Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1274 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 1274 conjugacy classes of subgroups — too many to draw. Only its 109 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 | #13107840 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13104932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13104804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13103946 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13103935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13103928 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13103880 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #41×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 9 | C5×#4150 | C4 | 1 | 2 | yes | complemented |
| 10 | Q8×D52 | — | 2 | 1 | no | — |
| 11 | #11717481 | — | 2 | 1 | no | — |
| 12 | #11717477 | — | 2 | 1 | no | — |
| 13 | #11717477 | — | 2 | 2 | no | — |
| 14 | #11717474 | — | 2 | 1 | no | — |
| 15 | #11717474 | — | 2 | 2 | no | — |
| 16 | #11717471 | — | 2 | 1 | no | — |
| 17 | #11717471 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#87872 | — | 2 | 1 | no | — |
| 19 | C2×#87872 | C22 | 1 | 1 | yes | characteristic |
| 20 | #11717462 | — | 2 | 2 | no | — |
| 21 | #11717462 | C4 | 1 | 2 | yes | complemented |
| 22 | C2×C4⋊#1044 | C22 | 1 | 1 | yes | characteristic |
| 23 | #11717448 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C4×#1043 | C22 | 1 | 1 | yes | characteristic |
| 25 | #11717435 | C22 | 1 | 1 | yes | characteristic |
| 26 | #11716902 | — | 2 | 1 | no | — |
| 27 | #11716900 | — | 2 | 1 | no | — |
| 28 | #11716878 | — | 2 | 1 | no | — |
| 29 | #11716876 | — | 2 | 1 | no | — |
| 30 | #11716782 | — | 2 | 2 | no | — |
| 31 | #11716776 | — | 2 | 2 | no | — |
| 32 | #11716770 | — | 2 | 2 | no | — |
| 33 | #11716768 | — | 2 | 1 | no | — |
| 34 | #11716766 | — | 2 | 1 | no | — |
| 35 | #10605019 | — | 5 | 2 | no | maximal |
| 36 | C22×#1044 | — | 2 | 1 | no | — |
| 37 | C22×#1043 | — | 2 | 1 | no | — |
| 38 | C52×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | #87904 | D4 | 1 | 1 | yes | characteristic |
| 40 | Q8×C5⋊D5 | D4 | 1 | 1 | yes | characteristic |
| 41 | #87902 | — | 2 | 1 | no | — |
| 42 | #87902 | D4 | 1 | 1 | yes | characteristic |
| 43 | D4×C5⋊D5 | — | 2 | 1 | no | — |
| 44 | D4×C5⋊D5 | D4 | 1 | 1 | yes | characteristic |
| 45 | #87900 | — | 2 | 1 | no | — |
| 46 | #87900 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 48 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 49 | C5×Q8×D5 | — | 2 | 2 | no | — |
| 50 | C5×#711 | — | 2 | 2 | no | — |
| 51 | C5×#711 | — | 2 | 4 | no | — |
| 52 | C5×#709 | — | 2 | 2 | no | — |
| 53 | C5×#709 | C2×C4 | 1 | 2 | yes | — |
| 54 | C2×C5×Dic10 | — | 2 | 2 | no | — |
| 55 | C2×C5×Dic10 | C2×C4 | 1 | 2 | yes | — |
| 56 | #87886 | — | 2 | 2 | no | — |
| 57 | #87886 | — | 2 | 1 | no | — |
| 58 | C2×#6039 | — | 2 | 2 | no | — |
| 59 | C2×#6039 | D4 | 1 | 2 | yes | — |
| 60 | C2×#6036 | — | 2 | 2 | no | — |
| 61 | C2×#6036 | D4 | 1 | 2 | yes | — |
| 62 | #87880 | — | 2 | 2 | no | — |
| 63 | #87880 | — | 2 | 1 | no | — |
| 64 | #87879 | — | 2 | 4 | no | — |
| 65 | #87879 | — | 2 | 4 | no | — |
| 66 | #87879 | — | 2 | 4 | no | — |
| 67 | #87877 | D4 | 1 | 1 | yes | characteristic |
| 68 | C4×D52 | — | 2 | 2 | no | — |
| 69 | C4×D52 | — | 2 | 1 | no | — |
| 70 | #87874 | — | 2 | 4 | no | — |
| 71 | #87874 | — | 2 | 2 | no | — |
| 72 | #87873 | — | 2 | 2 | no | — |
| 73 | #87873 | — | 2 | 1 | no | — |
| 74 | #87872 | — | 2 | 2 | no | — |
| 75 | #87872 | — | 2 | 2 | no | — |
| 76 | #87872 | — | 2 | 1 | no | — |
| 77 | #87872 | — | 2 | 1 | no | — |
| 78 | #87872 | — | 2 | 1 | no | — |
| 79 | #87872 | — | 2 | 1 | no | — |
| 80 | #87872 | — | 2 | 2 | no | — |
| 81 | #87872 | D4 | 1 | 1 | yes | characteristic |
| 82 | #87871 | — | 2 | 2 | no | — |
| 83 | #87871 | D4 | 1 | 2 | yes | — |
| 84 | D5×Dic10 | — | 2 | 4 | no | — |
| 85 | D5×Dic10 | — | 2 | 2 | no | — |
| 86 | #87867 | — | 2 | 1 | no | — |
| 87 | C4⋊#1044 | — | 2 | 1 | no | — |
| 88 | C4⋊#1044 | — | 2 | 1 | no | — |
| 89 | #87863 | — | 2 | 1 | no | — |
| 90 | #87862 | — | 2 | 1 | no | — |
| 91 | #87860 | — | 2 | 1 | no | — |
| 92 | C4×#1043 | — | 2 | 1 | no | — |
| 93 | C4×#1043 | — | 2 | 1 | no | — |
| 94 | #87856 | — | 2 | 1 | no | — |
| 95 | #87855 | — | 2 | 1 | no | — |
| 96 | D5×2−1+4 | — | 5 | 2 | no | — |
| 97 | #65793 | — | 5 | 2 | no | — |
| 98 | #65793 | — | 5 | 2 | no | — |
| 99 | D5⋊#104 | — | 5 | 2 | no | — |
| 100 | D5⋊#104 | — | 5 | 2 | no | — |
| 101 | D5⋊#104 | — | 10 | 2 | no | — |
| 102 | (C2×AGL(1,𝔽5))⋊Q8 | — | 5 | 2 | no | — |
| 103 | D5⋊#101 | — | 5 | 2 | no | — |
| 104 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 105 | C22×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C2×D52 | — | 2 | 1 | no | — |
| 107 | C2×#1044 | — | 4 | 2 | no | — |
| 108 | C2×#1044 | — | 4 | 1 | no | — |
| 109 | C2×#1043 | — | 2 | 2 | no | — |
| 110 | C2×#1043 | — | 4 | 1 | no | — |
| 111 | C2×#1043 | — | 4 | 1 | no | — |
| 112 | C52×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 113 | C52×D4 | — | 2 | 1 | no | — |
| 114 | C52×D4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C52 | — | 2 | 1 | no | — |
| 116 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 117 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 118 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 119 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 120 | C2×#1039 | — | 2 | 1 | no | — |
| 121 | C2×#1039 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 123 | C4⋊(C5⋊D5) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 124 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 125 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 126 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 127 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | #6045 | — | 2 | 1 | no | — |
| 132 | #6045 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 133 | C5×C22⋊D5 | — | 2 | 4 | no | — |
| 134 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 135 | C2×C5×Dic5 | — | 2 | 4 | no | — |
| 136 | C2×C5×Dic5 | C22⋊C4 | 1 | 4 | yes | — |
| 137 | C5×D20 | C22⋊C4 | 1 | 2 | yes | — |
| 138 | C4×C5×D5 | — | 2 | 4 | no | — |
| 139 | C4×C5×D5 | — | 2 | 2 | no | — |
| 140 | C5×Dic10 | — | 2 | 4 | no | — |
| 141 | C5×Dic10 | — | 2 | 2 | no | — |
| 142 | C5×Dic10 | — | 2 | 2 | no | — |
| 143 | C5×Dic10 | C22⋊C4 | 1 | 2 | yes | — |
| 144 | #6039 | — | 2 | 4 | no | — |
| 145 | #6039 | — | 2 | 2 | no | — |
| 146 | #6039 | — | 2 | 2 | no | — |
| 147 | #6039 | — | 2 | 1 | no | — |
| 148 | #6038 | — | 2 | 4 | no | — |
| 149 | #6038 | — | 2 | 2 | no | — |
| 150 | #6037 | — | 2 | 1 | no | — |
| 151 | #6036 | — | 2 | 4 | no | — |
| 152 | #6036 | — | 2 | 2 | no | — |
| 153 | #6036 | — | 2 | 1 | no | — |
| 154 | #6036 | — | 2 | 2 | no | — |
| 155 | D5×Dic5 | — | 2 | 4 | no | — |
| 156 | D5×Dic5 | — | 2 | 2 | no | — |
| 157 | #6034 | — | 4 | 1 | no | — |
| 158 | #6033 | — | 4 | 1 | no | — |
| 159 | C5×2−1+4 | — | 5 | 2 | no | — |
| 160 | #4150 | — | 5 | 2 | no | — |
| 161 | #4150 | — | 10 | 2 | no | — |
| 162 | #4150 | — | 10 | 4 | no | — |
| 163 | #4150 | — | 10 | 2 | no | — |
| 164 | #4150 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 165 | D5×#41 | — | 5 | 2 | no | — |
| 166 | D5×#41 | — | 5 | 2 | no | — |
| 167 | D5×#41 | — | 10 | 2 | no | — |
| 168 | D5×#41 | — | 10 | 4 | no | — |
| 169 | D5×#41 | — | 10 | 2 | no | — |
| 170 | D5×#41 | — | 10 | 2 | no | — |
| 171 | #4147 | — | 5 | 2 | no | — |
| 172 | #4147 | — | 10 | 2 | no | — |
| 173 | #4147 | — | 10 | 2 | no | — |
| 174 | C2×Q8×D5 | — | 5 | 2 | no | — |
| 175 | C2×Q8×D5 | — | 10 | 2 | no | — |
| 176 | C2×Q8×D5 | — | 10 | 2 | no | — |
| 177 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 178 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 179 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 180 | D5⋊M16 | — | 5 | 2 | no | — |
| 181 | D5⋊M16 | — | 5 | 2 | no | — |
| 182 | D5⋊M16 | — | 10 | 2 | no | — |
| 183 | #4010 | — | 10 | 2 | no | — |
| 184 | #4010 | — | 10 | 2 | no | — |
| 185 | #4010 | — | 10 | 4 | no | — |
| 186 | #4009 | — | 10 | 2 | no | — |
| 187 | #4009 | — | 10 | 2 | no | — |
| 188 | #4008 | — | 10 | 2 | no | — |
| 189 | #4008 | — | 10 | 2 | no | — |
| 190 | #4008 | — | 10 | 4 | no | — |
| 191 | #4007 | — | 10 | 2 | no | — |
| 192 | #4007 | — | 10 | 2 | no | — |
| 193 | (C2×AGL(1,𝔽5))⋊C4 | — | 10 | 4 | no | — |
| 194 | #4005 | — | 10 | 4 | no | — |
| 195 | #1793 | — | 25 | 1 | no | Sylow |
| 196 | C22×C52 | — | 2 | 1 | no | — |
| 197 | C22×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 198 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 199 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 200 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 201 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 202 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 203 | C2×C5⋊D5 | #120 | 1 | 1 | yes | characteristic |
| 204 | C2×C5⋊D5 | #120 | 1 | 1 | yes | characteristic |
| 205 | C2×C5×D5 | — | 2 | 2 | no | — |
| 206 | D52 | — | 4 | 1 | no | — |
| 207 | D52 | — | 4 | 1 | no | — |
| 208 | #1044 | — | 8 | 1 | no | — |
| 209 | #1043 | — | 4 | 2 | no | — |
| 210 | C4×C52 | — | 2 | 1 | no | — |
| 211 | C4×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 212 | C4×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 213 | #1039 | — | 2 | 1 | no | — |
| 214 | #1039 | #120 | 1 | 1 | yes | characteristic |
| 215 | #1039 | #120 | 1 | 1 | yes | characteristic |
| 216 | C5×Dic5 | — | 2 | 4 | no | — |
| 217 | C5×Dic5 | — | 2 | 2 | no | — |
| 218 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 219 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 220 | C22×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 221 | C5×#41 | — | 2 | 2 | no | — |
| 222 | C5×#41 | — | 5 | 2 | no | — |
| 223 | C5×#41 | — | 10 | 2 | no | — |
| 224 | C5×#41 | — | 10 | 4 | no | — |
| 225 | C5×#41 | — | 10 | 2 | no | — |
| 226 | C5×#41 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 227 | C2×C5×Q8 | — | 5 | 2 | no | — |
| 228 | C2×C5×Q8 | — | 10 | 2 | no | — |
| 229 | C2×C5×Q8 | — | 10 | 2 | no | — |
| 230 | #713 | — | 5 | 2 | no | — |
| 231 | #713 | — | 5 | 2 | no | — |
| 232 | #713 | — | 10 | 2 | no | — |
| 233 | #713 | — | 10 | 2 | no | — |
| 234 | #713 | — | 10 | 4 | no | — |
| 235 | #713 | — | 10 | 2 | no | — |
| 236 | Q8×D5 | — | 2 | 2 | no | — |
| 237 | Q8×D5 | — | 5 | 2 | no | — |
| 238 | Q8×D5 | — | 5 | 2 | no | — |
| 239 | Q8×D5 | — | 10 | 2 | no | — |
| 240 | Q8×D5 | — | 10 | 2 | no | — |
| 241 | Q8×D5 | — | 10 | 2 | no | — |
| 242 | Q8×D5 | — | 10 | 2 | no | — |
| 243 | Q8×D5 | — | 10 | 2 | no | — |
| 244 | Q8×D5 | — | 10 | 2 | no | — |
| 245 | Q8×D5 | — | 10 | 4 | no | — |
| 246 | Q8×D5 | — | 10 | 4 | no | — |
| 247 | Q8×D5 | — | 10 | 2 | no | — |
| 248 | Q8×D5 | — | 10 | 4 | no | — |
| 249 | Q8×D5 | — | 10 | 2 | no | — |
| 250 | #711 | — | 2 | 2 | no | — |
| 251 | #711 | — | 2 | 4 | no | — |
| 252 | #711 | — | 5 | 2 | no | — |
| 253 | #711 | — | 5 | 2 | no | — |
| 254 | #711 | — | 10 | 2 | no | — |
| 255 | #711 | — | 10 | 2 | no | — |
| 256 | #711 | — | 10 | 4 | no | — |
| 257 | #711 | — | 10 | 4 | no | — |
| 258 | #711 | — | 10 | 2 | no | — |
| 259 | #711 | — | 10 | 2 | no | — |
| 260 | #711 | — | 10 | 4 | no | — |
| 261 | #711 | — | 10 | 4 | no | — |
| 262 | #711 | — | 20 | 2 | no | — |
| 263 | D4×D5 | — | 5 | 2 | no | — |
| 264 | D4×D5 | — | 5 | 2 | no | — |
| 265 | D4×D5 | — | 10 | 2 | no | — |
| 266 | D4×D5 | — | 10 | 2 | no | — |
| 267 | D4×D5 | — | 10 | 4 | no | — |
| 268 | D4×D5 | — | 10 | 2 | no | — |
| 269 | D4×D5 | — | 20 | 2 | no | — |
| 270 | #709 | — | 2 | 2 | no | — |
| 271 | #709 | — | 5 | 2 | no | — |
| 272 | #709 | — | 10 | 2 | no | — |
| 273 | #709 | — | 10 | 2 | no | — |
| 274 | #709 | — | 10 | 4 | no | — |
| 275 | #709 | — | 10 | 2 | no | — |
| 276 | #709 | — | 10 | 4 | no | — |
| 277 | #709 | — | 10 | 2 | no | — |
| 278 | #709 | — | 10 | 4 | no | — |
| 279 | #709 | — | 10 | 4 | no | — |
| 280 | #709 | — | 10 | 4 | no | — |
| 281 | #709 | — | 20 | 2 | no | — |
| 282 | #709 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 283 | C2×C4×D5 | — | 5 | 2 | no | — |
| 284 | C2×C4×D5 | — | 5 | 4 | no | — |
| 285 | C2×C4×D5 | — | 10 | 2 | no | — |
| 286 | C2×C4×D5 | — | 10 | 2 | no | — |
| 287 | C2×C4×D5 | — | 10 | 4 | no | — |
| 288 | C2×C4×D5 | — | 10 | 2 | no | — |
| 289 | C2×C4×D5 | — | 10 | 4 | no | — |
| 290 | C2×C4×D5 | — | 20 | 2 | no | — |
| 291 | C2×Dic10 | — | 2 | 2 | no | — |
| 292 | C2×Dic10 | — | 5 | 4 | no | — |
| 293 | C2×Dic10 | — | 10 | 2 | no | — |
| 294 | C2×Dic10 | — | 10 | 4 | no | — |
| 295 | C2×Dic10 | — | 10 | 4 | no | — |
| 296 | C2×Dic10 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 297 | #704 | — | 10 | 2 | no | — |
| 298 | #704 | — | 10 | 2 | no | — |
| 299 | #704 | — | 20 | 2 | no | — |
| 300 | C4⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 301 | C4⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 302 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 303 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 304 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 305 | C4×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 306 | #700 | — | 10 | 2 | no | — |
| 307 | #700 | — | 10 | 2 | no | — |
| 308 | #700 | — | 10 | 4 | no | — |
| 309 | D5⋊C8 | — | 10 | 2 | no | — |
| 310 | D5⋊C8 | — | 10 | 2 | no | — |
| 311 | D5⋊C8 | — | 20 | 2 | no | — |
| 312 | C2×2−1+4 | — | 25 | 1 | no | — |
| 313 | C2×#104 | — | 25 | 1 | no | — |
| 314 | C2×#104 | — | 25 | 1 | no | — |
| 315 | #417 | — | 25 | 1 | no | — |
| 316 | #417 | — | 25 | 1 | no | — |
| 317 | C2×#101 | — | 25 | 1 | no | — |
| 318 | #391 | — | 25 | 1 | no | — |
| 319 | C2×C52 | — | 2 | 1 | no | — |
| 320 | C2×C52 | — | 4 | 1 | no | — |
| 321 | C2×C52 | #379 | 1 | 1 | yes | characteristic |
| 322 | C5⋊D5 | — | 2 | 1 | no | — |
| 323 | C5⋊D5 | — | 4 | 1 | no | — |
| 324 | C5⋊D5 | #454 | 1 | 1 | yes | characteristic |
| 325 | C5⋊D5 | #456 | 1 | 1 | yes | characteristic |
| 326 | C5×D5 | — | 4 | 2 | no | — |
| 327 | C22×D5 | — | 5 | 2 | no | — |
| 328 | C22×D5 | — | 10 | 2 | no | — |
| 329 | C22×D5 | — | 10 | 2 | no | — |
| 330 | C22×D5 | — | 10 | 2 | no | — |
| 331 | C22×D5 | — | 20 | 2 | no | — |
| 332 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 333 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 334 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 335 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 336 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 337 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 338 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 339 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 340 | C5×Q8 | — | 2 | 2 | no | — |
| 341 | C5×Q8 | — | 5 | 2 | no | — |
| 342 | C5×Q8 | — | 10 | 4 | no | — |
| 343 | C5×Q8 | — | 10 | 2 | no | — |
| 344 | C5×Q8 | — | 10 | 2 | no | — |
| 345 | C5×Q8 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 346 | C5×D4 | — | 2 | 2 | no | — |
| 347 | C5×D4 | — | 2 | 2 | no | — |
| 348 | C5×D4 | — | 4 | 2 | no | — |
| 349 | C5×D4 | — | 5 | 2 | no | — |
| 350 | C5×D4 | — | 10 | 4 | no | — |
| 351 | C5×D4 | — | 10 | 2 | no | — |
| 352 | C5×D4 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 353 | C2×C4×C5 | — | 2 | 2 | no | — |
| 354 | C2×C4×C5 | — | 2 | 2 | no | — |
| 355 | C2×C4×C5 | — | 4 | 2 | no | — |
| 356 | C2×C4×C5 | — | 5 | 4 | no | — |
| 357 | C2×C4×C5 | — | 10 | 4 | no | — |
| 358 | C2×C4×C5 | — | 10 | 4 | no | — |
| 359 | C2×C4×C5 | — | 10 | 2 | no | — |
| 360 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 361 | C22⋊D5 | — | 2 | 4 | no | — |
| 362 | C22⋊D5 | — | 2 | 2 | no | — |
| 363 | C22⋊D5 | — | 10 | 2 | no | — |
| 364 | C22⋊D5 | — | 10 | 4 | no | — |
| 365 | C22⋊D5 | — | 10 | 2 | no | — |
| 366 | C22⋊D5 | — | 10 | 2 | no | — |
| 367 | C22⋊D5 | — | 10 | 2 | no | — |
| 368 | C22⋊D5 | — | 10 | 2 | no | — |
| 369 | C22⋊D5 | — | 20 | 2 | no | — |
| 370 | C22⋊D5 | — | 20 | 2 | no | — |
| 371 | C22⋊D5 | — | 20 | 2 | no | — |
| 372 | C2×Dic5 | — | 2 | 4 | no | — |
| 373 | C2×Dic5 | — | 5 | 2 | no | — |
| 374 | C2×Dic5 | — | 10 | 2 | no | — |
| 375 | C2×Dic5 | — | 10 | 2 | no | — |
| 376 | C2×Dic5 | — | 10 | 4 | no | — |
| 377 | C2×Dic5 | — | 10 | 2 | no | — |
| 378 | C2×Dic5 | — | 20 | 2 | no | — |
| 379 | C2×Dic5 | C22⋊AGL(1,𝔽5) | 1 | 4 | yes | — |
| 380 | D20 | — | 5 | 2 | no | — |
| 381 | D20 | — | 10 | 2 | no | — |
| 382 | D20 | — | 10 | 2 | no | — |
| 383 | D20 | — | 10 | 2 | no | — |
| 384 | D20 | — | 10 | 4 | no | — |
| 385 | D20 | — | 20 | 2 | no | — |
| 386 | D20 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 387 | C4×D5 | — | 2 | 4 | no | — |
| 388 | C4×D5 | — | 2 | 2 | no | — |
| 389 | C4×D5 | — | 5 | 2 | no | — |
| 390 | C4×D5 | — | 5 | 2 | no | — |
| 391 | C4×D5 | — | 5 | 2 | no | — |
| 392 | C4×D5 | — | 5 | 2 | no | — |
| 393 | C4×D5 | — | 10 | 2 | no | — |
| 394 | C4×D5 | — | 10 | 2 | no | — |
| 395 | C4×D5 | — | 10 | 2 | no | — |
| 396 | C4×D5 | — | 10 | 2 | no | — |
| 397 | C4×D5 | — | 10 | 4 | no | — |
| 398 | C4×D5 | — | 10 | 4 | no | — |
| 399 | C4×D5 | — | 10 | 2 | no | — |
| 400 | C4×D5 | — | 10 | 4 | no | — |
| 401 | C4×D5 | — | 10 | 4 | no | — |
| 402 | C4×D5 | — | 10 | 2 | no | — |
| 403 | C4×D5 | — | 10 | 2 | no | — |
| 404 | C4×D5 | — | 10 | 2 | no | — |
| 405 | C4×D5 | — | 10 | 4 | no | — |
| 406 | C4×D5 | — | 10 | 2 | no | — |
| 407 | C4×D5 | — | 20 | 2 | no | — |
| 408 | C4×D5 | — | 20 | 2 | no | — |
| 409 | C4×D5 | — | 20 | 2 | no | — |
| 410 | Dic10 | — | 2 | 4 | no | — |
| 411 | Dic10 | — | 2 | 2 | no | — |
| 412 | Dic10 | — | 2 | 2 | no | — |
| 413 | Dic10 | — | 5 | 2 | no | — |
| 414 | Dic10 | — | 10 | 2 | no | — |
| 415 | Dic10 | — | 10 | 4 | no | — |
| 416 | Dic10 | — | 10 | 4 | no | — |
| 417 | Dic10 | — | 10 | 2 | no | — |
| 418 | Dic10 | — | 10 | 4 | no | — |
| 419 | Dic10 | — | 10 | 4 | no | — |
| 420 | Dic10 | — | 10 | 2 | no | — |
| 421 | Dic10 | — | 20 | 2 | no | — |
| 422 | Dic10 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 423 | #170 | — | 20 | 2 | no | — |
| 424 | #170 | — | 20 | 2 | no | — |
| 425 | #170 | — | 20 | 4 | no | — |
| 426 | 2−1+4 | — | 5 | 2 | no | — |
| 427 | 2−1+4 | — | 25 | 2 | no | — |
| 428 | 2−1+4 | — | 50 | 1 | no | — |
| 429 | 2−1+4 | — | 50 | 2 | no | — |
| 430 | 2−1+4 | — | 50 | 2 | no | — |
| 431 | 2−1+4 | — | 50 | 1 | no | — |
| 432 | C2×#41 | — | 25 | 1 | no | — |
| 433 | C2×#41 | — | 25 | 1 | no | — |
| 434 | C2×#41 | — | 50 | 2 | no | — |
| 435 | C2×#41 | — | 50 | 1 | no | — |
| 436 | C2×#41 | — | 50 | 1 | no | — |
| 437 | C22×Q8 | — | 25 | 1 | no | — |
| 438 | C22×Q8 | — | 50 | 1 | no | — |
| 439 | C22×Q8 | — | 50 | 1 | no | — |
| 440 | C2×M16 | — | 25 | 1 | no | — |
| 441 | C2×M16 | — | 25 | 1 | no | — |
| 442 | C2×C4⋊C4 | — | 25 | 1 | no | — |
| 443 | C2×C42 | — | 25 | 1 | no | — |
| 444 | #104 | — | 50 | 1 | no | — |
| 445 | #104 | — | 50 | 2 | no | — |
| 446 | #104 | — | 50 | 1 | no | — |
| 447 | #103 | — | 50 | 1 | no | — |
| 448 | #103 | — | 50 | 1 | no | — |
| 449 | #102 | — | 50 | 1 | no | — |
| 450 | #102 | — | 50 | 1 | no | — |
| 451 | #101 | — | 50 | 2 | no | — |
| 452 | #95 | — | 50 | 2 | no | — |
| 453 | C52 | #1793 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 454 | C22×C5 | — | 2 | 2 | no | — |
| 455 | C22×C5 | — | 2 | 2 | no | — |
| 456 | C22×C5 | — | 4 | 2 | no | — |
| 457 | C22×C5 | — | 10 | 2 | no | — |
| 458 | C22×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 459 | C2×D5 | — | 2 | 2 | no | — |
| 460 | C2×D5 | — | 5 | 2 | no | — |
| 461 | C2×D5 | — | 5 | 2 | no | — |
| 462 | C2×D5 | — | 10 | 2 | no | — |
| 463 | C2×D5 | — | 10 | 2 | no | — |
| 464 | C2×D5 | — | 10 | 2 | no | — |
| 465 | C2×D5 | — | 10 | 2 | no | — |
| 466 | C2×D5 | — | 10 | 2 | no | — |
| 467 | C2×D5 | — | 20 | 2 | no | — |
| 468 | C2×D5 | — | 20 | 2 | no | — |
| 469 | C2×D5 | — | 20 | 2 | no | — |
| 470 | C2×D5 | — | 20 | 2 | no | — |
| 471 | C2×D5 | — | 20 | 2 | no | — |
| 472 | C2×D5 | — | 20 | 2 | no | — |
| 473 | C2×D5 | — | 20 | 2 | no | — |
| 474 | C2×D5 | — | 40 | 2 | no | — |
| 475 | C2×D5 | — | 40 | 2 | no | — |
| 476 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 477 | AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 478 | AGL(1,𝔽5) | — | 40 | 2 | no | — |
| 479 | C4×C5 | — | 2 | 2 | no | — |
| 480 | C4×C5 | — | 2 | 2 | no | — |
| 481 | C4×C5 | — | 2 | 2 | no | — |
| 482 | C4×C5 | — | 4 | 2 | no | — |
| 483 | C4×C5 | — | 10 | 4 | no | — |
| 484 | C4×C5 | — | 10 | 2 | no | — |
| 485 | C4×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 486 | C4×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 487 | Dic5 | — | 2 | 4 | no | — |
| 488 | Dic5 | — | 2 | 2 | no | — |
| 489 | Dic5 | — | 5 | 2 | no | — |
| 490 | Dic5 | — | 5 | 2 | no | — |
| 491 | Dic5 | — | 10 | 2 | no | — |
| 492 | Dic5 | — | 10 | 2 | no | — |
| 493 | Dic5 | — | 10 | 2 | no | — |
| 494 | Dic5 | — | 20 | 2 | no | — |
| 495 | #41 | — | 5 | 2 | no | — |
| 496 | #41 | — | 10 | 2 | no | — |
| 497 | #41 | — | 10 | 4 | no | — |
| 498 | #41 | — | 10 | 2 | no | — |
| 499 | #41 | — | 25 | 2 | no | — |
| 500 | #41 | — | 25 | 1 | no | — |
| 501 | #41 | — | 25 | 1 | no | — |
| 502 | #41 | — | 25 | 1 | no | — |
| 503 | #41 | — | 50 | 1 | no | — |
| 504 | #41 | — | 50 | 4 | no | — |
| 505 | #41 | — | 50 | 1 | no | — |
| 506 | #41 | — | 50 | 2 | no | — |
| 507 | #41 | — | 50 | 4 | no | — |
| 508 | #41 | — | 50 | 4 | no | — |
| 509 | #41 | — | 50 | 2 | no | — |
| 510 | #41 | — | 50 | 4 | no | — |
| 511 | #41 | — | 50 | 1 | no | — |
| 512 | #41 | — | 50 | 1 | no | — |
| 513 | #41 | — | 50 | 2 | no | — |
| 514 | #41 | — | 50 | 2 | no | — |
| 515 | #41 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 516 | C2×Q8 | — | 5 | 2 | no | — |
| 517 | C2×Q8 | — | 10 | 2 | no | — |
| 518 | C2×Q8 | — | 10 | 2 | no | — |
| 519 | C2×Q8 | — | 25 | 2 | no | — |
| 520 | C2×Q8 | — | 25 | 1 | no | — |
| 521 | C2×Q8 | — | 25 | 1 | no | — |
| 522 | C2×Q8 | — | 50 | 2 | no | — |
| 523 | C2×Q8 | — | 50 | 2 | no | — |
| 524 | C2×Q8 | — | 50 | 4 | no | — |
| 525 | C2×Q8 | — | 50 | 1 | no | — |
| 526 | C2×Q8 | — | 50 | 1 | no | — |
| 527 | C2×Q8 | — | 50 | 1 | no | — |
| 528 | C2×Q8 | — | 50 | 1 | no | — |
| 529 | C2×Q8 | — | 50 | 2 | no | — |
| 530 | C2×Q8 | — | 50 | 2 | no | — |
| 531 | C2×Q8 | — | 50 | 2 | no | — |
| 532 | C2×D4 | — | 25 | 1 | no | — |
| 533 | C2×D4 | — | 25 | 1 | no | — |
| 534 | C2×D4 | — | 50 | 1 | no | — |
| 535 | C2×D4 | — | 50 | 1 | no | — |
| 536 | C2×D4 | — | 50 | 2 | no | — |
| 537 | C22×C4 | — | 25 | 2 | no | — |
| 538 | C22×C4 | — | 25 | 1 | no | — |
| 539 | C22×C4 | — | 50 | 1 | no | — |
| 540 | C22×C4 | — | 50 | 1 | no | — |
| 541 | C22×C4 | — | 50 | 2 | no | — |
| 542 | C22×C4 | — | 50 | 2 | no | — |
| 543 | C22×C4 | — | 50 | 1 | no | — |
| 544 | C22×C4 | — | 50 | 1 | no | — |
| 545 | M16 | — | 50 | 1 | no | — |
| 546 | M16 | — | 50 | 1 | no | — |
| 547 | M16 | — | 50 | 1 | no | — |
| 548 | M16 | — | 50 | 1 | no | — |
| 549 | C2×C8 | — | 50 | 1 | no | — |
| 550 | C2×C8 | — | 50 | 1 | no | — |
| 551 | C4⋊C4 | — | 50 | 1 | no | — |
| 552 | C4⋊C4 | — | 50 | 1 | no | — |
| 553 | C42 | — | 50 | 1 | no | — |
| 554 | C42 | — | 50 | 1 | no | — |
| 555 | C2×C5 | — | 2 | 2 | no | — |
| 556 | C2×C5 | — | 2 | 2 | no | — |
| 557 | C2×C5 | — | 4 | 2 | no | — |
| 558 | C2×C5 | — | 4 | 2 | no | — |
| 559 | C2×C5 | — | 8 | 2 | no | — |
| 560 | C2×C5 | — | 20 | 2 | no | — |
| 561 | C2×C5 | #65800 | 1 | 2 | yes | — |
| 562 | D5 | — | 4 | 2 | no | — |
| 563 | D5 | — | 5 | 2 | no | — |
| 564 | D5 | — | 5 | 2 | no | — |
| 565 | D5 | — | 10 | 2 | no | — |
| 566 | D5 | — | 10 | 2 | no | — |
| 567 | D5 | — | 10 | 2 | no | — |
| 568 | D5 | — | 20 | 2 | no | — |
| 569 | D5 | — | 20 | 2 | no | — |
| 570 | D5 | — | 40 | 2 | no | — |
| 571 | C23 | — | 25 | 1 | no | — |
| 572 | C23 | — | 50 | 1 | no | — |
| 573 | C23 | — | 50 | 1 | no | — |
| 574 | Q8 | — | 5 | 2 | no | — |
| 575 | Q8 | — | 10 | 4 | no | — |
| 576 | Q8 | — | 10 | 2 | no | — |
| 577 | Q8 | — | 10 | 2 | no | — |
| 578 | Q8 | — | 25 | 1 | no | — |
| 579 | Q8 | — | 50 | 1 | no | — |
| 580 | Q8 | — | 50 | 2 | no | — |
| 581 | Q8 | — | 50 | 2 | no | — |
| 582 | Q8 | — | 50 | 1 | no | — |
| 583 | Q8 | — | 50 | 4 | no | — |
| 584 | Q8 | #87831 | 1 | 1 | yes | characteristic |
| 585 | D4 | — | 2 | 1 | no | — |
| 586 | D4 | — | 5 | 2 | no | — |
| 587 | D4 | — | 10 | 4 | no | — |
| 588 | D4 | — | 10 | 2 | no | — |
| 589 | D4 | — | 25 | 1 | no | — |
| 590 | D4 | — | 50 | 1 | no | — |
| 591 | D4 | — | 50 | 2 | no | — |
| 592 | D4 | — | 50 | 4 | no | — |
| 593 | D4 | — | 50 | 1 | no | — |
| 594 | D4 | — | 50 | 1 | no | — |
| 595 | D4 | — | 50 | 1 | no | — |
| 596 | D4 | — | 50 | 1 | no | — |
| 597 | D4 | #87831 | 1 | 1 | yes | characteristic |
| 598 | C2×C4 | — | 2 | 1 | no | — |
| 599 | C2×C4 | — | 5 | 4 | no | — |
| 600 | C2×C4 | — | 10 | 4 | no | — |
| 601 | C2×C4 | — | 10 | 4 | no | — |
| 602 | C2×C4 | — | 10 | 2 | no | — |
| 603 | C2×C4 | — | 25 | 1 | no | — |
| 604 | C2×C4 | — | 25 | 1 | no | — |
| 605 | C2×C4 | — | 25 | 1 | no | — |
| 606 | C2×C4 | — | 25 | 1 | no | — |
| 607 | C2×C4 | — | 25 | 1 | no | — |
| 608 | C2×C4 | — | 50 | 1 | no | — |
| 609 | C2×C4 | — | 50 | 1 | no | — |
| 610 | C2×C4 | — | 50 | 2 | no | — |
| 611 | C2×C4 | — | 50 | 2 | no | — |
| 612 | C2×C4 | — | 50 | 1 | no | — |
| 613 | C2×C4 | — | 50 | 4 | no | — |
| 614 | C2×C4 | — | 50 | 2 | no | — |
| 615 | C2×C4 | — | 50 | 4 | no | — |
| 616 | C2×C4 | — | 50 | 1 | no | — |
| 617 | C2×C4 | — | 50 | 1 | no | — |
| 618 | C2×C4 | — | 50 | 2 | no | — |
| 619 | C2×C4 | — | 100 | 1 | no | — |
| 620 | C2×C4 | — | 100 | 1 | no | — |
| 621 | C2×C4 | — | 100 | 1 | no | — |
| 622 | C2×C4 | — | 100 | 2 | no | — |
| 623 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 624 | C8 | — | 100 | 1 | no | — |
| 625 | C8 | — | 100 | 1 | no | — |
| 626 | C5 | — | 2 | 2 | no | — |
| 627 | C5 | #10605019 | 1 | 2 | yes | complemented |
| 628 | C22 | — | 2 | 1 | no | — |
| 629 | C22 | — | 10 | 2 | no | — |
| 630 | C22 | — | 25 | 1 | no | — |
| 631 | C22 | — | 25 | 1 | no | — |
| 632 | C22 | — | 50 | 1 | no | — |
| 633 | C22 | — | 50 | 1 | no | — |
| 634 | C22 | — | 50 | 1 | no | — |
| 635 | C22 | — | 100 | 1 | no | — |
| 636 | C22 | — | 100 | 1 | no | — |
| 637 | C22 | — | 100 | 1 | no | — |
| 638 | C22 | — | 100 | 1 | no | — |
| 639 | C22 | D5⋊(C22⋊AGL(1,𝔽5)) | 1 | 1 | yes | characteristic |
| 640 | C4 | — | 2 | 1 | no | — |
| 641 | C4 | — | 10 | 4 | no | — |
| 642 | C4 | — | 10 | 2 | no | — |
| 643 | C4 | — | 25 | 1 | no | — |
| 644 | C4 | — | 25 | 1 | no | — |
| 645 | C4 | — | 50 | 1 | no | — |
| 646 | C4 | — | 100 | 2 | no | — |
| 647 | C4 | — | 200 | 1 | no | — |
| 648 | C4 | C2×#87831 | 1 | 1 | yes | characteristic |
| 649 | C4 | D5⋊(C22⋊AGL(1,𝔽5)) | 1 | 1 | yes | characteristic |
| 650 | C2 | — | 2 | 1 | no | — |
| 651 | C2 | — | 4 | 1 | no | — |
| 652 | C2 | — | 20 | 2 | no | — |
| 653 | C2 | — | 25 | 1 | no | — |
| 654 | C2 | — | 25 | 1 | no | — |
| 655 | C2 | — | 50 | 1 | no | — |
| 656 | C2 | — | 100 | 1 | no | — |
| 657 | C2 | #13104117 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13104932 | C2 | semidirect |
| 3. #13104804 | C2 | semidirect |
| 4. #13103946 | C2 | semidirect |
| 5. #13103935 | C2 | semidirect |
| 6. #13103928 | C2 | semidirect |
| 7. #13103880 | C2 | semidirect |
| 9. C5×#4150 | C4 | semidirect |
| 21. #11717462 | C4 | semidirect |
| 164. #4150 | AGL(1,𝔽5) | semidirect |
| 453. C52 | #1793 | semidirect |
| 627. C5 | #10605019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107840 | 2 |
| #13104932 | 2 |
| #13104804 | 2 |
| #13103946 | 2 |
| #13103935 | 2 |
| #13103928 | 2 |
| #13103880 | 2 |
| #10605019 | 5 |