Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1120 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1120 conjugacy classes of subgroups — too many to draw. Only its 172 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 | C5×#66169 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13106547 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13103105 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13101863 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13101856 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13101850 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13101713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13101697 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13101687 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C52×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×#4149 | C22 | 1 | 2 | yes | complemented |
| 12 | #11717473 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #11717269 | C22 | 1 | 2 | yes | complemented |
| 14 | #11717260 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C5×#4096 | — | 2 | 2 | no | — |
| 16 | C5×#4096 | C22 | 1 | 2 | yes | — |
| 17 | C5×#4095 | — | 2 | 2 | no | — |
| 18 | C5×#4095 | C22 | 1 | 2 | yes | complemented |
| 19 | C5×#4094 | C22 | 1 | 2 | yes | complemented |
| 20 | C5×#4078 | — | 2 | 2 | no | — |
| 21 | C5×#4078 | C22 | 1 | 2 | yes | complemented |
| 22 | C2×C5×#686 | — | 2 | 2 | no | — |
| 23 | C2×C5×#686 | C22 | 1 | 2 | yes | complemented |
| 24 | #11717067 | — | 2 | 2 | no | — |
| 25 | #11717057 | — | 2 | 2 | no | — |
| 26 | #11717052 | — | 2 | 2 | no | — |
| 27 | D5×#686 | — | 2 | 2 | no | — |
| 28 | #11717032 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#87771 | C22 | 1 | 2 | yes | complemented |
| 30 | #11716941 | C22 | 1 | 2 | yes | complemented |
| 31 | #11716932 | C22 | 1 | 2 | yes | complemented |
| 32 | #11716704 | C22 | 1 | 2 | yes | complemented |
| 33 | #11716700 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #11716618 | C22 | 1 | 2 | yes | complemented |
| 35 | #11716609 | C22 | 1 | 2 | yes | complemented |
| 36 | #11716600 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #11716599 | C22 | 1 | 2 | yes | complemented |
| 38 | #11716594 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #10615741 | — | 5 | 2 | no | maximal |
| 40 | C52×#41 | — | 2 | 2 | no | — |
| 41 | C52×#41 | C23 | 1 | 2 | yes | — |
| 42 | C2×C52×D4 | — | 2 | 2 | no | — |
| 43 | C2×C52×D4 | — | 4 | 1 | no | — |
| 44 | C2×C52×D4 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×C22⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 46 | C2×C4⋊(C5⋊D5) | C23 | 1 | 1 | yes | characteristic |
| 47 | C5×#713 | — | 2 | 2 | no | — |
| 48 | C5×D4×D5 | — | 2 | 2 | no | — |
| 49 | C5×D4×D5 | — | 4 | 2 | no | — |
| 50 | C5×#709 | — | 2 | 2 | no | — |
| 51 | C5×#709 | C23 | 1 | 2 | yes | — |
| 52 | C2×C5×D20 | — | 2 | 2 | no | — |
| 53 | C2×C5×D20 | C23 | 1 | 2 | yes | — |
| 54 | #87886 | — | 4 | 1 | no | — |
| 55 | C2×#6037 | — | 4 | 1 | no | — |
| 56 | D5×D20 | — | 2 | 2 | no | — |
| 57 | #87874 | — | 2 | 2 | no | — |
| 58 | #87811 | — | 2 | 2 | no | — |
| 59 | #87809 | — | 2 | 2 | no | — |
| 60 | C4×#1039 | C23 | 1 | 1 | yes | characteristic |
| 61 | #87804 | C23 | 1 | 2 | yes | — |
| 62 | C5×#689 | D4 | 1 | 2 | yes | complemented |
| 63 | C5×#688 | — | 2 | 2 | no | — |
| 64 | C5×#688 | D4 | 1 | 2 | yes | complemented |
| 65 | C5×#687 | — | 2 | 2 | no | — |
| 66 | C5×#687 | D4 | 1 | 2 | yes | complemented |
| 67 | C5×#686 | — | 2 | 2 | no | — |
| 68 | C5×#686 | — | 2 | 2 | no | — |
| 69 | C5×#686 | — | 2 | 2 | no | — |
| 70 | C5×#686 | — | 2 | 2 | no | — |
| 71 | C5×#686 | D4 | 1 | 2 | yes | complemented |
| 72 | C5×#681 | — | 2 | 2 | no | — |
| 73 | C5×#681 | C23 | 1 | 2 | yes | — |
| 74 | C2×C5×#168 | — | 2 | 2 | no | — |
| 75 | C2×C5×#168 | C23 | 1 | 2 | yes | — |
| 76 | #87772 | — | 2 | 2 | no | — |
| 77 | #87771 | — | 2 | 2 | no | — |
| 78 | #87771 | — | 2 | 2 | no | — |
| 79 | #87770 | — | 2 | 2 | no | — |
| 80 | #87768 | — | 2 | 2 | no | — |
| 81 | D5×#168 | — | 2 | 2 | no | — |
| 82 | C5×#576 | — | 5 | 2 | no | — |
| 83 | #66169 | — | 5 | 2 | no | — |
| 84 | #66169 | D5 | 1 | 2 | yes | complemented |
| 85 | #66103 | — | 5 | 2 | no | — |
| 86 | #65530 | — | 5 | 2 | no | — |
| 87 | #65530 | — | 5 | 2 | no | — |
| 88 | #65530 | — | 10 | 2 | no | — |
| 89 | #65488 | — | 5 | 2 | no | — |
| 90 | #65488 | — | 5 | 2 | no | — |
| 91 | #65487 | — | 5 | 2 | no | — |
| 92 | #65487 | — | 5 | 2 | no | — |
| 93 | #65485 | — | 5 | 2 | no | — |
| 94 | #65449 | — | 5 | 2 | no | — |
| 95 | #65440 | — | 5 | 2 | no | — |
| 96 | #65433 | — | 5 | 2 | no | — |
| 97 | #65431 | — | 5 | 2 | no | — |
| 98 | C23×C52 | — | 2 | 1 | no | — |
| 99 | C23×C52 | — | 4 | 1 | no | — |
| 100 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 101 | C22×C5×D5 | — | 2 | 2 | no | — |
| 102 | C22×C5×D5 | — | 4 | 2 | no | — |
| 103 | C2×D52 | — | 4 | 1 | no | — |
| 104 | C52×Q8 | C2×D4 | 1 | 2 | yes | — |
| 105 | C52×D4 | — | 2 | 2 | no | — |
| 106 | C52×D4 | — | 2 | 2 | no | — |
| 107 | C52×D4 | — | 4 | 2 | no | — |
| 108 | C52×D4 | C2×D4 | 1 | 2 | yes | — |
| 109 | C2×C4×C52 | — | 2 | 2 | no | — |
| 110 | C2×C4×C52 | — | 4 | 1 | no | — |
| 111 | C2×C4×C52 | C24 | 1 | 1 | yes | characteristic |
| 112 | C22⋊(C5⋊D5) | — | 8 | 2 | no | — |
| 113 | C2×#1039 | — | 2 | 1 | no | — |
| 114 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 115 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 116 | C5×C22⋊D5 | — | 4 | 2 | no | — |
| 117 | C5×D20 | — | 2 | 2 | no | — |
| 118 | C5×D20 | — | 2 | 2 | no | — |
| 119 | C5×D20 | — | 4 | 2 | no | — |
| 120 | C5×D20 | C2×D4 | 1 | 2 | yes | — |
| 121 | C4×C5×D5 | — | 2 | 2 | no | — |
| 122 | C4×C5×D5 | — | 4 | 2 | no | — |
| 123 | C5×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 124 | #6038 | — | 4 | 2 | no | — |
| 125 | #6037 | — | 8 | 2 | no | — |
| 126 | #6036 | — | 4 | 1 | no | — |
| 127 | #6029 | — | 2 | 2 | no | — |
| 128 | C5×#168 | — | 2 | 2 | no | — |
| 129 | C5×#168 | C2×D4 | 1 | 2 | yes | — |
| 130 | C5×#168 | C2×D4 | 1 | 2 | yes | — |
| 131 | C5×H(5,𝔽2) | — | 2 | 2 | no | — |
| 132 | C5×H(5,𝔽2) | — | 5 | 2 | no | — |
| 133 | C5×H(5,𝔽2) | C2×D5 | 1 | 2 | yes | complemented |
| 134 | #4149 | — | 5 | 2 | no | — |
| 135 | #4149 | C2×D5 | 1 | 2 | yes | complemented |
| 136 | C5×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 137 | C5×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 138 | C5×AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 139 | C5×AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 140 | C5×#135 | — | 5 | 2 | no | — |
| 141 | C5×#135 | — | 10 | 2 | no | — |
| 142 | C2×C5×D8 | — | 5 | 2 | no | — |
| 143 | C2×C5×D8 | — | 10 | 2 | no | — |
| 144 | C5×#131 | — | 5 | 2 | no | — |
| 145 | #4096 | — | 2 | 2 | no | — |
| 146 | #4096 | — | 10 | 2 | no | — |
| 147 | #4096 | C2×D5 | 1 | 2 | yes | — |
| 148 | #4095 | — | 2 | 2 | no | — |
| 149 | #4095 | — | 5 | 2 | no | — |
| 150 | #4095 | — | 5 | 2 | no | — |
| 151 | #4095 | — | 5 | 2 | no | — |
| 152 | #4095 | — | 10 | 4 | no | — |
| 153 | #4095 | — | 10 | 2 | no | — |
| 154 | #4095 | C2×D5 | 1 | 2 | yes | complemented |
| 155 | #4094 | — | 5 | 2 | no | — |
| 156 | #4094 | C2×D5 | 1 | 2 | yes | complemented |
| 157 | #4086 | — | 5 | 2 | no | — |
| 158 | #4086 | — | 5 | 2 | no | — |
| 159 | #4086 | — | 10 | 2 | no | — |
| 160 | #4078 | — | 2 | 2 | no | — |
| 161 | #4078 | — | 5 | 2 | no | — |
| 162 | #4078 | — | 10 | 2 | no | — |
| 163 | #4078 | C2×D5 | 1 | 2 | yes | complemented |
| 164 | C2×#686 | — | 2 | 2 | no | — |
| 165 | C2×#686 | — | 5 | 2 | no | — |
| 166 | C2×#686 | — | 10 | 2 | no | — |
| 167 | C2×#686 | C2×D5 | 1 | 2 | yes | complemented |
| 168 | #4065 | — | 10 | 2 | no | — |
| 169 | #4060 | — | 10 | 2 | no | — |
| 170 | #4060 | — | 10 | 2 | no | — |
| 171 | D5×D8 | — | 10 | 2 | no | — |
| 172 | C2×D40 | — | 5 | 2 | no | — |
| 173 | #4047 | — | 5 | 2 | no | — |
| 174 | #3969 | — | 5 | 2 | no | — |
| 175 | #3969 | — | 5 | 2 | no | — |
| 176 | #3969 | — | 5 | 2 | no | — |
| 177 | #3969 | — | 10 | 4 | no | — |
| 178 | #3965 | — | 5 | 2 | no | — |
| 179 | #3965 | — | 5 | 2 | no | — |
| 180 | #3965 | — | 10 | 2 | no | — |
| 181 | #3957 | — | 5 | 2 | no | — |
| 182 | #3955 | — | 5 | 2 | no | — |
| 183 | #3955 | — | 5 | 2 | no | — |
| 184 | #3954 | — | 5 | 2 | no | — |
| 185 | #3951 | — | 5 | 2 | no | — |
| 186 | C8×Dic5 | — | 5 | 2 | no | — |
| 187 | #3292 | — | 25 | 1 | no | Sylow |
| 188 | C22×C52 | — | 2 | 2 | no | — |
| 189 | C22×C52 | — | 4 | 1 | no | — |
| 190 | C22×C52 | — | 8 | 1 | no | — |
| 191 | C22×C52 | — | 16 | 1 | no | — |
| 192 | C22×C52 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 193 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 194 | C2×C5⋊D5 | — | 8 | 1 | no | — |
| 195 | C2×C5×D5 | — | 2 | 2 | no | — |
| 196 | C2×C5×D5 | — | 4 | 2 | no | — |
| 197 | C2×C5×D5 | — | 8 | 2 | no | — |
| 198 | C2×C5×D5 | — | 16 | 2 | no | — |
| 199 | D52 | — | 16 | 1 | no | — |
| 200 | C4×C52 | — | 2 | 2 | no | — |
| 201 | C4×C52 | C22×D4 | 1 | 2 | yes | — |
| 202 | #1039 | — | 2 | 2 | no | — |
| 203 | C5×Dic5 | — | 2 | 2 | no | — |
| 204 | C5×#41 | — | 2 | 2 | no | — |
| 205 | C5×#41 | — | 2 | 2 | no | — |
| 206 | C5×#41 | — | 2 | 4 | no | — |
| 207 | C5×#41 | — | 4 | 4 | no | — |
| 208 | C5×#41 | — | 5 | 2 | no | — |
| 209 | C5×#41 | — | 10 | 2 | no | — |
| 210 | C5×#41 | — | 10 | 2 | no | — |
| 211 | C5×#41 | C22×D5 | 1 | 2 | yes | — |
| 212 | C5×#41 | C22×D5 | 1 | 2 | yes | — |
| 213 | C2×C5×D4 | — | 2 | 2 | no | — |
| 214 | C2×C5×D4 | — | 2 | 2 | no | — |
| 215 | C2×C5×D4 | — | 2 | 2 | no | — |
| 216 | C2×C5×D4 | — | 4 | 4 | no | — |
| 217 | C2×C5×D4 | — | 4 | 2 | no | — |
| 218 | C2×C5×D4 | — | 4 | 4 | no | — |
| 219 | C2×C5×D4 | — | 5 | 2 | no | — |
| 220 | C2×C5×D4 | — | 10 | 2 | no | — |
| 221 | C2×C5×D4 | — | 10 | 2 | no | — |
| 222 | C2×C5×D4 | — | 20 | 2 | no | — |
| 223 | C2×C5×D4 | C22×D5 | 1 | 2 | yes | — |
| 224 | C2×C22⋊D5 | — | 20 | 2 | no | — |
| 225 | C2×C22⋊D5 | — | 20 | 2 | no | — |
| 226 | C2×C22⋊D5 | — | 20 | 4 | no | — |
| 227 | #713 | — | 2 | 2 | no | — |
| 228 | #713 | — | 10 | 2 | no | — |
| 229 | D4×D5 | — | 2 | 2 | no | — |
| 230 | D4×D5 | — | 4 | 2 | no | — |
| 231 | D4×D5 | — | 10 | 2 | no | — |
| 232 | D4×D5 | — | 20 | 2 | no | — |
| 233 | #709 | — | 2 | 2 | no | — |
| 234 | #709 | — | 10 | 2 | no | — |
| 235 | #709 | C22×D5 | 1 | 2 | yes | — |
| 236 | C2×D20 | — | 2 | 2 | no | — |
| 237 | C2×D20 | — | 5 | 2 | no | — |
| 238 | C2×D20 | — | 10 | 2 | no | — |
| 239 | C2×D20 | — | 10 | 2 | no | — |
| 240 | C2×D20 | C22×D5 | 1 | 2 | yes | — |
| 241 | C5×Q16 | — | 5 | 2 | no | — |
| 242 | C5×SD16 | — | 5 | 2 | no | — |
| 243 | C5×SD16 | — | 5 | 2 | no | — |
| 244 | C5×SD16 | — | 10 | 2 | no | — |
| 245 | C5×SD16 | — | 10 | 2 | no | — |
| 246 | C5×D8 | — | 5 | 2 | no | — |
| 247 | C5×D8 | — | 10 | 2 | no | — |
| 248 | C5×D8 | — | 10 | 2 | no | — |
| 249 | C5×D8 | — | 10 | 2 | no | — |
| 250 | C5×D8 | — | 10 | 2 | no | — |
| 251 | C5×M16 | — | 5 | 2 | no | — |
| 252 | C5×M16 | — | 10 | 2 | no | — |
| 253 | C2×C5×C8 | — | 5 | 2 | no | — |
| 254 | C2×C5×C8 | — | 10 | 2 | no | — |
| 255 | #689 | C22⋊D5 | 1 | 2 | yes | complemented |
| 256 | #688 | — | 2 | 2 | no | — |
| 257 | #688 | — | 10 | 2 | no | — |
| 258 | #688 | — | 10 | 2 | no | — |
| 259 | #688 | — | 10 | 2 | no | — |
| 260 | #688 | — | 20 | 4 | no | — |
| 261 | #688 | C22⋊D5 | 1 | 2 | yes | complemented |
| 262 | #687 | — | 2 | 2 | no | — |
| 263 | #687 | — | 10 | 2 | no | — |
| 264 | #687 | C22⋊D5 | 1 | 2 | yes | complemented |
| 265 | #686 | — | 2 | 2 | no | — |
| 266 | #686 | — | 2 | 2 | no | — |
| 267 | #686 | — | 2 | 2 | no | — |
| 268 | #686 | — | 2 | 2 | no | — |
| 269 | #686 | — | 10 | 2 | no | — |
| 270 | #686 | — | 10 | 2 | no | — |
| 271 | #686 | — | 10 | 2 | no | — |
| 272 | #686 | — | 10 | 2 | no | — |
| 273 | #686 | — | 10 | 2 | no | — |
| 274 | #686 | — | 10 | 2 | no | — |
| 275 | #686 | — | 20 | 4 | no | — |
| 276 | #686 | C22⋊D5 | 1 | 2 | yes | complemented |
| 277 | C4×Dic5 | — | 5 | 2 | no | — |
| 278 | C4×Dic5 | — | 10 | 2 | no | — |
| 279 | #681 | — | 2 | 2 | no | — |
| 280 | #681 | — | 5 | 2 | no | — |
| 281 | #681 | — | 5 | 2 | no | — |
| 282 | #681 | — | 10 | 4 | no | — |
| 283 | #681 | — | 10 | 2 | no | — |
| 284 | #681 | C22×D5 | 1 | 2 | yes | — |
| 285 | C2×#168 | — | 2 | 2 | no | — |
| 286 | C2×#168 | — | 10 | 2 | no | — |
| 287 | C2×#168 | C22×D5 | 1 | 2 | yes | — |
| 288 | D40 | — | 10 | 2 | no | — |
| 289 | D40 | — | 10 | 2 | no | — |
| 290 | #676 | — | 10 | 2 | no | — |
| 291 | C8×D5 | — | 10 | 2 | no | — |
| 292 | #576 | — | 5 | 2 | no | — |
| 293 | #576 | — | 25 | 2 | no | — |
| 294 | #493 | — | 25 | 1 | no | — |
| 295 | #472 | — | 25 | 2 | no | — |
| 296 | #472 | — | 25 | 2 | no | — |
| 297 | #453 | — | 25 | 1 | no | — |
| 298 | #453 | — | 25 | 2 | no | — |
| 299 | #453 | — | 25 | 1 | no | — |
| 300 | #443 | — | 25 | 2 | no | — |
| 301 | C2×C52 | — | 2 | 1 | no | — |
| 302 | C2×C52 | — | 4 | 2 | no | — |
| 303 | C2×C52 | — | 8 | 1 | no | — |
| 304 | C2×C52 | D42 | 1 | 1 | yes | characteristic |
| 305 | C5⋊D5 | — | 8 | 1 | no | — |
| 306 | C5×D5 | — | 4 | 2 | no | — |
| 307 | C5×D5 | — | 8 | 2 | no | — |
| 308 | C23×C5 | — | 2 | 4 | no | — |
| 309 | C23×C5 | — | 2 | 2 | no | — |
| 310 | C23×C5 | — | 4 | 2 | no | — |
| 311 | C23×C5 | — | 4 | 4 | no | — |
| 312 | C23×C5 | — | 10 | 2 | no | — |
| 313 | C23×C5 | — | 20 | 2 | no | — |
| 314 | C22×D5 | — | 2 | 2 | no | — |
| 315 | C22×D5 | — | 4 | 2 | no | — |
| 316 | C22×D5 | — | 10 | 2 | no | — |
| 317 | C22×D5 | — | 20 | 2 | no | — |
| 318 | C22×D5 | — | 20 | 2 | no | — |
| 319 | C5×Q8 | — | 2 | 4 | no | — |
| 320 | C5×Q8 | — | 5 | 2 | no | — |
| 321 | C5×Q8 | D4×D5 | 1 | 2 | yes | — |
| 322 | C5×Q8 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 323 | C5×D4 | — | 2 | 2 | no | — |
| 324 | C5×D4 | — | 2 | 2 | no | — |
| 325 | C5×D4 | — | 2 | 2 | no | — |
| 326 | C5×D4 | — | 2 | 2 | no | — |
| 327 | C5×D4 | — | 2 | 4 | no | — |
| 328 | C5×D4 | — | 4 | 4 | no | — |
| 329 | C5×D4 | — | 4 | 4 | no | — |
| 330 | C5×D4 | — | 4 | 2 | no | — |
| 331 | C5×D4 | — | 4 | 2 | no | — |
| 332 | C5×D4 | — | 4 | 8 | no | — |
| 333 | C5×D4 | — | 5 | 2 | no | — |
| 334 | C5×D4 | — | 10 | 2 | no | — |
| 335 | C5×D4 | — | 10 | 2 | no | — |
| 336 | C5×D4 | — | 10 | 2 | no | — |
| 337 | C5×D4 | — | 20 | 2 | no | — |
| 338 | C5×D4 | — | 20 | 2 | no | — |
| 339 | C5×D4 | D4×D5 | 1 | 2 | yes | — |
| 340 | C5×D4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 341 | C2×C4×C5 | — | 2 | 2 | no | — |
| 342 | C2×C4×C5 | — | 2 | 2 | no | — |
| 343 | C2×C4×C5 | — | 2 | 2 | no | — |
| 344 | C2×C4×C5 | — | 4 | 4 | no | — |
| 345 | C2×C4×C5 | — | 4 | 2 | no | — |
| 346 | C2×C4×C5 | — | 4 | 4 | no | — |
| 347 | C2×C4×C5 | — | 10 | 2 | no | — |
| 348 | C2×C4×C5 | — | 20 | 2 | no | — |
| 349 | C2×C4×C5 | C23×D5 | 1 | 2 | yes | — |
| 350 | C22⋊D5 | — | 2 | 2 | no | — |
| 351 | C22⋊D5 | — | 4 | 2 | no | — |
| 352 | C22⋊D5 | — | 20 | 2 | no | — |
| 353 | C22⋊D5 | — | 40 | 4 | no | — |
| 354 | C22⋊D5 | — | 40 | 4 | no | — |
| 355 | C22⋊D5 | — | 40 | 8 | no | — |
| 356 | C2×Dic5 | — | 10 | 2 | no | — |
| 357 | C2×Dic5 | — | 20 | 2 | no | — |
| 358 | D20 | — | 2 | 2 | no | — |
| 359 | D20 | — | 2 | 2 | no | — |
| 360 | D20 | — | 4 | 2 | no | — |
| 361 | D20 | — | 10 | 2 | no | — |
| 362 | D20 | — | 10 | 2 | no | — |
| 363 | D20 | — | 20 | 4 | no | — |
| 364 | D20 | — | 20 | 2 | no | — |
| 365 | D20 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 366 | C4×D5 | — | 2 | 2 | no | — |
| 367 | C4×D5 | — | 4 | 2 | no | — |
| 368 | C4×D5 | — | 20 | 2 | no | — |
| 369 | Dic10 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 370 | C5×C8 | — | 5 | 2 | no | — |
| 371 | C5×C8 | — | 5 | 2 | no | — |
| 372 | C5×C8 | — | 10 | 2 | no | — |
| 373 | #168 | — | 2 | 2 | no | — |
| 374 | #168 | — | 10 | 2 | no | — |
| 375 | #168 | — | 10 | 2 | no | — |
| 376 | #168 | — | 20 | 4 | no | — |
| 377 | #168 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 378 | #168 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 379 | H(5,𝔽2) | — | 5 | 2 | no | — |
| 380 | H(5,𝔽2) | — | 25 | 1 | no | — |
| 381 | H(5,𝔽2) | D52 | 1 | 1 | yes | characteristic, complemented |
| 382 | AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 383 | AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 384 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 385 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 386 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 387 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 388 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 389 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 390 | #135 | — | 5 | 2 | no | — |
| 391 | #135 | — | 10 | 2 | no | — |
| 392 | #135 | — | 50 | 2 | no | — |
| 393 | C2×D8 | — | 5 | 2 | no | — |
| 394 | C2×D8 | — | 10 | 2 | no | — |
| 395 | C2×D8 | — | 25 | 2 | no | — |
| 396 | C2×D8 | — | 50 | 2 | no | — |
| 397 | #131 | — | 5 | 2 | no | — |
| 398 | #131 | — | 25 | 2 | no | — |
| 399 | #127 | — | 25 | 1 | no | — |
| 400 | #127 | — | 25 | 1 | no | — |
| 401 | #108 | — | 25 | 2 | no | — |
| 402 | #104 | — | 25 | 2 | no | — |
| 403 | #104 | — | 25 | 2 | no | — |
| 404 | #100 | — | 25 | 1 | no | — |
| 405 | #100 | — | 25 | 2 | no | — |
| 406 | #100 | — | 25 | 1 | no | — |
| 407 | C4×C8 | — | 25 | 1 | no | — |
| 408 | C52 | #3292 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 409 | C22×C5 | — | 2 | 2 | no | — |
| 410 | C22×C5 | — | 2 | 2 | no | — |
| 411 | C22×C5 | — | 2 | 2 | no | — |
| 412 | C22×C5 | — | 4 | 4 | no | — |
| 413 | C22×C5 | — | 4 | 4 | no | — |
| 414 | C22×C5 | — | 4 | 2 | no | — |
| 415 | C22×C5 | — | 8 | 2 | no | — |
| 416 | C22×C5 | — | 8 | 4 | no | — |
| 417 | C22×C5 | — | 10 | 2 | no | — |
| 418 | C22×C5 | — | 16 | 2 | no | — |
| 419 | C22×C5 | — | 16 | 4 | no | — |
| 420 | C22×C5 | — | 20 | 2 | no | — |
| 421 | C22×C5 | — | 40 | 2 | no | — |
| 422 | C22×C5 | — | 80 | 2 | no | — |
| 423 | C22×C5 | #4144 | 1 | 2 | yes | — |
| 424 | C2×D5 | — | 2 | 2 | no | — |
| 425 | C2×D5 | — | 4 | 2 | no | — |
| 426 | C2×D5 | — | 8 | 2 | no | — |
| 427 | C2×D5 | — | 16 | 2 | no | — |
| 428 | C2×D5 | — | 20 | 2 | no | — |
| 429 | C2×D5 | — | 40 | 2 | no | — |
| 430 | C2×D5 | — | 40 | 2 | no | — |
| 431 | C2×D5 | — | 40 | 4 | no | — |
| 432 | C2×D5 | — | 80 | 2 | no | — |
| 433 | C4×C5 | — | 2 | 2 | no | — |
| 434 | C4×C5 | — | 2 | 2 | no | — |
| 435 | C4×C5 | — | 2 | 4 | no | — |
| 436 | C4×C5 | — | 4 | 4 | no | — |
| 437 | C4×C5 | — | 10 | 2 | no | — |
| 438 | C4×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 439 | C4×C5 | C22×C22⋊D5 | 1 | 2 | yes | — |
| 440 | Dic5 | — | 2 | 2 | no | — |
| 441 | Dic5 | — | 10 | 4 | no | — |
| 442 | Dic5 | — | 20 | 4 | no | — |
| 443 | #41 | — | 2 | 2 | no | — |
| 444 | #41 | — | 5 | 2 | no | — |
| 445 | #41 | — | 10 | 2 | no | — |
| 446 | #41 | — | 10 | 2 | no | — |
| 447 | #41 | — | 50 | 2 | no | — |
| 448 | #41 | C2×D52 | 1 | 2 | yes | — |
| 449 | C2×D4 | — | 2 | 2 | no | — |
| 450 | C2×D4 | — | 4 | 1 | no | — |
| 451 | C2×D4 | — | 5 | 2 | no | — |
| 452 | C2×D4 | — | 10 | 2 | no | — |
| 453 | C2×D4 | — | 10 | 2 | no | — |
| 454 | C2×D4 | — | 20 | 2 | no | — |
| 455 | C2×D4 | — | 25 | 1 | no | — |
| 456 | C2×D4 | — | 50 | 2 | no | — |
| 457 | C2×D4 | — | 100 | 1 | no | — |
| 458 | C2×D4 | — | 100 | 1 | no | — |
| 459 | C2×D4 | — | 100 | 1 | no | — |
| 460 | C2×D4 | C2×D52 | 1 | 1 | yes | characteristic |
| 461 | Q16 | — | 5 | 2 | no | — |
| 462 | SD16 | — | 5 | 2 | no | — |
| 463 | SD16 | — | 5 | 2 | no | — |
| 464 | SD16 | — | 10 | 2 | no | — |
| 465 | SD16 | — | 10 | 2 | no | — |
| 466 | SD16 | — | 50 | 2 | no | — |
| 467 | SD16 | — | 50 | 2 | no | — |
| 468 | D8 | — | 5 | 2 | no | — |
| 469 | D8 | — | 10 | 2 | no | — |
| 470 | D8 | — | 10 | 2 | no | — |
| 471 | D8 | — | 10 | 2 | no | — |
| 472 | D8 | — | 10 | 2 | no | — |
| 473 | D8 | — | 50 | 2 | no | — |
| 474 | D8 | — | 50 | 2 | no | — |
| 475 | D8 | — | 50 | 2 | no | — |
| 476 | D8 | — | 50 | 2 | no | — |
| 477 | M16 | — | 5 | 2 | no | — |
| 478 | M16 | — | 10 | 2 | no | — |
| 479 | M16 | — | 25 | 2 | no | — |
| 480 | M16 | — | 50 | 2 | no | — |
| 481 | C2×C8 | — | 5 | 2 | no | — |
| 482 | C2×C8 | — | 10 | 2 | no | — |
| 483 | C2×C8 | — | 50 | 2 | no | — |
| 484 | C42 | — | 25 | 1 | no | — |
| 485 | C2×C5 | — | 2 | 2 | no | — |
| 486 | C2×C5 | — | 2 | 2 | no | — |
| 487 | C2×C5 | — | 4 | 2 | no | — |
| 488 | C2×C5 | — | 4 | 2 | no | — |
| 489 | C2×C5 | — | 4 | 2 | no | — |
| 490 | C2×C5 | — | 8 | 4 | no | — |
| 491 | C2×C5 | — | 8 | 4 | no | — |
| 492 | C2×C5 | — | 8 | 2 | no | — |
| 493 | C2×C5 | — | 20 | 2 | no | — |
| 494 | C2×C5 | — | 40 | 2 | no | — |
| 495 | C2×C5 | D4×C22⋊D5 | 1 | 2 | yes | — |
| 496 | D5 | — | 4 | 2 | no | — |
| 497 | D5 | — | 8 | 2 | no | — |
| 498 | D5 | — | 40 | 2 | no | — |
| 499 | D5 | — | 80 | 2 | no | — |
| 500 | C23 | — | 2 | 1 | no | — |
| 501 | C23 | — | 4 | 1 | no | — |
| 502 | C23 | — | 10 | 2 | no | — |
| 503 | C23 | — | 20 | 2 | no | — |
| 504 | C23 | — | 50 | 1 | no | — |
| 505 | C23 | — | 100 | 1 | no | — |
| 506 | Q8 | — | 5 | 2 | no | — |
| 507 | Q8 | D5×C22⋊D5 | 1 | 2 | yes | — |
| 508 | D4 | — | 2 | 2 | no | — |
| 509 | D4 | — | 2 | 2 | no | — |
| 510 | D4 | — | 4 | 2 | no | — |
| 511 | D4 | — | 5 | 2 | no | — |
| 512 | D4 | — | 10 | 2 | no | — |
| 513 | D4 | — | 10 | 2 | no | — |
| 514 | D4 | — | 10 | 2 | no | — |
| 515 | D4 | — | 20 | 2 | no | — |
| 516 | D4 | — | 20 | 2 | no | — |
| 517 | D4 | — | 50 | 2 | no | — |
| 518 | D4 | — | 100 | 2 | no | — |
| 519 | D4 | — | 200 | 2 | no | — |
| 520 | D4 | — | 200 | 2 | no | — |
| 521 | D4 | D5×C22⋊D5 | 1 | 2 | yes | — |
| 522 | C2×C4 | — | 2 | 2 | no | — |
| 523 | C2×C4 | — | 4 | 1 | no | — |
| 524 | C2×C4 | — | 10 | 2 | no | — |
| 525 | C2×C4 | — | 20 | 2 | no | — |
| 526 | C2×C4 | — | 50 | 1 | no | — |
| 527 | C2×C4 | — | 100 | 1 | no | — |
| 528 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 529 | C8 | — | 5 | 2 | no | — |
| 530 | C8 | — | 5 | 2 | no | — |
| 531 | C8 | — | 10 | 2 | no | — |
| 532 | C8 | — | 50 | 2 | no | — |
| 533 | C5 | — | 2 | 2 | no | — |
| 534 | C5 | #10615741 | 1 | 2 | yes | complemented |
| 535 | C22 | — | 2 | 2 | no | — |
| 536 | C22 | — | 4 | 1 | no | — |
| 537 | C22 | — | 8 | 1 | no | — |
| 538 | C22 | — | 10 | 2 | no | — |
| 539 | C22 | — | 16 | 1 | no | — |
| 540 | C22 | — | 20 | 2 | no | — |
| 541 | C22 | — | 40 | 2 | no | — |
| 542 | C22 | — | 80 | 2 | no | — |
| 543 | C22 | — | 100 | 1 | no | — |
| 544 | C22 | — | 400 | 1 | no | — |
| 545 | C22 | — | 200 | 1 | no | — |
| 546 | C22 | #11717495 | 1 | 1 | yes | characteristic |
| 547 | C4 | — | 2 | 2 | no | — |
| 548 | C4 | — | 10 | 2 | no | — |
| 549 | C4 | — | 50 | 2 | no | — |
| 550 | C4 | C2×D5×C22⋊D5 | 1 | 2 | yes | — |
| 551 | C2 | — | 2 | 1 | no | — |
| 552 | C2 | — | 4 | 2 | no | — |
| 553 | C2 | — | 8 | 1 | no | — |
| 554 | C2 | — | 20 | 2 | no | — |
| 555 | C2 | — | 40 | 2 | no | — |
| 556 | C2 | — | 200 | 1 | no | — |
| 557 | C2 | C22⋊D52 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#66169 | C2 | semidirect |
| 2. #13106547 | C2 | semidirect |
| 3. #13103105 | C2 | semidirect |
| 4. #13101863 | C2 | semidirect |
| 5. #13101856 | C2 | semidirect |
| 6. #13101850 | C2 | semidirect |
| 7. #13101713 | C2 | semidirect |
| 8. #13101697 | C2 | semidirect |
| 9. #13101687 | C2 | semidirect |
| 10. C52×H(5,𝔽2) | C22 | semidirect |
| 11. C5×#4149 | C22 | semidirect |
| 12. #11717473 | C22 | semidirect |
| 13. #11717269 | C22 | semidirect |
| 14. #11717260 | C22 | semidirect |
| 18. C5×#4095 | C22 | semidirect |
| 19. C5×#4094 | C22 | semidirect |
| 21. C5×#4078 | C22 | semidirect |
| 23. C2×C5×#686 | C22 | semidirect |
| 28. #11717032 | C22 | semidirect |
| 29. C2×#87771 | C22 | semidirect |
| 30. #11716941 | C22 | semidirect |
| 31. #11716932 | C22 | semidirect |
| 32. #11716704 | C22 | semidirect |
| 33. #11716700 | C22 | semidirect |
| 34. #11716618 | C22 | semidirect |
| 35. #11716609 | C22 | semidirect |
| 36. #11716600 | C22 | semidirect |
| 37. #11716599 | C22 | semidirect |
| 38. #11716594 | C22 | semidirect |
| 62. C5×#689 | D4 | semidirect |
| 64. C5×#688 | D4 | semidirect |
| 66. C5×#687 | D4 | semidirect |
| 71. C5×#686 | D4 | semidirect |
| 84. #66169 | D5 | semidirect |
| 133. C5×H(5,𝔽2) | C2×D5 | semidirect |
| 135. #4149 | C2×D5 | semidirect |
| 154. #4095 | C2×D5 | semidirect |
| 156. #4094 | C2×D5 | semidirect |
| 163. #4078 | C2×D5 | semidirect |
| 167. C2×#686 | C2×D5 | semidirect |
| 255. #689 | C22⋊D5 | semidirect |
| 261. #688 | C22⋊D5 | semidirect |
| 264. #687 | C22⋊D5 | semidirect |
| 276. #686 | C22⋊D5 | semidirect |
| 381. H(5,𝔽2) | D52 | semidirect |
| 408. C52 | #3292 | semidirect |
| 534. C5 | #10615741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#66169 | 2 |
| #13106547 | 2 |
| #13103105 | 2 |
| #13101863 | 2 |
| #13101856 | 2 |
| #13101850 | 2 |
| #13101713 | 2 |
| #13101697 | 2 |
| #13101687 | 2 |
| #10615741 | 5 |