Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
942 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #13107619 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D5×#4020 | 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 | D5⋊#3955 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13100146 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C5×#64862 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×D5×D20 | — | 2 | 2 | no | — |
| 9 | C2×D5×D20 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×D5×D20 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11717425 | C22 | 1 | 1 | yes | characteristic |
| 12 | D5⋊#681 | C22 | 1 | 1 | yes | characteristic |
| 13 | C5×#4130 | C22 | 1 | 1 | yes | characteristic |
| 14 | C5×D5⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 15 | D5×C22⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 16 | #11717337 | — | 2 | 2 | no | — |
| 17 | AGL(1,𝔽5)×D20 | — | 2 | 2 | no | — |
| 18 | #11717194 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | C5×#4020 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | C42×C5×D5 | C22 | 1 | 1 | yes | characteristic |
| 21 | #11717029 | — | 2 | 2 | no | — |
| 22 | #11717029 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #11717029 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #11716757 | — | 2 | 2 | no | — |
| 25 | #11716735 | — | 2 | 2 | no | — |
| 26 | #11716734 | — | 2 | 2 | no | — |
| 27 | #10604614 | — | 5 | 1 | no | maximal |
| 28 | #10599553 | — | 5 | 1 | no | maximal |
| 29 | C22×D52 | — | 2 | 1 | no | — |
| 30 | C22×D52 | D4 | 1 | 2 | yes | — |
| 31 | C2×D5×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 32 | C2×C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 33 | C2×C4⋊(C5⋊D5) | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×C4⋊(C5⋊D5) | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×C5×D20 | — | 2 | 2 | no | — |
| 36 | C2×C5×D20 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×C5×D20 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×C4×C5×D5 | — | 2 | 1 | no | — |
| 39 | C2×C4×C5×D5 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×#6038 | — | 2 | 2 | no | — |
| 41 | C2×#6038 | — | 2 | 2 | no | — |
| 42 | C2×#6038 | — | 2 | 1 | no | — |
| 43 | C2×#6038 | D4 | 1 | 2 | yes | — |
| 44 | D5×D20 | — | 2 | 1 | no | — |
| 45 | D5×D20 | — | 2 | 1 | no | — |
| 46 | D5×D20 | — | 2 | 1 | no | — |
| 47 | D5×D20 | — | 2 | 1 | no | — |
| 48 | D5×D20 | — | 2 | 1 | no | — |
| 49 | D5×D20 | — | 2 | 1 | no | — |
| 50 | D5×D20 | — | 2 | 1 | no | — |
| 51 | D5×D20 | — | 2 | 1 | no | — |
| 52 | D5×D20 | — | 4 | 8 | no | — |
| 53 | C22⋊#1042 | — | 2 | 1 | no | — |
| 54 | #87853 | — | 2 | 1 | no | — |
| 55 | C4⋊#1042 | D4 | 1 | 2 | yes | complemented |
| 56 | C4×#1042 | — | 2 | 1 | no | — |
| 57 | #87849 | — | 2 | 1 | no | — |
| 58 | D5⋊#168 | — | 2 | 1 | no | — |
| 59 | C5×C22⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 60 | C5×#704 | — | 2 | 1 | no | — |
| 61 | C5×C4⋊AGL(1,𝔽5) | D4 | 1 | 2 | yes | complemented |
| 62 | C4×C5×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 63 | C5×#700 | — | 2 | 1 | no | — |
| 64 | C5×D5⋊C8 | — | 2 | 1 | no | — |
| 65 | (C2×AGL(1,𝔽5))⋊D5 | — | 2 | 4 | no | — |
| 66 | C42×C52 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 67 | C4×C5×Dic5 | — | 2 | 1 | no | — |
| 68 | C4×C5×Dic5 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 69 | #66258 | — | 5 | 1 | no | — |
| 70 | D5×#127 | — | 5 | 1 | no | — |
| 71 | #65855 | — | 5 | 1 | no | — |
| 72 | C2×#4020 | — | 5 | 1 | no | — |
| 73 | D5⋊#100 | — | 5 | 1 | no | — |
| 74 | #65767 | — | 5 | 1 | no | — |
| 75 | #65767 | — | 5 | 1 | no | — |
| 76 | #65420 | — | 5 | 1 | no | — |
| 77 | C2×#3955 | — | 5 | 1 | no | — |
| 78 | #65290 | — | 5 | 1 | no | — |
| 79 | #64862 | — | 5 | 1 | no | — |
| 80 | #64862 | D5 | 1 | 1 | yes | characteristic, complemented |
| 81 | C5×#339 | — | 5 | 1 | no | — |
| 82 | #64743 | — | 5 | 1 | no | — |
| 83 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 84 | C22×C5⋊D5 | C22⋊C4 | 1 | 2 | yes | — |
| 85 | C22×C5×D5 | — | 2 | 1 | no | — |
| 86 | C22×C5×D5 | C22⋊C4 | 1 | 2 | yes | — |
| 87 | C22×C5×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C2×D52 | — | 2 | 2 | no | — |
| 89 | C2×D52 | — | 2 | 2 | no | — |
| 90 | C2×D52 | — | 4 | 4 | no | — |
| 91 | C2×D52 | — | 4 | 4 | no | — |
| 92 | C2×D52 | — | 4 | 1 | no | — |
| 93 | C2×D52 | — | 4 | 1 | no | — |
| 94 | C2×#1042 | — | 2 | 2 | no | — |
| 95 | C2×C5×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 96 | D5×AGL(1,𝔽5) | — | 8 | 4 | no | — |
| 97 | C2×C4×C52 | — | 2 | 1 | no | — |
| 98 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 99 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 100 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 101 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 102 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 103 | C4⋊(C5⋊D5) | — | 4 | 4 | no | — |
| 104 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 105 | C2×C5×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C5×D20 | — | 2 | 1 | no | — |
| 107 | C5×D20 | — | 2 | 1 | no | — |
| 108 | C5×D20 | — | 2 | 1 | no | — |
| 109 | C5×D20 | — | 2 | 1 | no | — |
| 110 | C5×D20 | — | 4 | 4 | no | — |
| 111 | C4×C5×D5 | — | 2 | 4 | no | — |
| 112 | C4×C5×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C4×C5×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C4×C5×D5 | #41 | 1 | 1 | yes | characteristic |
| 115 | C4×C5×D5 | #41 | 1 | 1 | yes | characteristic |
| 116 | #6038 | — | 2 | 2 | no | — |
| 117 | #6038 | — | 2 | 2 | no | — |
| 118 | #6038 | — | 4 | 4 | no | — |
| 119 | #6038 | — | 4 | 4 | no | — |
| 120 | #6038 | — | 4 | 1 | no | — |
| 121 | #6038 | — | 4 | 1 | no | — |
| 122 | #6032 | — | 4 | 1 | no | — |
| 123 | C5×#170 | — | 4 | 1 | no | — |
| 124 | C2×D4×D5 | — | 5 | 1 | no | — |
| 125 | C2×D4×D5 | — | 5 | 1 | no | — |
| 126 | C2×D4×D5 | — | 10 | 2 | no | — |
| 127 | C22×D20 | — | 5 | 1 | no | — |
| 128 | C22×D20 | — | 5 | 1 | no | — |
| 129 | C22×D20 | — | 10 | 2 | no | — |
| 130 | C2×C22⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 131 | D4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 132 | D4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 133 | #4130 | — | 5 | 1 | no | — |
| 134 | #4130 | C2×D5 | 1 | 1 | yes | characteristic |
| 135 | D5⋊M16 | — | 5 | 1 | no | — |
| 136 | D5⋊M16 | C2×D5 | 1 | 1 | yes | characteristic |
| 137 | C2×C5×M16 | — | 5 | 1 | no | — |
| 138 | C5×#127 | — | 5 | 1 | no | — |
| 139 | C5×#117 | — | 5 | 1 | no | — |
| 140 | C2×C42×C5 | — | 5 | 1 | no | — |
| 141 | #4086 | — | 5 | 1 | no | — |
| 142 | #4086 | — | 5 | 1 | no | — |
| 143 | #4086 | — | 10 | 2 | no | — |
| 144 | #4072 | — | 5 | 1 | no | — |
| 145 | C2×#681 | — | 5 | 1 | no | — |
| 146 | #4039 | — | 10 | 2 | no | — |
| 147 | D5×C22⋊C4 | — | 10 | 2 | no | — |
| 148 | #4020 | — | 5 | 1 | no | — |
| 149 | #4020 | — | 5 | 1 | no | — |
| 150 | #4020 | — | 5 | 1 | no | — |
| 151 | #4020 | — | 5 | 1 | no | — |
| 152 | #4020 | — | 10 | 2 | no | — |
| 153 | #4020 | — | 20 | 1 | no | — |
| 154 | #4020 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 155 | C4×D20 | — | 10 | 2 | no | — |
| 156 | C42×D5 | C2×D5 | 1 | 1 | yes | characteristic |
| 157 | #4013 | — | 10 | 2 | no | — |
| 158 | #4007 | — | 10 | 2 | no | — |
| 159 | #4007 | — | 10 | 2 | no | — |
| 160 | #3955 | — | 10 | 2 | no | — |
| 161 | #3953 | — | 10 | 2 | no | — |
| 162 | #3941 | — | 10 | 2 | no | — |
| 163 | #1887 | — | 25 | 1 | no | Sylow |
| 164 | C22×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 166 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 167 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 168 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 169 | C2×C5×D5 | — | 2 | 2 | no | — |
| 170 | C2×C5×D5 | — | 2 | 2 | no | — |
| 171 | C2×C5×D5 | — | 4 | 2 | no | — |
| 172 | C2×C5×D5 | — | 4 | 2 | no | — |
| 173 | C2×C5×D5 | — | 4 | 1 | no | — |
| 174 | C2×C5×D5 | #120 | 1 | 1 | yes | characteristic |
| 175 | C2×C5×D5 | #123 | 1 | 1 | yes | characteristic |
| 176 | D52 | — | 4 | 4 | no | — |
| 177 | D52 | — | 8 | 2 | no | — |
| 178 | D52 | — | 8 | 2 | no | — |
| 179 | D52 | — | 8 | 2 | no | — |
| 180 | #1042 | — | 4 | 2 | no | — |
| 181 | C5×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 182 | C4×C52 | — | 2 | 2 | no | — |
| 183 | C4×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 184 | C4×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 185 | C5×Dic5 | — | 2 | 2 | no | — |
| 186 | C5×Dic5 | #121 | 1 | 1 | yes | characteristic |
| 187 | C5×Dic5 | #121 | 1 | 1 | yes | characteristic |
| 188 | C23×D5 | — | 5 | 2 | no | — |
| 189 | C23×D5 | — | 5 | 2 | no | — |
| 190 | C23×D5 | — | 10 | 1 | no | — |
| 191 | C23×D5 | — | 10 | 1 | no | — |
| 192 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 193 | C2×C5×D4 | — | 5 | 1 | no | — |
| 194 | C2×C5×D4 | — | 5 | 1 | no | — |
| 195 | C2×C5×D4 | — | 10 | 2 | no | — |
| 196 | C22×C4×C5 | — | 5 | 1 | no | — |
| 197 | C22×C4×C5 | — | 10 | 1 | no | — |
| 198 | C2×C22⋊D5 | — | 5 | 2 | no | — |
| 199 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 200 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 201 | C2×C22⋊D5 | — | 10 | 1 | no | — |
| 202 | D4×D5 | — | 10 | 1 | no | — |
| 203 | D4×D5 | — | 10 | 1 | no | — |
| 204 | D4×D5 | — | 10 | 1 | no | — |
| 205 | D4×D5 | — | 10 | 1 | no | — |
| 206 | D4×D5 | — | 10 | 1 | no | — |
| 207 | D4×D5 | — | 10 | 1 | no | — |
| 208 | D4×D5 | — | 10 | 1 | no | — |
| 209 | D4×D5 | — | 10 | 1 | no | — |
| 210 | D4×D5 | — | 20 | 8 | no | — |
| 211 | C2×D20 | — | 2 | 2 | no | — |
| 212 | C2×D20 | — | 5 | 2 | no | — |
| 213 | C2×D20 | — | 5 | 1 | no | — |
| 214 | C2×D20 | — | 5 | 1 | no | — |
| 215 | C2×D20 | — | 5 | 1 | no | — |
| 216 | C2×D20 | — | 5 | 1 | no | — |
| 217 | C2×D20 | — | 10 | 1 | no | — |
| 218 | C2×D20 | — | 10 | 1 | no | — |
| 219 | C2×D20 | — | 10 | 1 | no | — |
| 220 | C2×D20 | — | 10 | 1 | no | — |
| 221 | C2×D20 | — | 10 | 1 | no | — |
| 222 | C2×D20 | — | 10 | 1 | no | — |
| 223 | C2×D20 | — | 10 | 1 | no | — |
| 224 | C2×D20 | — | 10 | 1 | no | — |
| 225 | C2×D20 | — | 10 | 2 | no | — |
| 226 | C2×D20 | — | 10 | 2 | no | — |
| 227 | C2×D20 | — | 10 | 1 | no | — |
| 228 | C2×D20 | — | 10 | 2 | no | — |
| 229 | C2×D20 | — | 10 | 2 | no | — |
| 230 | C2×D20 | — | 20 | 1 | no | — |
| 231 | C2×D20 | — | 20 | 1 | no | — |
| 232 | C2×D20 | — | 20 | 4 | no | — |
| 233 | C2×D20 | — | 20 | 8 | no | — |
| 234 | C2×D20 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 235 | C2×D20 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 236 | C2×C4×D5 | — | 2 | 1 | no | — |
| 237 | C2×C4×D5 | — | 10 | 4 | no | — |
| 238 | C2×C4×D5 | C22×D5 | 1 | 1 | yes | characteristic |
| 239 | C22⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 240 | C22⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 241 | C22⋊AGL(1,𝔽5) | — | 10 | 1 | no | — |
| 242 | #704 | — | 2 | 1 | no | — |
| 243 | #704 | — | 10 | 1 | no | — |
| 244 | C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 245 | C4⋊AGL(1,𝔽5) | D20 | 1 | 2 | yes | complemented |
| 246 | C4×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 247 | C4×AGL(1,𝔽5) | — | 10 | 1 | no | — |
| 248 | #700 | — | 2 | 1 | no | — |
| 249 | #700 | — | 10 | 1 | no | — |
| 250 | D5⋊C8 | — | 2 | 1 | no | — |
| 251 | D5⋊C8 | — | 10 | 1 | no | — |
| 252 | C5×M16 | — | 10 | 1 | no | — |
| 253 | C5×M16 | — | 10 | 1 | no | — |
| 254 | C2×C5×C8 | — | 10 | 1 | no | — |
| 255 | C5×C4⋊C4 | — | 5 | 2 | no | — |
| 256 | C5×C22⋊C4 | — | 10 | 1 | no | — |
| 257 | C42×C5 | — | 4 | 1 | no | — |
| 258 | C42×C5 | — | 5 | 1 | no | — |
| 259 | C42×C5 | — | 10 | 1 | no | — |
| 260 | C42×C5 | — | 10 | 1 | no | — |
| 261 | C42×C5 | C4×D5 | 1 | 1 | yes | characteristic, complemented |
| 262 | C42×C5 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 263 | C22⋊Dic5 | — | 10 | 1 | no | — |
| 264 | #685 | — | 10 | 4 | no | — |
| 265 | C4⋊Dic5 | — | 5 | 2 | no | — |
| 266 | C4×Dic5 | — | 2 | 1 | no | — |
| 267 | C4×Dic5 | — | 10 | 1 | no | — |
| 268 | C4×Dic5 | C4×D5 | 1 | 1 | yes | characteristic, complemented |
| 269 | #681 | — | 10 | 1 | no | — |
| 270 | #681 | — | 10 | 1 | no | — |
| 271 | C2×#168 | — | 10 | 1 | no | — |
| 272 | C2×#127 | — | 25 | 1 | no | — |
| 273 | #518 | — | 25 | 1 | no | — |
| 274 | #418 | — | 25 | 1 | no | — |
| 275 | #418 | — | 25 | 1 | no | — |
| 276 | C2×#100 | — | 25 | 1 | no | — |
| 277 | #339 | — | 5 | 1 | no | — |
| 278 | #339 | — | 25 | 1 | no | — |
| 279 | C2×C52 | — | 2 | 1 | no | — |
| 280 | C2×C52 | #386 | 1 | 1 | yes | characteristic |
| 281 | C5⋊D5 | — | 4 | 2 | no | — |
| 282 | C5⋊D5 | — | 8 | 1 | no | — |
| 283 | C5×D5 | — | 2 | 1 | no | — |
| 284 | C5×D5 | — | 4 | 2 | no | — |
| 285 | C5×D5 | — | 8 | 1 | no | — |
| 286 | C5×D5 | #453 | 1 | 2 | yes | — |
| 287 | C23×C5 | — | 5 | 1 | no | — |
| 288 | C23×C5 | — | 5 | 2 | no | — |
| 289 | C23×C5 | — | 10 | 1 | no | — |
| 290 | C22×D5 | — | 2 | 1 | no | — |
| 291 | C22×D5 | — | 5 | 2 | no | — |
| 292 | C22×D5 | — | 5 | 2 | no | — |
| 293 | C22×D5 | — | 10 | 2 | no | — |
| 294 | C22×D5 | — | 10 | 2 | no | — |
| 295 | C22×D5 | — | 10 | 2 | no | — |
| 296 | C22×D5 | — | 10 | 2 | no | — |
| 297 | C22×D5 | — | 10 | 1 | no | — |
| 298 | C22×D5 | — | 10 | 1 | no | — |
| 299 | C22×D5 | — | 20 | 2 | no | — |
| 300 | C22×D5 | — | 20 | 2 | no | — |
| 301 | C22×D5 | — | 20 | 4 | no | — |
| 302 | C22×D5 | — | 20 | 4 | no | — |
| 303 | C22×D5 | — | 20 | 4 | no | — |
| 304 | C22×D5 | — | 20 | 1 | no | — |
| 305 | C22×D5 | — | 20 | 1 | no | — |
| 306 | C22×D5 | — | 20 | 4 | no | — |
| 307 | C22×D5 | — | 20 | 1 | no | — |
| 308 | C22×D5 | — | 20 | 1 | no | — |
| 309 | C22×D5 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 310 | C22×D5 | D4×D5 | 1 | 1 | yes | characteristic |
| 311 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 312 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 313 | C2×AGL(1,𝔽5) | — | 40 | 4 | no | — |
| 314 | C5×D4 | — | 10 | 1 | no | — |
| 315 | C5×D4 | — | 10 | 1 | no | — |
| 316 | C5×D4 | — | 10 | 1 | no | — |
| 317 | C5×D4 | — | 10 | 1 | no | — |
| 318 | C5×D4 | — | 20 | 4 | no | — |
| 319 | C2×C4×C5 | — | 2 | 1 | no | — |
| 320 | C2×C4×C5 | — | 2 | 1 | no | — |
| 321 | C2×C4×C5 | — | 4 | 2 | no | — |
| 322 | C2×C4×C5 | — | 4 | 1 | no | — |
| 323 | C2×C4×C5 | — | 5 | 1 | no | — |
| 324 | C2×C4×C5 | — | 5 | 1 | no | — |
| 325 | C2×C4×C5 | — | 5 | 1 | no | — |
| 326 | C2×C4×C5 | — | 5 | 1 | no | — |
| 327 | C2×C4×C5 | — | 5 | 1 | no | — |
| 328 | C2×C4×C5 | — | 10 | 4 | no | — |
| 329 | C2×C4×C5 | — | 10 | 1 | no | — |
| 330 | C2×C4×C5 | — | 10 | 2 | no | — |
| 331 | C2×C4×C5 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 332 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 333 | C22⋊D5 | — | 10 | 2 | no | — |
| 334 | C22⋊D5 | — | 10 | 2 | no | — |
| 335 | C22⋊D5 | — | 20 | 4 | no | — |
| 336 | C22⋊D5 | — | 20 | 4 | no | — |
| 337 | C22⋊D5 | — | 20 | 1 | no | — |
| 338 | C22⋊D5 | — | 20 | 1 | no | — |
| 339 | C2×Dic5 | — | 2 | 1 | no | — |
| 340 | C2×Dic5 | — | 10 | 2 | no | — |
| 341 | C2×Dic5 | D4×D5 | 1 | 1 | yes | characteristic |
| 342 | D20 | — | 2 | 1 | no | — |
| 343 | D20 | — | 2 | 1 | no | — |
| 344 | D20 | — | 2 | 1 | no | — |
| 345 | D20 | — | 2 | 1 | no | — |
| 346 | D20 | — | 4 | 4 | no | — |
| 347 | D20 | — | 10 | 2 | no | — |
| 348 | D20 | — | 10 | 2 | no | — |
| 349 | D20 | — | 10 | 1 | no | — |
| 350 | D20 | — | 10 | 1 | no | — |
| 351 | D20 | — | 10 | 1 | no | — |
| 352 | D20 | — | 10 | 1 | no | — |
| 353 | D20 | — | 10 | 1 | no | — |
| 354 | D20 | — | 10 | 1 | no | — |
| 355 | D20 | — | 10 | 1 | no | — |
| 356 | D20 | — | 10 | 1 | no | — |
| 357 | D20 | — | 20 | 4 | no | — |
| 358 | D20 | — | 20 | 4 | no | — |
| 359 | D20 | — | 20 | 1 | no | — |
| 360 | D20 | — | 20 | 1 | no | — |
| 361 | D20 | — | 20 | 4 | no | — |
| 362 | D20 | — | 20 | 4 | no | — |
| 363 | D20 | — | 40 | 1 | no | — |
| 364 | D20 | — | 40 | 1 | no | — |
| 365 | D20 | — | 40 | 1 | no | — |
| 366 | D20 | — | 40 | 1 | no | — |
| 367 | D20 | — | 40 | 8 | no | — |
| 368 | C4×D5 | — | 2 | 4 | no | — |
| 369 | C4×D5 | — | 40 | 4 | no | — |
| 370 | C4×D5 | C2×D20 | 1 | 1 | yes | characteristic |
| 371 | C4×D5 | #709 | 1 | 1 | yes | characteristic |
| 372 | C4×D5 | D4×D5 | 1 | 1 | yes | characteristic |
| 373 | C4×D5 | #713 | 1 | 1 | yes | characteristic |
| 374 | #170 | — | 4 | 1 | no | — |
| 375 | #170 | — | 20 | 1 | no | — |
| 376 | C5×C8 | — | 20 | 1 | no | — |
| 377 | #168 | — | 20 | 1 | no | — |
| 378 | C22×D4 | — | 25 | 1 | no | — |
| 379 | C22×D4 | — | 25 | 1 | no | — |
| 380 | C22×D4 | — | 50 | 2 | no | — |
| 381 | C2×M16 | — | 5 | 1 | no | — |
| 382 | C2×M16 | — | 25 | 1 | no | — |
| 383 | #127 | — | 5 | 1 | no | — |
| 384 | #127 | — | 25 | 1 | no | — |
| 385 | #127 | — | 25 | 1 | no | — |
| 386 | #127 | — | 25 | 1 | no | — |
| 387 | #127 | — | 50 | 2 | no | — |
| 388 | C4×D4 | — | 50 | 2 | no | — |
| 389 | C4×D4 | — | 50 | 2 | no | — |
| 390 | #117 | — | 5 | 1 | no | — |
| 391 | #117 | — | 25 | 1 | no | — |
| 392 | C2×C22⋊C4 | — | 50 | 2 | no | — |
| 393 | C2×C42 | — | 5 | 1 | no | — |
| 394 | #102 | — | 50 | 2 | no | — |
| 395 | #102 | — | 50 | 2 | no | — |
| 396 | #100 | — | 50 | 2 | no | — |
| 397 | C52 | #1887 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 398 | C22×C5 | — | 4 | 1 | no | — |
| 399 | C22×C5 | — | 5 | 1 | no | — |
| 400 | C22×C5 | — | 5 | 1 | no | — |
| 401 | C22×C5 | — | 10 | 2 | no | — |
| 402 | C22×C5 | — | 10 | 2 | no | — |
| 403 | C22×C5 | — | 20 | 2 | no | — |
| 404 | C22×C5 | — | 20 | 2 | no | — |
| 405 | C22×C5 | — | 20 | 1 | no | — |
| 406 | C22×C5 | D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 407 | C22×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 408 | C2×D5 | — | 2 | 2 | no | — |
| 409 | C2×D5 | — | 2 | 2 | no | — |
| 410 | C2×D5 | — | 4 | 2 | no | — |
| 411 | C2×D5 | — | 4 | 2 | no | — |
| 412 | C2×D5 | — | 4 | 1 | no | — |
| 413 | C2×D5 | — | 10 | 2 | no | — |
| 414 | C2×D5 | — | 10 | 2 | no | — |
| 415 | C2×D5 | — | 20 | 4 | no | — |
| 416 | C2×D5 | — | 20 | 4 | no | — |
| 417 | C2×D5 | — | 20 | 2 | no | — |
| 418 | C2×D5 | — | 20 | 2 | no | — |
| 419 | C2×D5 | — | 20 | 2 | no | — |
| 420 | C2×D5 | — | 20 | 2 | no | — |
| 421 | C2×D5 | — | 20 | 1 | no | — |
| 422 | C2×D5 | — | 20 | 1 | no | — |
| 423 | C2×D5 | — | 40 | 2 | no | — |
| 424 | C2×D5 | — | 40 | 4 | no | — |
| 425 | C2×D5 | — | 40 | 4 | no | — |
| 426 | C2×D5 | — | 40 | 2 | no | — |
| 427 | C2×D5 | — | 40 | 2 | no | — |
| 428 | C2×D5 | — | 40 | 2 | no | — |
| 429 | C2×D5 | — | 40 | 2 | no | — |
| 430 | C2×D5 | — | 40 | 2 | no | — |
| 431 | C2×D5 | — | 40 | 2 | no | — |
| 432 | C2×D5 | — | 40 | 2 | no | — |
| 433 | C2×D5 | #4028 | 1 | 1 | yes | characteristic |
| 434 | C2×D5 | #4040 | 1 | 1 | yes | characteristic |
| 435 | AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 436 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 437 | C4×C5 | — | 2 | 2 | no | — |
| 438 | C4×C5 | — | 2 | 2 | no | — |
| 439 | C4×C5 | — | 4 | 4 | no | — |
| 440 | C4×C5 | — | 4 | 1 | no | — |
| 441 | C4×C5 | — | 4 | 1 | no | — |
| 442 | C4×C5 | — | 5 | 1 | no | — |
| 443 | C4×C5 | — | 5 | 1 | no | — |
| 444 | C4×C5 | — | 10 | 2 | no | — |
| 445 | C4×C5 | — | 20 | 2 | no | — |
| 446 | C4×C5 | C4×D20 | 1 | 1 | yes | characteristic |
| 447 | C4×C5 | #4039 | 1 | 1 | yes | characteristic |
| 448 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 449 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 450 | Dic5 | — | 2 | 2 | no | — |
| 451 | Dic5 | — | 20 | 2 | no | — |
| 452 | Dic5 | #4030 | 1 | 1 | yes | characteristic |
| 453 | Dic5 | #4041 | 1 | 1 | yes | characteristic |
| 454 | C24 | — | 25 | 2 | no | — |
| 455 | C24 | — | 50 | 1 | no | — |
| 456 | C2×D4 | — | 5 | 1 | no | — |
| 457 | C2×D4 | — | 5 | 1 | no | — |
| 458 | C2×D4 | — | 10 | 2 | no | — |
| 459 | C2×D4 | — | 25 | 2 | no | — |
| 460 | C2×D4 | — | 25 | 1 | no | — |
| 461 | C2×D4 | — | 25 | 1 | no | — |
| 462 | C2×D4 | — | 50 | 2 | no | — |
| 463 | C2×D4 | — | 50 | 1 | no | — |
| 464 | C2×D4 | — | 50 | 1 | no | — |
| 465 | C2×D4 | — | 50 | 1 | no | — |
| 466 | C2×D4 | — | 50 | 1 | no | — |
| 467 | C2×D4 | — | 50 | 1 | no | — |
| 468 | C2×D4 | — | 50 | 1 | no | — |
| 469 | C2×D4 | — | 50 | 1 | no | — |
| 470 | C2×D4 | — | 50 | 1 | no | — |
| 471 | C2×D4 | — | 50 | 1 | no | — |
| 472 | C2×D4 | — | 50 | 2 | no | — |
| 473 | C2×D4 | — | 50 | 2 | no | — |
| 474 | C2×D4 | — | 100 | 8 | no | — |
| 475 | C22×C4 | — | 5 | 1 | no | — |
| 476 | C22×C4 | — | 10 | 1 | no | — |
| 477 | C22×C4 | — | 50 | 4 | no | — |
| 478 | M16 | — | 10 | 1 | no | — |
| 479 | M16 | — | 10 | 1 | no | — |
| 480 | M16 | — | 50 | 1 | no | — |
| 481 | M16 | — | 50 | 1 | no | — |
| 482 | C2×C8 | — | 10 | 1 | no | — |
| 483 | C2×C8 | — | 50 | 1 | no | — |
| 484 | C4⋊C4 | — | 5 | 2 | no | — |
| 485 | C4⋊C4 | — | 25 | 2 | no | — |
| 486 | C22⋊C4 | — | 10 | 1 | no | — |
| 487 | C22⋊C4 | — | 50 | 4 | no | — |
| 488 | C22⋊C4 | — | 50 | 1 | no | — |
| 489 | C42 | — | 5 | 1 | no | — |
| 490 | C42 | — | 10 | 1 | no | — |
| 491 | C42 | — | 10 | 1 | no | — |
| 492 | C42 | — | 50 | 1 | no | — |
| 493 | C42 | D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 494 | C2×C5 | — | 2 | 1 | no | — |
| 495 | C2×C5 | — | 2 | 1 | no | — |
| 496 | C2×C5 | — | 4 | 2 | no | — |
| 497 | C2×C5 | — | 4 | 1 | no | — |
| 498 | C2×C5 | — | 5 | 2 | no | — |
| 499 | C2×C5 | — | 10 | 1 | no | — |
| 500 | C2×C5 | — | 20 | 2 | no | — |
| 501 | C2×C5 | — | 40 | 1 | no | — |
| 502 | C2×C5 | #64954 | 1 | 1 | yes | characteristic |
| 503 | C2×C5 | #65779 | 1 | 1 | yes | characteristic |
| 504 | D5 | — | 2 | 1 | no | — |
| 505 | D5 | — | 4 | 2 | no | — |
| 506 | D5 | — | 8 | 1 | no | — |
| 507 | D5 | — | 20 | 2 | no | — |
| 508 | D5 | — | 20 | 2 | no | — |
| 509 | D5 | — | 40 | 1 | no | — |
| 510 | D5 | — | 40 | 1 | no | — |
| 511 | D5 | — | 80 | 2 | no | — |
| 512 | D5 | — | 80 | 2 | no | — |
| 513 | D5 | #65111 | 1 | 2 | yes | — |
| 514 | C23 | — | 5 | 1 | no | — |
| 515 | C23 | — | 5 | 2 | no | — |
| 516 | C23 | — | 10 | 1 | no | — |
| 517 | C23 | — | 25 | 2 | no | — |
| 518 | C23 | — | 50 | 2 | no | — |
| 519 | C23 | — | 50 | 2 | no | — |
| 520 | C23 | — | 50 | 1 | no | — |
| 521 | C23 | — | 100 | 1 | no | — |
| 522 | C23 | — | 100 | 1 | no | — |
| 523 | C23 | — | 100 | 4 | no | — |
| 524 | C23 | — | 100 | 4 | no | — |
| 525 | D4 | — | 10 | 1 | no | — |
| 526 | D4 | — | 10 | 1 | no | — |
| 527 | D4 | — | 10 | 1 | no | — |
| 528 | D4 | — | 10 | 1 | no | — |
| 529 | D4 | — | 20 | 4 | no | — |
| 530 | D4 | — | 50 | 2 | no | — |
| 531 | D4 | — | 50 | 2 | no | — |
| 532 | D4 | — | 50 | 1 | no | — |
| 533 | D4 | — | 50 | 1 | no | — |
| 534 | D4 | — | 50 | 1 | no | — |
| 535 | D4 | — | 50 | 1 | no | — |
| 536 | D4 | — | 100 | 4 | no | — |
| 537 | D4 | — | 100 | 1 | no | — |
| 538 | D4 | — | 100 | 1 | no | — |
| 539 | D4 | — | 100 | 4 | no | — |
| 540 | D4 | — | 100 | 4 | no | — |
| 541 | C2×C4 | — | 2 | 1 | no | — |
| 542 | C2×C4 | — | 5 | 1 | no | — |
| 543 | C2×C4 | — | 5 | 1 | no | — |
| 544 | C2×C4 | — | 5 | 1 | no | — |
| 545 | C2×C4 | — | 5 | 1 | no | — |
| 546 | C2×C4 | — | 5 | 1 | no | — |
| 547 | C2×C4 | — | 10 | 4 | no | — |
| 548 | C2×C4 | — | 10 | 1 | no | — |
| 549 | C2×C4 | — | 10 | 2 | no | — |
| 550 | C2×C4 | — | 50 | 2 | no | — |
| 551 | C2×C4 | — | 200 | 4 | no | — |
| 552 | C2×C4 | C2×D5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 553 | C8 | — | 20 | 1 | no | — |
| 554 | C8 | — | 100 | 1 | no | — |
| 555 | C5 | — | 4 | 1 | no | — |
| 556 | C5 | #10599553 | 1 | 1 | yes | characteristic, complemented |
| 557 | C5 | #10604614 | 1 | 1 | yes | characteristic, complemented |
| 558 | C22 | — | 5 | 1 | no | — |
| 559 | C22 | — | 5 | 1 | no | — |
| 560 | C22 | — | 10 | 2 | no | — |
| 561 | C22 | — | 10 | 2 | no | — |
| 562 | C22 | — | 20 | 2 | no | — |
| 563 | C22 | — | 20 | 2 | no | — |
| 564 | C22 | — | 20 | 1 | no | — |
| 565 | C22 | — | 50 | 2 | no | — |
| 566 | C22 | — | 100 | 2 | no | — |
| 567 | C22 | — | 100 | 2 | no | — |
| 568 | C22 | — | 100 | 4 | no | — |
| 569 | C22 | — | 100 | 1 | no | — |
| 570 | C22 | — | 200 | 2 | no | — |
| 571 | C22 | — | 200 | 2 | no | — |
| 572 | C22 | — | 200 | 2 | no | — |
| 573 | C22 | D5×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 574 | C4 | — | 2 | 2 | no | — |
| 575 | C4 | — | 5 | 1 | no | — |
| 576 | C4 | — | 5 | 1 | no | — |
| 577 | C4 | — | 10 | 2 | no | — |
| 578 | C4 | — | 20 | 2 | no | — |
| 579 | C4 | — | 100 | 2 | no | — |
| 580 | C4 | AGL(1,𝔽5)×D20 | 1 | 1 | yes | characteristic |
| 581 | C4 | #11717337 | 1 | 1 | yes | characteristic |
| 582 | C2 | — | 2 | 1 | no | — |
| 583 | C2 | — | 5 | 2 | no | — |
| 584 | C2 | — | 10 | 1 | no | — |
| 585 | C2 | — | 20 | 2 | no | — |
| 586 | C2 | — | 40 | 1 | no | — |
| 587 | C2 | — | 100 | 2 | no | — |
| 588 | C2 | — | 200 | 1 | no | — |
| 589 | C2 | #13103713 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107619 | C2 | semidirect |
| 3. #13103546 | C2 | semidirect |
| 4. #13103543 | C2 | semidirect |
| 5. D5⋊#3955 | C2 | semidirect |
| 6. #13100146 | C2 | semidirect |
| 7. C5×#64862 | C2 | semidirect |
| 18. #11717194 | C4 | semidirect |
| 19. C5×#4020 | C4 | semidirect |
| 22. #11717029 | C4 | semidirect |
| 23. #11717029 | C4 | semidirect |
| 34. C2×C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 37. C2×C5×D20 | C2×C4 | semidirect |
| 55. C4⋊#1042 | D4 | semidirect |
| 61. C5×C4⋊AGL(1,𝔽5) | D4 | semidirect |
| 66. C42×C52 | C2×C4 | semidirect |
| 68. C4×C5×Dic5 | C2×C4 | semidirect |
| 80. #64862 | D5 | semidirect |
| 154. #4020 | AGL(1,𝔽5) | semidirect |
| 235. C2×D20 | C2×AGL(1,𝔽5) | semidirect |
| 245. C4⋊AGL(1,𝔽5) | D20 | semidirect |
| 261. C42×C5 | C4×D5 | semidirect |
| 262. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 268. C4×Dic5 | C4×D5 | semidirect |
| 397. C52 | #1887 | semidirect |
| 493. C42 | D5×AGL(1,𝔽5) | semidirect |
| 556. C5 | #10599553 | semidirect |
| 557. C5 | #10604614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107619 | 2 |
| D5×#4020 | 2 |
| #13103546 | 2 |
| #13103543 | 2 |
| D5⋊#3955 | 2 |
| #13100146 | 2 |
| C5×#64862 | 2 |
| #10604614 | 5 |
| #10599553 | 5 |