Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1072 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1072 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 | #13105771 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13105770 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13102576 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#65006 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13101105 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13101101 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13100582 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13100579 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13100578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11717473 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11717473 | C22 | 1 | 2 | yes | complemented |
| 12 | #11717463 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×#87801 | C22 | 1 | 2 | yes | complemented |
| 14 | C2×#87800 | C22 | 1 | 2 | yes | complemented |
| 15 | #11717195 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #11717194 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C5×#4050 | C22 | 1 | 2 | yes | — |
| 18 | C5×#4047 | C22 | 1 | 2 | yes | complemented |
| 19 | C5×#4047 | C22 | 1 | 2 | yes | complemented |
| 20 | #11716949 | C22 | 1 | 2 | yes | complemented |
| 21 | #11716943 | C22 | 1 | 2 | yes | — |
| 22 | #11716943 | C22 | 1 | 2 | yes | complemented |
| 23 | #11716943 | C22 | 1 | 2 | yes | complemented |
| 24 | #11716926 | — | 2 | 2 | no | — |
| 25 | #11716924 | — | 2 | 2 | no | — |
| 26 | #11716919 | — | 2 | 2 | no | — |
| 27 | #11716913 | — | 2 | 2 | no | — |
| 28 | #11716912 | — | 2 | 2 | no | — |
| 29 | #11716912 | — | 2 | 2 | no | — |
| 30 | D5×D40 | — | 2 | 2 | no | — |
| 31 | D5×#677 | — | 2 | 2 | no | — |
| 32 | C52×#97 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | C5×#3951 | C22 | 1 | 2 | yes | complemented |
| 34 | C5×#3937 | C22 | 1 | 2 | yes | complemented |
| 35 | C5×#3937 | C22 | 1 | 2 | yes | complemented |
| 36 | #11716602 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #11716600 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #11716600 | C22 | 1 | 2 | yes | complemented |
| 39 | #10611631 | — | 5 | 2 | no | maximal |
| 40 | C2×C4⋊(C5⋊D5) | — | 4 | 1 | no | — |
| 41 | C2×C4⋊(C5⋊D5) | C23 | 1 | 2 | yes | — |
| 42 | C2×C4⋊(C5⋊D5) | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×#6045 | C23 | 1 | 1 | yes | characteristic |
| 44 | C5×#709 | C23 | 1 | 2 | yes | — |
| 45 | C5×#709 | C23 | 1 | 2 | yes | — |
| 46 | #87886 | — | 4 | 1 | no | — |
| 47 | #87886 | — | 4 | 2 | no | — |
| 48 | #87880 | — | 4 | 1 | no | — |
| 49 | D5×D20 | — | 2 | 2 | no | — |
| 50 | D5×D20 | — | 2 | 2 | no | — |
| 51 | D5×D20 | — | 2 | 2 | no | — |
| 52 | #87874 | — | 2 | 2 | no | — |
| 53 | #87874 | — | 2 | 2 | no | — |
| 54 | #87874 | — | 2 | 2 | no | — |
| 55 | #87870 | — | 2 | 2 | no | — |
| 56 | D5×Dic10 | — | 2 | 2 | no | — |
| 57 | C2×C52×C8 | C23 | 1 | 2 | yes | — |
| 58 | C42×C52 | C23 | 1 | 1 | yes | characteristic |
| 59 | #87808 | — | 4 | 1 | no | — |
| 60 | #87801 | — | 2 | 2 | no | — |
| 61 | #87801 | — | 2 | 2 | no | — |
| 62 | #87800 | — | 2 | 2 | no | — |
| 63 | #87800 | — | 2 | 2 | no | — |
| 64 | C5×#681 | C23 | 1 | 2 | yes | — |
| 65 | C5×#681 | C23 | 1 | 2 | yes | — |
| 66 | C5×Dic20 | D4 | 1 | 2 | yes | complemented |
| 67 | C5×D40 | D4 | 1 | 2 | yes | complemented |
| 68 | C5×#677 | D4 | 1 | 2 | yes | complemented |
| 69 | C5×#677 | D4 | 1 | 2 | yes | complemented |
| 70 | C5×#676 | — | 2 | 2 | no | — |
| 71 | C5×#676 | — | 2 | 2 | no | — |
| 72 | C5×C8×D5 | — | 2 | 2 | no | — |
| 73 | C5×C8×D5 | — | 2 | 2 | no | — |
| 74 | #87776 | — | 2 | 2 | no | — |
| 75 | #87774 | — | 2 | 2 | no | — |
| 76 | #87774 | — | 2 | 2 | no | — |
| 77 | #87774 | — | 2 | 2 | no | — |
| 78 | #87773 | — | 2 | 2 | no | — |
| 79 | #87771 | — | 2 | 2 | no | — |
| 80 | #87771 | — | 2 | 2 | no | — |
| 81 | #87771 | — | 2 | 2 | no | — |
| 82 | #66104 | — | 5 | 2 | no | — |
| 83 | #66103 | — | 5 | 2 | no | — |
| 84 | #66086 | — | 5 | 2 | no | — |
| 85 | #66085 | — | 5 | 2 | no | — |
| 86 | C5×#444 | — | 5 | 2 | no | — |
| 87 | #65431 | — | 5 | 2 | no | — |
| 88 | #65430 | — | 5 | 2 | no | — |
| 89 | #65187 | — | 5 | 2 | no | — |
| 90 | #65186 | — | 5 | 2 | no | — |
| 91 | #65116 | — | 5 | 2 | no | — |
| 92 | #65114 | — | 5 | 2 | no | — |
| 93 | #65111 | — | 5 | 2 | no | — |
| 94 | #65111 | — | 5 | 2 | no | — |
| 95 | #65006 | D5 | 1 | 2 | yes | complemented |
| 96 | #65001 | — | 5 | 2 | no | — |
| 97 | #65001 | — | 10 | 2 | no | — |
| 98 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 99 | C22×C5⋊D5 | — | 2 | 2 | no | — |
| 100 | C2×D52 | — | 4 | 2 | no | — |
| 101 | C2×D52 | — | 4 | 1 | no | — |
| 102 | C2×C4×C52 | — | 2 | 1 | no | — |
| 103 | C2×C4×C52 | C24 | 1 | 1 | yes | characteristic |
| 104 | C2×#1039 | — | 2 | 1 | no | — |
| 105 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 106 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 107 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 108 | C4⋊(C5⋊D5) | — | 8 | 2 | no | — |
| 109 | #6045 | — | 2 | 2 | no | — |
| 110 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 111 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 112 | C5×D20 | C2×D4 | 1 | 2 | yes | — |
| 113 | C5×D20 | C2×D4 | 1 | 2 | yes | — |
| 114 | C4×C5×D5 | — | 2 | 2 | no | — |
| 115 | C4×C5×D5 | — | 2 | 2 | no | — |
| 116 | C5×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 117 | C5×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 118 | #6039 | — | 4 | 1 | no | — |
| 119 | #6038 | — | 4 | 2 | no | — |
| 120 | #6038 | — | 4 | 2 | no | — |
| 121 | #6038 | — | 4 | 2 | no | — |
| 122 | #6037 | — | 4 | 1 | no | — |
| 123 | #6036 | — | 4 | 2 | no | — |
| 124 | #6036 | — | 4 | 1 | no | — |
| 125 | D5×Dic5 | — | 4 | 2 | no | — |
| 126 | C52×C8 | C2×D4 | 1 | 2 | yes | — |
| 127 | C52×C8 | C2×D4 | 1 | 2 | yes | — |
| 128 | C5×#168 | — | 2 | 2 | no | — |
| 129 | C5×#168 | — | 2 | 2 | no | — |
| 130 | #4150 | — | 5 | 2 | no | — |
| 131 | #4149 | — | 5 | 2 | no | — |
| 132 | #4149 | — | 5 | 2 | no | — |
| 133 | #4149 | — | 5 | 2 | no | — |
| 134 | C5×#135 | — | 5 | 2 | no | — |
| 135 | C5×#131 | — | 5 | 2 | no | — |
| 136 | C5×#131 | — | 5 | 2 | no | — |
| 137 | #4097 | — | 5 | 2 | no | — |
| 138 | #4095 | — | 5 | 2 | no | — |
| 139 | #4095 | — | 5 | 2 | no | — |
| 140 | #4095 | — | 5 | 2 | no | — |
| 141 | #4065 | — | 10 | 2 | no | — |
| 142 | #4064 | — | 10 | 2 | no | — |
| 143 | #4062 | — | 10 | 2 | no | — |
| 144 | #4060 | — | 10 | 2 | no | — |
| 145 | #4060 | — | 10 | 2 | no | — |
| 146 | D5×SD16 | — | 10 | 2 | no | — |
| 147 | #4057 | — | 10 | 2 | no | — |
| 148 | D5×D8 | — | 10 | 2 | no | — |
| 149 | #4055 | — | 5 | 2 | no | — |
| 150 | #4055 | — | 10 | 2 | no | — |
| 151 | #4054 | — | 5 | 2 | no | — |
| 152 | #4054 | — | 5 | 2 | no | — |
| 153 | #4054 | — | 5 | 2 | no | — |
| 154 | #4054 | — | 10 | 2 | no | — |
| 155 | #4054 | — | 10 | 2 | no | — |
| 156 | #4054 | — | 10 | 2 | no | — |
| 157 | #4050 | — | 10 | 2 | no | — |
| 158 | #4050 | — | 10 | 2 | no | — |
| 159 | #4050 | C2×D5 | 1 | 2 | yes | — |
| 160 | C2×D40 | — | 5 | 2 | no | — |
| 161 | C2×D40 | — | 5 | 2 | no | — |
| 162 | C2×D40 | — | 10 | 4 | no | — |
| 163 | C2×D40 | — | 10 | 2 | no | — |
| 164 | C2×#677 | — | 5 | 2 | no | — |
| 165 | C2×#677 | — | 5 | 2 | no | — |
| 166 | C2×#677 | — | 10 | 4 | no | — |
| 167 | C2×#677 | — | 10 | 2 | no | — |
| 168 | #4047 | C2×D5 | 1 | 2 | yes | complemented |
| 169 | #4047 | C2×D5 | 1 | 2 | yes | complemented |
| 170 | #4021 | — | 5 | 2 | no | — |
| 171 | #4021 | — | 10 | 2 | no | — |
| 172 | #4020 | — | 5 | 2 | no | — |
| 173 | #4020 | — | 10 | 2 | no | — |
| 174 | C5×#108 | — | 5 | 2 | no | — |
| 175 | C5×#104 | — | 5 | 2 | no | — |
| 176 | C5×#104 | — | 5 | 2 | no | — |
| 177 | C5×#97 | — | 2 | 2 | no | — |
| 178 | C5×#97 | C2×D5 | 1 | 2 | yes | complemented |
| 179 | #3956 | — | 5 | 2 | no | — |
| 180 | #3955 | — | 5 | 2 | no | — |
| 181 | #3955 | — | 5 | 2 | no | — |
| 182 | #3955 | — | 5 | 2 | no | — |
| 183 | #3951 | C2×D5 | 1 | 2 | yes | complemented |
| 184 | #3937 | C2×D5 | 1 | 2 | yes | complemented |
| 185 | #3937 | C2×D5 | 1 | 2 | yes | complemented |
| 186 | #3288 | — | 25 | 1 | no | Sylow |
| 187 | C22×C52 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 188 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 189 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 190 | C2×C5⋊D5 | — | 8 | 2 | no | — |
| 191 | C2×C5⋊D5 | — | 8 | 1 | no | — |
| 192 | C2×C5×D5 | — | 2 | 2 | no | — |
| 193 | C2×C5×D5 | — | 2 | 2 | no | — |
| 194 | D52 | — | 16 | 1 | no | — |
| 195 | D52 | — | 16 | 2 | no | — |
| 196 | C4×C52 | — | 4 | 1 | no | — |
| 197 | C4×C52 | C22×D4 | 1 | 2 | yes | — |
| 198 | #1039 | — | 4 | 1 | no | — |
| 199 | C5×Dic5 | — | 2 | 2 | no | — |
| 200 | C5×Dic5 | — | 2 | 2 | no | — |
| 201 | C5×#41 | — | 5 | 2 | no | — |
| 202 | C5×#41 | — | 5 | 2 | no | — |
| 203 | #713 | — | 10 | 2 | no | — |
| 204 | #713 | — | 10 | 2 | no | — |
| 205 | #713 | — | 10 | 2 | no | — |
| 206 | Q8×D5 | — | 10 | 2 | no | — |
| 207 | #711 | — | 10 | 2 | no | — |
| 208 | #711 | — | 20 | 2 | no | — |
| 209 | D4×D5 | — | 10 | 2 | no | — |
| 210 | D4×D5 | — | 10 | 2 | no | — |
| 211 | D4×D5 | — | 10 | 2 | no | — |
| 212 | D4×D5 | — | 20 | 2 | no | — |
| 213 | D4×D5 | — | 20 | 2 | no | — |
| 214 | D4×D5 | — | 20 | 2 | no | — |
| 215 | #709 | — | 10 | 2 | no | — |
| 216 | #709 | — | 10 | 2 | no | — |
| 217 | #709 | — | 10 | 2 | no | — |
| 218 | #709 | — | 10 | 2 | no | — |
| 219 | #709 | C22×D5 | 1 | 2 | yes | — |
| 220 | #709 | C22×D5 | 1 | 2 | yes | — |
| 221 | C2×D20 | — | 5 | 2 | no | — |
| 222 | C2×D20 | — | 5 | 2 | no | — |
| 223 | C2×D20 | — | 5 | 2 | no | — |
| 224 | C2×D20 | — | 10 | 4 | no | — |
| 225 | C2×D20 | — | 10 | 2 | no | — |
| 226 | C2×D20 | — | 10 | 2 | no | — |
| 227 | C2×D20 | — | 10 | 2 | no | — |
| 228 | C2×D20 | — | 10 | 2 | no | — |
| 229 | C2×D20 | — | 20 | 2 | no | — |
| 230 | C2×D20 | — | 20 | 4 | no | — |
| 231 | C2×Dic10 | — | 5 | 2 | no | — |
| 232 | C2×Dic10 | — | 10 | 2 | no | — |
| 233 | C2×Dic10 | — | 10 | 2 | no | — |
| 234 | C5×Q16 | — | 5 | 2 | no | — |
| 235 | C5×SD16 | — | 5 | 2 | no | — |
| 236 | C5×SD16 | — | 5 | 2 | no | — |
| 237 | C5×D8 | — | 5 | 2 | no | — |
| 238 | C5×M16 | — | 5 | 2 | no | — |
| 239 | C5×M16 | — | 5 | 2 | no | — |
| 240 | C5×M16 | — | 10 | 2 | no | — |
| 241 | C5×M16 | — | 10 | 2 | no | — |
| 242 | C2×C5×C8 | — | 2 | 4 | no | — |
| 243 | C2×C5×C8 | — | 10 | 2 | no | — |
| 244 | C2×C5×C8 | — | 10 | 2 | no | — |
| 245 | C2×C5×C8 | C22×D5 | 1 | 2 | yes | — |
| 246 | C2×C5×C8 | C22×D5 | 1 | 2 | yes | — |
| 247 | C42×C5 | — | 2 | 2 | no | — |
| 248 | C42×C5 | C22×D5 | 1 | 2 | yes | — |
| 249 | #689 | — | 10 | 2 | no | — |
| 250 | #688 | — | 10 | 2 | no | — |
| 251 | #688 | — | 10 | 2 | no | — |
| 252 | #688 | — | 10 | 2 | no | — |
| 253 | #687 | — | 10 | 2 | no | — |
| 254 | #686 | — | 10 | 2 | no | — |
| 255 | #686 | — | 10 | 2 | no | — |
| 256 | #686 | — | 10 | 2 | no | — |
| 257 | #685 | — | 20 | 2 | no | — |
| 258 | #685 | — | 20 | 4 | no | — |
| 259 | #681 | C22×D5 | 1 | 2 | yes | — |
| 260 | #681 | C22×D5 | 1 | 2 | yes | — |
| 261 | Dic20 | — | 10 | 2 | no | — |
| 262 | Dic20 | D20 | 1 | 2 | yes | complemented |
| 263 | D40 | — | 10 | 2 | no | — |
| 264 | D40 | — | 10 | 2 | no | — |
| 265 | D40 | — | 10 | 2 | no | — |
| 266 | D40 | — | 10 | 2 | no | — |
| 267 | D40 | — | 10 | 2 | no | — |
| 268 | D40 | — | 10 | 2 | no | — |
| 269 | D40 | — | 10 | 2 | no | — |
| 270 | D40 | — | 20 | 4 | no | — |
| 271 | D40 | — | 20 | 4 | no | — |
| 272 | D40 | D20 | 1 | 2 | yes | complemented |
| 273 | #677 | — | 10 | 2 | no | — |
| 274 | #677 | — | 10 | 2 | no | — |
| 275 | #677 | — | 10 | 2 | no | — |
| 276 | #677 | — | 10 | 2 | no | — |
| 277 | #677 | — | 10 | 2 | no | — |
| 278 | #677 | — | 10 | 2 | no | — |
| 279 | #677 | — | 10 | 2 | no | — |
| 280 | #677 | — | 10 | 2 | no | — |
| 281 | #677 | — | 20 | 4 | no | — |
| 282 | #677 | — | 20 | 4 | no | — |
| 283 | #677 | D20 | 1 | 2 | yes | complemented |
| 284 | #677 | D20 | 1 | 2 | yes | complemented |
| 285 | #676 | — | 2 | 2 | no | — |
| 286 | #676 | — | 2 | 2 | no | — |
| 287 | C8×D5 | — | 2 | 2 | no | — |
| 288 | C8×D5 | — | 2 | 2 | no | — |
| 289 | #577 | — | 25 | 2 | no | — |
| 290 | #576 | — | 25 | 2 | no | — |
| 291 | #496 | — | 25 | 1 | no | — |
| 292 | #472 | — | 25 | 2 | no | — |
| 293 | #471 | — | 25 | 2 | no | — |
| 294 | #455 | — | 25 | 1 | no | — |
| 295 | #454 | — | 25 | 1 | no | — |
| 296 | #453 | — | 25 | 2 | no | — |
| 297 | #444 | — | 5 | 2 | no | — |
| 298 | C2×C52 | — | 2 | 1 | no | — |
| 299 | C2×C52 | D42 | 1 | 1 | yes | characteristic |
| 300 | C5⋊D5 | — | 8 | 2 | no | — |
| 301 | C5⋊D5 | — | 8 | 1 | no | — |
| 302 | C5×D5 | — | 4 | 2 | no | — |
| 303 | C5×D5 | — | 4 | 2 | no | — |
| 304 | C22×D5 | — | 10 | 2 | no | — |
| 305 | C22×D5 | — | 10 | 2 | no | — |
| 306 | C22×D5 | — | 10 | 2 | no | — |
| 307 | C22×D5 | — | 20 | 2 | no | — |
| 308 | C22×D5 | — | 20 | 4 | no | — |
| 309 | C22×D5 | — | 20 | 2 | no | — |
| 310 | C22×D5 | — | 20 | 2 | no | — |
| 311 | C22×D5 | — | 20 | 2 | no | — |
| 312 | C5×Q8 | — | 5 | 2 | no | — |
| 313 | C5×Q8 | — | 5 | 2 | no | — |
| 314 | C5×D4 | — | 5 | 2 | no | — |
| 315 | C5×D4 | — | 5 | 2 | no | — |
| 316 | C5×D4 | — | 10 | 2 | no | — |
| 317 | C5×D4 | — | 10 | 2 | no | — |
| 318 | C2×C4×C5 | — | 2 | 4 | no | — |
| 319 | C2×C4×C5 | — | 2 | 2 | no | — |
| 320 | C2×C4×C5 | — | 2 | 2 | no | — |
| 321 | C2×C4×C5 | — | 10 | 2 | no | — |
| 322 | C2×C4×C5 | — | 10 | 2 | no | — |
| 323 | C2×C4×C5 | C23×D5 | 1 | 2 | yes | — |
| 324 | C22⋊D5 | — | 2 | 2 | no | — |
| 325 | C22⋊D5 | — | 2 | 2 | no | — |
| 326 | C22⋊D5 | — | 20 | 2 | no | — |
| 327 | C22⋊D5 | — | 20 | 2 | no | — |
| 328 | C22⋊D5 | — | 20 | 2 | no | — |
| 329 | C22⋊D5 | — | 20 | 2 | no | — |
| 330 | C2×Dic5 | — | 10 | 2 | no | — |
| 331 | C2×Dic5 | — | 20 | 2 | no | — |
| 332 | C2×Dic5 | — | 20 | 2 | no | — |
| 333 | D20 | — | 10 | 2 | no | — |
| 334 | D20 | — | 10 | 2 | no | — |
| 335 | D20 | — | 10 | 2 | no | — |
| 336 | D20 | — | 10 | 2 | no | — |
| 337 | D20 | — | 10 | 2 | no | — |
| 338 | D20 | — | 10 | 2 | no | — |
| 339 | D20 | — | 20 | 4 | no | — |
| 340 | D20 | — | 20 | 4 | no | — |
| 341 | D20 | — | 20 | 4 | no | — |
| 342 | D20 | — | 20 | 2 | no | — |
| 343 | D20 | — | 20 | 2 | no | — |
| 344 | D20 | — | 20 | 2 | no | — |
| 345 | D20 | — | 40 | 4 | no | — |
| 346 | D20 | — | 40 | 8 | no | — |
| 347 | D20 | C2×D20 | 1 | 2 | yes | — |
| 348 | D20 | C2×D20 | 1 | 2 | yes | — |
| 349 | C4×D5 | — | 2 | 2 | no | — |
| 350 | C4×D5 | — | 2 | 2 | no | — |
| 351 | C4×D5 | — | 20 | 2 | no | — |
| 352 | C4×D5 | — | 20 | 2 | no | — |
| 353 | C4×D5 | — | 20 | 2 | no | — |
| 354 | C4×D5 | — | 20 | 2 | no | — |
| 355 | Dic10 | — | 10 | 2 | no | — |
| 356 | Dic10 | — | 10 | 2 | no | — |
| 357 | Dic10 | — | 20 | 4 | no | — |
| 358 | Dic10 | — | 20 | 2 | no | — |
| 359 | Dic10 | C2×D20 | 1 | 2 | yes | — |
| 360 | Dic10 | C2×D20 | 1 | 2 | yes | — |
| 361 | C5×C8 | — | 2 | 4 | no | — |
| 362 | C5×C8 | — | 2 | 4 | no | — |
| 363 | C5×C8 | — | 10 | 2 | no | — |
| 364 | C5×C8 | — | 10 | 2 | no | — |
| 365 | C5×C8 | C2×D20 | 1 | 2 | yes | — |
| 366 | C5×C8 | C2×D20 | 1 | 2 | yes | — |
| 367 | C5×C8 | D4×D5 | 1 | 2 | yes | — |
| 368 | C5×C8 | D4×D5 | 1 | 2 | yes | — |
| 369 | #168 | — | 2 | 2 | no | — |
| 370 | #168 | — | 2 | 2 | no | — |
| 371 | 2−1+4 | — | 25 | 1 | no | — |
| 372 | H(5,𝔽2) | — | 25 | 1 | no | — |
| 373 | H(5,𝔽2) | — | 25 | 2 | no | — |
| 374 | #137 | — | 25 | 2 | no | — |
| 375 | #137 | — | 50 | 2 | no | — |
| 376 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 377 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 378 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 379 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 380 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 381 | AGL(1,ℤ/8) | — | 50 | 2 | no | — |
| 382 | #135 | — | 5 | 2 | no | — |
| 383 | #135 | — | 50 | 2 | no | — |
| 384 | #135 | — | 50 | 2 | no | — |
| 385 | C2×SD16 | — | 25 | 2 | no | — |
| 386 | C2×SD16 | — | 50 | 2 | no | — |
| 387 | C2×D8 | — | 25 | 2 | no | — |
| 388 | C2×D8 | — | 50 | 2 | no | — |
| 389 | #131 | — | 5 | 2 | no | — |
| 390 | #131 | — | 5 | 2 | no | — |
| 391 | #127 | — | 25 | 1 | no | — |
| 392 | #124 | — | 25 | 1 | no | — |
| 393 | #108 | — | 5 | 2 | no | — |
| 394 | #104 | — | 5 | 2 | no | — |
| 395 | #104 | — | 5 | 2 | no | — |
| 396 | #101 | — | 25 | 1 | no | — |
| 397 | #100 | — | 25 | 2 | no | — |
| 398 | #100 | — | 25 | 1 | no | — |
| 399 | #97 | D52 | 1 | 1 | yes | characteristic, complemented |
| 400 | C52 | #3288 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 401 | C22×C5 | — | 2 | 2 | no | — |
| 402 | C22×C5 | — | 10 | 2 | no | — |
| 403 | C22×C5 | — | 10 | 2 | no | — |
| 404 | C22×C5 | #4149 | 1 | 2 | yes | — |
| 405 | C2×D5 | — | 2 | 2 | no | — |
| 406 | C2×D5 | — | 2 | 2 | no | — |
| 407 | C2×D5 | — | 20 | 2 | no | — |
| 408 | C2×D5 | — | 20 | 2 | no | — |
| 409 | C2×D5 | — | 20 | 2 | no | — |
| 410 | C2×D5 | — | 40 | 4 | no | — |
| 411 | C2×D5 | — | 40 | 2 | no | — |
| 412 | C2×D5 | — | 40 | 2 | no | — |
| 413 | C2×D5 | — | 40 | 2 | no | — |
| 414 | C2×D5 | — | 40 | 2 | no | — |
| 415 | C2×D5 | — | 40 | 8 | no | — |
| 416 | C2×D5 | — | 40 | 4 | no | — |
| 417 | C2×D5 | — | 80 | 2 | no | — |
| 418 | C2×D5 | — | 80 | 2 | no | — |
| 419 | C2×D5 | — | 80 | 2 | no | — |
| 420 | C4×C5 | — | 2 | 4 | no | — |
| 421 | C4×C5 | — | 4 | 4 | no | — |
| 422 | C4×C5 | — | 4 | 2 | no | — |
| 423 | C4×C5 | — | 10 | 2 | no | — |
| 424 | C4×C5 | — | 10 | 2 | no | — |
| 425 | C4×C5 | C22×D20 | 1 | 2 | yes | — |
| 426 | C4×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 427 | Dic5 | — | 2 | 2 | no | — |
| 428 | Dic5 | — | 2 | 2 | no | — |
| 429 | Dic5 | — | 20 | 2 | no | — |
| 430 | Dic5 | — | 40 | 2 | no | — |
| 431 | #41 | — | 5 | 2 | no | — |
| 432 | #41 | — | 5 | 2 | no | — |
| 433 | #41 | — | 50 | 2 | no | — |
| 434 | #41 | — | 50 | 2 | no | — |
| 435 | #41 | — | 50 | 2 | no | — |
| 436 | #41 | — | 50 | 2 | no | — |
| 437 | #41 | — | 100 | 1 | no | — |
| 438 | C2×Q8 | — | 25 | 1 | no | — |
| 439 | C2×Q8 | — | 50 | 2 | no | — |
| 440 | C2×D4 | — | 25 | 1 | no | — |
| 441 | C2×D4 | — | 25 | 2 | no | — |
| 442 | C2×D4 | — | 50 | 2 | no | — |
| 443 | C2×D4 | — | 50 | 2 | no | — |
| 444 | C2×D4 | — | 50 | 2 | no | — |
| 445 | C2×D4 | — | 100 | 1 | no | — |
| 446 | C2×D4 | — | 100 | 1 | no | — |
| 447 | C2×D4 | — | 100 | 2 | no | — |
| 448 | Q16 | — | 5 | 2 | no | — |
| 449 | Q16 | — | 50 | 2 | no | — |
| 450 | SD16 | — | 5 | 2 | no | — |
| 451 | SD16 | — | 5 | 2 | no | — |
| 452 | SD16 | — | 50 | 2 | no | — |
| 453 | SD16 | — | 50 | 2 | no | — |
| 454 | SD16 | — | 50 | 2 | no | — |
| 455 | SD16 | — | 50 | 2 | no | — |
| 456 | SD16 | — | 50 | 2 | no | — |
| 457 | SD16 | — | 50 | 2 | no | — |
| 458 | D8 | — | 5 | 2 | no | — |
| 459 | D8 | — | 50 | 2 | no | — |
| 460 | D8 | — | 50 | 2 | no | — |
| 461 | D8 | — | 50 | 2 | no | — |
| 462 | D8 | — | 50 | 2 | no | — |
| 463 | D8 | — | 50 | 2 | no | — |
| 464 | M16 | — | 5 | 2 | no | — |
| 465 | M16 | — | 5 | 2 | no | — |
| 466 | M16 | — | 10 | 2 | no | — |
| 467 | M16 | — | 10 | 2 | no | — |
| 468 | C2×C8 | — | 10 | 2 | no | — |
| 469 | C2×C8 | — | 10 | 2 | no | — |
| 470 | C2×C8 | C2×D52 | 1 | 2 | yes | — |
| 471 | C22⋊C4 | — | 100 | 1 | no | — |
| 472 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 473 | C2×C5 | — | 2 | 4 | no | — |
| 474 | C2×C5 | — | 2 | 2 | no | — |
| 475 | C2×C5 | — | 2 | 2 | no | — |
| 476 | C2×C5 | — | 20 | 2 | no | — |
| 477 | C2×C5 | — | 20 | 2 | no | — |
| 478 | C2×C5 | D4×D20 | 1 | 2 | yes | — |
| 479 | D5 | — | 4 | 2 | no | — |
| 480 | D5 | — | 4 | 2 | no | — |
| 481 | D5 | — | 40 | 2 | no | — |
| 482 | D5 | — | 40 | 2 | no | — |
| 483 | D5 | — | 40 | 2 | no | — |
| 484 | D5 | — | 80 | 4 | no | — |
| 485 | D5 | — | 80 | 2 | no | — |
| 486 | C23 | — | 50 | 1 | no | — |
| 487 | C23 | — | 50 | 2 | no | — |
| 488 | C23 | — | 100 | 2 | no | — |
| 489 | C23 | — | 100 | 1 | no | — |
| 490 | Q8 | — | 5 | 2 | no | — |
| 491 | Q8 | — | 5 | 2 | no | — |
| 492 | Q8 | — | 50 | 2 | no | — |
| 493 | Q8 | — | 100 | 1 | no | — |
| 494 | D4 | — | 5 | 2 | no | — |
| 495 | D4 | — | 5 | 2 | no | — |
| 496 | D4 | — | 10 | 2 | no | — |
| 497 | D4 | — | 10 | 2 | no | — |
| 498 | D4 | — | 50 | 2 | no | — |
| 499 | D4 | — | 50 | 2 | no | — |
| 500 | D4 | — | 50 | 2 | no | — |
| 501 | D4 | — | 100 | 2 | no | — |
| 502 | D4 | — | 100 | 2 | no | — |
| 503 | D4 | — | 100 | 2 | no | — |
| 504 | D4 | — | 100 | 1 | no | — |
| 505 | D4 | — | 200 | 2 | no | — |
| 506 | C2×C4 | — | 2 | 1 | no | — |
| 507 | C2×C4 | — | 10 | 2 | no | — |
| 508 | C2×C4 | — | 10 | 2 | no | — |
| 509 | C2×C4 | — | 50 | 1 | no | — |
| 510 | C2×C4 | — | 100 | 1 | no | — |
| 511 | C2×C4 | — | 100 | 2 | no | — |
| 512 | C2×C4 | — | 100 | 2 | no | — |
| 513 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 514 | C8 | — | 10 | 2 | no | — |
| 515 | C8 | — | 10 | 2 | no | — |
| 516 | C8 | D5×D20 | 1 | 2 | yes | — |
| 517 | C8 | D5×D20 | 1 | 2 | yes | — |
| 518 | C5 | — | 2 | 2 | no | — |
| 519 | C5 | #10611631 | 1 | 2 | yes | complemented |
| 520 | C22 | — | 10 | 2 | no | — |
| 521 | C22 | — | 10 | 2 | no | — |
| 522 | C22 | — | 100 | 1 | no | — |
| 523 | C22 | — | 100 | 2 | no | — |
| 524 | C22 | — | 400 | 1 | no | — |
| 525 | C22 | — | 400 | 2 | no | — |
| 526 | C22 | — | 200 | 2 | no | — |
| 527 | C22 | — | 200 | 1 | no | — |
| 528 | C22 | #11717473 | 1 | 1 | yes | characteristic |
| 529 | C4 | — | 4 | 1 | no | — |
| 530 | C4 | — | 10 | 2 | no | — |
| 531 | C4 | — | 10 | 2 | no | — |
| 532 | C4 | — | 100 | 1 | no | — |
| 533 | C4 | C2×D5×D20 | 1 | 2 | yes | — |
| 534 | C2 | — | 2 | 1 | no | — |
| 535 | C2 | — | 20 | 2 | no | — |
| 536 | C2 | — | 20 | 2 | no | — |
| 537 | C2 | — | 200 | 2 | no | — |
| 538 | C2 | — | 200 | 1 | no | — |
| 539 | C2 | D202 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D202 |
| commutator, cosocle | C2×C4×C52 | C24 |
| Frattini | C2×C4 | C22×D52 |
| Fitting | C52×#97 | C22 |
| socle | C2×C52 | D42 |
| hypercenter | #97 | D52 |
| hypocenter | C52 | #3288 |
| LCS | G ▷ C2×C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13105771 | C2 | semidirect |
| 2. #13105770 | C2 | semidirect |
| 3. #13102576 | C2 | semidirect |
| 4. C5×#65006 | C2 | semidirect |
| 5. #13101105 | C2 | semidirect |
| 6. #13101101 | C2 | semidirect |
| 7. #13100582 | C2 | semidirect |
| 8. #13100579 | C2 | semidirect |
| 9. #13100578 | C2 | semidirect |
| 11. #11717473 | C22 | semidirect |
| 12. #11717463 | C22 | semidirect |
| 13. C2×#87801 | C22 | semidirect |
| 14. C2×#87800 | C22 | semidirect |
| 15. #11717195 | C22 | semidirect |
| 16. #11717194 | C22 | semidirect |
| 18. C5×#4047 | C22 | semidirect |
| 19. C5×#4047 | C22 | semidirect |
| 20. #11716949 | C22 | semidirect |
| 22. #11716943 | C22 | semidirect |
| 23. #11716943 | C22 | semidirect |
| 32. C52×#97 | C22 | semidirect |
| 33. C5×#3951 | C22 | semidirect |
| 34. C5×#3937 | C22 | semidirect |
| 35. C5×#3937 | C22 | semidirect |
| 36. #11716602 | C22 | semidirect |
| 37. #11716600 | C22 | semidirect |
| 38. #11716600 | C22 | semidirect |
| 66. C5×Dic20 | D4 | semidirect |
| 67. C5×D40 | D4 | semidirect |
| 68. C5×#677 | D4 | semidirect |
| 69. C5×#677 | D4 | semidirect |
| 95. #65006 | D5 | semidirect |
| 168. #4047 | C2×D5 | semidirect |
| 169. #4047 | C2×D5 | semidirect |
| 178. C5×#97 | C2×D5 | semidirect |
| 183. #3951 | C2×D5 | semidirect |
| 184. #3937 | C2×D5 | semidirect |
| 185. #3937 | C2×D5 | semidirect |
| 262. Dic20 | D20 | semidirect |
| 272. D40 | D20 | semidirect |
| 283. #677 | D20 | semidirect |
| 284. #677 | D20 | semidirect |
| 399. #97 | D52 | semidirect |
| 400. C52 | #3288 | semidirect |
| 519. C5 | #10611631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13105771 | 2 |
| #13105770 | 2 |
| #13102576 | 2 |
| C5×#65006 | 2 |
| #13101105 | 2 |
| #13101101 | 2 |
| #13100582 | 2 |
| #13100579 | 2 |
| #13100578 | 2 |
| #10611631 | 5 |