Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
742 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13107609 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13105092 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13103546 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13103543 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13103536 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13100147 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C5×#64863 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×D5×D20 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#87874 | C22 | 1 | 1 | yes | characteristic |
| 10 | #11717425 | C22 | 1 | 1 | yes | characteristic |
| 11 | D5⋊#681 | C22 | 1 | 1 | yes | characteristic |
| 12 | C5×#4130 | C22 | 1 | 1 | yes | characteristic |
| 13 | C5×D5⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11717347 | — | 2 | 2 | no | — |
| 15 | #11717332 | — | 2 | 2 | no | — |
| 16 | #11717330 | — | 2 | 2 | no | — |
| 17 | #11717194 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | C5×#4021 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | C5×#4018 | C22 | 1 | 1 | yes | characteristic |
| 20 | #11717041 | — | 2 | 2 | no | — |
| 21 | #11717029 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #11717028 | — | 2 | 2 | no | — |
| 23 | #11716982 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #11716756 | — | 2 | 2 | no | — |
| 25 | #11716735 | — | 2 | 2 | no | — |
| 26 | #11716734 | — | 2 | 2 | no | — |
| 27 | #10604571 | — | 5 | 1 | no | maximal |
| 28 | #10599506 | — | 5 | 1 | no | maximal |
| 29 | C22×D52 | — | 2 | 1 | no | — |
| 30 | C2×C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 31 | C2×C4⋊(C5⋊D5) | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C2×C4⋊(C5⋊D5) | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C2×C5×D20 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×C4×C5×D5 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×C5×Dic10 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×#6038 | — | 2 | 1 | no | — |
| 37 | C2×#6038 | — | 2 | 2 | no | — |
| 38 | C2×#6038 | D4 | 1 | 2 | yes | — |
| 39 | C2×#6036 | D4 | 1 | 2 | yes | — |
| 40 | D5×D20 | — | 2 | 1 | no | — |
| 41 | D5×D20 | — | 2 | 1 | no | — |
| 42 | D5×D20 | — | 2 | 1 | no | — |
| 43 | D5×D20 | — | 2 | 1 | no | — |
| 44 | #87874 | — | 2 | 1 | no | — |
| 45 | #87874 | — | 2 | 1 | no | — |
| 46 | #87874 | — | 2 | 1 | no | — |
| 47 | #87874 | — | 2 | 1 | no | — |
| 48 | C22⋊#1042 | — | 2 | 1 | no | — |
| 49 | #87853 | — | 2 | 1 | no | — |
| 50 | C4⋊#1042 | — | 2 | 1 | no | — |
| 51 | C4×#1042 | — | 2 | 1 | no | — |
| 52 | #87849 | — | 2 | 1 | no | — |
| 53 | D5⋊#168 | D4 | 1 | 2 | yes | complemented |
| 54 | C5×C22⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 55 | C5×#704 | — | 2 | 1 | no | — |
| 56 | C5×C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 57 | C4×C5×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 58 | C5×#700 | — | 2 | 1 | no | — |
| 59 | C5×D5⋊C8 | D4 | 1 | 2 | yes | complemented |
| 60 | #87829 | — | 2 | 4 | no | — |
| 61 | #87827 | — | 2 | 4 | no | — |
| 62 | C42×C52 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C5×#685 | — | 2 | 1 | no | — |
| 64 | C5×#685 | — | 2 | 2 | no | — |
| 65 | C5×#683 | — | 2 | 1 | no | — |
| 66 | C4×C5×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #87779 | — | 2 | 2 | no | — |
| 68 | #66260 | — | 5 | 1 | no | — |
| 69 | #66079 | — | 5 | 1 | no | — |
| 70 | #66008 | — | 5 | 1 | no | — |
| 71 | #65859 | — | 5 | 1 | no | — |
| 72 | #65785 | — | 5 | 1 | no | — |
| 73 | #65767 | — | 5 | 1 | no | — |
| 74 | #65767 | — | 5 | 1 | no | — |
| 75 | #65420 | — | 5 | 1 | no | — |
| 76 | #65295 | — | 5 | 1 | no | — |
| 77 | #65290 | — | 5 | 1 | no | — |
| 78 | #64863 | — | 5 | 1 | no | — |
| 79 | #64863 | D5 | 1 | 1 | yes | characteristic, complemented |
| 80 | C5×H(3,ℤ/4) | — | 5 | 1 | no | — |
| 81 | #64751 | — | 5 | 1 | no | — |
| 82 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 83 | C22×C5⋊D5 | C22⋊C4 | 1 | 2 | yes | — |
| 84 | C22×C5×D5 | — | 2 | 1 | no | — |
| 85 | C22×C5×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C2×D52 | — | 4 | 1 | no | — |
| 87 | C2×D52 | — | 4 | 1 | no | — |
| 88 | C2×D52 | — | 8 | 2 | no | — |
| 89 | C2×#1042 | — | 4 | 1 | no | — |
| 90 | C2×C5×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 91 | C2×C4×C52 | — | 2 | 1 | no | — |
| 92 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 93 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 94 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 95 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 96 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 97 | C4⋊(C5⋊D5) | — | 8 | 2 | no | — |
| 98 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 99 | C2×C5×Dic5 | C22⋊C4 | 1 | 2 | yes | — |
| 100 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C5×D20 | — | 2 | 1 | no | — |
| 102 | C5×D20 | — | 2 | 1 | no | — |
| 103 | C4×C5×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C4×C5×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C4×C5×D5 | #41 | 1 | 1 | yes | characteristic |
| 106 | C4×C5×D5 | #41 | 1 | 1 | yes | characteristic |
| 107 | C5×Dic10 | — | 2 | 1 | no | — |
| 108 | C5×Dic10 | — | 2 | 1 | no | — |
| 109 | #6038 | — | 2 | 2 | no | — |
| 110 | #6038 | — | 2 | 2 | no | — |
| 111 | #6038 | — | 4 | 1 | no | — |
| 112 | #6038 | — | 4 | 1 | no | — |
| 113 | #6038 | — | 8 | 2 | no | — |
| 114 | #6036 | — | 2 | 2 | no | — |
| 115 | #6036 | — | 2 | 2 | no | — |
| 116 | #6032 | — | 2 | 2 | no | — |
| 117 | C5×#170 | — | 2 | 2 | no | — |
| 118 | C2×#713 | — | 5 | 1 | no | — |
| 119 | C2×D4×D5 | — | 5 | 1 | no | — |
| 120 | C2×#709 | — | 5 | 1 | no | — |
| 121 | C22×D20 | — | 5 | 1 | no | — |
| 122 | #4133 | — | 10 | 2 | no | — |
| 123 | #4133 | — | 10 | 2 | no | — |
| 124 | #4130 | — | 5 | 1 | no | — |
| 125 | #4130 | C2×D5 | 1 | 1 | yes | characteristic |
| 126 | D5⋊M16 | — | 5 | 1 | no | — |
| 127 | D5⋊M16 | — | 10 | 2 | no | — |
| 128 | D5⋊M16 | C2×D5 | 1 | 1 | yes | characteristic |
| 129 | C2×C5×M16 | — | 5 | 1 | no | — |
| 130 | C5×#124 | — | 5 | 1 | no | — |
| 131 | C5×#117 | — | 5 | 1 | no | — |
| 132 | C5×#117 | — | 5 | 1 | no | — |
| 133 | #4093 | — | 5 | 1 | no | — |
| 134 | #4086 | — | 5 | 1 | no | — |
| 135 | #4072 | — | 5 | 1 | no | — |
| 136 | C2×#681 | — | 5 | 1 | no | — |
| 137 | #4053 | — | 10 | 2 | no | — |
| 138 | D5×M16 | — | 10 | 2 | no | — |
| 139 | #4047 | — | 10 | 2 | no | — |
| 140 | #4041 | — | 10 | 2 | no | — |
| 141 | #4030 | — | 10 | 2 | no | — |
| 142 | #4028 | — | 10 | 2 | no | — |
| 143 | #4028 | — | 10 | 2 | no | — |
| 144 | #4021 | — | 5 | 1 | no | — |
| 145 | #4021 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 146 | #4020 | — | 5 | 1 | no | — |
| 147 | #4020 | — | 5 | 1 | no | — |
| 148 | #4020 | — | 5 | 1 | no | — |
| 149 | #4020 | — | 20 | 1 | no | — |
| 150 | #4018 | C2×D5 | 1 | 1 | yes | characteristic |
| 151 | #4007 | — | 10 | 2 | no | — |
| 152 | #4007 | — | 10 | 2 | no | — |
| 153 | #3999 | — | 10 | 2 | no | — |
| 154 | #3953 | — | 10 | 2 | no | — |
| 155 | #3941 | — | 10 | 2 | no | — |
| 156 | #3938 | — | 10 | 2 | no | — |
| 157 | #1910 | — | 25 | 1 | no | Sylow |
| 158 | C22×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 159 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 160 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 161 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 162 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 163 | C2×C5×D5 | — | 4 | 1 | no | — |
| 164 | C2×C5×D5 | — | 4 | 2 | no | — |
| 165 | C2×C5×D5 | — | 4 | 1 | no | — |
| 166 | C2×C5×D5 | #121 | 1 | 1 | yes | characteristic |
| 167 | C2×C5×D5 | #121 | 1 | 1 | yes | characteristic |
| 168 | D52 | — | 8 | 2 | no | — |
| 169 | D52 | — | 8 | 2 | no | — |
| 170 | #1042 | — | 8 | 1 | no | — |
| 171 | C5×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 172 | C4×C52 | — | 4 | 1 | no | — |
| 173 | C4×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 174 | C4×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 175 | C5×Dic5 | — | 2 | 2 | no | — |
| 176 | C5×Dic5 | — | 4 | 1 | no | — |
| 177 | C5×Dic5 | #120 | 1 | 1 | yes | characteristic |
| 178 | C5×Dic5 | #123 | 1 | 1 | yes | characteristic |
| 179 | C23×D5 | — | 10 | 1 | no | — |
| 180 | C23×D5 | — | 10 | 1 | no | — |
| 181 | C2×C5×Q8 | — | 5 | 1 | no | — |
| 182 | C2×C5×D4 | — | 5 | 1 | no | — |
| 183 | C22×C4×C5 | — | 5 | 1 | no | — |
| 184 | C2×C22⋊D5 | — | 5 | 2 | no | — |
| 185 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 186 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 187 | #713 | — | 10 | 1 | no | — |
| 188 | #713 | — | 10 | 1 | no | — |
| 189 | #713 | — | 10 | 1 | no | — |
| 190 | #713 | — | 10 | 1 | no | — |
| 191 | D4×D5 | — | 10 | 1 | no | — |
| 192 | D4×D5 | — | 10 | 1 | no | — |
| 193 | D4×D5 | — | 10 | 1 | no | — |
| 194 | D4×D5 | — | 10 | 1 | no | — |
| 195 | #709 | — | 10 | 1 | no | — |
| 196 | #709 | — | 10 | 1 | no | — |
| 197 | #709 | — | 10 | 1 | no | — |
| 198 | #709 | — | 10 | 1 | no | — |
| 199 | C2×D20 | — | 5 | 2 | no | — |
| 200 | C2×D20 | — | 5 | 1 | no | — |
| 201 | C2×D20 | — | 5 | 1 | no | — |
| 202 | C2×D20 | — | 5 | 1 | no | — |
| 203 | C2×D20 | — | 5 | 1 | no | — |
| 204 | C2×D20 | — | 10 | 1 | no | — |
| 205 | C2×D20 | — | 10 | 1 | no | — |
| 206 | C2×D20 | — | 10 | 1 | no | — |
| 207 | C2×D20 | — | 10 | 1 | no | — |
| 208 | C2×D20 | — | 10 | 1 | no | — |
| 209 | C2×D20 | — | 10 | 2 | no | — |
| 210 | C2×D20 | — | 10 | 2 | no | — |
| 211 | C2×D20 | — | 10 | 2 | no | — |
| 212 | C2×D20 | — | 20 | 1 | no | — |
| 213 | C2×D20 | — | 20 | 1 | no | — |
| 214 | C2×D20 | — | 20 | 4 | no | — |
| 215 | C2×D20 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 216 | C2×C4×D5 | — | 5 | 2 | no | — |
| 217 | C2×C4×D5 | — | 5 | 2 | no | — |
| 218 | C2×C4×D5 | C22×D5 | 1 | 1 | yes | characteristic |
| 219 | C2×Dic10 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 220 | C22⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 221 | C22⋊AGL(1,𝔽5) | — | 10 | 1 | no | — |
| 222 | #704 | — | 2 | 1 | no | — |
| 223 | #704 | — | 10 | 1 | no | — |
| 224 | C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 225 | C4⋊AGL(1,𝔽5) | — | 10 | 1 | no | — |
| 226 | C4×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 227 | C4×AGL(1,𝔽5) | — | 10 | 1 | no | — |
| 228 | #700 | — | 2 | 1 | no | — |
| 229 | #700 | — | 10 | 4 | no | — |
| 230 | #700 | — | 10 | 1 | no | — |
| 231 | D5⋊C8 | — | 5 | 2 | no | — |
| 232 | D5⋊C8 | — | 10 | 4 | no | — |
| 233 | D5⋊C8 | D20 | 1 | 2 | yes | complemented |
| 234 | C5×M16 | — | 10 | 1 | no | — |
| 235 | C5×M16 | — | 10 | 1 | no | — |
| 236 | C2×C5×C8 | — | 5 | 2 | no | — |
| 237 | C5×C4⋊C4 | — | 10 | 1 | no | — |
| 238 | C5×C4⋊C4 | — | 10 | 1 | no | — |
| 239 | C5×C22⋊C4 | — | 10 | 2 | no | — |
| 240 | C5×C22⋊C4 | — | 10 | 1 | no | — |
| 241 | C5×C22⋊C4 | — | 10 | 1 | no | — |
| 242 | C42×C5 | — | 4 | 1 | no | — |
| 243 | C42×C5 | — | 5 | 1 | no | — |
| 244 | C42×C5 | — | 10 | 1 | no | — |
| 245 | C42×C5 | C4×D5 | 1 | 1 | yes | characteristic |
| 246 | C42×C5 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 247 | C22⋊Dic5 | — | 10 | 1 | no | — |
| 248 | #685 | — | 2 | 1 | no | — |
| 249 | #685 | — | 2 | 2 | no | — |
| 250 | #685 | — | 10 | 2 | no | — |
| 251 | #685 | — | 10 | 2 | no | — |
| 252 | C4⋊Dic5 | — | 10 | 1 | no | — |
| 253 | #683 | — | 2 | 1 | no | — |
| 254 | C4×Dic5 | — | 10 | 1 | no | — |
| 255 | C4×Dic5 | C4×D5 | 1 | 1 | yes | characteristic |
| 256 | #681 | — | 10 | 1 | no | — |
| 257 | #681 | — | 10 | 1 | no | — |
| 258 | C2×#168 | — | 5 | 2 | no | — |
| 259 | #676 | — | 10 | 4 | no | — |
| 260 | C8×D5 | — | 10 | 4 | no | — |
| 261 | #568 | — | 25 | 1 | no | — |
| 262 | #535 | — | 25 | 1 | no | — |
| 263 | #418 | — | 25 | 1 | no | — |
| 264 | #418 | — | 25 | 1 | no | — |
| 265 | #410 | — | 25 | 1 | no | — |
| 266 | H(3,ℤ/4) | — | 5 | 1 | no | — |
| 267 | H(3,ℤ/4) | — | 25 | 1 | no | — |
| 268 | C2×C52 | — | 2 | 1 | no | — |
| 269 | C2×C52 | #386 | 1 | 1 | yes | characteristic |
| 270 | C5⋊D5 | — | 4 | 2 | no | — |
| 271 | C5⋊D5 | — | 8 | 1 | no | — |
| 272 | C5×D5 | — | 2 | 1 | no | — |
| 273 | C5×D5 | — | 2 | 1 | no | — |
| 274 | C5×D5 | — | 8 | 1 | no | — |
| 275 | C23×C5 | — | 5 | 1 | no | — |
| 276 | C23×C5 | — | 10 | 1 | no | — |
| 277 | C22×D5 | — | 2 | 1 | no | — |
| 278 | C22×D5 | — | 5 | 2 | no | — |
| 279 | C22×D5 | — | 5 | 2 | no | — |
| 280 | C22×D5 | — | 10 | 1 | no | — |
| 281 | C22×D5 | — | 10 | 1 | no | — |
| 282 | C22×D5 | — | 20 | 2 | no | — |
| 283 | C22×D5 | — | 20 | 2 | no | — |
| 284 | C22×D5 | — | 20 | 1 | no | — |
| 285 | C22×D5 | — | 20 | 1 | no | — |
| 286 | C22×D5 | — | 20 | 1 | no | — |
| 287 | C22×D5 | — | 20 | 1 | no | — |
| 288 | C22×D5 | — | 40 | 2 | no | — |
| 289 | C22×D5 | — | 40 | 2 | no | — |
| 290 | C22×D5 | D4×D5 | 1 | 1 | yes | characteristic |
| 291 | C2×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 292 | C2×AGL(1,𝔽5) | — | 20 | 1 | no | — |
| 293 | C5×Q8 | — | 10 | 1 | no | — |
| 294 | C5×Q8 | — | 10 | 1 | no | — |
| 295 | C5×D4 | — | 10 | 1 | no | — |
| 296 | C5×D4 | — | 10 | 1 | no | — |
| 297 | C2×C4×C5 | — | 2 | 1 | no | — |
| 298 | C2×C4×C5 | — | 2 | 1 | no | — |
| 299 | C2×C4×C5 | — | 4 | 2 | no | — |
| 300 | C2×C4×C5 | — | 4 | 1 | no | — |
| 301 | C2×C4×C5 | — | 5 | 1 | no | — |
| 302 | C2×C4×C5 | — | 5 | 1 | no | — |
| 303 | C2×C4×C5 | — | 5 | 1 | no | — |
| 304 | C2×C4×C5 | — | 5 | 1 | no | — |
| 305 | C2×C4×C5 | — | 5 | 1 | no | — |
| 306 | C2×C4×C5 | — | 5 | 2 | no | — |
| 307 | C2×C4×C5 | — | 10 | 1 | no | — |
| 308 | C2×C4×C5 | — | 20 | 1 | no | — |
| 309 | C2×C4×C5 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 310 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 311 | C22⋊D5 | — | 10 | 2 | no | — |
| 312 | C22⋊D5 | — | 10 | 2 | no | — |
| 313 | C22⋊D5 | — | 20 | 1 | no | — |
| 314 | C22⋊D5 | — | 20 | 1 | no | — |
| 315 | C22⋊D5 | — | 40 | 2 | no | — |
| 316 | C2×Dic5 | — | 2 | 1 | no | — |
| 317 | C2×Dic5 | — | 20 | 1 | no | — |
| 318 | C2×Dic5 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 319 | C2×Dic5 | D4×D5 | 1 | 1 | yes | characteristic |
| 320 | D20 | — | 2 | 1 | no | — |
| 321 | D20 | — | 2 | 1 | no | — |
| 322 | D20 | — | 10 | 2 | no | — |
| 323 | D20 | — | 10 | 2 | no | — |
| 324 | D20 | — | 10 | 1 | no | — |
| 325 | D20 | — | 10 | 1 | no | — |
| 326 | D20 | — | 10 | 1 | no | — |
| 327 | D20 | — | 10 | 1 | no | — |
| 328 | D20 | — | 10 | 1 | no | — |
| 329 | D20 | — | 10 | 1 | no | — |
| 330 | D20 | — | 10 | 1 | no | — |
| 331 | D20 | — | 10 | 1 | no | — |
| 332 | D20 | — | 20 | 1 | no | — |
| 333 | D20 | — | 20 | 1 | no | — |
| 334 | D20 | — | 40 | 1 | no | — |
| 335 | D20 | — | 40 | 1 | no | — |
| 336 | D20 | — | 40 | 1 | no | — |
| 337 | D20 | — | 40 | 1 | no | — |
| 338 | D20 | — | 40 | 2 | no | — |
| 339 | D20 | — | 40 | 2 | no | — |
| 340 | D20 | — | 40 | 8 | no | — |
| 341 | D20 | — | 40 | 2 | no | — |
| 342 | C4×D5 | — | 10 | 2 | no | — |
| 343 | C4×D5 | — | 10 | 2 | no | — |
| 344 | C4×D5 | — | 10 | 2 | no | — |
| 345 | C4×D5 | — | 10 | 2 | no | — |
| 346 | C4×D5 | C2×D20 | 1 | 1 | yes | characteristic |
| 347 | C4×D5 | #709 | 1 | 1 | yes | characteristic |
| 348 | C4×D5 | D4×D5 | 1 | 1 | yes | characteristic |
| 349 | C4×D5 | #713 | 1 | 1 | yes | characteristic |
| 350 | Dic10 | — | 2 | 1 | no | — |
| 351 | Dic10 | — | 2 | 1 | no | — |
| 352 | #170 | — | 2 | 2 | no | — |
| 353 | #170 | — | 10 | 2 | no | — |
| 354 | C5×C8 | — | 10 | 2 | no | — |
| 355 | #168 | — | 10 | 2 | no | — |
| 356 | C2×#41 | — | 25 | 1 | no | — |
| 357 | C22×D4 | — | 25 | 1 | no | — |
| 358 | #131 | — | 50 | 2 | no | — |
| 359 | #131 | — | 50 | 2 | no | — |
| 360 | C2×M16 | — | 5 | 1 | no | — |
| 361 | C2×M16 | — | 25 | 1 | no | — |
| 362 | C2×M16 | — | 50 | 2 | no | — |
| 363 | #127 | — | 25 | 1 | no | — |
| 364 | #127 | — | 25 | 1 | no | — |
| 365 | #124 | — | 5 | 1 | no | — |
| 366 | #124 | — | 25 | 1 | no | — |
| 367 | #121 | — | 50 | 2 | no | — |
| 368 | #120 | — | 50 | 2 | no | — |
| 369 | #117 | — | 5 | 1 | no | — |
| 370 | #117 | — | 5 | 1 | no | — |
| 371 | #117 | — | 25 | 1 | no | — |
| 372 | #102 | — | 50 | 2 | no | — |
| 373 | #102 | — | 50 | 2 | no | — |
| 374 | #99 | — | 50 | 2 | no | — |
| 375 | C52 | #1910 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 376 | C22×C5 | — | 4 | 1 | no | — |
| 377 | C22×C5 | — | 5 | 1 | no | — |
| 378 | C22×C5 | — | 5 | 1 | no | — |
| 379 | C22×C5 | — | 20 | 1 | no | — |
| 380 | C22×C5 | — | 20 | 2 | no | — |
| 381 | C22×C5 | — | 20 | 1 | no | — |
| 382 | C22×C5 | D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 383 | C22×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 384 | C2×D5 | — | 4 | 1 | no | — |
| 385 | C2×D5 | — | 4 | 2 | no | — |
| 386 | C2×D5 | — | 4 | 1 | no | — |
| 387 | C2×D5 | — | 10 | 2 | no | — |
| 388 | C2×D5 | — | 10 | 2 | no | — |
| 389 | C2×D5 | — | 20 | 2 | no | — |
| 390 | C2×D5 | — | 20 | 2 | no | — |
| 391 | C2×D5 | — | 20 | 2 | no | — |
| 392 | C2×D5 | — | 20 | 2 | no | — |
| 393 | C2×D5 | — | 20 | 1 | no | — |
| 394 | C2×D5 | — | 20 | 1 | no | — |
| 395 | C2×D5 | — | 40 | 2 | no | — |
| 396 | C2×D5 | — | 40 | 4 | no | — |
| 397 | C2×D5 | — | 40 | 4 | no | — |
| 398 | C2×D5 | — | 40 | 2 | no | — |
| 399 | C2×D5 | — | 40 | 2 | no | — |
| 400 | C2×D5 | — | 40 | 2 | no | — |
| 401 | C2×D5 | — | 40 | 2 | no | — |
| 402 | C2×D5 | — | 40 | 2 | no | — |
| 403 | C2×D5 | #4030 | 1 | 1 | yes | characteristic |
| 404 | C2×D5 | #4041 | 1 | 1 | yes | characteristic |
| 405 | AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 406 | AGL(1,𝔽5) | — | 40 | 1 | no | — |
| 407 | C4×C5 | — | 4 | 1 | no | — |
| 408 | C4×C5 | — | 4 | 1 | no | — |
| 409 | C4×C5 | — | 4 | 4 | no | — |
| 410 | C4×C5 | — | 4 | 1 | no | — |
| 411 | C4×C5 | — | 4 | 1 | no | — |
| 412 | C4×C5 | — | 5 | 1 | no | — |
| 413 | C4×C5 | — | 5 | 1 | no | — |
| 414 | C4×C5 | — | 10 | 2 | no | — |
| 415 | C4×C5 | — | 20 | 1 | no | — |
| 416 | C4×C5 | — | 40 | 1 | no | — |
| 417 | C4×C5 | C4×D20 | 1 | 1 | yes | characteristic |
| 418 | C4×C5 | #4039 | 1 | 1 | yes | characteristic |
| 419 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 420 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 421 | Dic5 | — | 2 | 2 | no | — |
| 422 | Dic5 | — | 4 | 1 | no | — |
| 423 | Dic5 | — | 40 | 1 | no | — |
| 424 | Dic5 | #4028 | 1 | 1 | yes | characteristic |
| 425 | Dic5 | #4040 | 1 | 1 | yes | characteristic |
| 426 | C24 | — | 50 | 1 | no | — |
| 427 | #41 | — | 50 | 1 | no | — |
| 428 | #41 | — | 50 | 1 | no | — |
| 429 | #41 | — | 50 | 1 | no | — |
| 430 | #41 | — | 50 | 1 | no | — |
| 431 | C2×Q8 | — | 5 | 1 | no | — |
| 432 | C2×D4 | — | 5 | 1 | no | — |
| 433 | C2×D4 | — | 25 | 2 | no | — |
| 434 | C2×D4 | — | 25 | 1 | no | — |
| 435 | C2×D4 | — | 25 | 1 | no | — |
| 436 | C2×D4 | — | 50 | 2 | no | — |
| 437 | C2×D4 | — | 50 | 1 | no | — |
| 438 | C2×D4 | — | 50 | 1 | no | — |
| 439 | C2×D4 | — | 50 | 1 | no | — |
| 440 | C2×D4 | — | 50 | 1 | no | — |
| 441 | C2×D4 | — | 50 | 1 | no | — |
| 442 | C2×D4 | — | 50 | 2 | no | — |
| 443 | C22×C4 | — | 5 | 1 | no | — |
| 444 | C22×C4 | — | 25 | 2 | no | — |
| 445 | M16 | — | 10 | 1 | no | — |
| 446 | M16 | — | 10 | 1 | no | — |
| 447 | M16 | — | 50 | 4 | no | — |
| 448 | M16 | — | 50 | 1 | no | — |
| 449 | M16 | — | 50 | 1 | no | — |
| 450 | C2×C8 | — | 5 | 2 | no | — |
| 451 | C2×C8 | — | 25 | 2 | no | — |
| 452 | C2×C8 | — | 50 | 4 | no | — |
| 453 | C4⋊C4 | — | 10 | 1 | no | — |
| 454 | C4⋊C4 | — | 10 | 1 | no | — |
| 455 | C4⋊C4 | — | 50 | 1 | no | — |
| 456 | C22⋊C4 | — | 10 | 2 | no | — |
| 457 | C22⋊C4 | — | 10 | 1 | no | — |
| 458 | C22⋊C4 | — | 10 | 1 | no | — |
| 459 | C22⋊C4 | — | 50 | 2 | no | — |
| 460 | C22⋊C4 | — | 50 | 1 | no | — |
| 461 | C42 | — | 5 | 1 | no | — |
| 462 | C42 | — | 10 | 1 | no | — |
| 463 | C42 | — | 50 | 1 | no | — |
| 464 | C42 | D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 465 | C2×C5 | — | 2 | 1 | no | — |
| 466 | C2×C5 | — | 2 | 1 | no | — |
| 467 | C2×C5 | — | 4 | 2 | no | — |
| 468 | C2×C5 | — | 4 | 1 | no | — |
| 469 | C2×C5 | — | 10 | 1 | no | — |
| 470 | C2×C5 | — | 10 | 1 | no | — |
| 471 | C2×C5 | — | 40 | 1 | no | — |
| 472 | C2×C5 | #64954 | 1 | 1 | yes | characteristic |
| 473 | C2×C5 | #65779 | 1 | 1 | yes | characteristic |
| 474 | D5 | — | 2 | 1 | no | — |
| 475 | D5 | — | 2 | 1 | no | — |
| 476 | D5 | — | 8 | 1 | no | — |
| 477 | D5 | — | 20 | 2 | no | — |
| 478 | D5 | — | 20 | 2 | no | — |
| 479 | D5 | — | 40 | 1 | no | — |
| 480 | D5 | — | 40 | 1 | no | — |
| 481 | D5 | — | 80 | 2 | no | — |
| 482 | D5 | — | 80 | 2 | no | — |
| 483 | C23 | — | 5 | 1 | no | — |
| 484 | C23 | — | 10 | 1 | no | — |
| 485 | C23 | — | 25 | 2 | no | — |
| 486 | C23 | — | 50 | 1 | no | — |
| 487 | C23 | — | 100 | 1 | no | — |
| 488 | C23 | — | 100 | 1 | no | — |
| 489 | C23 | — | 200 | 2 | no | — |
| 490 | Q8 | — | 10 | 1 | no | — |
| 491 | Q8 | — | 10 | 1 | no | — |
| 492 | D4 | — | 10 | 1 | no | — |
| 493 | D4 | — | 10 | 1 | no | — |
| 494 | D4 | — | 50 | 2 | no | — |
| 495 | D4 | — | 50 | 2 | no | — |
| 496 | D4 | — | 50 | 1 | no | — |
| 497 | D4 | — | 50 | 1 | no | — |
| 498 | D4 | — | 50 | 1 | no | — |
| 499 | D4 | — | 50 | 1 | no | — |
| 500 | D4 | — | 100 | 1 | no | — |
| 501 | D4 | — | 100 | 1 | no | — |
| 502 | D4 | — | 200 | 2 | no | — |
| 503 | D4 | — | 200 | 2 | no | — |
| 504 | C2×C4 | — | 2 | 1 | no | — |
| 505 | C2×C4 | — | 5 | 1 | no | — |
| 506 | C2×C4 | — | 5 | 1 | no | — |
| 507 | C2×C4 | — | 5 | 1 | no | — |
| 508 | C2×C4 | — | 5 | 1 | no | — |
| 509 | C2×C4 | — | 5 | 1 | no | — |
| 510 | C2×C4 | — | 5 | 2 | no | — |
| 511 | C2×C4 | — | 10 | 1 | no | — |
| 512 | C2×C4 | — | 20 | 1 | no | — |
| 513 | C2×C4 | — | 50 | 2 | no | — |
| 514 | C2×C4 | — | 50 | 2 | no | — |
| 515 | C2×C4 | — | 100 | 1 | no | — |
| 516 | C2×C4 | C2×D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 517 | C8 | — | 10 | 2 | no | — |
| 518 | C8 | — | 50 | 2 | no | — |
| 519 | C5 | — | 4 | 1 | no | — |
| 520 | C5 | #10599506 | 1 | 1 | yes | characteristic, complemented |
| 521 | C5 | #10604571 | 1 | 1 | yes | characteristic, complemented |
| 522 | C22 | — | 5 | 1 | no | — |
| 523 | C22 | — | 5 | 1 | no | — |
| 524 | C22 | — | 20 | 1 | no | — |
| 525 | C22 | — | 20 | 2 | no | — |
| 526 | C22 | — | 20 | 1 | no | — |
| 527 | C22 | — | 50 | 2 | no | — |
| 528 | C22 | — | 100 | 2 | no | — |
| 529 | C22 | — | 100 | 2 | no | — |
| 530 | C22 | — | 100 | 1 | no | — |
| 531 | C22 | — | 200 | 2 | no | — |
| 532 | C22 | — | 200 | 2 | no | — |
| 533 | C22 | D5×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 534 | C4 | — | 4 | 1 | no | — |
| 535 | C4 | — | 5 | 1 | no | — |
| 536 | C4 | — | 5 | 1 | no | — |
| 537 | C4 | — | 10 | 2 | no | — |
| 538 | C4 | — | 20 | 1 | no | — |
| 539 | C4 | — | 40 | 1 | no | — |
| 540 | C4 | — | 200 | 1 | no | — |
| 541 | C4 | AGL(1,𝔽5)×D20 | 1 | 1 | yes | characteristic |
| 542 | C4 | #11717337 | 1 | 1 | yes | characteristic |
| 543 | C2 | — | 2 | 1 | no | — |
| 544 | C2 | — | 10 | 1 | no | — |
| 545 | C2 | — | 10 | 1 | no | — |
| 546 | C2 | — | 40 | 1 | no | — |
| 547 | C2 | — | 100 | 2 | no | — |
| 548 | C2 | — | 200 | 1 | no | — |
| 549 | C2 | #13103713 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107609 | C2 | semidirect |
| 3. #13103546 | C2 | semidirect |
| 4. #13103543 | C2 | semidirect |
| 5. #13103536 | C2 | semidirect |
| 6. #13100147 | C2 | semidirect |
| 7. C5×#64863 | C2 | semidirect |
| 17. #11717194 | C4 | semidirect |
| 18. C5×#4021 | C4 | semidirect |
| 21. #11717029 | C4 | semidirect |
| 23. #11716982 | C4 | semidirect |
| 53. D5⋊#168 | D4 | semidirect |
| 59. C5×D5⋊C8 | D4 | semidirect |
| 79. #64863 | D5 | semidirect |
| 145. #4021 | AGL(1,𝔽5) | semidirect |
| 233. D5⋊C8 | D20 | semidirect |
| 375. C52 | #1910 | semidirect |
| 520. C5 | #10599506 | semidirect |
| 521. C5 | #10604571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107609 | 2 |
| #13105092 | 2 |
| #13103546 | 2 |
| #13103543 | 2 |
| #13103536 | 2 |
| #13100147 | 2 |
| C5×#64863 | 2 |
| #10604571 | 5 |
| #10599506 | 5 |