Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1882 conjugacy classes of subgroups.
The subgroup lattice has 887 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D52×#41 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C4×D5⋊AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D5⋊(D5⋊M16) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13104930 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13104804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | D5⋊#4010 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | D5⋊#4008 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #13103946 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13103942 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×D5⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 11 | #41×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 12 | C5×D5×#41 | C4 | 1 | 2 | yes | complemented |
| 13 | #11717484 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | D5×#713 | C22 | 1 | 2 | yes | — |
| 15 | Q8×D52 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | #11717477 | — | 2 | 1 | no | — |
| 17 | #11717477 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | D5×#711 | — | 2 | 2 | no | — |
| 19 | D5×#711 | C22 | 1 | 2 | yes | — |
| 20 | D4×D52 | — | 2 | 1 | no | — |
| 21 | D4×D52 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #11717471 | — | 2 | 1 | no | — |
| 23 | #11717471 | C22 | 1 | 1 | yes | characteristic |
| 24 | D5×#709 | — | 2 | 2 | no | — |
| 25 | D5×#709 | C4 | 1 | 2 | yes | complemented |
| 26 | C2×C4×D52 | — | 2 | 1 | no | — |
| 27 | C2×C4×D52 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C4×#1044 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #11717448 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×C4×#1043 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #11717435 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | D5⋊#704 | — | 2 | 2 | no | — |
| 33 | C2×#87830 | — | 2 | 1 | no | — |
| 34 | C4×D5⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 35 | C4×D5⋊AGL(1,𝔽5) | C22 | 1 | 4 | yes | complemented |
| 36 | #11717361 | — | 2 | 1 | no | — |
| 37 | D5⋊#700 | C22 | 1 | 4 | yes | complemented |
| 38 | D5⋊(D5⋊C8) | — | 2 | 1 | no | — |
| 39 | #11716903 | C22 | 1 | 2 | yes | complemented |
| 40 | #11716901 | C22 | 1 | 2 | yes | complemented |
| 41 | #11716878 | C22 | 1 | 2 | yes | complemented |
| 42 | #11716876 | C22 | 1 | 2 | yes | complemented |
| 43 | #11716770 | C22 | 1 | 4 | yes | complemented |
| 44 | #11716769 | C22 | 1 | 4 | yes | complemented |
| 45 | C2×D5⋊#104 | — | 5 | 2 | no | maximal |
| 46 | C22×D52 | — | 2 | 1 | no | — |
| 47 | C22×D52 | D4 | 1 | 1 | yes | characteristic |
| 48 | C22×#1044 | — | 2 | 1 | no | — |
| 49 | C22×#1043 | — | 2 | 1 | no | — |
| 50 | C2×D5⋊AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 51 | C2×D5⋊AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 52 | C52×#41 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 53 | #87904 | C23 | 1 | 1 | yes | characteristic |
| 54 | Q8×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 55 | #87902 | — | 2 | 1 | no | — |
| 56 | #87902 | C23 | 1 | 1 | yes | characteristic |
| 57 | D4×C5⋊D5 | — | 2 | 1 | no | — |
| 58 | D4×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 59 | #87900 | — | 2 | 1 | no | — |
| 60 | #87900 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 62 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 63 | C5×#713 | C2×C4 | 1 | 2 | yes | complemented |
| 64 | C5×Q8×D5 | C2×C4 | 1 | 2 | yes | complemented |
| 65 | C5×#711 | — | 2 | 2 | no | — |
| 66 | C5×#711 | C2×C4 | 1 | 2 | yes | complemented |
| 67 | C5×D4×D5 | — | 2 | 2 | no | — |
| 68 | C5×D4×D5 | C2×C4 | 1 | 2 | yes | complemented |
| 69 | C5×#709 | — | 2 | 2 | no | — |
| 70 | C5×#709 | C2×C4 | 1 | 2 | yes | complemented |
| 71 | C2×C4×C5×D5 | — | 2 | 2 | no | — |
| 72 | C2×C4×C5×D5 | C2×C4 | 1 | 2 | yes | — |
| 73 | #87886 | — | 2 | 1 | no | — |
| 74 | #87886 | — | 2 | 1 | no | — |
| 75 | #87886 | — | 2 | 1 | no | — |
| 76 | D5×C22⋊D5 | — | 2 | 2 | no | — |
| 77 | D5×C22⋊D5 | — | 2 | 2 | no | — |
| 78 | D5×C22⋊D5 | — | 2 | 2 | no | — |
| 79 | C2×#6036 | — | 2 | 1 | no | — |
| 80 | C2×#6036 | D4 | 1 | 1 | yes | characteristic |
| 81 | #87880 | — | 2 | 1 | no | — |
| 82 | #87880 | — | 2 | 2 | no | — |
| 83 | #87879 | — | 2 | 2 | no | — |
| 84 | #87879 | — | 2 | 2 | no | — |
| 85 | #87879 | — | 2 | 2 | no | — |
| 86 | C2×D5×Dic5 | — | 2 | 2 | no | — |
| 87 | C2×D5×Dic5 | D4 | 1 | 2 | yes | — |
| 88 | #87877 | — | 2 | 1 | no | — |
| 89 | #87877 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 90 | D5×D20 | — | 2 | 2 | no | — |
| 91 | D5×D20 | C2×C4 | 1 | 2 | yes | complemented |
| 92 | C4×D52 | — | 2 | 1 | no | — |
| 93 | C4×D52 | — | 2 | 1 | no | — |
| 94 | C4×D52 | — | 2 | 2 | no | — |
| 95 | C4×D52 | — | 2 | 1 | no | — |
| 96 | C4×D52 | — | 2 | 2 | no | — |
| 97 | C4×D52 | C2×C4 | 1 | 1 | yes | characteristic |
| 98 | C4×D52 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | C4×D52 | D4 | 1 | 2 | yes | — |
| 100 | C4×D52 | D4 | 1 | 1 | yes | characteristic |
| 101 | C4×D52 | D4 | 1 | 1 | yes | characteristic |
| 102 | C4×D52 | C23 | 1 | 2 | yes | — |
| 103 | #87874 | — | 2 | 2 | no | — |
| 104 | #87874 | C2×C4 | 1 | 2 | yes | complemented |
| 105 | #87873 | — | 2 | 1 | no | — |
| 106 | #87873 | — | 2 | 2 | no | — |
| 107 | #87872 | — | 2 | 1 | no | — |
| 108 | #87872 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 109 | #87871 | — | 2 | 2 | no | — |
| 110 | #87871 | C23 | 1 | 2 | yes | — |
| 111 | #87870 | — | 2 | 2 | no | — |
| 112 | #87870 | C2×C4 | 1 | 2 | yes | complemented |
| 113 | D5×Dic10 | — | 2 | 2 | no | — |
| 114 | D5×Dic10 | C2×C4 | 1 | 2 | yes | complemented |
| 115 | #87867 | — | 2 | 1 | no | — |
| 116 | C4×#1044 | — | 2 | 1 | no | — |
| 117 | C4×#1044 | C23 | 1 | 2 | yes | complemented |
| 118 | #87863 | C23 | 1 | 2 | yes | complemented |
| 119 | #87862 | — | 2 | 1 | no | — |
| 120 | #87860 | — | 2 | 1 | no | — |
| 121 | C4×#1043 | — | 2 | 1 | no | — |
| 122 | C4×#1043 | C23 | 1 | 2 | yes | complemented |
| 123 | #87856 | C23 | 1 | 2 | yes | complemented |
| 124 | #87855 | — | 2 | 1 | no | — |
| 125 | #87834 | — | 2 | 4 | no | — |
| 126 | D5⋊#170 | — | 2 | 4 | no | — |
| 127 | #87830 | — | 2 | 4 | no | — |
| 128 | C2×D5×#41 | — | 5 | 2 | no | — |
| 129 | C22×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 130 | C2×D5⋊M16 | — | 5 | 2 | no | — |
| 131 | D5⋊#104 | — | 5 | 2 | no | — |
| 132 | D5⋊#104 | — | 5 | 2 | no | — |
| 133 | D5⋊#104 | — | 5 | 2 | no | — |
| 134 | D5⋊#104 | — | 5 | 2 | no | — |
| 135 | D5⋊#104 | — | 5 | 4 | no | — |
| 136 | D5⋊#104 | — | 5 | 4 | no | — |
| 137 | D5⋊#104 | — | 10 | 2 | no | — |
| 138 | C2×#4010 | — | 5 | 4 | no | — |
| 139 | C2×#4008 | — | 5 | 4 | no | — |
| 140 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 141 | C22×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C22×C5×D5 | — | 2 | 2 | no | — |
| 143 | C22×C5×D5 | C22⋊C4 | 1 | 2 | yes | — |
| 144 | C2×D52 | — | 2 | 4 | no | — |
| 145 | C2×D52 | — | 2 | 1 | no | — |
| 146 | C2×D52 | — | 2 | 2 | no | — |
| 147 | C2×D52 | — | 4 | 4 | no | — |
| 148 | C2×D52 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 149 | C2×D52 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 151 | C2×#1044 | — | 2 | 4 | no | — |
| 152 | C2×#1044 | — | 2 | 2 | no | — |
| 153 | C2×#1043 | — | 2 | 4 | no | — |
| 154 | C2×#1043 | — | 2 | 2 | no | — |
| 155 | D5⋊AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 156 | C52×Q8 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 157 | C52×D4 | — | 2 | 1 | no | — |
| 158 | C52×D4 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 159 | C2×C4×C52 | — | 2 | 1 | no | — |
| 160 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 161 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 162 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 163 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 164 | C2×#1039 | — | 2 | 1 | no | — |
| 165 | C2×#1039 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 167 | C4⋊(C5⋊D5) | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 168 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 169 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 170 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 171 | C4×C5⋊D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 172 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C4×C5⋊D5 | C24 | 1 | 1 | yes | characteristic |
| 175 | #6045 | — | 2 | 1 | no | — |
| 176 | #6045 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 177 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 178 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 179 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 180 | C2×C5×Dic5 | — | 2 | 2 | no | — |
| 181 | C2×C5×Dic5 | C22⋊C4 | 1 | 2 | yes | — |
| 182 | C5×D20 | — | 2 | 2 | no | — |
| 183 | C5×D20 | C22×C4 | 1 | 2 | yes | complemented |
| 184 | C4×C5×D5 | — | 2 | 2 | no | — |
| 185 | C4×C5×D5 | — | 2 | 2 | no | — |
| 186 | C4×C5×D5 | — | 2 | 2 | no | — |
| 187 | C4×C5×D5 | C22⋊C4 | 1 | 2 | yes | — |
| 188 | C4×C5×D5 | C22⋊C4 | 1 | 2 | yes | — |
| 189 | C4×C5×D5 | C22×C4 | 1 | 2 | yes | — |
| 190 | C4×C5×D5 | C22×C4 | 1 | 2 | yes | — |
| 191 | C5×Dic10 | — | 2 | 2 | no | — |
| 192 | C5×Dic10 | C22×C4 | 1 | 2 | yes | complemented |
| 193 | #6039 | — | 2 | 1 | no | — |
| 194 | #6039 | — | 2 | 2 | no | — |
| 195 | #6038 | — | 2 | 2 | no | — |
| 196 | #6038 | — | 2 | 2 | no | — |
| 197 | #6038 | — | 2 | 2 | no | — |
| 198 | #6037 | — | 2 | 2 | no | — |
| 199 | #6037 | — | 2 | 1 | no | — |
| 200 | #6036 | — | 2 | 1 | no | — |
| 201 | #6036 | — | 2 | 2 | no | — |
| 202 | #6036 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 203 | #6036 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 204 | #6036 | C2×D4 | 1 | 2 | yes | — |
| 205 | D5×Dic5 | — | 2 | 2 | no | — |
| 206 | D5×Dic5 | — | 2 | 2 | no | — |
| 207 | D5×Dic5 | — | 2 | 2 | no | — |
| 208 | D5×Dic5 | C22⋊C4 | 1 | 2 | yes | — |
| 209 | D5×Dic5 | C22⋊C4 | 1 | 2 | yes | — |
| 210 | D5×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 211 | D5×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 212 | #6034 | — | 2 | 2 | no | — |
| 213 | #6033 | — | 2 | 2 | no | — |
| 214 | C23×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 215 | C2×C5×#41 | — | 5 | 2 | no | — |
| 216 | D5×#41 | — | 5 | 2 | no | — |
| 217 | D5×#41 | — | 5 | 2 | no | — |
| 218 | D5×#41 | — | 5 | 2 | no | — |
| 219 | D5×#41 | — | 5 | 2 | no | — |
| 220 | D5×#41 | — | 5 | 2 | no | — |
| 221 | D5×#41 | — | 5 | 2 | no | — |
| 222 | D5×#41 | — | 5 | 2 | no | — |
| 223 | D5×#41 | — | 10 | 2 | no | — |
| 224 | D5×#41 | — | 10 | 2 | no | — |
| 225 | D5×#41 | — | 10 | 2 | no | — |
| 226 | D5×#41 | — | 10 | 2 | no | — |
| 227 | D5×#41 | — | 10 | 2 | no | — |
| 228 | D5×#41 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 229 | C2×#713 | — | 5 | 2 | no | — |
| 230 | C2×Q8×D5 | — | 5 | 2 | no | — |
| 231 | C2×#711 | — | 5 | 2 | no | — |
| 232 | C2×#711 | — | 10 | 2 | no | — |
| 233 | C2×D4×D5 | — | 5 | 2 | no | — |
| 234 | C2×D4×D5 | — | 10 | 2 | no | — |
| 235 | C2×#709 | — | 5 | 2 | no | — |
| 236 | C2×#709 | — | 10 | 2 | no | — |
| 237 | C22×C4×D5 | — | 5 | 2 | no | — |
| 238 | C22×C4×D5 | — | 10 | 2 | no | — |
| 239 | C2×#704 | — | 10 | 2 | no | — |
| 240 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 241 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 242 | C2×C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 243 | C2×C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 244 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 245 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 246 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 247 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 248 | D5⋊M16 | — | 5 | 2 | no | — |
| 249 | D5⋊M16 | — | 5 | 2 | no | — |
| 250 | D5⋊M16 | — | 5 | 4 | no | — |
| 251 | D5⋊M16 | — | 10 | 2 | no | — |
| 252 | D5⋊M16 | — | 10 | 2 | no | — |
| 253 | D5⋊M16 | — | 10 | 2 | no | — |
| 254 | C2×#700 | — | 5 | 4 | no | — |
| 255 | C2×D5⋊C8 | — | 10 | 2 | no | — |
| 256 | #4010 | — | 5 | 4 | no | — |
| 257 | #4010 | — | 5 | 4 | no | — |
| 258 | #4010 | — | 5 | 4 | no | — |
| 259 | #4010 | — | 5 | 4 | no | — |
| 260 | #4010 | — | 10 | 4 | no | — |
| 261 | #4008 | — | 5 | 4 | no | — |
| 262 | #4008 | — | 5 | 4 | no | — |
| 263 | #4008 | — | 5 | 4 | no | — |
| 264 | #4008 | — | 5 | 4 | no | — |
| 265 | #4008 | — | 10 | 4 | no | — |
| 266 | C22×#104 | — | 25 | 1 | no | Sylow |
| 267 | C22×C52 | — | 2 | 1 | no | — |
| 268 | C22×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 269 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 270 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 271 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 272 | C2×C5⋊D5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 273 | C2×C5⋊D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 274 | C2×C5×D5 | — | 2 | 4 | no | — |
| 275 | C2×C5×D5 | — | 2 | 2 | no | — |
| 276 | C2×C5×D5 | — | 4 | 4 | no | — |
| 277 | C2×C5×D5 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 278 | C2×C5×D5 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 279 | D52 | — | 2 | 4 | no | — |
| 280 | D52 | — | 2 | 2 | no | — |
| 281 | D52 | — | 4 | 4 | no | — |
| 282 | D52 | — | 4 | 2 | no | — |
| 283 | D52 | #104 | 1 | 4 | yes | complemented |
| 284 | #1044 | — | 2 | 4 | no | — |
| 285 | #1043 | — | 2 | 4 | no | — |
| 286 | C4×C52 | — | 2 | 1 | no | — |
| 287 | C4×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 288 | C4×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 289 | #1039 | — | 2 | 1 | no | — |
| 290 | #1039 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 291 | #1039 | C22×D4 | 1 | 1 | yes | characteristic |
| 292 | C5×Dic5 | — | 2 | 2 | no | — |
| 293 | C5×Dic5 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 294 | C5×Dic5 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 295 | C23×D5 | — | 5 | 2 | no | — |
| 296 | C23×D5 | — | 10 | 2 | no | — |
| 297 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 298 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 299 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 300 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 301 | C22×AGL(1,𝔽5) | — | 10 | 16 | no | — |
| 302 | C22×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 303 | C5×#41 | — | 2 | 2 | no | — |
| 304 | C5×#41 | — | 5 | 2 | no | — |
| 305 | C5×#41 | — | 5 | 2 | no | — |
| 306 | C5×#41 | — | 5 | 2 | no | — |
| 307 | C5×#41 | — | 10 | 2 | no | — |
| 308 | C5×#41 | — | 10 | 2 | no | — |
| 309 | C5×#41 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 310 | C2×C5×Q8 | — | 5 | 2 | no | — |
| 311 | C2×C5×D4 | — | 5 | 2 | no | — |
| 312 | C2×C5×D4 | — | 10 | 2 | no | — |
| 313 | C22×C4×C5 | — | 5 | 2 | no | — |
| 314 | C22×C4×C5 | — | 10 | 2 | no | — |
| 315 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 316 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 317 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 318 | C22×Dic5 | — | 5 | 2 | no | — |
| 319 | C22×Dic5 | — | 10 | 2 | no | — |
| 320 | #713 | — | 5 | 2 | no | — |
| 321 | #713 | — | 5 | 2 | no | — |
| 322 | #713 | — | 5 | 2 | no | — |
| 323 | #713 | — | 10 | 2 | no | — |
| 324 | #713 | — | 10 | 2 | no | — |
| 325 | #713 | — | 10 | 2 | no | — |
| 326 | #713 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 327 | Q8×D5 | — | 5 | 2 | no | — |
| 328 | Q8×D5 | — | 5 | 2 | no | — |
| 329 | Q8×D5 | — | 5 | 2 | no | — |
| 330 | Q8×D5 | — | 10 | 2 | no | — |
| 331 | Q8×D5 | — | 10 | 2 | no | — |
| 332 | Q8×D5 | — | 10 | 2 | no | — |
| 333 | Q8×D5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 334 | #711 | — | 2 | 2 | no | — |
| 335 | #711 | — | 5 | 2 | no | — |
| 336 | #711 | — | 5 | 2 | no | — |
| 337 | #711 | — | 5 | 2 | no | — |
| 338 | #711 | — | 10 | 2 | no | — |
| 339 | #711 | — | 10 | 2 | no | — |
| 340 | #711 | — | 10 | 2 | no | — |
| 341 | #711 | — | 10 | 2 | no | — |
| 342 | #711 | — | 10 | 2 | no | — |
| 343 | #711 | — | 10 | 2 | no | — |
| 344 | #711 | — | 10 | 2 | no | — |
| 345 | #711 | — | 10 | 2 | no | — |
| 346 | #711 | — | 10 | 2 | no | — |
| 347 | #711 | — | 10 | 2 | no | — |
| 348 | #711 | — | 20 | 2 | no | — |
| 349 | #711 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 350 | D4×D5 | — | 2 | 2 | no | — |
| 351 | D4×D5 | — | 5 | 2 | no | — |
| 352 | D4×D5 | — | 5 | 2 | no | — |
| 353 | D4×D5 | — | 5 | 2 | no | — |
| 354 | D4×D5 | — | 10 | 2 | no | — |
| 355 | D4×D5 | — | 10 | 2 | no | — |
| 356 | D4×D5 | — | 10 | 2 | no | — |
| 357 | D4×D5 | — | 10 | 2 | no | — |
| 358 | D4×D5 | — | 10 | 2 | no | — |
| 359 | D4×D5 | — | 10 | 2 | no | — |
| 360 | D4×D5 | — | 10 | 2 | no | — |
| 361 | D4×D5 | — | 10 | 2 | no | — |
| 362 | D4×D5 | — | 10 | 2 | no | — |
| 363 | D4×D5 | — | 10 | 2 | no | — |
| 364 | D4×D5 | — | 20 | 2 | no | — |
| 365 | D4×D5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 366 | #709 | — | 2 | 2 | no | — |
| 367 | #709 | — | 5 | 2 | no | — |
| 368 | #709 | — | 5 | 2 | no | — |
| 369 | #709 | — | 5 | 2 | no | — |
| 370 | #709 | — | 10 | 2 | no | — |
| 371 | #709 | — | 10 | 2 | no | — |
| 372 | #709 | — | 10 | 2 | no | — |
| 373 | #709 | — | 10 | 2 | no | — |
| 374 | #709 | — | 10 | 2 | no | — |
| 375 | #709 | — | 10 | 2 | no | — |
| 376 | #709 | — | 10 | 2 | no | — |
| 377 | #709 | — | 10 | 2 | no | — |
| 378 | #709 | — | 10 | 2 | no | — |
| 379 | #709 | — | 10 | 2 | no | — |
| 380 | #709 | — | 20 | 2 | no | — |
| 381 | #709 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 382 | C2×D20 | — | 5 | 2 | no | — |
| 383 | C2×D20 | — | 10 | 2 | no | — |
| 384 | C2×C4×D5 | — | 2 | 2 | no | — |
| 385 | C2×C4×D5 | — | 5 | 2 | no | — |
| 386 | C2×C4×D5 | — | 5 | 2 | no | — |
| 387 | C2×C4×D5 | — | 5 | 2 | no | — |
| 388 | C2×C4×D5 | — | 5 | 2 | no | — |
| 389 | C2×C4×D5 | — | 5 | 2 | no | — |
| 390 | C2×C4×D5 | — | 5 | 2 | no | — |
| 391 | C2×C4×D5 | — | 5 | 2 | no | — |
| 392 | C2×C4×D5 | — | 5 | 2 | no | — |
| 393 | C2×C4×D5 | — | 5 | 2 | no | — |
| 394 | C2×C4×D5 | — | 5 | 2 | no | — |
| 395 | C2×C4×D5 | — | 5 | 2 | no | — |
| 396 | C2×C4×D5 | — | 10 | 2 | no | — |
| 397 | C2×C4×D5 | — | 10 | 2 | no | — |
| 398 | C2×C4×D5 | — | 10 | 2 | no | — |
| 399 | C2×C4×D5 | — | 10 | 2 | no | — |
| 400 | C2×C4×D5 | — | 10 | 2 | no | — |
| 401 | C2×C4×D5 | — | 10 | 2 | no | — |
| 402 | C2×C4×D5 | — | 10 | 2 | no | — |
| 403 | C2×C4×D5 | — | 10 | 2 | no | — |
| 404 | C2×C4×D5 | — | 10 | 2 | no | — |
| 405 | C2×C4×D5 | — | 10 | 2 | no | — |
| 406 | C2×C4×D5 | — | 10 | 2 | no | — |
| 407 | C2×C4×D5 | — | 20 | 2 | no | — |
| 408 | C2×C4×D5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 409 | C2×Dic10 | — | 5 | 2 | no | — |
| 410 | C2×Dic10 | — | 10 | 2 | no | — |
| 411 | #704 | — | 10 | 4 | no | — |
| 412 | #704 | — | 10 | 2 | no | — |
| 413 | #704 | — | 10 | 2 | no | — |
| 414 | #704 | — | 20 | 2 | no | — |
| 415 | C2×#170 | — | 10 | 4 | no | — |
| 416 | C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 417 | C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 418 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 419 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 420 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 421 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 422 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 423 | C4×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 424 | #700 | — | 5 | 4 | no | — |
| 425 | #700 | — | 5 | 4 | no | — |
| 426 | #700 | — | 10 | 4 | no | — |
| 427 | #700 | — | 10 | 4 | no | — |
| 428 | D5⋊C8 | — | 10 | 4 | no | — |
| 429 | D5⋊C8 | — | 10 | 2 | no | — |
| 430 | D5⋊C8 | — | 10 | 2 | no | — |
| 431 | D5⋊C8 | — | 20 | 2 | no | — |
| 432 | C22×#41 | — | 25 | 1 | no | — |
| 433 | C22×M16 | — | 25 | 1 | no | — |
| 434 | C22×C42 | — | 25 | 1 | no | — |
| 435 | C2×#104 | — | 25 | 1 | no | — |
| 436 | C2×#104 | — | 25 | 1 | no | — |
| 437 | C2×#104 | — | 25 | 1 | no | — |
| 438 | C2×#104 | — | 25 | 1 | no | — |
| 439 | C2×#104 | — | 25 | 4 | no | — |
| 440 | C2×#104 | — | 25 | 4 | no | — |
| 441 | C2×C52 | — | 2 | 1 | no | — |
| 442 | C2×C52 | — | 4 | 1 | no | — |
| 443 | C2×C52 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 444 | C5⋊D5 | — | 2 | 1 | no | — |
| 445 | C5⋊D5 | — | 4 | 1 | no | — |
| 446 | C5⋊D5 | C2×#104 | 1 | 2 | yes | complemented |
| 447 | C5×D5 | — | 2 | 2 | no | — |
| 448 | C5×D5 | — | 4 | 2 | no | — |
| 449 | C5×D5 | C2×#104 | 1 | 4 | yes | complemented |
| 450 | C23×C5 | — | 5 | 2 | no | — |
| 451 | C23×C5 | — | 10 | 2 | no | — |
| 452 | C22×D5 | — | 2 | 2 | no | — |
| 453 | C22×D5 | — | 5 | 2 | no | — |
| 454 | C22×D5 | — | 5 | 2 | no | — |
| 455 | C22×D5 | — | 5 | 2 | no | — |
| 456 | C22×D5 | — | 5 | 2 | no | — |
| 457 | C22×D5 | — | 5 | 2 | no | — |
| 458 | C22×D5 | — | 10 | 2 | no | — |
| 459 | C22×D5 | — | 10 | 8 | no | — |
| 460 | C22×D5 | — | 10 | 2 | no | — |
| 461 | C22×D5 | — | 10 | 2 | no | — |
| 462 | C22×D5 | — | 10 | 2 | no | — |
| 463 | C22×D5 | — | 10 | 2 | no | — |
| 464 | C22×D5 | — | 20 | 2 | no | — |
| 465 | C22×D5 | — | 20 | 8 | no | — |
| 466 | C22×D5 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 467 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 468 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 469 | C2×AGL(1,𝔽5) | — | 10 | 16 | no | — |
| 470 | C2×AGL(1,𝔽5) | — | 10 | 16 | no | — |
| 471 | C2×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 472 | C2×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 473 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 474 | C2×AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 475 | C5×Q8 | — | 2 | 2 | no | — |
| 476 | C5×Q8 | — | 5 | 2 | no | — |
| 477 | C5×Q8 | — | 10 | 2 | no | — |
| 478 | C5×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 479 | C5×D4 | — | 2 | 2 | no | — |
| 480 | C5×D4 | — | 2 | 2 | no | — |
| 481 | C5×D4 | — | 4 | 2 | no | — |
| 482 | C5×D4 | — | 5 | 2 | no | — |
| 483 | C5×D4 | — | 10 | 2 | no | — |
| 484 | C5×D4 | — | 10 | 2 | no | — |
| 485 | C5×D4 | — | 10 | 2 | no | — |
| 486 | C5×D4 | — | 10 | 2 | no | — |
| 487 | C5×D4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 488 | C2×C4×C5 | — | 2 | 2 | no | — |
| 489 | C2×C4×C5 | — | 2 | 2 | no | — |
| 490 | C2×C4×C5 | — | 4 | 2 | no | — |
| 491 | C2×C4×C5 | — | 5 | 2 | no | — |
| 492 | C2×C4×C5 | — | 5 | 2 | no | — |
| 493 | C2×C4×C5 | — | 5 | 2 | no | — |
| 494 | C2×C4×C5 | — | 5 | 2 | no | — |
| 495 | C2×C4×C5 | — | 5 | 2 | no | — |
| 496 | C2×C4×C5 | — | 10 | 2 | no | — |
| 497 | C2×C4×C5 | — | 10 | 2 | no | — |
| 498 | C2×C4×C5 | — | 10 | 2 | no | — |
| 499 | C2×C4×C5 | — | 10 | 2 | no | — |
| 500 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 501 | C22⋊D5 | — | 2 | 2 | no | — |
| 502 | C22⋊D5 | — | 2 | 2 | no | — |
| 503 | C22⋊D5 | — | 2 | 2 | no | — |
| 504 | C22⋊D5 | — | 10 | 2 | no | — |
| 505 | C22⋊D5 | — | 10 | 2 | no | — |
| 506 | C22⋊D5 | — | 10 | 2 | no | — |
| 507 | C22⋊D5 | — | 10 | 2 | no | — |
| 508 | C22⋊D5 | — | 10 | 2 | no | — |
| 509 | C22⋊D5 | — | 10 | 2 | no | — |
| 510 | C22⋊D5 | — | 10 | 2 | no | — |
| 511 | C22⋊D5 | — | 10 | 2 | no | — |
| 512 | C22⋊D5 | — | 10 | 2 | no | — |
| 513 | C22⋊D5 | — | 20 | 2 | no | — |
| 514 | C22⋊D5 | — | 20 | 2 | no | — |
| 515 | C22⋊D5 | — | 20 | 2 | no | — |
| 516 | C2×Dic5 | — | 2 | 2 | no | — |
| 517 | C2×Dic5 | — | 5 | 2 | no | — |
| 518 | C2×Dic5 | — | 5 | 2 | no | — |
| 519 | C2×Dic5 | — | 5 | 2 | no | — |
| 520 | C2×Dic5 | — | 5 | 2 | no | — |
| 521 | C2×Dic5 | — | 5 | 2 | no | — |
| 522 | C2×Dic5 | — | 10 | 2 | no | — |
| 523 | C2×Dic5 | — | 10 | 2 | no | — |
| 524 | C2×Dic5 | — | 10 | 2 | no | — |
| 525 | C2×Dic5 | — | 10 | 2 | no | — |
| 526 | C2×Dic5 | — | 10 | 2 | no | — |
| 527 | C2×Dic5 | — | 20 | 2 | no | — |
| 528 | C2×Dic5 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 529 | D20 | — | 2 | 2 | no | — |
| 530 | D20 | — | 5 | 2 | no | — |
| 531 | D20 | — | 10 | 2 | no | — |
| 532 | D20 | — | 10 | 2 | no | — |
| 533 | D20 | — | 10 | 2 | no | — |
| 534 | D20 | — | 10 | 2 | no | — |
| 535 | D20 | — | 10 | 2 | no | — |
| 536 | D20 | — | 20 | 2 | no | — |
| 537 | D20 | C22×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 538 | C4×D5 | — | 2 | 2 | no | — |
| 539 | C4×D5 | — | 2 | 2 | no | — |
| 540 | C4×D5 | — | 2 | 2 | no | — |
| 541 | C4×D5 | — | 5 | 2 | no | — |
| 542 | C4×D5 | — | 5 | 2 | no | — |
| 543 | C4×D5 | — | 5 | 2 | no | — |
| 544 | C4×D5 | — | 5 | 2 | no | — |
| 545 | C4×D5 | — | 5 | 2 | no | — |
| 546 | C4×D5 | — | 5 | 2 | no | — |
| 547 | C4×D5 | — | 5 | 2 | no | — |
| 548 | C4×D5 | — | 5 | 2 | no | — |
| 549 | C4×D5 | — | 5 | 2 | no | — |
| 550 | C4×D5 | — | 5 | 2 | no | — |
| 551 | C4×D5 | — | 5 | 2 | no | — |
| 552 | C4×D5 | — | 5 | 2 | no | — |
| 553 | C4×D5 | — | 10 | 2 | no | — |
| 554 | C4×D5 | — | 10 | 2 | no | — |
| 555 | C4×D5 | — | 10 | 2 | no | — |
| 556 | C4×D5 | — | 10 | 2 | no | — |
| 557 | C4×D5 | — | 10 | 2 | no | — |
| 558 | C4×D5 | — | 10 | 2 | no | — |
| 559 | C4×D5 | — | 10 | 2 | no | — |
| 560 | C4×D5 | — | 10 | 2 | no | — |
| 561 | C4×D5 | — | 10 | 2 | no | — |
| 562 | C4×D5 | — | 10 | 2 | no | — |
| 563 | C4×D5 | — | 10 | 2 | no | — |
| 564 | C4×D5 | — | 10 | 2 | no | — |
| 565 | C4×D5 | — | 10 | 2 | no | — |
| 566 | C4×D5 | — | 20 | 2 | no | — |
| 567 | C4×D5 | — | 20 | 2 | no | — |
| 568 | C4×D5 | — | 20 | 2 | no | — |
| 569 | C4×D5 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 570 | C4×D5 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 571 | C4×D5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 572 | C4×D5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 573 | Dic10 | — | 2 | 2 | no | — |
| 574 | Dic10 | — | 5 | 2 | no | — |
| 575 | Dic10 | — | 10 | 2 | no | — |
| 576 | Dic10 | — | 10 | 2 | no | — |
| 577 | Dic10 | — | 10 | 2 | no | — |
| 578 | Dic10 | — | 10 | 2 | no | — |
| 579 | Dic10 | — | 10 | 2 | no | — |
| 580 | Dic10 | — | 20 | 2 | no | — |
| 581 | Dic10 | C22×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 582 | #170 | — | 10 | 4 | no | — |
| 583 | #170 | — | 10 | 4 | no | — |
| 584 | #170 | — | 20 | 4 | no | — |
| 585 | C2×#41 | — | 5 | 2 | no | — |
| 586 | C2×#41 | — | 25 | 2 | no | — |
| 587 | C2×#41 | — | 25 | 2 | no | — |
| 588 | C2×#41 | — | 25 | 2 | no | — |
| 589 | C2×#41 | — | 25 | 1 | no | — |
| 590 | C2×#41 | — | 25 | 1 | no | — |
| 591 | C2×#41 | — | 25 | 1 | no | — |
| 592 | C2×#41 | — | 25 | 1 | no | — |
| 593 | C2×#41 | — | 50 | 2 | no | — |
| 594 | C2×#41 | — | 50 | 2 | no | — |
| 595 | C2×#41 | — | 50 | 1 | no | — |
| 596 | C2×#41 | — | 50 | 1 | no | — |
| 597 | C22×Q8 | — | 25 | 1 | no | — |
| 598 | C22×D4 | — | 25 | 1 | no | — |
| 599 | C22×D4 | — | 50 | 1 | no | — |
| 600 | C23×C4 | — | 25 | 1 | no | — |
| 601 | C23×C4 | — | 50 | 1 | no | — |
| 602 | C23×C4 | — | 50 | 1 | no | — |
| 603 | C2×M16 | — | 25 | 4 | no | — |
| 604 | C2×M16 | — | 25 | 1 | no | — |
| 605 | C2×M16 | — | 25 | 1 | no | — |
| 606 | C2×M16 | — | 50 | 1 | no | — |
| 607 | C2×M16 | — | 50 | 2 | no | — |
| 608 | C22×C8 | — | 50 | 1 | no | — |
| 609 | C2×C42 | — | 25 | 1 | no | — |
| 610 | C2×C42 | — | 25 | 1 | no | — |
| 611 | C2×C42 | — | 25 | 4 | no | — |
| 612 | C2×C42 | — | 50 | 1 | no | — |
| 613 | C2×C42 | — | 50 | 2 | no | — |
| 614 | #104 | — | 25 | 2 | no | — |
| 615 | #104 | — | 25 | 2 | no | — |
| 616 | #104 | — | 25 | 4 | no | — |
| 617 | #104 | — | 25 | 4 | no | — |
| 618 | #104 | — | 25 | 2 | no | — |
| 619 | #104 | — | 25 | 2 | no | — |
| 620 | C52 | C22×#104 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 621 | C22×C5 | — | 2 | 2 | no | — |
| 622 | C22×C5 | — | 2 | 2 | no | — |
| 623 | C22×C5 | — | 4 | 2 | no | — |
| 624 | C22×C5 | — | 5 | 2 | no | — |
| 625 | C22×C5 | — | 5 | 2 | no | — |
| 626 | C22×C5 | — | 10 | 4 | no | — |
| 627 | C22×C5 | — | 10 | 2 | no | — |
| 628 | C22×C5 | — | 20 | 4 | no | — |
| 629 | C22×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 630 | C2×D5 | — | 2 | 4 | no | — |
| 631 | C2×D5 | — | 2 | 2 | no | — |
| 632 | C2×D5 | — | 4 | 4 | no | — |
| 633 | C2×D5 | — | 5 | 2 | no | — |
| 634 | C2×D5 | — | 5 | 8 | no | — |
| 635 | C2×D5 | — | 5 | 2 | no | — |
| 636 | C2×D5 | — | 10 | 2 | no | — |
| 637 | C2×D5 | — | 10 | 2 | no | — |
| 638 | C2×D5 | — | 10 | 4 | no | — |
| 639 | C2×D5 | — | 10 | 4 | no | — |
| 640 | C2×D5 | — | 10 | 4 | no | — |
| 641 | C2×D5 | — | 10 | 4 | no | — |
| 642 | C2×D5 | — | 10 | 2 | no | — |
| 643 | C2×D5 | — | 20 | 4 | no | — |
| 644 | C2×D5 | — | 20 | 2 | no | — |
| 645 | C2×D5 | — | 20 | 4 | no | — |
| 646 | C2×D5 | — | 20 | 4 | no | — |
| 647 | C2×D5 | — | 20 | 4 | no | — |
| 648 | C2×D5 | — | 20 | 4 | no | — |
| 649 | C2×D5 | — | 40 | 4 | no | — |
| 650 | C2×D5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 651 | C2×D5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 652 | AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 653 | AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 654 | AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 655 | C4×C5 | — | 2 | 2 | no | — |
| 656 | C4×C5 | — | 2 | 2 | no | — |
| 657 | C4×C5 | — | 2 | 2 | no | — |
| 658 | C4×C5 | — | 4 | 2 | no | — |
| 659 | C4×C5 | — | 5 | 2 | no | — |
| 660 | C4×C5 | — | 5 | 2 | no | — |
| 661 | C4×C5 | — | 10 | 2 | no | — |
| 662 | C4×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 663 | C4×C5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 664 | Dic5 | — | 2 | 2 | no | — |
| 665 | Dic5 | — | 5 | 2 | no | — |
| 666 | Dic5 | — | 5 | 2 | no | — |
| 667 | Dic5 | — | 10 | 2 | no | — |
| 668 | Dic5 | — | 10 | 2 | no | — |
| 669 | Dic5 | — | 10 | 2 | no | — |
| 670 | Dic5 | — | 20 | 2 | no | — |
| 671 | Dic5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 672 | Dic5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 673 | C24 | — | 25 | 1 | no | — |
| 674 | C24 | — | 50 | 1 | no | — |
| 675 | #41 | — | 5 | 2 | no | — |
| 676 | #41 | — | 5 | 2 | no | — |
| 677 | #41 | — | 5 | 2 | no | — |
| 678 | #41 | — | 10 | 2 | no | — |
| 679 | #41 | — | 10 | 2 | no | — |
| 680 | #41 | — | 25 | 2 | no | — |
| 681 | #41 | — | 25 | 2 | no | — |
| 682 | #41 | — | 25 | 2 | no | — |
| 683 | #41 | — | 25 | 1 | no | — |
| 684 | #41 | — | 25 | 1 | no | — |
| 685 | #41 | — | 25 | 1 | no | — |
| 686 | #41 | — | 50 | 1 | no | — |
| 687 | #41 | — | 50 | 2 | no | — |
| 688 | #41 | — | 50 | 2 | no | — |
| 689 | #41 | — | 50 | 1 | no | — |
| 690 | #41 | — | 50 | 2 | no | — |
| 691 | #41 | — | 50 | 2 | no | — |
| 692 | #41 | — | 50 | 2 | no | — |
| 693 | #41 | — | 50 | 2 | no | — |
| 694 | #41 | — | 50 | 1 | no | — |
| 695 | #41 | — | 50 | 2 | no | — |
| 696 | #41 | — | 50 | 1 | no | — |
| 697 | #41 | — | 50 | 2 | no | — |
| 698 | #41 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 699 | C2×Q8 | — | 5 | 2 | no | — |
| 700 | C2×Q8 | — | 25 | 2 | no | — |
| 701 | C2×Q8 | — | 25 | 1 | no | — |
| 702 | C2×Q8 | — | 25 | 1 | no | — |
| 703 | C2×Q8 | — | 50 | 2 | no | — |
| 704 | C2×Q8 | — | 50 | 1 | no | — |
| 705 | C2×D4 | — | 5 | 2 | no | — |
| 706 | C2×D4 | — | 10 | 2 | no | — |
| 707 | C2×D4 | — | 25 | 2 | no | — |
| 708 | C2×D4 | — | 25 | 1 | no | — |
| 709 | C2×D4 | — | 25 | 1 | no | — |
| 710 | C2×D4 | — | 50 | 2 | no | — |
| 711 | C2×D4 | — | 50 | 1 | no | — |
| 712 | C2×D4 | — | 50 | 2 | no | — |
| 713 | C2×D4 | — | 50 | 1 | no | — |
| 714 | C2×D4 | — | 50 | 1 | no | — |
| 715 | C2×D4 | — | 50 | 1 | no | — |
| 716 | C2×D4 | — | 50 | 1 | no | — |
| 717 | C2×D4 | — | 50 | 2 | no | — |
| 718 | C2×D4 | — | 50 | 2 | no | — |
| 719 | C22×C4 | — | 5 | 2 | no | — |
| 720 | C22×C4 | — | 10 | 2 | no | — |
| 721 | C22×C4 | — | 25 | 2 | no | — |
| 722 | C22×C4 | — | 25 | 1 | no | — |
| 723 | C22×C4 | — | 25 | 2 | no | — |
| 724 | C22×C4 | — | 25 | 1 | no | — |
| 725 | C22×C4 | — | 25 | 1 | no | — |
| 726 | C22×C4 | — | 25 | 1 | no | — |
| 727 | C22×C4 | — | 25 | 1 | no | — |
| 728 | C22×C4 | — | 25 | 2 | no | — |
| 729 | C22×C4 | — | 25 | 1 | no | — |
| 730 | C22×C4 | — | 50 | 1 | no | — |
| 731 | C22×C4 | — | 50 | 2 | no | — |
| 732 | C22×C4 | — | 50 | 1 | no | — |
| 733 | C22×C4 | — | 50 | 2 | no | — |
| 734 | C22×C4 | — | 50 | 1 | no | — |
| 735 | C22×C4 | — | 50 | 1 | no | — |
| 736 | C22×C4 | — | 50 | 1 | no | — |
| 737 | C22×C4 | — | 50 | 2 | no | — |
| 738 | C22×C4 | — | 50 | 1 | no | — |
| 739 | C22×C4 | — | 50 | 4 | no | — |
| 740 | C22×C4 | — | 50 | 1 | no | — |
| 741 | C22×C4 | — | 50 | 8 | no | — |
| 742 | M16 | — | 25 | 2 | no | — |
| 743 | M16 | — | 25 | 2 | no | — |
| 744 | M16 | — | 50 | 4 | no | — |
| 745 | M16 | — | 50 | 1 | no | — |
| 746 | M16 | — | 50 | 1 | no | — |
| 747 | C2×C8 | — | 50 | 1 | no | — |
| 748 | C2×C8 | — | 50 | 1 | no | — |
| 749 | C2×C8 | — | 50 | 4 | no | — |
| 750 | C42 | — | 25 | 2 | no | — |
| 751 | C42 | — | 25 | 2 | no | — |
| 752 | C42 | — | 50 | 4 | no | — |
| 753 | C42 | — | 50 | 1 | no | — |
| 754 | C42 | — | 50 | 1 | no | — |
| 755 | C2×C5 | — | 2 | 2 | no | — |
| 756 | C2×C5 | — | 2 | 2 | no | — |
| 757 | C2×C5 | — | 4 | 2 | no | — |
| 758 | C2×C5 | — | 4 | 2 | no | — |
| 759 | C2×C5 | — | 5 | 4 | no | — |
| 760 | C2×C5 | — | 8 | 2 | no | — |
| 761 | C2×C5 | — | 10 | 2 | no | — |
| 762 | C2×C5 | — | 20 | 2 | no | — |
| 763 | C2×C5 | C22×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 764 | D5 | — | 2 | 2 | no | — |
| 765 | D5 | — | 4 | 2 | no | — |
| 766 | D5 | — | 5 | 4 | no | — |
| 767 | D5 | — | 10 | 4 | no | — |
| 768 | D5 | — | 10 | 2 | no | — |
| 769 | D5 | — | 20 | 2 | no | — |
| 770 | D5 | — | 20 | 2 | no | — |
| 771 | D5 | — | 40 | 2 | no | — |
| 772 | D5 | D5⋊#104 | 1 | 4 | yes | complemented |
| 773 | C23 | — | 5 | 2 | no | — |
| 774 | C23 | — | 10 | 2 | no | — |
| 775 | C23 | — | 25 | 1 | no | — |
| 776 | C23 | — | 25 | 2 | no | — |
| 777 | C23 | — | 25 | 1 | no | — |
| 778 | C23 | — | 25 | 1 | no | — |
| 779 | C23 | — | 50 | 1 | no | — |
| 780 | C23 | — | 50 | 2 | no | — |
| 781 | C23 | — | 50 | 4 | no | — |
| 782 | C23 | — | 50 | 1 | no | — |
| 783 | C23 | — | 100 | 4 | no | — |
| 784 | Q8 | — | 5 | 2 | no | — |
| 785 | Q8 | — | 10 | 2 | no | — |
| 786 | Q8 | — | 25 | 1 | no | — |
| 787 | Q8 | — | 50 | 1 | no | — |
| 788 | Q8 | — | 50 | 2 | no | — |
| 789 | Q8 | — | 50 | 1 | no | — |
| 790 | Q8 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 791 | D4 | — | 2 | 1 | no | — |
| 792 | D4 | — | 5 | 2 | no | — |
| 793 | D4 | — | 10 | 2 | no | — |
| 794 | D4 | — | 10 | 2 | no | — |
| 795 | D4 | — | 10 | 2 | no | — |
| 796 | D4 | — | 10 | 2 | no | — |
| 797 | D4 | — | 25 | 1 | no | — |
| 798 | D4 | — | 50 | 1 | no | — |
| 799 | D4 | — | 50 | 2 | no | — |
| 800 | D4 | — | 50 | 2 | no | — |
| 801 | D4 | — | 50 | 2 | no | — |
| 802 | D4 | — | 50 | 1 | no | — |
| 803 | D4 | — | 50 | 1 | no | — |
| 804 | D4 | — | 50 | 1 | no | — |
| 805 | D4 | — | 50 | 2 | no | — |
| 806 | D4 | — | 50 | 1 | no | — |
| 807 | D4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 808 | C2×C4 | — | 2 | 1 | no | — |
| 809 | C2×C4 | — | 5 | 2 | no | — |
| 810 | C2×C4 | — | 5 | 2 | no | — |
| 811 | C2×C4 | — | 5 | 2 | no | — |
| 812 | C2×C4 | — | 5 | 2 | no | — |
| 813 | C2×C4 | — | 5 | 2 | no | — |
| 814 | C2×C4 | — | 10 | 2 | no | — |
| 815 | C2×C4 | — | 10 | 2 | no | — |
| 816 | C2×C4 | — | 10 | 2 | no | — |
| 817 | C2×C4 | — | 10 | 2 | no | — |
| 818 | C2×C4 | — | 25 | 2 | no | — |
| 819 | C2×C4 | — | 25 | 1 | no | — |
| 820 | C2×C4 | — | 25 | 1 | no | — |
| 821 | C2×C4 | — | 25 | 2 | no | — |
| 822 | C2×C4 | — | 25 | 2 | no | — |
| 823 | C2×C4 | — | 25 | 2 | no | — |
| 824 | C2×C4 | — | 25 | 2 | no | — |
| 825 | C2×C4 | — | 25 | 1 | no | — |
| 826 | C2×C4 | — | 25 | 1 | no | — |
| 827 | C2×C4 | — | 25 | 1 | no | — |
| 828 | C2×C4 | — | 25 | 1 | no | — |
| 829 | C2×C4 | — | 25 | 1 | no | — |
| 830 | C2×C4 | — | 50 | 1 | no | — |
| 831 | C2×C4 | — | 50 | 1 | no | — |
| 832 | C2×C4 | — | 50 | 2 | no | — |
| 833 | C2×C4 | — | 50 | 2 | no | — |
| 834 | C2×C4 | — | 50 | 1 | no | — |
| 835 | C2×C4 | — | 50 | 2 | no | — |
| 836 | C2×C4 | — | 50 | 2 | no | — |
| 837 | C2×C4 | — | 50 | 1 | no | — |
| 838 | C2×C4 | — | 50 | 2 | no | — |
| 839 | C2×C4 | — | 50 | 2 | no | — |
| 840 | C2×C4 | — | 50 | 4 | no | — |
| 841 | C2×C4 | — | 50 | 16 | no | — |
| 842 | C2×C4 | — | 50 | 4 | no | — |
| 843 | C2×C4 | — | 50 | 1 | no | — |
| 844 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 845 | C8 | — | 50 | 2 | no | — |
| 846 | C8 | — | 50 | 2 | no | — |
| 847 | C5 | — | 2 | 2 | no | — |
| 848 | C5 | C2×D5⋊#104 | 1 | 2 | yes | complemented |
| 849 | C22 | — | 2 | 1 | no | — |
| 850 | C22 | — | 5 | 2 | no | — |
| 851 | C22 | — | 5 | 2 | no | — |
| 852 | C22 | — | 10 | 4 | no | — |
| 853 | C22 | — | 10 | 2 | no | — |
| 854 | C22 | — | 20 | 4 | no | — |
| 855 | C22 | — | 25 | 4 | no | — |
| 856 | C22 | — | 25 | 1 | no | — |
| 857 | C22 | — | 25 | 1 | no | — |
| 858 | C22 | — | 50 | 2 | no | — |
| 859 | C22 | — | 50 | 4 | no | — |
| 860 | C22 | — | 50 | 2 | no | — |
| 861 | C22 | — | 50 | 1 | no | — |
| 862 | C22 | — | 100 | 2 | no | — |
| 863 | C22 | — | 100 | 4 | no | — |
| 864 | C22 | — | 100 | 2 | no | — |
| 865 | C22 | D5⋊(C22⋊AGL(1,𝔽5)) | 1 | 1 | yes | characteristic |
| 866 | C4 | — | 2 | 1 | no | — |
| 867 | C4 | — | 5 | 2 | no | — |
| 868 | C4 | — | 5 | 2 | no | — |
| 869 | C4 | — | 10 | 2 | no | — |
| 870 | C4 | — | 25 | 1 | no | — |
| 871 | C4 | — | 25 | 1 | no | — |
| 872 | C4 | — | 50 | 4 | no | — |
| 873 | C4 | — | 50 | 4 | no | — |
| 874 | C4 | — | 50 | 1 | no | — |
| 875 | C4 | D5⋊(C22⋊AGL(1,𝔽5)) | 1 | 1 | yes | characteristic |
| 876 | C4 | C22×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 877 | C2 | — | 2 | 1 | no | — |
| 878 | C2 | — | 4 | 1 | no | — |
| 879 | C2 | — | 5 | 4 | no | — |
| 880 | C2 | — | 10 | 2 | no | — |
| 881 | C2 | — | 20 | 2 | no | — |
| 882 | C2 | — | 25 | 2 | no | — |
| 883 | C2 | — | 50 | 1 | no | — |
| 884 | C2 | — | 100 | 1 | no | — |
| 885 | C2 | C2×D5⋊(C22⋊AGL(1,𝔽5)) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D5⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. D5⋊(D5⋊M16) | C2 | semidirect |
| 4. #13104930 | C2 | semidirect |
| 5. #13104804 | C2 | semidirect |
| 6. D5⋊#4010 | C2 | semidirect |
| 7. D5⋊#4008 | C2 | semidirect |
| 8. #13103946 | C2 | semidirect |
| 9. #13103942 | C2 | semidirect |
| 12. C5×D5×#41 | C4 | semidirect |
| 13. #11717484 | C4 | semidirect |
| 15. Q8×D52 | C4 | semidirect |
| 17. #11717477 | C4 | semidirect |
| 21. D4×D52 | C4 | semidirect |
| 25. D5×#709 | C4 | semidirect |
| 28. C2×C4×#1044 | C22 | semidirect |
| 29. #11717448 | C22 | semidirect |
| 30. C2×C4×#1043 | C22 | semidirect |
| 31. #11717435 | C22 | semidirect |
| 35. C4×D5⋊AGL(1,𝔽5) | C22 | semidirect |
| 37. D5⋊#700 | C22 | semidirect |
| 39. #11716903 | C22 | semidirect |
| 40. #11716901 | C22 | semidirect |
| 41. #11716878 | C22 | semidirect |
| 42. #11716876 | C22 | semidirect |
| 43. #11716770 | C22 | semidirect |
| 44. #11716769 | C22 | semidirect |
| 52. C52×#41 | C2×C4 | semidirect |
| 54. Q8×C5⋊D5 | C2×C4 | semidirect |
| 58. D4×C5⋊D5 | C2×C4 | semidirect |
| 60. #87900 | C2×C4 | semidirect |
| 63. C5×#713 | C2×C4 | semidirect |
| 64. C5×Q8×D5 | C2×C4 | semidirect |
| 66. C5×#711 | C2×C4 | semidirect |
| 68. C5×D4×D5 | C2×C4 | semidirect |
| 70. C5×#709 | C2×C4 | semidirect |
| 89. #87877 | C2×C4 | semidirect |
| 91. D5×D20 | C2×C4 | semidirect |
| 104. #87874 | C2×C4 | semidirect |
| 108. #87872 | C2×C4 | semidirect |
| 112. #87870 | C2×C4 | semidirect |
| 114. D5×Dic10 | C2×C4 | semidirect |
| 117. C4×#1044 | C23 | semidirect |
| 118. #87863 | C23 | semidirect |
| 122. C4×#1043 | C23 | semidirect |
| 123. #87856 | C23 | semidirect |
| 156. C52×Q8 | C22×C4 | semidirect |
| 158. C52×D4 | C22×C4 | semidirect |
| 167. C4⋊(C5⋊D5) | C22×C4 | semidirect |
| 176. #6045 | C22×C4 | semidirect |
| 183. C5×D20 | C22×C4 | semidirect |
| 192. C5×Dic10 | C22×C4 | semidirect |
| 228. D5×#41 | AGL(1,𝔽5) | semidirect |
| 283. D52 | #104 | semidirect |
| 309. C5×#41 | C2×AGL(1,𝔽5) | semidirect |
| 326. #713 | C2×AGL(1,𝔽5) | semidirect |
| 333. Q8×D5 | C2×AGL(1,𝔽5) | semidirect |
| 349. #711 | C2×AGL(1,𝔽5) | semidirect |
| 365. D4×D5 | C2×AGL(1,𝔽5) | semidirect |
| 381. #709 | C2×AGL(1,𝔽5) | semidirect |
| 446. C5⋊D5 | C2×#104 | semidirect |
| 449. C5×D5 | C2×#104 | semidirect |
| 478. C5×Q8 | C22×AGL(1,𝔽5) | semidirect |
| 487. C5×D4 | C22×AGL(1,𝔽5) | semidirect |
| 537. D20 | C22×AGL(1,𝔽5) | semidirect |
| 581. Dic10 | C22×AGL(1,𝔽5) | semidirect |
| 620. C52 | C22×#104 | semidirect |
| 698. #41 | D5⋊AGL(1,𝔽5) | semidirect |
| 772. D5 | D5⋊#104 | semidirect |
| 790. Q8 | C2×D5⋊AGL(1,𝔽5) | semidirect |
| 807. D4 | C2×D5⋊AGL(1,𝔽5) | semidirect |
| 848. C5 | C2×D5⋊#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D52×#41 | 2 |
| C2×C4×D5⋊AGL(1,𝔽5) | 2 |
| D5⋊(D5⋊M16) | 2 |
| #13104930 | 2 |
| #13104804 | 2 |
| D5⋊#4010 | 2 |
| D5⋊#4008 | 2 |
| #13103946 | 2 |
| #13103942 | 2 |
| C2×D5⋊#104 | 5 |