← #72221502
Subgroups — #72221502
Order 3200.
3038 conjugacy classes of subgroups.
The subgroup lattice has 828 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11717477 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13107786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#66256 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#11717347 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #13107645 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13107624 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #13107622 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #13107609 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | D5×D5⋊M16 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×D4×C5⋊D5 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×C5×#711 | C4 | 1 | 1 | yes | characteristic |
| 12 | C2×C5×#711 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#87886 | C4 | 1 | 2 | yes | — |
| 14 | C22×#6036 | C22 | 1 | 2 | yes | — |
| 15 | C2×#87879 | C4 | 1 | 2 | yes | — |
| 16 | C2×#87879 | C22 | 1 | 2 | yes | — |
| 17 | #11717477 | C4 | 1 | 4 | yes | — |
| 18 | #11717477 | C4 | 1 | 4 | yes | — |
| 19 | #11717477 | C22 | 1 | 4 | yes | — |
| 20 | #11717477 | C22 | 1 | 4 | yes | — |
| 21 | C2×C4×D52 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#87874 | C4 | 1 | 1 | yes | characteristic |
| 23 | C2×#87874 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#87872 | C4 | 1 | 1 | yes | characteristic |
| 25 | C2×#87853 | C22 | 1 | 4 | yes | complemented |
| 26 | #11717426 | C22 | 1 | 8 | yes | complemented |
| 27 | D5⋊#681 | C22 | 1 | 2 | yes | complemented |
| 28 | C2×C5×#704 | C22 | 1 | 4 | yes | complemented |
| 29 | C5×#4131 | C22 | 1 | 8 | yes | complemented |
| 30 | C5×D5⋊M16 | C22 | 1 | 2 | yes | complemented |
| 31 | C2×#87829 | C22 | 1 | 8 | yes | complemented |
| 32 | #11717347 | C22 | 1 | 4 | yes | — |
| 33 | #11717347 | C22 | 1 | 8 | yes | complemented |
| 34 | #11717347 | C22 | 1 | 8 | yes | complemented |
| 35 | #11717347 | C22 | 1 | 8 | yes | complemented |
| 36 | C2×#87827 | C22 | 1 | 8 | yes | complemented |
| 37 | #11717345 | C22 | 1 | 16 | yes | complemented |
| 38 | D5×#704 | C22 | 1 | 4 | yes | complemented |
| 39 | #11717343 | C22 | 1 | 16 | yes | complemented |
| 40 | D5⋊#676 | C22 | 1 | 4 | yes | complemented |
| 41 | #11717332 | C22 | 1 | 8 | yes | complemented |
| 42 | #11717331 | C22 | 1 | 4 | yes | complemented |
| 43 | #11717330 | C22 | 1 | 8 | yes | complemented |
| 44 | D5×#700 | C22 | 1 | 4 | yes | complemented |
| 45 | D5×D5⋊C8 | C22 | 1 | 4 | yes | complemented |
| 46 | D5⋊#568 | — | 5 | 1 | no | maximal |
| 47 | D5×#568 | — | 5 | 1 | no | maximal |
| 48 | C23×C5⋊D5 | C2×C4 | 1 | 2 | yes | — |
| 49 | C22×D52 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×C52×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×C22⋊(C5⋊D5) | C2×C4 | 1 | 2 | yes | — |
| 52 | D4×C5⋊D5 | C2×C4 | 1 | 4 | yes | — |
| 53 | D4×C5⋊D5 | C2×C4 | 1 | 4 | yes | — |
| 54 | C2×C4⋊(C5⋊D5) | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×C4×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C2×C5×C22⋊D5 | C2×C4 | 1 | 2 | yes | — |
| 57 | C2×C5×C22⋊D5 | C2×C4 | 1 | 2 | yes | — |
| 58 | C22×C5×Dic5 | C2×C4 | 1 | 2 | yes | — |
| 59 | C22×C5×Dic5 | C23 | 1 | 2 | yes | — |
| 60 | C5×#711 | C2×C4 | 1 | 4 | yes | — |
| 61 | C5×#711 | C2×C4 | 1 | 4 | yes | — |
| 62 | C5×#711 | C2×C4 | 1 | 4 | yes | — |
| 63 | C5×#711 | C23 | 1 | 4 | yes | — |
| 64 | C2×C4×C5×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×C5×D5 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C5×Dic10 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | C2×C5×Dic10 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | #87886 | C2×C4 | 1 | 8 | yes | — |
| 69 | #87886 | C2×C4 | 1 | 8 | yes | — |
| 70 | C2×#6039 | C2×C4 | 1 | 2 | yes | — |
| 71 | C2×#6038 | C2×C4 | 1 | 2 | yes | — |
| 72 | C2×#6038 | C2×C4 | 1 | 2 | yes | — |
| 73 | C2×#6036 | C2×C4 | 1 | 2 | yes | — |
| 74 | C2×#6036 | C2×C4 | 1 | 2 | yes | — |
| 75 | C2×#6036 | C2×C4 | 1 | 4 | yes | — |
| 76 | C2×#6036 | C2×C4 | 1 | 4 | yes | — |
| 77 | C2×#6036 | C23 | 1 | 2 | yes | — |
| 78 | C2×#6036 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#6036 | C23 | 1 | 4 | yes | — |
| 80 | C2×#6036 | C23 | 1 | 4 | yes | — |
| 81 | #87879 | C2×C4 | 1 | 8 | yes | — |
| 82 | #87879 | C2×C4 | 1 | 8 | yes | — |
| 83 | #87879 | C2×C4 | 1 | 8 | yes | — |
| 84 | #87879 | C23 | 1 | 8 | yes | — |
| 85 | C2×D5×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | C2×D5×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 87 | C4×D52 | C2×C4 | 1 | 2 | yes | — |
| 88 | C4×D52 | C2×C4 | 1 | 2 | yes | — |
| 89 | C4×D52 | C23 | 1 | 2 | yes | — |
| 90 | C4×D52 | C23 | 1 | 2 | yes | — |
| 91 | #87874 | C2×C4 | 1 | 4 | yes | — |
| 92 | #87874 | C2×C4 | 1 | 4 | yes | — |
| 93 | #87874 | C2×C4 | 1 | 4 | yes | — |
| 94 | #87874 | C23 | 1 | 4 | yes | — |
| 95 | #87872 | C2×C4 | 1 | 4 | yes | — |
| 96 | #87872 | C2×C4 | 1 | 4 | yes | — |
| 97 | #87853 | C23 | 1 | 4 | yes | — |
| 98 | #87853 | C23 | 1 | 8 | yes | complemented |
| 99 | C2×#6032 | C23 | 1 | 8 | yes | complemented |
| 100 | #87849 | C23 | 1 | 4 | yes | complemented |
| 101 | D5⋊#168 | C23 | 1 | 4 | yes | complemented |
| 102 | C5×#704 | C23 | 1 | 4 | yes | — |
| 103 | C5×#704 | C23 | 1 | 8 | yes | complemented |
| 104 | C2×C5×#170 | C23 | 1 | 8 | yes | complemented |
| 105 | C5×#700 | C23 | 1 | 4 | yes | complemented |
| 106 | C5×D5⋊C8 | C23 | 1 | 4 | yes | complemented |
| 107 | #87829 | C23 | 1 | 8 | yes | — |
| 108 | #87829 | C23 | 1 | 16 | yes | complemented |
| 109 | #87828 | C23 | 1 | 8 | yes | complemented |
| 110 | #87827 | C23 | 1 | 8 | yes | — |
| 111 | #87827 | C23 | 1 | 16 | yes | complemented |
| 112 | D5×#170 | C23 | 1 | 8 | yes | complemented |
| 113 | C2×D5×#41 | — | 5 | 1 | no | — |
| 114 | C2×D5×#41 | — | 5 | 1 | no | — |
| 115 | #66264 | — | 5 | 8 | no | — |
| 116 | D5⋊#131 | — | 5 | 8 | no | — |
| 117 | #66260 | — | 5 | 2 | no | — |
| 118 | #66256 | — | 5 | 1 | no | — |
| 119 | #66256 | — | 5 | 4 | no | — |
| 120 | #66256 | D5 | 1 | 1 | yes | characteristic, complemented |
| 121 | C2×D5⋊M16 | — | 5 | 4 | no | — |
| 122 | C2×D5⋊M16 | — | 5 | 2 | no | — |
| 123 | C5×#568 | — | 5 | 1 | no | — |
| 124 | #66153 | — | 5 | 1 | no | — |
| 125 | #66084 | — | 5 | 8 | no | — |
| 126 | D5×#131 | — | 5 | 8 | no | — |
| 127 | #66079 | — | 5 | 2 | no | — |
| 128 | #66079 | — | 5 | 4 | no | — |
| 129 | C2×D5×M16 | — | 5 | 2 | no | — |
| 130 | C2×D5×M16 | — | 5 | 4 | no | — |
| 131 | C23×C52 | C22×C4 | 1 | 2 | yes | — |
| 132 | C22×C5⋊D5 | — | 4 | 4 | no | — |
| 133 | C22×C5⋊D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 134 | C22×C5⋊D5 | C22×C4 | 1 | 4 | yes | — |
| 135 | C22×C5⋊D5 | C22×C4 | 1 | 2 | yes | — |
| 136 | C22×C5⋊D5 | C22×C4 | 1 | 4 | yes | — |
| 137 | C22×C5×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 138 | C22×C5×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 139 | C2×D52 | — | 4 | 2 | no | — |
| 140 | C2×D52 | C22×C4 | 1 | 2 | yes | — |
| 141 | C2×D52 | C22×C4 | 1 | 2 | yes | — |
| 142 | C52×D4 | C22×C4 | 1 | 4 | yes | — |
| 143 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 144 | C22⋊(C5⋊D5) | C22×C4 | 1 | 8 | yes | — |
| 145 | C2×#1039 | C22×C4 | 1 | 1 | yes | characteristic |
| 146 | C4⋊(C5⋊D5) | C22×C4 | 1 | 4 | yes | — |
| 147 | C4×C5⋊D5 | C22×C4 | 1 | 2 | yes | — |
| 148 | C4×C5⋊D5 | C22×C4 | 1 | 2 | yes | — |
| 149 | C5×C22⋊D5 | C22×C4 | 1 | 8 | yes | — |
| 150 | C5×C22⋊D5 | C22×C4 | 1 | 8 | yes | — |
| 151 | C2×C5×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 152 | C2×C5×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 153 | C2×C5×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 154 | C2×C5×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 155 | C2×C5×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 156 | C2×C5×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 157 | C2×C5×Dic5 | C24 | 1 | 4 | yes | — |
| 158 | C2×C5×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 159 | C4×C5×D5 | C22×C4 | 1 | 2 | yes | — |
| 160 | C4×C5×D5 | C22×C4 | 1 | 2 | yes | — |
| 161 | C4×C5×D5 | C22×C4 | 1 | 2 | yes | — |
| 162 | C4×C5×D5 | C24 | 1 | 2 | yes | — |
| 163 | C5×Dic10 | C22×C4 | 1 | 4 | yes | — |
| 164 | C5×Dic10 | C22×C4 | 1 | 4 | yes | — |
| 165 | #6039 | C22×C4 | 1 | 8 | yes | — |
| 166 | #6038 | C22×C4 | 1 | 8 | yes | — |
| 167 | #6038 | C22×C4 | 1 | 8 | yes | — |
| 168 | #6036 | C22×C4 | 1 | 4 | yes | — |
| 169 | #6036 | C22×C4 | 1 | 4 | yes | — |
| 170 | #6036 | C22×C4 | 1 | 4 | yes | — |
| 171 | #6036 | C22×C4 | 1 | 4 | yes | — |
| 172 | #6036 | C22×C4 | 1 | 4 | yes | — |
| 173 | #6036 | C22×C4 | 1 | 1 | yes | characteristic |
| 174 | #6036 | C22×C4 | 1 | 1 | yes | characteristic |
| 175 | #6036 | C24 | 1 | 1 | yes | characteristic |
| 176 | #6036 | C24 | 1 | 4 | yes | — |
| 177 | #6036 | C24 | 1 | 1 | yes | characteristic |
| 178 | D5×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 179 | D5×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 180 | D5×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 181 | D5×Dic5 | C24 | 1 | 2 | yes | — |
| 182 | #6032 | C24 | 1 | 8 | yes | — |
| 183 | C5×#170 | C24 | 1 | 8 | yes | — |
| 184 | C2×C5×#41 | — | 5 | 1 | no | — |
| 185 | C2×C5×#41 | — | 5 | 1 | no | — |
| 186 | D5×#41 | — | 5 | 4 | no | — |
| 187 | D5×#41 | — | 5 | 4 | no | — |
| 188 | D5×#41 | — | 5 | 4 | no | — |
| 189 | D5×#41 | — | 5 | 4 | no | — |
| 190 | D5×#41 | — | 5 | 4 | no | — |
| 191 | D5×#41 | — | 5 | 4 | no | — |
| 192 | D5×#41 | — | 5 | 4 | no | — |
| 193 | D5×#41 | — | 5 | 4 | no | — |
| 194 | C2×#713 | — | 5 | 1 | no | — |
| 195 | C2×#713 | — | 5 | 1 | no | — |
| 196 | C2×Q8×D5 | — | 5 | 1 | no | — |
| 197 | C2×Q8×D5 | — | 5 | 1 | no | — |
| 198 | C2×#711 | — | 5 | 2 | no | — |
| 199 | C2×#711 | — | 5 | 2 | no | — |
| 200 | C2×#711 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 201 | C2×#711 | C2×D5 | 1 | 1 | yes | characteristic |
| 202 | C2×D4×D5 | — | 5 | 1 | no | — |
| 203 | C2×D4×D5 | — | 5 | 1 | no | — |
| 204 | C2×D4×D5 | — | 5 | 2 | no | — |
| 205 | C2×D4×D5 | — | 5 | 2 | no | — |
| 206 | C2×D4×D5 | — | 20 | 1 | no | — |
| 207 | C2×#709 | — | 5 | 2 | no | — |
| 208 | C2×#709 | — | 5 | 2 | no | — |
| 209 | C2×#709 | — | 5 | 1 | no | — |
| 210 | C2×#709 | — | 5 | 1 | no | — |
| 211 | C22×C4×D5 | — | 5 | 2 | no | — |
| 212 | C22×C4×D5 | — | 5 | 2 | no | — |
| 213 | C22×C4×D5 | — | 5 | 1 | no | — |
| 214 | C22×C4×D5 | — | 5 | 1 | no | — |
| 215 | C2×#704 | — | 5 | 4 | no | — |
| 216 | C2×#704 | — | 5 | 4 | no | — |
| 217 | C2×#704 | C2×D5 | 1 | 4 | yes | complemented |
| 218 | #4133 | — | 5 | 8 | no | — |
| 219 | #4133 | — | 5 | 8 | no | — |
| 220 | #4131 | — | 5 | 8 | no | — |
| 221 | #4131 | — | 5 | 16 | no | — |
| 222 | #4131 | — | 5 | 16 | no | — |
| 223 | #4131 | C2×D5 | 1 | 8 | yes | complemented |
| 224 | D5⋊M16 | — | 5 | 2 | no | — |
| 225 | D5⋊M16 | — | 5 | 4 | no | — |
| 226 | D5⋊M16 | — | 5 | 8 | no | — |
| 227 | D5⋊M16 | — | 5 | 8 | no | — |
| 228 | D5⋊M16 | — | 5 | 8 | no | — |
| 229 | D5⋊M16 | — | 5 | 4 | no | — |
| 230 | D5⋊M16 | — | 5 | 4 | no | — |
| 231 | D5⋊M16 | C2×D5 | 1 | 2 | yes | complemented |
| 232 | C2×#700 | — | 5 | 8 | no | — |
| 233 | C2×#700 | — | 5 | 4 | no | — |
| 234 | C2×D5⋊C8 | — | 5 | 8 | no | — |
| 235 | C2×D5⋊C8 | — | 5 | 4 | no | — |
| 236 | C5×#131 | — | 5 | 8 | no | — |
| 237 | C2×C5×M16 | — | 5 | 2 | no | — |
| 238 | C2×C5×M16 | — | 5 | 4 | no | — |
| 239 | #4094 | — | 5 | 8 | no | — |
| 240 | C2×#681 | — | 5 | 2 | no | — |
| 241 | C2×#681 | — | 5 | 4 | no | — |
| 242 | #4053 | — | 5 | 8 | no | — |
| 243 | #4053 | — | 5 | 16 | no | — |
| 244 | D5×M16 | — | 5 | 4 | no | — |
| 245 | D5×M16 | — | 5 | 4 | no | — |
| 246 | D5×M16 | — | 5 | 8 | no | — |
| 247 | D5×M16 | — | 5 | 4 | no | — |
| 248 | D5×M16 | — | 5 | 8 | no | — |
| 249 | D5×M16 | — | 5 | 4 | no | — |
| 250 | D5×M16 | — | 5 | 8 | no | — |
| 251 | #4047 | — | 5 | 8 | no | — |
| 252 | #4047 | — | 5 | 16 | no | — |
| 253 | C2×#676 | — | 5 | 4 | no | — |
| 254 | C2×#676 | — | 5 | 8 | no | — |
| 255 | C2×C8×D5 | — | 5 | 4 | no | — |
| 256 | C2×C8×D5 | — | 5 | 8 | no | — |
| 257 | C2×#568 | — | 25 | 1 | no | Sylow |
| 258 | C22×C52 | — | 4 | 2 | no | — |
| 259 | C22×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 260 | C22×C52 | C23×C4 | 1 | 4 | yes | — |
| 261 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 262 | C2×C5⋊D5 | — | 2 | 8 | no | — |
| 263 | C2×C5⋊D5 | — | 4 | 4 | no | — |
| 264 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 265 | C2×C5⋊D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 266 | C2×C5⋊D5 | C23×C4 | 1 | 4 | yes | — |
| 267 | C2×C5⋊D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 268 | C2×C5×D5 | — | 4 | 1 | no | — |
| 269 | C2×C5×D5 | — | 4 | 1 | no | — |
| 270 | C2×C5×D5 | C23×C4 | 1 | 2 | yes | — |
| 271 | C2×C5×D5 | C23×C4 | 1 | 2 | yes | — |
| 272 | D52 | — | 2 | 4 | no | — |
| 273 | D52 | — | 4 | 2 | no | — |
| 274 | C4×C52 | C23×C4 | 1 | 2 | yes | — |
| 275 | #1039 | C23×C4 | 1 | 2 | yes | — |
| 276 | C5×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 277 | C5×Dic5 | C23×C4 | 1 | 4 | yes | — |
| 278 | C5×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 279 | C5×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 280 | C5×Dic5 | C23×C4 | 1 | 4 | yes | — |
| 281 | C5×Dic5 | C25 | 1 | 1 | yes | characteristic |
| 282 | C23×D5 | — | 5 | 2 | no | — |
| 283 | C23×D5 | — | 5 | 2 | no | — |
| 284 | C23×D5 | — | 5 | 1 | no | — |
| 285 | C23×D5 | — | 5 | 1 | no | — |
| 286 | C23×D5 | — | 20 | 2 | no | — |
| 287 | C5×#41 | — | 5 | 4 | no | — |
| 288 | C5×#41 | — | 5 | 4 | no | — |
| 289 | C5×#41 | — | 5 | 4 | no | — |
| 290 | C5×#41 | — | 5 | 4 | no | — |
| 291 | C2×C5×Q8 | — | 5 | 1 | no | — |
| 292 | C2×C5×Q8 | — | 5 | 1 | no | — |
| 293 | C2×C5×D4 | — | 4 | 1 | no | — |
| 294 | C2×C5×D4 | — | 5 | 2 | no | — |
| 295 | C2×C5×D4 | — | 5 | 2 | no | — |
| 296 | C2×C5×D4 | C4×D5 | 1 | 1 | yes | characteristic |
| 297 | C2×C5×D4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 298 | C22×C4×C5 | — | 5 | 2 | no | — |
| 299 | C22×C4×C5 | — | 5 | 2 | no | — |
| 300 | C22×C4×C5 | — | 5 | 1 | no | — |
| 301 | C22×C4×C5 | — | 5 | 1 | no | — |
| 302 | C2×C22⋊D5 | — | 5 | 2 | no | — |
| 303 | C2×C22⋊D5 | — | 5 | 2 | no | — |
| 304 | C2×C22⋊D5 | — | 5 | 2 | no | — |
| 305 | C2×C22⋊D5 | — | 5 | 2 | no | — |
| 306 | C2×C22⋊D5 | — | 20 | 2 | no | — |
| 307 | C2×C22⋊D5 | C4×D5 | 1 | 2 | yes | — |
| 308 | C2×C22⋊D5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 309 | C22×Dic5 | — | 5 | 1 | no | — |
| 310 | C22×Dic5 | — | 5 | 1 | no | — |
| 311 | C22×Dic5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 312 | C22×Dic5 | C22×D5 | 1 | 2 | yes | — |
| 313 | #713 | — | 5 | 4 | no | — |
| 314 | #713 | — | 5 | 4 | no | — |
| 315 | #713 | — | 5 | 4 | no | — |
| 316 | #713 | — | 5 | 4 | no | — |
| 317 | Q8×D5 | — | 5 | 4 | no | — |
| 318 | Q8×D5 | — | 5 | 4 | no | — |
| 319 | Q8×D5 | — | 5 | 4 | no | — |
| 320 | Q8×D5 | — | 5 | 4 | no | — |
| 321 | #711 | — | 5 | 8 | no | — |
| 322 | #711 | — | 5 | 8 | no | — |
| 323 | #711 | — | 5 | 8 | no | — |
| 324 | #711 | — | 5 | 8 | no | — |
| 325 | #711 | C4×D5 | 1 | 4 | yes | — |
| 326 | #711 | C2×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 327 | #711 | C2×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 328 | #711 | C22×D5 | 1 | 4 | yes | — |
| 329 | D4×D5 | — | 5 | 4 | no | — |
| 330 | D4×D5 | — | 5 | 4 | no | — |
| 331 | D4×D5 | — | 5 | 4 | no | — |
| 332 | D4×D5 | — | 5 | 4 | no | — |
| 333 | D4×D5 | — | 5 | 8 | no | — |
| 334 | D4×D5 | — | 5 | 8 | no | — |
| 335 | D4×D5 | — | 5 | 8 | no | — |
| 336 | D4×D5 | — | 5 | 8 | no | — |
| 337 | D4×D5 | — | 20 | 4 | no | — |
| 338 | D4×D5 | — | 20 | 4 | no | — |
| 339 | #709 | — | 5 | 8 | no | — |
| 340 | #709 | — | 5 | 8 | no | — |
| 341 | #709 | — | 5 | 8 | no | — |
| 342 | #709 | — | 5 | 8 | no | — |
| 343 | #709 | — | 5 | 4 | no | — |
| 344 | #709 | — | 5 | 4 | no | — |
| 345 | #709 | — | 5 | 4 | no | — |
| 346 | #709 | — | 5 | 4 | no | — |
| 347 | C2×D20 | — | 5 | 2 | no | — |
| 348 | C2×D20 | — | 5 | 2 | no | — |
| 349 | C2×D20 | — | 5 | 1 | no | — |
| 350 | C2×D20 | — | 5 | 1 | no | — |
| 351 | C2×D20 | — | 20 | 1 | no | — |
| 352 | C2×C4×D5 | — | 5 | 1 | no | — |
| 353 | C2×C4×D5 | — | 5 | 1 | no | — |
| 354 | C2×C4×D5 | — | 5 | 1 | no | — |
| 355 | C2×C4×D5 | — | 5 | 1 | no | — |
| 356 | C2×C4×D5 | — | 5 | 2 | no | — |
| 357 | C2×C4×D5 | — | 5 | 2 | no | — |
| 358 | C2×C4×D5 | — | 5 | 4 | no | — |
| 359 | C2×C4×D5 | — | 5 | 4 | no | — |
| 360 | C2×C4×D5 | — | 5 | 1 | no | — |
| 361 | C2×C4×D5 | — | 5 | 2 | no | — |
| 362 | C2×C4×D5 | — | 5 | 2 | no | — |
| 363 | C2×C4×D5 | — | 5 | 2 | no | — |
| 364 | C2×C4×D5 | — | 5 | 4 | no | — |
| 365 | C2×C4×D5 | — | 5 | 4 | no | — |
| 366 | C2×C4×D5 | — | 5 | 4 | no | — |
| 367 | C2×C4×D5 | — | 5 | 4 | no | — |
| 368 | C2×C4×D5 | — | 5 | 4 | no | — |
| 369 | C2×C4×D5 | — | 5 | 4 | no | — |
| 370 | C2×C4×D5 | — | 5 | 1 | no | — |
| 371 | C2×C4×D5 | — | 5 | 2 | no | — |
| 372 | C2×C4×D5 | — | 5 | 2 | no | — |
| 373 | C2×C4×D5 | — | 5 | 2 | no | — |
| 374 | C2×C4×D5 | — | 5 | 2 | no | — |
| 375 | C2×C4×D5 | — | 5 | 2 | no | — |
| 376 | C2×C4×D5 | — | 5 | 2 | no | — |
| 377 | C2×C4×D5 | — | 5 | 2 | no | — |
| 378 | C2×C4×D5 | — | 5 | 2 | no | — |
| 379 | C2×C4×D5 | — | 5 | 2 | no | — |
| 380 | C2×C4×D5 | — | 20 | 1 | no | — |
| 381 | C2×C4×D5 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 382 | C2×C4×D5 | C22×D5 | 1 | 1 | yes | characteristic |
| 383 | C2×Dic10 | — | 5 | 2 | no | — |
| 384 | C2×Dic10 | — | 5 | 2 | no | — |
| 385 | C2×Dic10 | C4×D5 | 1 | 1 | yes | characteristic |
| 386 | C2×Dic10 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 387 | #704 | — | 5 | 4 | no | — |
| 388 | #704 | — | 5 | 8 | no | — |
| 389 | #704 | — | 5 | 8 | no | — |
| 390 | #704 | C22×D5 | 1 | 4 | yes | — |
| 391 | #704 | C22×D5 | 1 | 8 | yes | complemented |
| 392 | C2×#170 | — | 5 | 8 | no | — |
| 393 | C2×#170 | — | 5 | 8 | no | — |
| 394 | C2×#170 | C22×D5 | 1 | 8 | yes | complemented |
| 395 | #700 | — | 5 | 4 | no | — |
| 396 | #700 | — | 5 | 8 | no | — |
| 397 | #700 | — | 5 | 16 | no | — |
| 398 | #700 | C22×D5 | 1 | 4 | yes | complemented |
| 399 | D5⋊C8 | — | 5 | 4 | no | — |
| 400 | D5⋊C8 | — | 5 | 8 | no | — |
| 401 | D5⋊C8 | — | 5 | 16 | no | — |
| 402 | D5⋊C8 | C22×D5 | 1 | 4 | yes | complemented |
| 403 | C5×M16 | — | 5 | 4 | no | — |
| 404 | C5×M16 | — | 5 | 4 | no | — |
| 405 | C5×M16 | — | 5 | 8 | no | — |
| 406 | C2×C5×C8 | — | 5 | 4 | no | — |
| 407 | C2×C5×C8 | — | 5 | 8 | no | — |
| 408 | #681 | — | 5 | 4 | no | — |
| 409 | #681 | — | 5 | 4 | no | — |
| 410 | #681 | — | 5 | 8 | no | — |
| 411 | C2×#168 | — | 5 | 4 | no | — |
| 412 | C2×#168 | — | 5 | 8 | no | — |
| 413 | #676 | — | 5 | 8 | no | — |
| 414 | #676 | — | 5 | 8 | no | — |
| 415 | #676 | — | 5 | 16 | no | — |
| 416 | C8×D5 | — | 5 | 8 | no | — |
| 417 | C8×D5 | — | 5 | 8 | no | — |
| 418 | C8×D5 | — | 5 | 16 | no | — |
| 419 | C22×#41 | — | 25 | 1 | no | — |
| 420 | #568 | — | 5 | 1 | no | — |
| 421 | #568 | — | 25 | 4 | no | — |
| 422 | #568 | — | 25 | 2 | no | — |
| 423 | #568 | — | 25 | 8 | no | — |
| 424 | #568 | — | 25 | 1 | no | — |
| 425 | C2×#131 | — | 25 | 8 | no | — |
| 426 | C22×M16 | — | 25 | 2 | no | — |
| 427 | C22×M16 | — | 25 | 4 | no | — |
| 428 | C2×C52 | — | 2 | 1 | no | — |
| 429 | C2×C52 | — | 2 | 4 | no | — |
| 430 | C2×C52 | C24×C4 | 1 | 1 | yes | characteristic |
| 431 | C5⋊D5 | — | 2 | 1 | no | — |
| 432 | C5⋊D5 | — | 2 | 4 | no | — |
| 433 | C5⋊D5 | #568 | 1 | 2 | yes | complemented |
| 434 | C5×D5 | — | 2 | 2 | no | — |
| 435 | C5×D5 | — | 2 | 2 | no | — |
| 436 | C23×C5 | — | 4 | 2 | no | — |
| 437 | C23×C5 | — | 5 | 1 | no | — |
| 438 | C23×C5 | — | 5 | 1 | no | — |
| 439 | C23×C5 | C2×C4×D5 | 1 | 2 | yes | — |
| 440 | C23×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 441 | C22×D5 | — | 5 | 1 | no | — |
| 442 | C22×D5 | — | 5 | 4 | no | — |
| 443 | C22×D5 | — | 5 | 1 | no | — |
| 444 | C22×D5 | — | 5 | 4 | no | — |
| 445 | C22×D5 | — | 5 | 2 | no | — |
| 446 | C22×D5 | — | 5 | 4 | no | — |
| 447 | C22×D5 | — | 5 | 2 | no | — |
| 448 | C22×D5 | — | 5 | 4 | no | — |
| 449 | C22×D5 | — | 5 | 2 | no | — |
| 450 | C22×D5 | — | 5 | 2 | no | — |
| 451 | C22×D5 | — | 5 | 2 | no | — |
| 452 | C22×D5 | — | 5 | 2 | no | — |
| 453 | C22×D5 | — | 20 | 1 | no | — |
| 454 | C22×D5 | — | 20 | 2 | no | — |
| 455 | C22×D5 | — | 20 | 4 | no | — |
| 456 | C22×D5 | — | 20 | 4 | no | — |
| 457 | C22×D5 | — | 20 | 2 | no | — |
| 458 | C22×D5 | — | 20 | 2 | no | — |
| 459 | C22×D5 | — | 20 | 4 | no | — |
| 460 | C22×D5 | — | 20 | 4 | no | — |
| 461 | C22×D5 | — | 40 | 8 | no | — |
| 462 | C22×D5 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 463 | C22×D5 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 464 | C5×Q8 | — | 5 | 4 | no | — |
| 465 | C5×Q8 | — | 5 | 4 | no | — |
| 466 | C5×D4 | — | 4 | 4 | no | — |
| 467 | C5×D4 | — | 5 | 8 | no | — |
| 468 | C5×D4 | — | 5 | 8 | no | — |
| 469 | C5×D4 | C2×C4×D5 | 1 | 4 | yes | — |
| 470 | C5×D4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 471 | C2×C4×C5 | — | 4 | 1 | no | — |
| 472 | C2×C4×C5 | — | 5 | 2 | no | — |
| 473 | C2×C4×C5 | — | 5 | 1 | no | — |
| 474 | C2×C4×C5 | — | 5 | 4 | no | — |
| 475 | C2×C4×C5 | — | 5 | 4 | no | — |
| 476 | C2×C4×C5 | — | 5 | 2 | no | — |
| 477 | C2×C4×C5 | — | 5 | 4 | no | — |
| 478 | C2×C4×C5 | — | 5 | 4 | no | — |
| 479 | C2×C4×C5 | — | 5 | 1 | no | — |
| 480 | C2×C4×C5 | — | 5 | 2 | no | — |
| 481 | C2×C4×C5 | — | 5 | 2 | no | — |
| 482 | C2×C4×C5 | — | 5 | 2 | no | — |
| 483 | C2×C4×C5 | — | 5 | 2 | no | — |
| 484 | C2×C4×C5 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 485 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 486 | C22⋊D5 | — | 5 | 8 | no | — |
| 487 | C22⋊D5 | — | 5 | 8 | no | — |
| 488 | C22⋊D5 | — | 5 | 8 | no | — |
| 489 | C22⋊D5 | — | 5 | 8 | no | — |
| 490 | C22⋊D5 | — | 20 | 8 | no | — |
| 491 | C22⋊D5 | C2×C4×D5 | 1 | 8 | yes | — |
| 492 | C22⋊D5 | C22×AGL(1,𝔽5) | 1 | 8 | yes | — |
| 493 | C2×Dic5 | — | 5 | 1 | no | — |
| 494 | C2×Dic5 | — | 5 | 1 | no | — |
| 495 | C2×Dic5 | — | 5 | 2 | no | — |
| 496 | C2×Dic5 | — | 5 | 2 | no | — |
| 497 | C2×Dic5 | — | 5 | 2 | no | — |
| 498 | C2×Dic5 | — | 5 | 2 | no | — |
| 499 | C2×Dic5 | — | 20 | 1 | no | — |
| 500 | C2×Dic5 | C2×C4×D5 | 1 | 2 | yes | — |
| 501 | C2×Dic5 | C2×C4×D5 | 1 | 4 | yes | — |
| 502 | C2×Dic5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 503 | C2×Dic5 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 504 | C2×Dic5 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 505 | C2×Dic5 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 506 | C2×Dic5 | C23×D5 | 1 | 4 | yes | — |
| 507 | C2×Dic5 | C23×D5 | 1 | 1 | yes | characteristic |
| 508 | D20 | — | 5 | 8 | no | — |
| 509 | D20 | — | 5 | 8 | no | — |
| 510 | D20 | — | 5 | 4 | no | — |
| 511 | D20 | — | 5 | 4 | no | — |
| 512 | D20 | — | 20 | 4 | no | — |
| 513 | C4×D5 | — | 5 | 2 | no | — |
| 514 | C4×D5 | — | 5 | 2 | no | — |
| 515 | C4×D5 | — | 5 | 2 | no | — |
| 516 | C4×D5 | — | 5 | 2 | no | — |
| 517 | C4×D5 | — | 5 | 2 | no | — |
| 518 | C4×D5 | — | 5 | 2 | no | — |
| 519 | C4×D5 | — | 5 | 2 | no | — |
| 520 | C4×D5 | — | 5 | 2 | no | — |
| 521 | C4×D5 | — | 5 | 1 | no | — |
| 522 | C4×D5 | — | 5 | 1 | no | — |
| 523 | C4×D5 | — | 5 | 4 | no | — |
| 524 | C4×D5 | — | 5 | 4 | no | — |
| 525 | C4×D5 | — | 5 | 4 | no | — |
| 526 | C4×D5 | — | 5 | 4 | no | — |
| 527 | C4×D5 | — | 5 | 4 | no | — |
| 528 | C4×D5 | — | 5 | 1 | no | — |
| 529 | C4×D5 | — | 5 | 1 | no | — |
| 530 | C4×D5 | — | 5 | 4 | no | — |
| 531 | C4×D5 | — | 5 | 4 | no | — |
| 532 | C4×D5 | — | 5 | 4 | no | — |
| 533 | C4×D5 | — | 5 | 4 | no | — |
| 534 | C4×D5 | — | 5 | 4 | no | — |
| 535 | C4×D5 | — | 5 | 1 | no | — |
| 536 | C4×D5 | — | 5 | 4 | no | — |
| 537 | C4×D5 | — | 5 | 1 | no | — |
| 538 | C4×D5 | — | 5 | 1 | no | — |
| 539 | C4×D5 | — | 5 | 4 | no | — |
| 540 | C4×D5 | — | 5 | 1 | no | — |
| 541 | C4×D5 | — | 20 | 2 | no | — |
| 542 | C4×D5 | — | 20 | 2 | no | — |
| 543 | C4×D5 | C2×C4×D5 | 1 | 2 | yes | — |
| 544 | C4×D5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 545 | C4×D5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 546 | C4×D5 | C23×D5 | 1 | 2 | yes | — |
| 547 | Dic10 | — | 5 | 8 | no | — |
| 548 | Dic10 | — | 5 | 8 | no | — |
| 549 | Dic10 | C2×C4×D5 | 1 | 4 | yes | — |
| 550 | Dic10 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 551 | #170 | — | 5 | 8 | no | — |
| 552 | #170 | C23×D5 | 1 | 8 | yes | — |
| 553 | C5×C8 | — | 5 | 8 | no | — |
| 554 | #168 | — | 5 | 8 | no | — |
| 555 | C2×#41 | — | 5 | 1 | no | — |
| 556 | C2×#41 | — | 5 | 1 | no | — |
| 557 | C2×#41 | — | 25 | 2 | no | — |
| 558 | C2×#41 | — | 25 | 2 | no | — |
| 559 | C2×#41 | — | 25 | 1 | no | — |
| 560 | C2×#41 | — | 25 | 1 | no | — |
| 561 | C2×#41 | — | 25 | 4 | no | — |
| 562 | C2×#41 | — | 25 | 4 | no | — |
| 563 | C2×#41 | — | 25 | 4 | no | — |
| 564 | C2×#41 | — | 25 | 4 | no | — |
| 565 | C22×Q8 | — | 25 | 1 | no | — |
| 566 | C22×D4 | — | 25 | 2 | no | — |
| 567 | C22×D4 | — | 25 | 1 | no | — |
| 568 | C23×C4 | — | 25 | 2 | no | — |
| 569 | C23×C4 | — | 25 | 1 | no | — |
| 570 | #131 | — | 5 | 8 | no | — |
| 571 | #131 | — | 25 | 16 | no | — |
| 572 | #131 | — | 25 | 8 | no | — |
| 573 | #131 | — | 25 | 16 | no | — |
| 574 | #131 | — | 25 | 8 | no | — |
| 575 | #131 | — | 25 | 8 | no | — |
| 576 | C2×M16 | — | 5 | 2 | no | — |
| 577 | C2×M16 | — | 5 | 4 | no | — |
| 578 | C2×M16 | — | 25 | 8 | no | — |
| 579 | C2×M16 | — | 25 | 4 | no | — |
| 580 | C2×M16 | — | 25 | 4 | no | — |
| 581 | C2×M16 | — | 25 | 4 | no | — |
| 582 | C2×M16 | — | 25 | 4 | no | — |
| 583 | C2×M16 | — | 25 | 8 | no | — |
| 584 | C2×M16 | — | 25 | 8 | no | — |
| 585 | C2×M16 | — | 25 | 8 | no | — |
| 586 | C2×M16 | — | 25 | 4 | no | — |
| 587 | C2×M16 | — | 25 | 2 | no | — |
| 588 | C2×M16 | — | 25 | 4 | no | — |
| 589 | C22×C8 | — | 25 | 4 | no | — |
| 590 | C22×C8 | — | 25 | 8 | no | — |
| 591 | C52 | C2×#568 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 592 | C22×C5 | — | 4 | 2 | no | — |
| 593 | C22×C5 | — | 4 | 2 | no | — |
| 594 | C22×C5 | — | 4 | 1 | no | — |
| 595 | C22×C5 | — | 4 | 4 | no | — |
| 596 | C22×C5 | — | 5 | 2 | no | — |
| 597 | C22×C5 | — | 5 | 2 | no | — |
| 598 | C22×C5 | — | 8 | 4 | no | — |
| 599 | C22×C5 | — | 20 | 1 | no | — |
| 600 | C22×C5 | — | 20 | 1 | no | — |
| 601 | C22×C5 | C22×C4×D5 | 1 | 1 | yes | characteristic |
| 602 | C22×C5 | C22×C4×D5 | 1 | 4 | yes | — |
| 603 | C22×C5 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 604 | C22×C5 | C23×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 605 | C2×D5 | — | 4 | 1 | no | — |
| 606 | C2×D5 | — | 4 | 1 | no | — |
| 607 | C2×D5 | — | 5 | 1 | no | — |
| 608 | C2×D5 | — | 5 | 1 | no | — |
| 609 | C2×D5 | — | 5 | 1 | no | — |
| 610 | C2×D5 | — | 5 | 4 | no | — |
| 611 | C2×D5 | — | 5 | 1 | no | — |
| 612 | C2×D5 | — | 5 | 4 | no | — |
| 613 | C2×D5 | — | 10 | 4 | no | — |
| 614 | C2×D5 | — | 10 | 4 | no | — |
| 615 | C2×D5 | — | 10 | 8 | no | — |
| 616 | C2×D5 | — | 10 | 8 | no | — |
| 617 | C2×D5 | — | 10 | 2 | no | — |
| 618 | C2×D5 | — | 10 | 2 | no | — |
| 619 | C2×D5 | — | 20 | 1 | no | — |
| 620 | C2×D5 | — | 20 | 1 | no | — |
| 621 | C2×D5 | — | 20 | 4 | no | — |
| 622 | C2×D5 | — | 20 | 4 | no | — |
| 623 | C2×D5 | — | 20 | 2 | no | — |
| 624 | C2×D5 | — | 20 | 2 | no | — |
| 625 | C2×D5 | — | 20 | 2 | no | — |
| 626 | C2×D5 | — | 20 | 4 | no | — |
| 627 | C2×D5 | — | 20 | 2 | no | — |
| 628 | C2×D5 | — | 20 | 4 | no | — |
| 629 | C2×D5 | — | 40 | 8 | no | — |
| 630 | C2×D5 | — | 40 | 8 | no | — |
| 631 | C2×D5 | — | 40 | 4 | no | — |
| 632 | C2×D5 | C22×C4×D5 | 1 | 2 | yes | — |
| 633 | C2×D5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 634 | C4×C5 | — | 4 | 2 | no | — |
| 635 | C4×C5 | — | 5 | 4 | no | — |
| 636 | C4×C5 | — | 5 | 1 | no | — |
| 637 | C4×C5 | — | 5 | 1 | no | — |
| 638 | C4×C5 | — | 5 | 4 | no | — |
| 639 | C4×C5 | — | 5 | 1 | no | — |
| 640 | C4×C5 | — | 5 | 1 | no | — |
| 641 | C4×C5 | C22×C4×D5 | 1 | 2 | yes | — |
| 642 | C4×C5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 643 | Dic5 | — | 5 | 2 | no | — |
| 644 | Dic5 | — | 5 | 2 | no | — |
| 645 | Dic5 | — | 20 | 2 | no | — |
| 646 | Dic5 | C22×C4×D5 | 1 | 4 | yes | — |
| 647 | Dic5 | C22×C4×D5 | 1 | 1 | yes | characteristic |
| 648 | Dic5 | C23×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 649 | Dic5 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 650 | Dic5 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 651 | Dic5 | C24×D5 | 1 | 1 | yes | characteristic |
| 652 | C24 | — | 25 | 1 | no | — |
| 653 | C24 | — | 25 | 2 | no | — |
| 654 | #41 | — | 5 | 4 | no | — |
| 655 | #41 | — | 5 | 4 | no | — |
| 656 | #41 | — | 5 | 4 | no | — |
| 657 | #41 | — | 5 | 4 | no | — |
| 658 | #41 | — | 25 | 8 | no | — |
| 659 | #41 | — | 25 | 8 | no | — |
| 660 | #41 | — | 25 | 8 | no | — |
| 661 | #41 | — | 25 | 8 | no | — |
| 662 | #41 | — | 25 | 4 | no | — |
| 663 | #41 | — | 25 | 4 | no | — |
| 664 | #41 | — | 25 | 4 | no | — |
| 665 | #41 | — | 25 | 4 | no | — |
| 666 | C2×Q8 | — | 5 | 1 | no | — |
| 667 | C2×Q8 | — | 5 | 1 | no | — |
| 668 | C2×Q8 | — | 25 | 2 | no | — |
| 669 | C2×Q8 | — | 25 | 4 | no | — |
| 670 | C2×Q8 | — | 25 | 4 | no | — |
| 671 | C2×D4 | — | 5 | 2 | no | — |
| 672 | C2×D4 | — | 5 | 2 | no | — |
| 673 | C2×D4 | — | 25 | 2 | no | — |
| 674 | C2×D4 | — | 25 | 2 | no | — |
| 675 | C2×D4 | — | 25 | 8 | no | — |
| 676 | C2×D4 | — | 25 | 8 | no | — |
| 677 | C2×D4 | — | 25 | 2 | no | — |
| 678 | C2×D4 | — | 25 | 4 | no | — |
| 679 | C2×D4 | — | 25 | 4 | no | — |
| 680 | C2×D4 | — | 25 | 1 | no | — |
| 681 | C2×D4 | D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 682 | C22×C4 | — | 5 | 2 | no | — |
| 683 | C22×C4 | — | 5 | 2 | no | — |
| 684 | C22×C4 | — | 5 | 1 | no | — |
| 685 | C22×C4 | — | 5 | 1 | no | — |
| 686 | C22×C4 | — | 25 | 4 | no | — |
| 687 | C22×C4 | — | 25 | 2 | no | — |
| 688 | C22×C4 | — | 25 | 1 | no | — |
| 689 | C22×C4 | — | 25 | 4 | no | — |
| 690 | C22×C4 | — | 25 | 2 | no | — |
| 691 | C22×C4 | — | 25 | 2 | no | — |
| 692 | C22×C4 | — | 25 | 2 | no | — |
| 693 | C22×C4 | — | 25 | 2 | no | — |
| 694 | C22×C4 | — | 25 | 4 | no | — |
| 695 | C22×C4 | — | 25 | 4 | no | — |
| 696 | C22×C4 | — | 25 | 2 | no | — |
| 697 | C22×C4 | — | 25 | 2 | no | — |
| 698 | C22×C4 | — | 25 | 1 | no | — |
| 699 | C22×C4 | — | 25 | 1 | no | — |
| 700 | C22×C4 | — | 25 | 1 | no | — |
| 701 | M16 | — | 5 | 4 | no | — |
| 702 | M16 | — | 5 | 4 | no | — |
| 703 | M16 | — | 5 | 8 | no | — |
| 704 | M16 | — | 25 | 8 | no | — |
| 705 | M16 | — | 25 | 16 | no | — |
| 706 | M16 | — | 25 | 8 | no | — |
| 707 | M16 | — | 25 | 4 | no | — |
| 708 | M16 | — | 25 | 4 | no | — |
| 709 | M16 | — | 25 | 8 | no | — |
| 710 | C2×C8 | — | 5 | 4 | no | — |
| 711 | C2×C8 | — | 5 | 8 | no | — |
| 712 | C2×C8 | — | 25 | 8 | no | — |
| 713 | C2×C8 | — | 25 | 16 | no | — |
| 714 | C2×C8 | — | 25 | 8 | no | — |
| 715 | C2×C8 | — | 25 | 4 | no | — |
| 716 | C2×C8 | — | 25 | 8 | no | — |
| 717 | C2×C5 | — | 2 | 1 | no | — |
| 718 | C2×C5 | — | 2 | 4 | no | — |
| 719 | C2×C5 | — | 2 | 1 | no | — |
| 720 | C2×C5 | — | 2 | 4 | no | — |
| 721 | C2×C5 | — | 4 | 2 | no | — |
| 722 | C2×C5 | — | 4 | 1 | no | — |
| 723 | C2×C5 | — | 8 | 4 | no | — |
| 724 | C2×C5 | — | 10 | 2 | no | — |
| 725 | C2×C5 | — | 10 | 2 | no | — |
| 726 | C2×C5 | C23×C4×D5 | 1 | 1 | yes | characteristic |
| 727 | C2×C5 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 728 | D5 | — | 2 | 2 | no | — |
| 729 | D5 | — | 2 | 2 | no | — |
| 730 | D5 | — | 5 | 2 | no | — |
| 731 | D5 | — | 5 | 2 | no | — |
| 732 | D5 | — | 10 | 4 | no | — |
| 733 | D5 | — | 10 | 1 | no | — |
| 734 | D5 | — | 10 | 4 | no | — |
| 735 | D5 | — | 10 | 1 | no | — |
| 736 | D5 | — | 20 | 2 | no | — |
| 737 | D5 | — | 20 | 2 | no | — |
| 738 | D5 | — | 40 | 4 | no | — |
| 739 | C23 | — | 5 | 1 | no | — |
| 740 | C23 | — | 5 | 1 | no | — |
| 741 | C23 | — | 25 | 2 | no | — |
| 742 | C23 | — | 25 | 2 | no | — |
| 743 | C23 | — | 25 | 1 | no | — |
| 744 | C23 | — | 25 | 4 | no | — |
| 745 | C23 | — | 25 | 4 | no | — |
| 746 | C23 | — | 25 | 2 | no | — |
| 747 | C23 | — | 100 | 4 | no | — |
| 748 | C23 | — | 100 | 2 | no | — |
| 749 | C23 | C2×D5×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 750 | Q8 | — | 5 | 4 | no | — |
| 751 | Q8 | — | 5 | 4 | no | — |
| 752 | Q8 | — | 25 | 8 | no | — |
| 753 | D4 | — | 5 | 8 | no | — |
| 754 | D4 | — | 5 | 8 | no | — |
| 755 | D4 | — | 25 | 8 | no | — |
| 756 | D4 | — | 25 | 8 | no | — |
| 757 | D4 | — | 25 | 8 | no | — |
| 758 | D4 | — | 25 | 4 | no | — |
| 759 | D4 | C2×D5×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 760 | C2×C4 | — | 5 | 4 | no | — |
| 761 | C2×C4 | — | 5 | 1 | no | — |
| 762 | C2×C4 | — | 5 | 1 | no | — |
| 763 | C2×C4 | — | 5 | 2 | no | — |
| 764 | C2×C4 | — | 5 | 2 | no | — |
| 765 | C2×C4 | — | 5 | 4 | no | — |
| 766 | C2×C4 | — | 5 | 4 | no | — |
| 767 | C2×C4 | — | 5 | 4 | no | — |
| 768 | C2×C4 | — | 5 | 2 | no | — |
| 769 | C2×C4 | — | 5 | 2 | no | — |
| 770 | C2×C4 | — | 5 | 2 | no | — |
| 771 | C2×C4 | — | 5 | 2 | no | — |
| 772 | C2×C4 | — | 25 | 1 | no | — |
| 773 | C2×C4 | — | 25 | 4 | no | — |
| 774 | C2×C4 | — | 25 | 1 | no | — |
| 775 | C2×C4 | — | 25 | 1 | no | — |
| 776 | C2×C4 | — | 25 | 1 | no | — |
| 777 | C2×C4 | — | 25 | 4 | no | — |
| 778 | C2×C4 | — | 25 | 4 | no | — |
| 779 | C2×C4 | — | 25 | 4 | no | — |
| 780 | C2×C4 | — | 25 | 4 | no | — |
| 781 | C2×C4 | — | 25 | 4 | no | — |
| 782 | C2×C4 | — | 25 | 2 | no | — |
| 783 | C2×C4 | — | 25 | 2 | no | — |
| 784 | C2×C4 | — | 25 | 2 | no | — |
| 785 | C2×C4 | — | 25 | 2 | no | — |
| 786 | C2×C4 | — | 25 | 1 | no | — |
| 787 | C2×C4 | — | 25 | 2 | no | — |
| 788 | C2×C4 | — | 25 | 2 | no | — |
| 789 | C2×C4 | C2×D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 790 | C8 | — | 5 | 8 | no | — |
| 791 | C8 | — | 25 | 8 | no | — |
| 792 | C5 | — | 4 | 1 | no | — |
| 793 | C5 | D5×#568 | 1 | 1 | yes | characteristic, complemented |
| 794 | C5 | D5⋊#568 | 1 | 1 | yes | characteristic, complemented |
| 795 | C22 | — | 4 | 2 | no | — |
| 796 | C22 | — | 5 | 2 | no | — |
| 797 | C22 | — | 5 | 2 | no | — |
| 798 | C22 | — | 20 | 1 | no | — |
| 799 | C22 | — | 20 | 1 | no | — |
| 800 | C22 | — | 25 | 1 | no | — |
| 801 | C22 | — | 25 | 1 | no | — |
| 802 | C22 | — | 25 | 4 | no | — |
| 803 | C22 | — | 50 | 2 | no | — |
| 804 | C22 | — | 50 | 8 | no | — |
| 805 | C22 | — | 50 | 4 | no | — |
| 806 | C22 | — | 100 | 2 | no | — |
| 807 | C22 | — | 100 | 4 | no | — |
| 808 | C22 | — | 100 | 2 | no | — |
| 809 | C22 | C22×D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 810 | C22 | C22×D5×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 811 | C4 | — | 5 | 1 | no | — |
| 812 | C4 | — | 5 | 1 | no | — |
| 813 | C4 | — | 5 | 1 | no | — |
| 814 | C4 | — | 5 | 1 | no | — |
| 815 | C4 | — | 5 | 4 | no | — |
| 816 | C4 | — | 5 | 4 | no | — |
| 817 | C4 | — | 25 | 2 | no | — |
| 818 | C4 | C22×D5×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 819 | C2 | — | 2 | 1 | no | — |
| 820 | C2 | — | 2 | 4 | no | — |
| 821 | C2 | — | 10 | 2 | no | — |
| 822 | C2 | — | 10 | 2 | no | — |
| 823 | C2 | — | 25 | 2 | no | — |
| 824 | C2 | — | 50 | 1 | no | — |
| 825 | C2 | — | 50 | 4 | no | — |
| 826 | C2 | C23×D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta