | — |
| 506 | C4×C5 | — | 10 | 1 | no | — |
| 507 | C4×C5 | — | 20 | 1 | no | — |
| 508 | Dic5 | — | 2 | 1 | no | — |
| 509 | Dic5 | — | 4 | 1 | no | — |
| 510 | Dic5 | — | 10 | 1 | no | — |
| 511 | Dic5 | — | 10 | 1 | no | — |
| 512 | Dic5 | — | 40 | 1 | no | — |
| 513 | Dic5 | #4028 | 1 | 1 | yes | characteristic |
| 514 | Dic5 | #4030 | 1 | 1 | yes | characteristic |
| 515 | Dic5 | #4040 | 1 | 1 | yes | characteristic |
| 516 | Dic5 | #4041 | 1 | 1 | yes | characteristic |
| 517 | C24 | — | 5 | 1 | no | — |
| 518 | C24 | — | 25 | 1 | no | — |
| 519 | #41 | — | 50 | 1 | no | — |
| 520 | #41 | — | 50 | 1 | no | — |
| 521 | #41 | — | 50 | 1 | no | — |
| 522 | #41 | — | 50 | 1 | no | — |
| 523 | C2×Q8 | — | 25 | 1 | no | — |
| 524 | C2×D4 | — | 5 | 1 | no | — |
| 525 | C2×D4 | — | 10 | 1 | no | — |
| 526 | C2×D4 | — | 25 | 1 | no | — |
| 527 | C2×D4 | — | 25 | 1 | no | — |
| 528 | C2×D4 | — | 50 | 1 | no | — |
| 529 | C2×D4 | — | 50 | 1 | no | — |
| 530 | C2×D4 | — | 50 | 1 | no | — |
| 531 | C2×D4 | — | 50 | 1 | no | — |
| 532 | C2×D4 | — | 50 | 1 | no | — |
| 533 | C2×D4 | — | 50 | 1 | no | — |
| 534 | C2×D4 | — | 50 | 1 | no | — |
| 535 | C2×D4 | — | 50 | 1 | no | — |
| 536 | C2×D4 | — | 50 | 1 | no | — |
| 537 | C22×C4 | — | 5 | 1 | no | — |
| 538 | C22×C4 | — | 25 | 1 | no | — |
| 539 | C22×C4 | — | 25 | 1 | no | — |
| 540 | M16 | — | 5 | 2 | no | — |
| 541 | M16 | — | 10 | 1 | no | — |
| 542 | M16 | — | 10 | 1 | no | — |
| 543 | M16 | — | 10 | 1 | no | — |
| 544 | M16 | — | 25 | 2 | no | — |
| 545 | M16 | — | 50 | 2 | no | — |
| 546 | M16 | — | 50 | 2 | no | — |
| 547 | M16 | — | 50 | 1 | no | — |
| 548 | M16 | — | 50 | 1 | no | — |
| 549 | M16 | — | 50 | 1 | no | — |
| 550 | C2×C8 | — | 10 | 1 | no | — |
| 551 | C2×C8 | — | 10 | 1 | no | — |
| 552 | C2×C8 | — | 50 | 2 | no | — |
| 553 | C2×C8 | — | 50 | 2 | no | — |
| 554 | C2×C8 | — | 50 | 1 | no | — |
| 555 | C2×C8 | — | 50 | 1 | no | — |
| 556 | C4⋊C4 | — | 10 | 1 | no | — |
| 557 | C22⋊C4 | — | 5 | 1 | no | — |
| 558 | C22⋊C4 | — | 10 | 1 | no | — |
| 559 | C22⋊C4 | — | 50 | 1 | no | — |
| 560 | C22⋊C4 | — | 50 | 1 | no | — |
| 561 | C22⋊C4 | — | 50 | 1 | no | — |
| 562 | C22⋊C4 | D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 563 | C42 | — | 10 | 1 | no | — |
| 564 | C2×C5 | — | 2 | 1 | no | — |
| 565 | C2×C5 | — | 2 | 1 | no | — |
| 566 | C2×C5 | — | 2 | 1 | no | — |
| 567 | C2×C5 | — | 2 | 1 | no | — |
| 568 | C2×C5 | — | 2 | 1 | no | — |
| 569 | C2×C5 | — | 2 | 1 | no | — |
| 570 | C2×C5 | — | 4 | 2 | no | — |
| 571 | C2×C5 | — | 4 | 1 | no | — |
| 572 | C2×C5 | — | 8 | 1 | no | — |
| 573 | C2×C5 | — | 8 | 1 | no | — |
| 574 | C2×C5 | — | 20 | 1 | no | — |
| 575 | C2×C5 | — | 40 | 1 | no | — |
| 576 | C2×C5 | #64954 | 1 | 1 | yes | characteristic |
| 577 | C2×C5 | #65779 | 1 | 1 | yes | characteristic |
| 578 | D5 | — | 4 | 1 | no | — |
| 579 | D5 | — | 8 | 1 | no | — |
| 580 | D5 | — | 20 | 1 | no | — |
| 581 | D5 | — | 20 | 1 | no | — |
| 582 | D5 | — | 40 | 4 | no | — |
| 583 | D5 | — | 40 | 1 | no | — |
| 584 | D5 | — | 40 | 1 | no | — |
| 585 | D5 | — | 80 | 1 | no | — |
| 586 | C23 | — | 5 | 1 | no | — |
| 587 | C23 | — | 10 | 1 | no | — |
| 588 | C23 | — | 10 | 1 | no | — |
| 589 | C23 | — | 10 | 1 | no | — |
| 590 | C23 | — | 25 | 1 | no | — |
| 591 | C23 | — | 40 | 1 | no | — |
| 592 | C23 | — | 50 | 1 | no | — |
| 593 | C23 | — | 50 | 1 | no | — |
| 594 | C23 | — | 50 | 1 | no | — |
| 595 | C23 | — | 200 | 1 | no | — |
| 596 | C23 | C2×D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 597 | Q8 | — | 50 | 1 | no | — |
| 598 | Q8 | — | 50 | 1 | no | — |
| 599 | D4 | — | 10 | 1 | no | — |
| 600 | D4 | — | 10 | 1 | no | — |
| 601 | D4 | — | 40 | 1 | no | — |
| 602 | D4 | — | 50 | 1 | no | — |
| 603 | D4 | — | 50 | 1 | no | — |
| 604 | D4 | — | 50 | 1 | no | — |
| 605 | D4 | — | 50 | 1 | no | — |
| 606 | D4 | — | 100 | 1 | no | — |
| 607 | D4 | — | 100 | 1 | no | — |
| 608 | D4 | — | 100 | 1 | no | — |
| 609 | D4 | — | 100 | 1 | no | — |
| 610 | D4 | — | 200 | 1 | no | — |
| 611 | D4 | — | 200 | 1 | no | — |
| 612 | D4 | — | 200 | 1 | no | — |
| 613 | C2×C4 | — | 2 | 1 | no | — |
| 614 | C2×C4 | — | 5 | 1 | no | — |
| 615 | C2×C4 | — | 5 | 1 | no | — |
| 616 | C2×C4 | — | 5 | 1 | no | — |
| 617 | C2×C4 | — | 5 | 1 | no | — |
| 618 | C2×C4 | — | 5 | 1 | no | — |
| 619 | C2×C4 | — | 5 | 1 | no | — |
| 620 | C2×C4 | — | 5 | 1 | no | — |
| 621 | C2×C4 | — | 10 | 1 | no | — |
| 622 | C2×C4 | — | 25 | 1 | no | — |
| 623 | C2×C4 | — | 50 | 1 | no | — |
| 624 | C2×C4 | — | 50 | 1 | no | — |
| 625 | C2×C4 | — | 50 | 1 | no | — |
| 626 | C2×C4 | — | 50 | 1 | no | — |
| 627 | C8 | — | 10 | 2 | no | — |
| 628 | C8 | — | 20 | 1 | no | — |
| 629 | C8 | — | 50 | 2 | no | — |
| 630 | C8 | — | 100 | 1 | no | — |
| 631 | C5 | — | 4 | 1 | no | — |
| 632 | C5 | #10599833 | 1 | 1 | yes | characteristic, complemented |
| 633 | C5 | #10604464 | 1 | 1 | yes | characteristic, complemented |
| 634 | C22 | — | 4 | 1 | no | — |
| 635 | C22 | — | 10 | 1 | no | — |
| 636 | C22 | — | 20 | 1 | no | — |
| 637 | C22 | — | 20 | 1 | no | — |
| 638 | C22 | — | 20 | 1 | no | — |
| 639 | C22 | — | 20 | 1 | no | — |
| 640 | C22 | — | 40 | 1 | no | — |
| 641 | C22 | — | 40 | 1 | no | — |
| 642 | C22 | — | 50 | 1 | no | — |
| 643 | C22 | — | 100 | 1 | no | — |
| 644 | C22 | — | 100 | 1 | no | — |
| 645 | C22 | — | 100 | 1 | no | — |
| 646 | C22 | — | 100 | 1 | no | — |
| 647 | C22 | — | 200 | 1 | no | — |
| 648 | C22 | — | 200 | 1 | no | — |
| 649 | C22 | AGL(1,𝔽5)×D20 | 1 | 1 | yes | characteristic |
| 650 | C22 | #11717337 | 1 | 1 | yes | characteristic |
| 651 | C22 | D5×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 652 | C4 | — | 4 | 1 | no | — |
| 653 | C4 | — | 5 | 1 | no | — |
| 654 | C4 | — | 5 | 1 | no | — |
| 655 | C4 | — | 5 | 1 | no | — |
| 656 | C4 | — | 5 | 1 | no | — |
| 657 | C4 | — | 10 | 1 | no | — |
| 658 | C4 | — | 20 | 1 | no | — |
| 659 | C4 | — | 50 | 1 | no | — |
| 660 | C2 | — | 2 | 1 | no | — |
| 661 | C2 | — | 2 | 1 | no | — |
| 662 | C2 | — | 2 | 1 | no | — |
| 663 | C2 | — | 20 | 1 | no | — |
| 664 | C2 | — | 40 | 1 | no | — |
| 665 | C2 | — | 100 | 1 | no | — |
| 666 | C2 | — | 200 | 1 | no | — |
| 667 | C2 | #13103713 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107645 | C2 | semidirect |
| 3. #13103784 | C2 | semidirect |
| 4. C2×#11716757 | C2 | semidirect |
| 5. C2×#11716757 | C2 | semidirect |
| 6. #13100151 | C2 | semidirect |
| 7. C5×#64867 | C2 | semidirect |
| 59. #87853 | D4 | semidirect |
| 65. C5×#704 | D4 | semidirect |
| 91. #64867 | D5 | semidirect |
| 270. #704 | D20 | semidirect |
| 451. C52 | #1914 | semidirect |
| 632. C5 | #10599833 | semidirect |
| 633. C5 | #10604464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107645 | 2 |
| #13105146 | 2 |
| #13103784 | 2 |
| C2×#11716757 | 2 |
| #13100151 | 2 |
| C5×#64867 | 2 |
| #10604464 | 5 |
| #10599833 | 5 |