Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
1540 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #72223216 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72223215 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72220909 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C5⋊D5×#492 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C2×SD16×C5⋊D5 | — | 2 | 2 | no | — |
| 6 | C4⋊Q8×C5⋊D5 | C4 | 1 | 1 | yes | characteristic |
| 7 | #127×C5⋊D5 | C4 | 1 | 1 | yes | characteristic |
| 8 | #13104853 | — | 2 | 2 | no | — |
| 9 | C52×#492 | C4 | 1 | 1 | yes | characteristic |
| 10 | #13103027 | — | 2 | 2 | no | — |
| 11 | #13102949 | C22 | 1 | 1 | yes | characteristic |
| 12 | #13102937 | C22 | 1 | 1 | yes | characteristic |
| 13 | #13102556 | C4 | 1 | 1 | yes | characteristic |
| 14 | C4×C8×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 15 | #13100361 | — | 2 | 2 | no | — |
| 16 | #13100331 | C22 | 1 | 4 | yes | complemented |
| 17 | D5⋊#1359 | — | 5 | 2 | no | maximal |
| 18 | C2×Q8×C5⋊D5 | — | 2 | 1 | no | — |
| 19 | C2×D4×C5⋊D5 | — | 2 | 1 | no | — |
| 20 | C2×D4×C5⋊D5 | — | 4 | 1 | no | — |
| 21 | C2×C52×SD16 | — | 2 | 2 | no | — |
| 22 | C52×C4⋊Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | C52×#127 | C2×C4 | 1 | 1 | yes | characteristic |
| 24 | #11717264 | — | 2 | 1 | no | — |
| 25 | C2×#87811 | — | 2 | 2 | no | — |
| 26 | #11717260 | — | 2 | 1 | no | — |
| 27 | #11717260 | — | 4 | 1 | no | — |
| 28 | C2×#87810 | — | 2 | 2 | no | — |
| 29 | SD16×C5⋊D5 | — | 4 | 2 | no | — |
| 30 | SD16×C5⋊D5 | — | 4 | 2 | no | — |
| 31 | SD16×C5⋊D5 | — | 4 | 2 | no | — |
| 32 | SD16×C5⋊D5 | — | 4 | 2 | no | — |
| 33 | C2×#87800 | — | 2 | 2 | no | — |
| 34 | C2×C8×C5⋊D5 | D4 | 1 | 2 | yes | — |
| 35 | C4⋊C4×C5⋊D5 | — | 4 | 1 | no | — |
| 36 | #11717208 | — | 4 | 1 | no | — |
| 37 | #11717194 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C42×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | #11717189 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | #11716891 | — | 2 | 4 | no | — |
| 41 | #11716883 | — | 4 | 2 | no | — |
| 42 | #11716882 | — | 4 | 2 | no | — |
| 43 | C4×C52×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C8×#1039 | D4 | 1 | 2 | yes | — |
| 45 | C4×#6029 | C23 | 1 | 1 | yes | characteristic |
| 46 | D5×#492 | — | 5 | 2 | no | — |
| 47 | D5×#492 | — | 10 | 2 | no | — |
| 48 | D5⋊#364 | — | 5 | 4 | no | — |
| 49 | #10598757 | — | 5 | 4 | no | — |
| 50 | #10598751 | — | 5 | 4 | no | — |
| 51 | C23×C5⋊D5 | — | 4 | 1 | no | — |
| 52 | C2×C52×Q8 | — | 2 | 1 | no | — |
| 53 | C2×C52×D4 | — | 2 | 1 | no | — |
| 54 | C2×C52×D4 | — | 4 | 1 | no | — |
| 55 | C2×C22⋊(C5⋊D5) | — | 4 | 2 | no | — |
| 56 | C2×C22⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 57 | Q8×C5⋊D5 | — | 4 | 2 | no | — |
| 58 | Q8×C5⋊D5 | — | 4 | 2 | no | — |
| 59 | D4×C5⋊D5 | — | 4 | 2 | no | — |
| 60 | D4×C5⋊D5 | — | 4 | 2 | no | — |
| 61 | D4×C5⋊D5 | — | 8 | 4 | no | — |
| 62 | C2×C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 63 | C2×C4⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 64 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 65 | C2×C4×C5⋊D5 | — | 4 | 1 | no | — |
| 66 | C2×C4×C5⋊D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 67 | C2×#6045 | — | 2 | 1 | no | — |
| 68 | C2×#6045 | — | 4 | 1 | no | — |
| 69 | C52×SD16 | — | 4 | 2 | no | — |
| 70 | C52×SD16 | — | 4 | 2 | no | — |
| 71 | C2×C52×C8 | C22⋊C4 | 1 | 2 | yes | — |
| 72 | C52×C4⋊C4 | — | 4 | 1 | no | — |
| 73 | C42×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 74 | #87811 | — | 4 | 2 | no | — |
| 75 | #87811 | — | 4 | 2 | no | — |
| 76 | #87810 | — | 4 | 2 | no | — |
| 77 | #87810 | — | 4 | 2 | no | — |
| 78 | C4⋊#1039 | — | 4 | 1 | no | — |
| 79 | #87806 | — | 4 | 2 | no | — |
| 80 | C4×#1039 | — | 2 | 1 | no | — |
| 81 | C4×#1039 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 82 | C2×#6029 | C2×D4 | 1 | 2 | yes | — |
| 83 | #87800 | — | 4 | 2 | no | — |
| 84 | #87800 | — | 4 | 2 | no | — |
| 85 | C8×C5⋊D5 | D8 | 1 | 2 | yes | — |
| 86 | C8×C5⋊D5 | D8 | 1 | 2 | yes | — |
| 87 | C8×C5⋊D5 | SD16 | 1 | 2 | yes | — |
| 88 | C8×C5⋊D5 | SD16 | 1 | 2 | yes | — |
| 89 | #87765 | — | 4 | 4 | no | — |
| 90 | C2×D5×SD16 | — | 10 | 4 | no | — |
| 91 | C2×D5×SD16 | — | 10 | 8 | no | — |
| 92 | D5×C4⋊Q8 | — | 5 | 2 | no | — |
| 93 | D5×C4⋊Q8 | — | 10 | 2 | no | — |
| 94 | D5×#127 | — | 5 | 2 | no | — |
| 95 | D5×#127 | — | 10 | 2 | no | — |
| 96 | D5⋊M32 | — | 10 | 4 | no | — |
| 97 | C5×#492 | — | 2 | 2 | no | — |
| 98 | C5×#492 | AGL(1,𝔽5) | 1 | 2 | yes | — |
| 99 | #65464 | — | 10 | 4 | no | — |
| 100 | #65464 | — | 10 | 8 | no | — |
| 101 | #65374 | — | 5 | 2 | no | — |
| 102 | #65374 | — | 10 | 2 | no | — |
| 103 | #65365 | — | 5 | 2 | no | — |
| 104 | #65365 | — | 10 | 2 | no | — |
| 105 | #64982 | — | 5 | 2 | no | — |
| 106 | #64982 | — | 10 | 2 | no | — |
| 107 | C4×C8×D5 | — | 5 | 2 | no | — |
| 108 | C4×C8×D5 | — | 10 | 2 | no | — |
| 109 | #64889 | — | 10 | 4 | no | — |
| 110 | #64861 | — | 5 | 8 | no | — |
| 111 | C2×#1359 | — | 25 | 1 | no | Sylow |
| 112 | C23×C52 | — | 4 | 1 | no | — |
| 113 | C22×C5⋊D5 | — | 4 | 1 | no | — |
| 114 | C22×C5⋊D5 | — | 8 | 4 | no | — |
| 115 | C22×C5⋊D5 | — | 8 | 1 | no | — |
| 116 | C22×C5⋊D5 | — | 8 | 1 | no | — |
| 117 | C22×C5⋊D5 | #100 | 1 | 1 | yes | characteristic |
| 118 | C52×Q8 | — | 4 | 2 | no | — |
| 119 | C52×D4 | — | 4 | 2 | no | — |
| 120 | C52×D4 | — | 8 | 2 | no | — |
| 121 | C2×C4×C52 | — | 2 | 1 | no | — |
| 122 | C2×C4×C52 | — | 4 | 1 | no | — |
| 123 | C2×C4×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 124 | C22⋊(C5⋊D5) | — | 8 | 4 | no | — |
| 125 | C22⋊(C5⋊D5) | — | 8 | 2 | no | — |
| 126 | C2×#1039 | — | 2 | 1 | no | — |
| 127 | C2×#1039 | — | 4 | 1 | no | — |
| 128 | C2×#1039 | #100 | 1 | 1 | yes | characteristic |
| 129 | C4⋊(C5⋊D5) | — | 4 | 2 | no | — |
| 130 | C4⋊(C5⋊D5) | — | 8 | 2 | no | — |
| 131 | C4×C5⋊D5 | — | 2 | 4 | no | — |
| 132 | C4×C5⋊D5 | — | 8 | 1 | no | — |
| 133 | C4×C5⋊D5 | — | 8 | 1 | no | — |
| 134 | C4×C5⋊D5 | #102 | 1 | 2 | yes | — |
| 135 | C4×C5⋊D5 | #102 | 1 | 2 | yes | — |
| 136 | #6045 | — | 4 | 2 | no | — |
| 137 | #6045 | — | 8 | 2 | no | — |
| 138 | C52×C8 | #102 | 1 | 2 | yes | — |
| 139 | C52×C8 | #102 | 1 | 2 | yes | — |
| 140 | #6029 | C2×D8 | 1 | 2 | yes | — |
| 141 | #6029 | C2×SD16 | 1 | 2 | yes | — |
| 142 | C2×Q8×D5 | — | 10 | 2 | no | — |
| 143 | C2×Q8×D5 | — | 10 | 4 | no | — |
| 144 | C2×D4×D5 | — | 10 | 2 | no | — |
| 145 | C2×D4×D5 | — | 10 | 4 | no | — |
| 146 | C2×D4×D5 | — | 20 | 2 | no | — |
| 147 | C2×D4×D5 | — | 20 | 4 | no | — |
| 148 | C2×C5×SD16 | — | 2 | 8 | no | — |
| 149 | C2×C5×SD16 | — | 2 | 4 | no | — |
| 150 | C5×C4⋊Q8 | — | 2 | 2 | no | — |
| 151 | C5×C4⋊Q8 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 152 | C5×#127 | — | 2 | 2 | no | — |
| 153 | C5×#127 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 154 | #4090 | — | 10 | 2 | no | — |
| 155 | #4090 | — | 10 | 4 | no | — |
| 156 | C2×#688 | — | 10 | 4 | no | — |
| 157 | C2×#688 | — | 10 | 8 | no | — |
| 158 | #4086 | — | 10 | 2 | no | — |
| 159 | #4086 | — | 10 | 4 | no | — |
| 160 | #4086 | — | 20 | 4 | no | — |
| 161 | #4086 | — | 20 | 2 | no | — |
| 162 | C2×#687 | — | 10 | 4 | no | — |
| 163 | C2×#687 | — | 10 | 8 | no | — |
| 164 | D5×SD16 | — | 20 | 4 | no | — |
| 165 | D5×SD16 | — | 20 | 4 | no | — |
| 166 | D5×SD16 | — | 20 | 4 | no | — |
| 167 | D5×SD16 | — | 20 | 4 | no | — |
| 168 | D5×SD16 | — | 20 | 8 | no | — |
| 169 | D5×SD16 | — | 20 | 8 | no | — |
| 170 | D5×SD16 | — | 20 | 8 | no | — |
| 171 | D5×SD16 | — | 20 | 8 | no | — |
| 172 | C2×#677 | — | 10 | 8 | no | — |
| 173 | C2×#677 | — | 10 | 4 | no | — |
| 174 | C2×C8×D5 | — | 5 | 4 | no | — |
| 175 | C2×C8×D5 | — | 10 | 4 | no | — |
| 176 | D5×C4⋊C4 | — | 20 | 2 | no | — |
| 177 | D5×C4⋊C4 | — | 20 | 4 | no | — |
| 178 | #4034 | — | 20 | 2 | no | — |
| 179 | #4034 | — | 20 | 4 | no | — |
| 180 | #4020 | — | 5 | 2 | no | — |
| 181 | #4020 | — | 10 | 2 | no | — |
| 182 | C42×D5 | — | 5 | 2 | no | — |
| 183 | C42×D5 | — | 10 | 2 | no | — |
| 184 | #4015 | — | 5 | 2 | no | — |
| 185 | #4015 | — | 10 | 2 | no | — |
| 186 | #3998 | — | 10 | 8 | no | — |
| 187 | #3990 | — | 20 | 4 | no | — |
| 188 | D5⋊C16 | — | 20 | 4 | no | — |
| 189 | C4×C5×C8 | — | 2 | 2 | no | — |
| 190 | C4×C5×C8 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 191 | C8×Dic5 | — | 5 | 4 | no | — |
| 192 | C8×Dic5 | — | 10 | 4 | no | — |
| 193 | C4×#168 | — | 5 | 2 | no | — |
| 194 | C4×#168 | — | 10 | 2 | no | — |
| 195 | C2×#492 | — | 25 | 1 | no | — |
| 196 | C2×#364 | — | 25 | 2 | no | — |
| 197 | #1359 | — | 25 | 2 | no | — |
| 198 | #1359 | — | 25 | 2 | no | — |
| 199 | C22×C52 | — | 8 | 2 | no | — |
| 200 | C22×C52 | — | 8 | 1 | no | — |
| 201 | C22×C52 | C2×#100 | 1 | 1 | yes | characteristic |
| 202 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 203 | C2×C5⋊D5 | — | 8 | 2 | no | — |
| 204 | C2×C5⋊D5 | — | 8 | 1 | no | — |
| 205 | C2×C5⋊D5 | — | 16 | 2 | no | — |
| 206 | C2×C5⋊D5 | — | 16 | 2 | no | — |
| 207 | C2×C5⋊D5 | #331 | 1 | 1 | yes | characteristic |
| 208 | C2×C5⋊D5 | #331 | 1 | 1 | yes | characteristic |
| 209 | C4×C52 | — | 2 | 2 | no | — |
| 210 | C4×C52 | — | 8 | 1 | no | — |
| 211 | C4×C52 | C2×#102 | 1 | 2 | yes | — |
| 212 | #1039 | — | 2 | 2 | no | — |
| 213 | #1039 | — | 8 | 1 | no | — |
| 214 | #1039 | #331 | 1 | 2 | yes | — |
| 215 | C23×D5 | — | 20 | 2 | no | — |
| 216 | C23×D5 | — | 20 | 4 | no | — |
| 217 | C2×C5×Q8 | — | 2 | 4 | no | — |
| 218 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 219 | C2×C5×D4 | — | 2 | 4 | no | — |
| 220 | C2×C5×D4 | — | 2 | 2 | no | — |
| 221 | C2×C5×D4 | — | 4 | 2 | no | — |
| 222 | C2×C5×D4 | — | 4 | 4 | no | — |
| 223 | C2×C22⋊D5 | — | 20 | 2 | no | — |
| 224 | C2×C22⋊D5 | — | 20 | 4 | no | — |
| 225 | C2×C22⋊D5 | — | 20 | 8 | no | — |
| 226 | C2×C22⋊D5 | — | 20 | 4 | no | — |
| 227 | Q8×D5 | — | 20 | 4 | no | — |
| 228 | Q8×D5 | — | 20 | 4 | no | — |
| 229 | Q8×D5 | — | 20 | 8 | no | — |
| 230 | Q8×D5 | — | 20 | 8 | no | — |
| 231 | D4×D5 | — | 20 | 4 | no | — |
| 232 | D4×D5 | — | 20 | 4 | no | — |
| 233 | D4×D5 | — | 20 | 8 | no | — |
| 234 | D4×D5 | — | 20 | 8 | no | — |
| 235 | D4×D5 | — | 40 | 8 | no | — |
| 236 | D4×D5 | — | 40 | 16 | no | — |
| 237 | C2×D20 | — | 10 | 4 | no | — |
| 238 | C2×D20 | — | 10 | 2 | no | — |
| 239 | C2×D20 | — | 20 | 2 | no | — |
| 240 | C2×D20 | — | 20 | 4 | no | — |
| 241 | C2×C4×D5 | — | 5 | 2 | no | — |
| 242 | C2×C4×D5 | — | 10 | 2 | no | — |
| 243 | C2×C4×D5 | — | 10 | 2 | no | — |
| 244 | C2×C4×D5 | — | 10 | 4 | no | — |
| 245 | C2×C4×D5 | — | 20 | 2 | no | — |
| 246 | C2×C4×D5 | — | 20 | 4 | no | — |
| 247 | C2×Dic10 | — | 10 | 4 | no | — |
| 248 | C2×Dic10 | — | 10 | 2 | no | — |
| 249 | C2×Dic10 | — | 20 | 2 | no | — |
| 250 | C2×Dic10 | — | 20 | 4 | no | — |
| 251 | C5×SD16 | — | 4 | 8 | no | — |
| 252 | C5×SD16 | — | 4 | 8 | no | — |
| 253 | C5×SD16 | — | 4 | 4 | no | — |
| 254 | C5×SD16 | — | 4 | 4 | no | — |
| 255 | C2×C5×C8 | — | 2 | 4 | no | — |
| 256 | C2×C5×C8 | C22⋊AGL(1,𝔽5) | 1 | 4 | yes | — |
| 257 | C5×C4⋊C4 | — | 4 | 2 | no | — |
| 258 | C5×C4⋊C4 | — | 4 | 4 | no | — |
| 259 | C42×C5 | — | 2 | 2 | no | — |
| 260 | C42×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 261 | #688 | — | 20 | 4 | no | — |
| 262 | #688 | — | 20 | 4 | no | — |
| 263 | #688 | — | 20 | 8 | no | — |
| 264 | #688 | — | 20 | 8 | no | — |
| 265 | #687 | — | 20 | 4 | no | — |
| 266 | #687 | — | 20 | 4 | no | — |
| 267 | #687 | — | 20 | 8 | no | — |
| 268 | #687 | — | 20 | 8 | no | — |
| 269 | C4⋊Dic5 | — | 20 | 4 | no | — |
| 270 | C4⋊Dic5 | — | 20 | 2 | no | — |
| 271 | #683 | — | 20 | 8 | no | — |
| 272 | #683 | — | 20 | 4 | no | — |
| 273 | C4×Dic5 | — | 5 | 2 | no | — |
| 274 | C4×Dic5 | — | 10 | 2 | no | — |
| 275 | C4×Dic5 | — | 10 | 2 | no | — |
| 276 | C4×Dic5 | — | 10 | 4 | no | — |
| 277 | C2×#168 | — | 5 | 4 | no | — |
| 278 | C2×#168 | — | 10 | 4 | no | — |
| 279 | #677 | — | 20 | 8 | no | — |
| 280 | #677 | — | 20 | 8 | no | — |
| 281 | #677 | — | 20 | 4 | no | — |
| 282 | #677 | — | 20 | 4 | no | — |
| 283 | C8×D5 | — | 5 | 4 | no | — |
| 284 | C8×D5 | — | 5 | 4 | no | — |
| 285 | C8×D5 | — | 5 | 4 | no | — |
| 286 | C8×D5 | — | 5 | 4 | no | — |
| 287 | C8×D5 | — | 10 | 4 | no | — |
| 288 | C8×D5 | — | 10 | 4 | no | — |
| 289 | C8×D5 | — | 10 | 4 | no | — |
| 290 | C8×D5 | — | 10 | 4 | no | — |
| 291 | #674 | — | 20 | 8 | no | — |
| 292 | C22×SD16 | — | 50 | 2 | no | — |
| 293 | C2×C4⋊Q8 | — | 25 | 1 | no | — |
| 294 | C2×#127 | — | 25 | 1 | no | — |
| 295 | C2×M32 | — | 50 | 2 | no | — |
| 296 | #492 | — | 25 | 1 | no | — |
| 297 | #492 | — | 25 | 1 | no | — |
| 298 | #492 | — | 25 | 1 | no | — |
| 299 | #492 | — | 50 | 2 | no | — |
| 300 | #492 | #1044 | 1 | 1 | yes | characteristic |
| 301 | C2×C4×C8 | — | 25 | 1 | no | — |
| 302 | #364 | — | 25 | 4 | no | — |
| 303 | #364 | — | 50 | 2 | no | — |
| 304 | C2×C52 | — | 2 | 1 | no | — |
| 305 | C2×C52 | — | 16 | 1 | no | — |
| 306 | C2×C52 | C2×#331 | 1 | 1 | yes | characteristic |
| 307 | C5⋊D5 | — | 2 | 1 | no | — |
| 308 | C5⋊D5 | — | 16 | 1 | no | — |
| 309 | C5⋊D5 | #1359 | 1 | 2 | yes | complemented |
| 310 | C23×C5 | — | 4 | 4 | no | — |
| 311 | C23×C5 | — | 4 | 2 | no | — |
| 312 | C22×D5 | — | 5 | 2 | no | — |
| 313 | C22×D5 | — | 10 | 2 | no | — |
| 314 | C22×D5 | — | 20 | 4 | no | — |
| 315 | C22×D5 | — | 20 | 2 | no | — |
| 316 | C22×D5 | — | 40 | 2 | no | — |
| 317 | C22×D5 | — | 40 | 2 | no | — |
| 318 | C22×D5 | — | 40 | 4 | no | — |
| 319 | C22×D5 | — | 40 | 4 | no | — |
| 320 | C22×D5 | — | 40 | 8 | no | — |
| 321 | C22×D5 | — | 40 | 16 | no | — |
| 322 | C5×Q8 | — | 4 | 8 | no | — |
| 323 | C5×Q8 | — | 4 | 4 | no | — |
| 324 | C5×D4 | — | 4 | 8 | no | — |
| 325 | C5×D4 | — | 4 | 4 | no | — |
| 326 | C5×D4 | — | 8 | 4 | no | — |
| 327 | C5×D4 | — | 8 | 8 | no | — |
| 328 | C2×C4×C5 | — | 2 | 4 | no | — |
| 329 | C2×C4×C5 | — | 2 | 2 | no | — |
| 330 | C2×C4×C5 | — | 2 | 2 | no | — |
| 331 | C2×C4×C5 | — | 4 | 4 | no | — |
| 332 | C2×C4×C5 | — | 4 | 2 | no | — |
| 333 | C2×C4×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 334 | C22⋊D5 | — | 40 | 4 | no | — |
| 335 | C22⋊D5 | — | 40 | 8 | no | — |
| 336 | C22⋊D5 | — | 40 | 16 | no | — |
| 337 | C22⋊D5 | — | 40 | 8 | no | — |
| 338 | C2×Dic5 | — | 5 | 2 | no | — |
| 339 | C2×Dic5 | — | 10 | 2 | no | — |
| 340 | C2×Dic5 | — | 10 | 4 | no | — |
| 341 | C2×Dic5 | — | 10 | 2 | no | — |
| 342 | C2×Dic5 | — | 20 | 4 | no | — |
| 343 | C2×Dic5 | — | 20 | 2 | no | — |
| 344 | D20 | — | 20 | 8 | no | — |
| 345 | D20 | — | 20 | 4 | no | — |
| 346 | D20 | — | 40 | 4 | no | — |
| 347 | D20 | — | 40 | 8 | no | — |
| 348 | C4×D5 | — | 5 | 4 | no | — |
| 349 | C4×D5 | — | 5 | 4 | no | — |
| 350 | C4×D5 | — | 10 | 4 | no | — |
| 351 | C4×D5 | — | 10 | 4 | no | — |
| 352 | C4×D5 | — | 10 | 8 | no | — |
| 353 | C4×D5 | — | 10 | 16 | no | — |
| 354 | C4×D5 | — | 40 | 2 | no | — |
| 355 | C4×D5 | — | 40 | 2 | no | — |
| 356 | C4×D5 | — | 40 | 4 | no | — |
| 357 | C4×D5 | — | 40 | 4 | no | — |
| 358 | Dic10 | — | 20 | 8 | no | — |
| 359 | Dic10 | — | 20 | 4 | no | — |
| 360 | Dic10 | — | 40 | 4 | no | — |
| 361 | Dic10 | — | 40 | 8 | no | — |
| 362 | C5×C8 | — | 2 | 4 | no | — |
| 363 | C5×C8 | — | 2 | 4 | no | — |
| 364 | C5×C8 | #4007 | 1 | 4 | yes | — |
| 365 | C5×C8 | #4007 | 1 | 4 | yes | — |
| 366 | #168 | — | 5 | 4 | no | — |
| 367 | #168 | — | 5 | 4 | no | — |
| 368 | #168 | — | 10 | 4 | no | — |
| 369 | #168 | — | 10 | 4 | no | — |
| 370 | C22×Q8 | — | 50 | 1 | no | — |
| 371 | C22×D4 | — | 50 | 1 | no | — |
| 372 | C22×D4 | — | 100 | 1 | no | — |
| 373 | C2×SD16 | — | 2 | 2 | no | — |
| 374 | C2×SD16 | — | 50 | 2 | no | — |
| 375 | C2×SD16 | — | 50 | 2 | no | — |
| 376 | C2×SD16 | — | 50 | 2 | no | — |
| 377 | C2×SD16 | — | 100 | 2 | no | — |
| 378 | C2×SD16 | — | 100 | 2 | no | — |
| 379 | C2×SD16 | — | 100 | 2 | no | — |
| 380 | C2×SD16 | — | 100 | 2 | no | — |
| 381 | C22×C8 | — | 25 | 2 | no | — |
| 382 | C4⋊Q8 | — | 25 | 1 | no | — |
| 383 | C4⋊Q8 | — | 50 | 1 | no | — |
| 384 | C4⋊Q8 | — | 100 | 1 | no | — |
| 385 | C4⋊Q8 | C2×#1044 | 1 | 1 | yes | characteristic |
| 386 | #127 | — | 25 | 1 | no | — |
| 387 | #127 | — | 50 | 1 | no | — |
| 388 | #127 | — | 100 | 1 | no | — |
| 389 | #127 | C2×#1044 | 1 | 1 | yes | characteristic |
| 390 | C2×C4⋊C4 | — | 100 | 1 | no | — |
| 391 | C2×C42 | — | 25 | 1 | no | — |
| 392 | M32 | — | 50 | 4 | no | — |
| 393 | M32 | — | 100 | 2 | no | — |
| 394 | C2×C16 | — | 100 | 2 | no | — |
| 395 | C4×C8 | — | 25 | 2 | no | — |
| 396 | C4×C8 | — | 25 | 1 | no | — |
| 397 | C4×C8 | C2×#1044 | 1 | 1 | yes | characteristic |
| 398 | C52 | C2×#1359 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 399 | C22×C5 | — | 2 | 2 | no | — |
| 400 | C22×C5 | — | 8 | 4 | no | — |
| 401 | C22×C5 | — | 8 | 8 | no | — |
| 402 | C22×C5 | — | 8 | 4 | no | — |
| 403 | C22×C5 | — | 8 | 2 | no | — |
| 404 | C22×C5 | D5⋊#100 | 1 | 2 | yes | — |
| 405 | C2×D5 | — | 5 | 2 | no | — |
| 406 | C2×D5 | — | 5 | 2 | no | — |
| 407 | C2×D5 | — | 10 | 2 | no | — |
| 408 | C2×D5 | — | 10 | 2 | no | — |
| 409 | C2×D5 | — | 10 | 4 | no | — |
| 410 | C2×D5 | — | 10 | 8 | no | — |
| 411 | C2×D5 | — | 40 | 4 | no | — |
| 412 | C2×D5 | — | 40 | 8 | no | — |
| 413 | C2×D5 | — | 40 | 4 | no | — |
| 414 | C2×D5 | — | 40 | 2 | no | — |
| 415 | C2×D5 | — | 80 | 4 | no | — |
| 416 | C2×D5 | — | 80 | 8 | no | — |
| 417 | C2×D5 | — | 80 | 8 | no | — |
| 418 | C2×D5 | — | 80 | 4 | no | — |
| 419 | C4×C5 | — | 2 | 8 | no | — |
| 420 | C4×C5 | — | 2 | 4 | no | — |
| 421 | C4×C5 | — | 2 | 4 | no | — |
| 422 | C4×C5 | — | 8 | 4 | no | — |
| 423 | C4×C5 | — | 8 | 2 | no | — |
| 424 | C4×C5 | C2×#4007 | 1 | 4 | yes | — |
| 425 | Dic5 | — | 5 | 4 | no | — |
| 426 | Dic5 | — | 10 | 4 | no | — |
| 427 | Dic5 | — | 10 | 8 | no | — |
| 428 | Dic5 | — | 10 | 4 | no | — |
| 429 | Dic5 | — | 40 | 4 | no | — |
| 430 | Dic5 | — | 40 | 2 | no | — |
| 431 | C24 | — | 100 | 1 | no | — |
| 432 | C2×Q8 | — | 2 | 1 | no | — |
| 433 | C2×Q8 | — | 50 | 1 | no | — |
| 434 | C2×Q8 | — | 100 | 1 | no | — |
| 435 | C2×Q8 | — | 100 | 2 | no | — |
| 436 | C2×Q8 | — | 100 | 2 | no | — |
| 437 | C2×D4 | — | 2 | 1 | no | — |
| 438 | C2×D4 | — | 4 | 1 | no | — |
| 439 | C2×D4 | — | 50 | 1 | no | — |
| 440 | C2×D4 | — | 100 | 1 | no | — |
| 441 | C2×D4 | — | 100 | 2 | no | — |
| 442 | C2×D4 | — | 100 | 2 | no | — |
| 443 | C2×D4 | — | 100 | 1 | no | — |
| 444 | C2×D4 | — | 100 | 2 | no | — |
| 445 | C2×D4 | — | 200 | 4 | no | — |
| 446 | C22×C4 | — | 25 | 1 | no | — |
| 447 | C22×C4 | — | 50 | 1 | no | — |
| 448 | C22×C4 | — | 100 | 1 | no | — |
| 449 | SD16 | — | 4 | 2 | no | — |
| 450 | SD16 | — | 4 | 2 | no | — |
| 451 | SD16 | — | 100 | 2 | no | — |
| 452 | SD16 | — | 100 | 2 | no | — |
| 453 | SD16 | — | 100 | 2 | no | — |
| 454 | SD16 | — | 100 | 2 | no | — |
| 455 | SD16 | — | 100 | 2 | no | — |
| 456 | SD16 | — | 100 | 2 | no | — |
| 457 | C2×C8 | — | 25 | 2 | no | — |
| 458 | C2×C8 | — | 25 | 2 | no | — |
| 459 | C2×C8 | — | 25 | 2 | no | — |
| 460 | C2×C8 | — | 25 | 2 | no | — |
| 461 | C2×C8 | — | 25 | 2 | no | — |
| 462 | C2×C8 | C22⋊#1044 | 1 | 2 | yes | — |
| 463 | C4⋊C4 | — | 4 | 1 | no | — |
| 464 | C4⋊C4 | — | 100 | 1 | no | — |
| 465 | C4⋊C4 | — | 100 | 2 | no | — |
| 466 | C42 | — | 25 | 1 | no | — |
| 467 | C42 | — | 50 | 1 | no | — |
| 468 | C42 | C22×#1044 | 1 | 1 | yes | characteristic |
| 469 | C16 | — | 100 | 4 | no | — |
| 470 | C2×C5 | — | 2 | 4 | no | — |
| 471 | C2×C5 | — | 2 | 2 | no | — |
| 472 | C2×C5 | — | 2 | 2 | no | — |
| 473 | C2×C5 | — | 16 | 4 | no | — |
| 474 | C2×C5 | — | 16 | 2 | no | — |
| 475 | C2×C5 | D5⋊#331 | 1 | 2 | yes | — |
| 476 | D5 | — | 5 | 4 | no | — |
| 477 | D5 | — | 10 | 4 | no | — |
| 478 | D5 | — | 10 | 4 | no | — |
| 479 | D5 | — | 10 | 2 | no | — |
| 480 | D5 | — | 80 | 4 | no | — |
| 481 | D5 | — | 80 | 2 | no | — |
| 482 | C23 | — | 4 | 1 | no | — |
| 483 | C23 | — | 25 | 1 | no | — |
| 484 | C23 | — | 100 | 1 | no | — |
| 485 | C23 | — | 200 | 1 | no | — |
| 486 | C23 | — | 200 | 1 | no | — |
| 487 | C23 | — | 200 | 4 | no | — |
| 488 | Q8 | — | 4 | 2 | no | — |
| 489 | Q8 | — | 100 | 2 | no | — |
| 490 | Q8 | — | 200 | 2 | no | — |
| 491 | D4 | — | 4 | 2 | no | — |
| 492 | D4 | — | 8 | 2 | no | — |
| 493 | D4 | — | 100 | 2 | no | — |
| 494 | D4 | — | 200 | 2 | no | — |
| 495 | D4 | — | 200 | 2 | no | — |
| 496 | D4 | — | 200 | 4 | no | — |
| 497 | C2×C4 | — | 2 | 1 | no | — |
| 498 | C2×C4 | — | 4 | 1 | no | — |
| 499 | C2×C4 | — | 25 | 1 | no | — |
| 500 | C2×C4 | — | 25 | 2 | no | — |
| 501 | C2×C4 | — | 25 | 2 | no | — |
| 502 | C2×C4 | — | 50 | 4 | no | — |
| 503 | C2×C4 | — | 50 | 1 | no | — |
| 504 | C2×C4 | — | 100 | 1 | no | — |
| 505 | C2×C4 | — | 200 | 1 | no | — |
| 506 | C2×C4 | — | 200 | 1 | no | — |
| 507 | C2×C4 | C2×C22⋊#1044 | 1 | 1 | yes | characteristic |
| 508 | C8 | — | 25 | 2 | no | — |
| 509 | C8 | — | 25 | 2 | no | — |
| 510 | C8 | #11716900 | 1 | 2 | yes | — |
| 511 | C8 | #11716900 | 1 | 2 | yes | — |
| 512 | C5 | — | 2 | 2 | no | — |
| 513 | C5 | D5⋊#1359 | 1 | 2 | yes | complemented |
| 514 | C22 | — | 8 | 2 | no | — |
| 515 | C22 | — | 8 | 1 | no | — |
| 516 | C22 | — | 25 | 1 | no | — |
| 517 | C22 | — | 25 | 1 | no | — |
| 518 | C22 | — | 50 | 2 | no | — |
| 519 | C22 | — | 400 | 2 | no | — |
| 520 | C22 | — | 400 | 2 | no | — |
| 521 | C22 | — | 200 | 2 | no | — |
| 522 | C22 | — | 200 | 1 | no | — |
| 523 | C22 | #13104916 | 1 | 1 | yes | characteristic |
| 524 | C4 | — | 2 | 2 | no | — |
| 525 | C4 | — | 8 | 1 | no | — |
| 526 | C4 | — | 25 | 2 | no | — |
| 527 | C4 | — | 50 | 2 | no | — |
| 528 | C4 | — | 200 | 1 | no | — |
| 529 | C4 | C2×#11716900 | 1 | 2 | yes | — |
| 530 | C2 | — | 2 | 1 | no | — |
| 531 | C2 | — | 16 | 1 | no | — |
| 532 | C2 | — | 25 | 2 | no | — |
| 533 | C2 | — | 50 | 1 | no | — |
| 534 | C2 | — | 400 | 1 | no | — |
| 535 | C2 | #72223212 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72223216 | C2 | semidirect |
| 2. #72223215 | C2 | semidirect |
| 3. #72220909 | C2 | semidirect |
| 16. #13100331 | C22 | semidirect |
| 309. C5⋊D5 | #1359 | semidirect |
| 398. C52 | C2×#1359 | semidirect |
| 513. C5 | D5⋊#1359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72223216 | 2 |
| #72223215 | 2 |
| #72220909 | 2 |
| C5⋊D5×#492 | 2 |
| D5⋊#1359 | 5 |