Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1850 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 1850 conjugacy classes of subgroups — too many to draw. Only its 174 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 | #13107821 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #124×C5⋊D5 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13106467 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C5×#65350 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13101839 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13101703 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13101682 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13100578 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13100574 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×Q8×C5⋊D5 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×D4×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 12 | C5×#4144 | C22 | 1 | 2 | yes | — |
| 13 | #11717495 | — | 2 | 2 | no | — |
| 14 | C2×#87886 | — | 2 | 2 | no | — |
| 15 | #11717479 | — | 2 | 4 | no | — |
| 16 | #11717477 | — | 2 | 2 | no | — |
| 17 | D4×D52 | — | 2 | 2 | no | — |
| 18 | #11717473 | C22 | 1 | 2 | yes | — |
| 19 | #11717471 | C22 | 1 | 2 | yes | — |
| 20 | C52×#124 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #11717267 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #11717256 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #11717205 | — | 2 | 2 | no | — |
| 24 | C22⋊C4×C5⋊D5 | — | 2 | 2 | no | — |
| 25 | #11717195 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C42×C5⋊D5 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C5×#4088 | C22 | 1 | 4 | yes | complemented |
| 28 | #11717069 | — | 2 | 4 | no | — |
| 29 | #11717062 | — | 2 | 2 | no | — |
| 30 | #11717058 | — | 2 | 2 | no | — |
| 31 | #11716949 | C22 | 1 | 4 | yes | complemented |
| 32 | #11716936 | C22 | 1 | 2 | yes | complemented |
| 33 | C5×#3965 | C22 | 1 | 2 | yes | complemented |
| 34 | C5×#3937 | C22 | 1 | 4 | yes | complemented |
| 35 | #11716609 | C22 | 1 | 4 | yes | complemented |
| 36 | #11716600 | C22 | 1 | 2 | yes | complemented |
| 37 | D5×#455 | — | 5 | 2 | no | maximal |
| 38 | C23×C5⋊D5 | D4 | 1 | 2 | yes | — |
| 39 | C22×D52 | — | 2 | 2 | no | — |
| 40 | C2×C52×Q8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×C52×D4 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×C22⋊(C5⋊D5) | D4 | 1 | 2 | yes | — |
| 43 | Q8×C5⋊D5 | — | 2 | 2 | no | — |
| 44 | Q8×C5⋊D5 | — | 2 | 2 | no | — |
| 45 | D4×C5⋊D5 | — | 2 | 2 | no | — |
| 46 | D4×C5⋊D5 | — | 2 | 2 | no | — |
| 47 | C2×C4⋊(C5⋊D5) | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 49 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 50 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 51 | C2×#6045 | — | 2 | 1 | no | — |
| 52 | C2×#6045 | C23 | 1 | 1 | yes | characteristic, complemented |
| 53 | C2×C5×C22⋊D5 | — | 2 | 4 | no | — |
| 54 | C5×#711 | — | 2 | 4 | no | — |
| 55 | C5×D4×D5 | — | 2 | 4 | no | — |
| 56 | C5×#709 | C23 | 1 | 4 | yes | — |
| 57 | #87886 | — | 2 | 4 | no | — |
| 58 | #87886 | — | 2 | 4 | no | — |
| 59 | #87886 | — | 2 | 2 | no | — |
| 60 | #87886 | — | 2 | 4 | no | — |
| 61 | D5×C22⋊D5 | — | 2 | 8 | no | — |
| 62 | C2×#6038 | — | 2 | 4 | no | — |
| 63 | C2×#6036 | — | 2 | 2 | no | — |
| 64 | #87880 | — | 2 | 2 | no | — |
| 65 | #87879 | — | 2 | 8 | no | — |
| 66 | #87877 | D4 | 1 | 2 | yes | — |
| 67 | D5×D20 | — | 2 | 4 | no | — |
| 68 | C4×D52 | — | 2 | 2 | no | — |
| 69 | #87874 | — | 2 | 4 | no | — |
| 70 | #87873 | — | 2 | 2 | no | — |
| 71 | #87872 | D4 | 1 | 2 | yes | — |
| 72 | #87871 | D4 | 1 | 4 | yes | — |
| 73 | C52×C22⋊C4 | — | 2 | 2 | no | — |
| 74 | C42×C52 | C23 | 1 | 1 | yes | characteristic, complemented |
| 75 | C22⋊#1039 | — | 2 | 2 | no | — |
| 76 | #87808 | — | 2 | 2 | no | — |
| 77 | #87808 | — | 2 | 2 | no | — |
| 78 | C4×#1039 | — | 2 | 1 | no | — |
| 79 | C4×#1039 | C23 | 1 | 1 | yes | characteristic, complemented |
| 80 | C5×#689 | — | 2 | 4 | no | — |
| 81 | C5×#688 | — | 2 | 4 | no | — |
| 82 | C5×#681 | C23 | 1 | 4 | yes | complemented |
| 83 | #87776 | — | 2 | 4 | no | — |
| 84 | #87773 | — | 2 | 4 | no | — |
| 85 | #87769 | — | 2 | 2 | no | — |
| 86 | #87767 | — | 2 | 2 | no | — |
| 87 | D5×H(5,𝔽2) | — | 5 | 2 | no | — |
| 88 | D5×#137 | — | 5 | 4 | no | — |
| 89 | D5×#124 | — | 5 | 2 | no | — |
| 90 | D5×#124 | — | 10 | 2 | no | — |
| 91 | C5×#455 | — | 5 | 2 | no | — |
| 92 | #65531 | — | 5 | 2 | no | — |
| 93 | #65491 | — | 5 | 4 | no | — |
| 94 | #65350 | D5 | 1 | 2 | yes | complemented |
| 95 | #65114 | — | 5 | 4 | no | — |
| 96 | D5×#104 | — | 5 | 4 | no | — |
| 97 | #65035 | — | 5 | 2 | no | — |
| 98 | D5×#100 | — | 5 | 2 | no | — |
| 99 | C23×C52 | C2×D4 | 1 | 2 | yes | — |
| 100 | C22×C5⋊D5 | — | 2 | 2 | no | — |
| 101 | C22×C5⋊D5 | — | 2 | 2 | no | — |
| 102 | C22×C5⋊D5 | — | 4 | 4 | no | — |
| 103 | C22×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C22×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 105 | C22×C5×D5 | — | 2 | 4 | no | — |
| 106 | C2×D52 | — | 2 | 2 | no | — |
| 107 | C2×D52 | — | 2 | 4 | no | — |
| 108 | C2×D52 | — | 8 | 4 | no | — |
| 109 | C52×Q8 | — | 2 | 2 | no | — |
| 110 | C52×D4 | — | 2 | 2 | no | — |
| 111 | C2×C4×C52 | — | 2 | 1 | no | — |
| 112 | C2×C4×C52 | — | 2 | 1 | no | — |
| 113 | C2×C4×C52 | C24 | 1 | 1 | yes | characteristic |
| 114 | C22⋊(C5⋊D5) | — | 2 | 4 | no | — |
| 115 | C2×#1039 | — | 2 | 1 | no | — |
| 116 | C2×#1039 | — | 2 | 1 | no | — |
| 117 | C2×#1039 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 119 | C4×C5⋊D5 | — | 4 | 2 | no | — |
| 120 | C4×C5⋊D5 | — | 4 | 1 | no | — |
| 121 | C4×C5⋊D5 | — | 4 | 1 | no | — |
| 122 | C4×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 123 | C4×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 124 | #6045 | — | 2 | 2 | no | — |
| 125 | #6045 | — | 4 | 2 | no | — |
| 126 | C5×C22⋊D5 | — | 2 | 8 | no | — |
| 127 | C5×C22⋊D5 | — | 2 | 4 | no | — |
| 128 | C2×C5×Dic5 | — | 2 | 4 | no | — |
| 129 | C5×D20 | C2×D4 | 1 | 4 | yes | — |
| 130 | C4×C5×D5 | — | 2 | 4 | no | — |
| 131 | C5×Dic10 | C2×D4 | 1 | 4 | yes | — |
| 132 | #6039 | — | 2 | 2 | no | — |
| 133 | #6038 | — | 2 | 8 | no | — |
| 134 | #6038 | — | 2 | 4 | no | — |
| 135 | #6037 | — | 2 | 2 | no | — |
| 136 | #6036 | — | 2 | 4 | no | — |
| 137 | #6036 | — | 2 | 2 | no | — |
| 138 | D5×Dic5 | — | 2 | 4 | no | — |
| 139 | C5×#168 | — | 2 | 4 | no | — |
| 140 | C5×H(5,𝔽2) | — | 5 | 2 | no | — |
| 141 | #4149 | — | 5 | 4 | no | — |
| 142 | #4149 | — | 10 | 4 | no | — |
| 143 | D5×#41 | — | 5 | 4 | no | — |
| 144 | D5×#41 | — | 10 | 4 | no | — |
| 145 | C2×Q8×D5 | — | 5 | 2 | no | — |
| 146 | C2×Q8×D5 | — | 10 | 2 | no | — |
| 147 | #4144 | — | 10 | 4 | no | — |
| 148 | #4144 | — | 10 | 4 | no | — |
| 149 | #4144 | C2×D5 | 1 | 2 | yes | — |
| 150 | C2×D4×D5 | — | 5 | 2 | no | — |
| 151 | C2×D4×D5 | — | 10 | 2 | no | — |
| 152 | C2×D4×D5 | — | 10 | 4 | no | — |
| 153 | C2×D4×D5 | — | 10 | 4 | no | — |
| 154 | C5×#137 | — | 5 | 4 | no | — |
| 155 | C5×#124 | — | 2 | 2 | no | — |
| 156 | C5×#124 | C2×D5 | 1 | 2 | yes | complemented |
| 157 | #4097 | — | 5 | 4 | no | — |
| 158 | #4093 | — | 5 | 2 | no | — |
| 159 | #4093 | — | 10 | 2 | no | — |
| 160 | #4088 | C2×D5 | 1 | 4 | yes | complemented |
| 161 | #4082 | — | 5 | 2 | no | — |
| 162 | #4082 | — | 10 | 2 | no | — |
| 163 | #4064 | — | 10 | 4 | no | — |
| 164 | D5×Q16 | — | 10 | 4 | no | — |
| 165 | #4061 | — | 10 | 4 | no | — |
| 166 | D5×SD16 | — | 10 | 4 | no | — |
| 167 | #4055 | — | 5 | 4 | no | — |
| 168 | D5×M16 | — | 5 | 4 | no | — |
| 169 | #4031 | — | 10 | 4 | no | — |
| 170 | #4031 | — | 10 | 8 | no | — |
| 171 | D5×C22⋊C4 | — | 10 | 4 | no | — |
| 172 | D5×C22⋊C4 | — | 10 | 8 | no | — |
| 173 | #4021 | — | 5 | 2 | no | — |
| 174 | #4021 | — | 10 | 2 | no | — |
| 175 | C42×D5 | — | 5 | 2 | no | — |
| 176 | C42×D5 | — | 10 | 2 | no | — |
| 177 | C5×#104 | — | 5 | 4 | no | — |
| 178 | C5×#100 | — | 5 | 2 | no | — |
| 179 | #3969 | — | 5 | 4 | no | — |
| 180 | #3965 | C2×D5 | 1 | 2 | yes | complemented |
| 181 | #3957 | — | 5 | 4 | no | — |
| 182 | #3955 | — | 5 | 4 | no | — |
| 183 | #3937 | C2×D5 | 1 | 4 | yes | complemented |
| 184 | C2×#455 | — | 25 | 1 | no | Sylow |
| 185 | C22×C52 | — | 2 | 2 | no | — |
| 186 | C22×C52 | — | 4 | 2 | no | — |
| 187 | C22×C52 | C22×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 189 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 190 | C2×C5⋊D5 | — | 4 | 4 | no | — |
| 191 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 192 | C2×C5⋊D5 | — | 8 | 2 | no | — |
| 193 | C2×C5⋊D5 | #120 | 1 | 1 | yes | characteristic |
| 194 | C2×C5⋊D5 | #120 | 1 | 1 | yes | characteristic |
| 195 | C2×C5×D5 | — | 2 | 4 | no | — |
| 196 | C2×C5×D5 | — | 8 | 4 | no | — |
| 197 | D52 | — | 4 | 4 | no | — |
| 198 | D52 | — | 8 | 4 | no | — |
| 199 | C4×C52 | — | 4 | 1 | no | — |
| 200 | C4×C52 | — | 4 | 1 | no | — |
| 201 | C4×C52 | C22×D4 | 1 | 2 | yes | — |
| 202 | #1039 | — | 4 | 1 | no | — |
| 203 | #1039 | — | 4 | 1 | no | — |
| 204 | #1039 | #120 | 1 | 2 | yes | — |
| 205 | C5×Dic5 | — | 2 | 4 | no | — |
| 206 | C23×D5 | — | 5 | 4 | no | — |
| 207 | C23×D5 | — | 10 | 4 | no | — |
| 208 | C23×D5 | — | 10 | 4 | no | — |
| 209 | C5×#41 | — | 5 | 4 | no | — |
| 210 | C5×#41 | — | 10 | 4 | no | — |
| 211 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 212 | C2×C5×Q8 | C22×D5 | 1 | 2 | yes | complemented |
| 213 | C2×C5×D4 | — | 2 | 2 | no | — |
| 214 | C2×C5×D4 | — | 10 | 4 | no | — |
| 215 | C2×C5×D4 | — | 10 | 4 | no | — |
| 216 | C2×C5×D4 | C22×D5 | 1 | 2 | yes | — |
| 217 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 218 | C2×C22⋊D5 | — | 5 | 4 | no | — |
| 219 | C2×C22⋊D5 | — | 10 | 4 | no | — |
| 220 | C2×C22⋊D5 | — | 10 | 4 | no | — |
| 221 | C2×C22⋊D5 | — | 10 | 8 | no | — |
| 222 | #713 | — | 5 | 4 | no | — |
| 223 | #713 | — | 10 | 4 | no | — |
| 224 | Q8×D5 | — | 5 | 4 | no | — |
| 225 | Q8×D5 | — | 10 | 4 | no | — |
| 226 | Q8×D5 | — | 10 | 4 | no | — |
| 227 | Q8×D5 | — | 20 | 4 | no | — |
| 228 | Q8×D5 | — | 20 | 4 | no | — |
| 229 | #711 | — | 2 | 4 | no | — |
| 230 | #711 | — | 5 | 4 | no | — |
| 231 | #711 | — | 10 | 8 | no | — |
| 232 | #711 | — | 10 | 4 | no | — |
| 233 | D4×D5 | — | 2 | 4 | no | — |
| 234 | D4×D5 | — | 5 | 4 | no | — |
| 235 | D4×D5 | — | 10 | 4 | no | — |
| 236 | D4×D5 | — | 10 | 4 | no | — |
| 237 | D4×D5 | — | 10 | 4 | no | — |
| 238 | D4×D5 | — | 10 | 4 | no | — |
| 239 | D4×D5 | — | 10 | 8 | no | — |
| 240 | D4×D5 | — | 10 | 8 | no | — |
| 241 | D4×D5 | — | 10 | 8 | no | — |
| 242 | D4×D5 | — | 10 | 8 | no | — |
| 243 | D4×D5 | — | 20 | 4 | no | — |
| 244 | D4×D5 | — | 20 | 4 | no | — |
| 245 | #709 | — | 10 | 4 | no | — |
| 246 | #709 | — | 10 | 8 | no | — |
| 247 | #709 | — | 10 | 4 | no | — |
| 248 | #709 | C22×D5 | 1 | 4 | yes | — |
| 249 | C2×D20 | — | 5 | 2 | no | — |
| 250 | C2×D20 | — | 10 | 2 | no | — |
| 251 | C2×D20 | — | 10 | 4 | no | — |
| 252 | C2×D20 | — | 10 | 4 | no | — |
| 253 | C2×C4×D5 | — | 5 | 2 | no | — |
| 254 | C2×C4×D5 | — | 10 | 2 | no | — |
| 255 | C2×C4×D5 | — | 10 | 4 | no | — |
| 256 | C2×C4×D5 | — | 10 | 4 | no | — |
| 257 | C2×C4×D5 | — | 10 | 2 | no | — |
| 258 | C2×C4×D5 | — | 10 | 2 | no | — |
| 259 | C2×C4×D5 | — | 10 | 4 | no | — |
| 260 | C2×C4×D5 | — | 10 | 4 | no | — |
| 261 | C2×Dic10 | — | 5 | 2 | no | — |
| 262 | C2×Dic10 | — | 10 | 2 | no | — |
| 263 | C2×Dic10 | — | 10 | 2 | no | — |
| 264 | C2×Dic10 | — | 10 | 4 | no | — |
| 265 | C5×Q16 | — | 10 | 4 | no | — |
| 266 | C5×SD16 | — | 10 | 4 | no | — |
| 267 | C5×M16 | — | 5 | 4 | no | — |
| 268 | C5×C22⋊C4 | — | 2 | 8 | no | — |
| 269 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 270 | C42×C5 | — | 2 | 2 | no | — |
| 271 | C42×C5 | C22×D5 | 1 | 2 | yes | complemented |
| 272 | C22⋊Dic5 | — | 10 | 8 | no | — |
| 273 | C22⋊Dic5 | — | 10 | 4 | no | — |
| 274 | #689 | — | 2 | 4 | no | — |
| 275 | #689 | — | 10 | 4 | no | — |
| 276 | #688 | — | 2 | 4 | no | — |
| 277 | #687 | — | 10 | 4 | no | — |
| 278 | #685 | — | 10 | 4 | no | — |
| 279 | #685 | — | 10 | 4 | no | — |
| 280 | #685 | — | 10 | 8 | no | — |
| 281 | #685 | — | 10 | 8 | no | — |
| 282 | C4×Dic5 | — | 5 | 2 | no | — |
| 283 | C4×Dic5 | — | 10 | 2 | no | — |
| 284 | C4×Dic5 | — | 10 | 2 | no | — |
| 285 | C4×Dic5 | — | 10 | 4 | no | — |
| 286 | #681 | C22×D5 | 1 | 4 | yes | complemented |
| 287 | Dic20 | — | 10 | 4 | no | — |
| 288 | #677 | — | 10 | 4 | no | — |
| 289 | #676 | — | 10 | 4 | no | — |
| 290 | C8×D5 | — | 10 | 4 | no | — |
| 291 | C2×H(5,𝔽2) | — | 25 | 1 | no | — |
| 292 | C2×#137 | — | 25 | 2 | no | — |
| 293 | C2×#124 | — | 25 | 1 | no | — |
| 294 | #455 | — | 5 | 2 | no | — |
| 295 | #455 | — | 25 | 2 | no | — |
| 296 | #455 | — | 25 | 2 | no | — |
| 297 | #455 | — | 25 | 2 | no | — |
| 298 | C2×#104 | — | 25 | 2 | no | — |
| 299 | C2×#100 | — | 25 | 1 | no | — |
| 300 | C2×C52 | — | 2 | 1 | no | — |
| 301 | C2×C52 | — | 4 | 2 | no | — |
| 302 | C2×C52 | C2×#120 | 1 | 1 | yes | characteristic |
| 303 | C5⋊D5 | — | 2 | 1 | no | — |
| 304 | C5⋊D5 | — | 4 | 2 | no | — |
| 305 | C5⋊D5 | #455 | 1 | 2 | yes | complemented |
| 306 | C5×D5 | — | 4 | 4 | no | — |
| 307 | C23×C5 | — | 2 | 4 | no | — |
| 308 | C23×C5 | — | 10 | 4 | no | — |
| 309 | C23×C5 | D4×D5 | 1 | 4 | yes | — |
| 310 | C22×D5 | — | 2 | 4 | no | — |
| 311 | C22×D5 | — | 5 | 2 | no | — |
| 312 | C22×D5 | — | 5 | 4 | no | — |
| 313 | C22×D5 | — | 10 | 2 | no | — |
| 314 | C22×D5 | — | 10 | 4 | no | — |
| 315 | C22×D5 | — | 10 | 4 | no | — |
| 316 | C22×D5 | — | 10 | 8 | no | — |
| 317 | C22×D5 | — | 10 | 4 | no | — |
| 318 | C22×D5 | — | 10 | 4 | no | — |
| 319 | C22×D5 | — | 20 | 4 | no | — |
| 320 | C22×D5 | — | 20 | 4 | no | — |
| 321 | C22×D5 | — | 20 | 8 | no | — |
| 322 | C22×D5 | — | 20 | 16 | no | — |
| 323 | C22×D5 | — | 40 | 8 | no | — |
| 324 | C5×Q8 | — | 2 | 4 | no | — |
| 325 | C5×Q8 | — | 4 | 4 | no | — |
| 326 | C5×Q8 | — | 5 | 4 | no | — |
| 327 | C5×D4 | — | 2 | 4 | no | — |
| 328 | C5×D4 | — | 4 | 4 | no | — |
| 329 | C5×D4 | — | 5 | 4 | no | — |
| 330 | C5×D4 | — | 10 | 8 | no | — |
| 331 | C5×D4 | — | 10 | 4 | no | — |
| 332 | C2×C4×C5 | — | 2 | 4 | no | — |
| 333 | C2×C4×C5 | — | 2 | 4 | no | — |
| 334 | C2×C4×C5 | — | 2 | 2 | no | — |
| 335 | C2×C4×C5 | — | 2 | 2 | no | — |
| 336 | C2×C4×C5 | — | 2 | 2 | no | — |
| 337 | C2×C4×C5 | — | 10 | 4 | no | — |
| 338 | C2×C4×C5 | — | 10 | 4 | no | — |
| 339 | C2×C4×C5 | C23×D5 | 1 | 2 | yes | — |
| 340 | C22⋊D5 | — | 2 | 8 | no | — |
| 341 | C22⋊D5 | — | 2 | 4 | no | — |
| 342 | C22⋊D5 | — | 10 | 4 | no | — |
| 343 | C22⋊D5 | — | 10 | 8 | no | — |
| 344 | C22⋊D5 | — | 10 | 4 | no | — |
| 345 | C22⋊D5 | — | 10 | 8 | no | — |
| 346 | C22⋊D5 | — | 20 | 8 | no | — |
| 347 | C2×Dic5 | — | 2 | 4 | no | — |
| 348 | C2×Dic5 | — | 5 | 2 | no | — |
| 349 | C2×Dic5 | — | 10 | 2 | no | — |
| 350 | C2×Dic5 | — | 10 | 4 | no | — |
| 351 | C2×Dic5 | — | 10 | 4 | no | — |
| 352 | C2×Dic5 | — | 10 | 4 | no | — |
| 353 | C2×Dic5 | — | 10 | 2 | no | — |
| 354 | C2×Dic5 | — | 10 | 2 | no | — |
| 355 | D20 | — | 10 | 4 | no | — |
| 356 | D20 | — | 10 | 8 | no | — |
| 357 | D20 | — | 10 | 4 | no | — |
| 358 | D20 | — | 20 | 4 | no | — |
| 359 | D20 | D4×D5 | 1 | 4 | yes | — |
| 360 | C4×D5 | — | 2 | 4 | no | — |
| 361 | C4×D5 | — | 5 | 4 | no | — |
| 362 | C4×D5 | — | 5 | 4 | no | — |
| 363 | C4×D5 | — | 10 | 4 | no | — |
| 364 | C4×D5 | — | 10 | 4 | no | — |
| 365 | C4×D5 | — | 10 | 4 | no | — |
| 366 | C4×D5 | — | 10 | 8 | no | — |
| 367 | C4×D5 | — | 10 | 4 | no | — |
| 368 | C4×D5 | — | 20 | 2 | no | — |
| 369 | C4×D5 | — | 20 | 2 | no | — |
| 370 | C4×D5 | — | 20 | 4 | no | — |
| 371 | C4×D5 | — | 20 | 8 | no | — |
| 372 | C4×D5 | — | 20 | 4 | no | — |
| 373 | C4×D5 | — | 20 | 4 | no | — |
| 374 | Dic10 | — | 10 | 4 | no | — |
| 375 | Dic10 | — | 10 | 4 | no | — |
| 376 | Dic10 | — | 20 | 4 | no | — |
| 377 | Dic10 | — | 20 | 4 | no | — |
| 378 | Dic10 | — | 20 | 8 | no | — |
| 379 | Dic10 | D4×D5 | 1 | 4 | yes | — |
| 380 | C5×C8 | — | 10 | 4 | no | — |
| 381 | #168 | — | 2 | 4 | no | — |
| 382 | H(5,𝔽2) | — | 5 | 2 | no | — |
| 383 | H(5,𝔽2) | — | 25 | 2 | no | — |
| 384 | H(5,𝔽2) | — | 50 | 2 | no | — |
| 385 | H(5,𝔽2) | — | 50 | 4 | no | — |
| 386 | C2×#41 | — | 25 | 2 | no | — |
| 387 | C2×#41 | — | 50 | 2 | no | — |
| 388 | C22×Q8 | — | 25 | 1 | no | — |
| 389 | C22×D4 | — | 25 | 1 | no | — |
| 390 | C22×D4 | — | 50 | 2 | no | — |
| 391 | C22×D4 | — | 50 | 2 | no | — |
| 392 | #137 | — | 5 | 4 | no | — |
| 393 | #137 | — | 25 | 4 | no | — |
| 394 | #137 | — | 50 | 4 | no | — |
| 395 | C2×Q16 | — | 50 | 2 | no | — |
| 396 | C2×SD16 | — | 50 | 2 | no | — |
| 397 | C2×M16 | — | 25 | 2 | no | — |
| 398 | #124 | — | 25 | 1 | no | — |
| 399 | #124 | — | 25 | 1 | no | — |
| 400 | #124 | — | 25 | 1 | no | — |
| 401 | #124 | — | 50 | 2 | no | — |
| 402 | #124 | D52 | 1 | 1 | yes | characteristic, complemented |
| 403 | C2×C22⋊C4 | — | 50 | 2 | no | — |
| 404 | C2×C42 | — | 25 | 1 | no | — |
| 405 | #104 | — | 5 | 4 | no | — |
| 406 | #104 | — | 25 | 4 | no | — |
| 407 | #100 | — | 5 | 2 | no | — |
| 408 | #100 | — | 25 | 2 | no | — |
| 409 | C52 | C2×#455 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 410 | C22×C5 | — | 2 | 4 | no | — |
| 411 | C22×C5 | — | 2 | 2 | no | — |
| 412 | C22×C5 | — | 4 | 4 | no | — |
| 413 | C22×C5 | — | 4 | 4 | no | — |
| 414 | C22×C5 | — | 4 | 8 | no | — |
| 415 | C22×C5 | — | 10 | 4 | no | — |
| 416 | C22×C5 | — | 40 | 4 | no | — |
| 417 | C22×C5 | C2×D4×D5 | 1 | 2 | yes | — |
| 418 | C2×D5 | — | 2 | 4 | no | — |
| 419 | C2×D5 | — | 5 | 2 | no | — |
| 420 | C2×D5 | — | 5 | 2 | no | — |
| 421 | C2×D5 | — | 8 | 4 | no | — |
| 422 | C2×D5 | — | 10 | 2 | no | — |
| 423 | C2×D5 | — | 10 | 2 | no | — |
| 424 | C2×D5 | — | 10 | 4 | no | — |
| 425 | C2×D5 | — | 10 | 8 | no | — |
| 426 | C2×D5 | — | 10 | 4 | no | — |
| 427 | C2×D5 | — | 20 | 4 | no | — |
| 428 | C2×D5 | — | 20 | 8 | no | — |
| 429 | C2×D5 | — | 20 | 8 | no | — |
| 430 | C2×D5 | — | 20 | 4 | no | — |
| 431 | C2×D5 | — | 20 | 8 | no | — |
| 432 | C2×D5 | — | 40 | 8 | no | — |
| 433 | C2×D5 | — | 40 | 8 | no | — |
| 434 | C2×D5 | — | 40 | 4 | no | — |
| 435 | C2×D5 | — | 40 | 8 | no | — |
| 436 | C4×C5 | — | 2 | 4 | no | — |
| 437 | C4×C5 | — | 4 | 4 | no | — |
| 438 | C4×C5 | — | 4 | 4 | no | — |
| 439 | C4×C5 | — | 4 | 2 | no | — |
| 440 | C4×C5 | — | 4 | 2 | no | — |
| 441 | C4×C5 | — | 10 | 4 | no | — |
| 442 | C4×C5 | C2×D4×D5 | 1 | 4 | yes | — |
| 443 | Dic5 | — | 2 | 4 | no | — |
| 444 | Dic5 | — | 5 | 4 | no | — |
| 445 | Dic5 | — | 10 | 4 | no | — |
| 446 | Dic5 | — | 20 | 4 | no | — |
| 447 | Dic5 | — | 20 | 4 | no | — |
| 448 | Dic5 | — | 20 | 2 | no | — |
| 449 | Dic5 | — | 20 | 2 | no | — |
| 450 | C24 | — | 25 | 2 | no | — |
| 451 | C24 | — | 50 | 2 | no | — |
| 452 | #41 | — | 5 | 4 | no | — |
| 453 | #41 | — | 10 | 4 | no | — |
| 454 | #41 | — | 25 | 4 | no | — |
| 455 | #41 | — | 50 | 2 | no | — |
| 456 | #41 | — | 50 | 8 | no | — |
| 457 | #41 | — | 50 | 4 | no | — |
| 458 | #41 | — | 50 | 2 | no | — |
| 459 | C2×Q8 | — | 25 | 2 | no | — |
| 460 | C2×Q8 | — | 25 | 1 | no | — |
| 461 | C2×Q8 | — | 50 | 1 | no | — |
| 462 | C2×Q8 | — | 50 | 2 | no | — |
| 463 | C2×Q8 | — | 50 | 2 | no | — |
| 464 | C2×Q8 | C2×D52 | 1 | 1 | yes | characteristic, complemented |
| 465 | C2×D4 | — | 10 | 4 | no | — |
| 466 | C2×D4 | — | 10 | 4 | no | — |
| 467 | C2×D4 | — | 25 | 2 | no | — |
| 468 | C2×D4 | — | 25 | 2 | no | — |
| 469 | C2×D4 | — | 25 | 1 | no | — |
| 470 | C2×D4 | — | 50 | 4 | no | — |
| 471 | C2×D4 | — | 50 | 4 | no | — |
| 472 | C2×D4 | — | 50 | 2 | no | — |
| 473 | C2×D4 | — | 50 | 2 | no | — |
| 474 | C2×D4 | — | 50 | 2 | no | — |
| 475 | C2×D4 | — | 50 | 4 | no | — |
| 476 | C2×D4 | — | 50 | 4 | no | — |
| 477 | C2×D4 | — | 50 | 4 | no | — |
| 478 | C2×D4 | — | 50 | 8 | no | — |
| 479 | C2×D4 | C2×D52 | 1 | 1 | yes | characteristic |
| 480 | C22×C4 | — | 25 | 1 | no | — |
| 481 | C22×C4 | — | 50 | 1 | no | — |
| 482 | C22×C4 | — | 50 | 1 | no | — |
| 483 | C22×C4 | — | 50 | 2 | no | — |
| 484 | C22×C4 | — | 50 | 2 | no | — |
| 485 | Q16 | — | 10 | 4 | no | — |
| 486 | Q16 | — | 50 | 4 | no | — |
| 487 | SD16 | — | 10 | 4 | no | — |
| 488 | SD16 | — | 50 | 4 | no | — |
| 489 | M16 | — | 5 | 4 | no | — |
| 490 | M16 | — | 50 | 2 | no | — |
| 491 | C2×C8 | — | 50 | 2 | no | — |
| 492 | C22⋊C4 | — | 2 | 2 | no | — |
| 493 | C22⋊C4 | — | 50 | 2 | no | — |
| 494 | C22⋊C4 | — | 50 | 2 | no | — |
| 495 | C22⋊C4 | — | 50 | 2 | no | — |
| 496 | C42 | — | 25 | 1 | no | — |
| 497 | C42 | — | 50 | 1 | no | — |
| 498 | C42 | C2×D52 | 1 | 1 | yes | characteristic, complemented |
| 499 | C2×C5 | — | 2 | 4 | no | — |
| 500 | C2×C5 | — | 2 | 2 | no | — |
| 501 | C2×C5 | — | 2 | 2 | no | — |
| 502 | C2×C5 | — | 4 | 4 | no | — |
| 503 | C2×C5 | — | 8 | 4 | no | — |
| 504 | C2×C5 | — | 20 | 4 | no | — |
| 505 | C2×C5 | D5×#120 | 1 | 2 | yes | — |
| 506 | D5 | — | 4 | 4 | no | — |
| 507 | D5 | — | 5 | 4 | no | — |
| 508 | D5 | — | 10 | 4 | no | — |
| 509 | D5 | — | 10 | 4 | no | — |
| 510 | D5 | — | 10 | 2 | no | — |
| 511 | D5 | — | 20 | 4 | no | — |
| 512 | D5 | — | 40 | 4 | no | — |
| 513 | C23 | — | 10 | 4 | no | — |
| 514 | C23 | — | 25 | 1 | no | — |
| 515 | C23 | — | 25 | 2 | no | — |
| 516 | C23 | — | 50 | 2 | no | — |
| 517 | C23 | — | 50 | 2 | no | — |
| 518 | C23 | — | 50 | 2 | no | — |
| 519 | C23 | — | 50 | 4 | no | — |
| 520 | C23 | — | 100 | 4 | no | — |
| 521 | C23 | — | 200 | 4 | no | — |
| 522 | C23 | #87886 | 1 | 2 | yes | — |
| 523 | Q8 | — | 2 | 2 | no | — |
| 524 | Q8 | — | 5 | 4 | no | — |
| 525 | Q8 | — | 50 | 2 | no | — |
| 526 | Q8 | — | 50 | 2 | no | — |
| 527 | Q8 | — | 100 | 2 | no | — |
| 528 | D4 | — | 2 | 2 | no | — |
| 529 | D4 | — | 5 | 4 | no | — |
| 530 | D4 | — | 10 | 8 | no | — |
| 531 | D4 | — | 10 | 4 | no | — |
| 532 | D4 | — | 50 | 4 | no | — |
| 533 | D4 | — | 50 | 8 | no | — |
| 534 | D4 | — | 50 | 4 | no | — |
| 535 | D4 | — | 50 | 2 | no | — |
| 536 | D4 | — | 50 | 2 | no | — |
| 537 | C2×C4 | — | 2 | 1 | no | — |
| 538 | C2×C4 | — | 2 | 1 | no | — |
| 539 | C2×C4 | — | 10 | 4 | no | — |
| 540 | C2×C4 | — | 10 | 4 | no | — |
| 541 | C2×C4 | — | 25 | 1 | no | — |
| 542 | C2×C4 | — | 25 | 2 | no | — |
| 543 | C2×C4 | — | 25 | 2 | no | — |
| 544 | C2×C4 | — | 50 | 2 | no | — |
| 545 | C2×C4 | — | 50 | 4 | no | — |
| 546 | C2×C4 | — | 50 | 4 | no | — |
| 547 | C2×C4 | — | 50 | 1 | no | — |
| 548 | C2×C4 | — | 50 | 1 | no | — |
| 549 | C2×C4 | — | 100 | 1 | no | — |
| 550 | C2×C4 | — | 100 | 1 | no | — |
| 551 | C2×C4 | — | 100 | 2 | no | — |
| 552 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 553 | C8 | — | 10 | 4 | no | — |
| 554 | C5 | — | 2 | 2 | no | — |
| 555 | C5 | D5×#455 | 1 | 2 | yes | complemented |
| 556 | C22 | — | 2 | 2 | no | — |
| 557 | C22 | — | 4 | 2 | no | — |
| 558 | C22 | — | 10 | 4 | no | — |
| 559 | C22 | — | 25 | 1 | no | — |
| 560 | C22 | — | 25 | 1 | no | — |
| 561 | C22 | — | 40 | 4 | no | — |
| 562 | C22 | — | 50 | 2 | no | — |
| 563 | C22 | — | 50 | 2 | no | — |
| 564 | C22 | — | 100 | 2 | no | — |
| 565 | C22 | — | 100 | 4 | no | — |
| 566 | C22 | — | 100 | 4 | no | — |
| 567 | C22 | — | 200 | 2 | no | — |
| 568 | C22 | — | 200 | 4 | no | — |
| 569 | C22 | C2×#87886 | 1 | 1 | yes | characteristic |
| 570 | C4 | — | 4 | 1 | no | — |
| 571 | C4 | — | 4 | 1 | no | — |
| 572 | C4 | — | 10 | 4 | no | — |
| 573 | C4 | — | 25 | 2 | no | — |
| 574 | C4 | — | 100 | 1 | no | — |
| 575 | C4 | — | 100 | 1 | no | — |
| 576 | C4 | D4×D52 | 1 | 2 | yes | — |
| 577 | C2 | — | 2 | 1 | no | — |
| 578 | C2 | — | 4 | 2 | no | — |
| 579 | C2 | — | 20 | 4 | no | — |
| 580 | C2 | — | 25 | 2 | no | — |
| 581 | C2 | — | 50 | 1 | no | — |
| 582 | C2 | — | 100 | 2 | no | — |
| 583 | C2 | #13106387 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #124×C5⋊D5 | C2 | semidirect |
| 3. #13106467 | C2 | semidirect |
| 4. C5×#65350 | C2 | semidirect |
| 5. #13101839 | C2 | semidirect |
| 6. #13101703 | C2 | semidirect |
| 7. #13101682 | C2 | semidirect |
| 8. #13100578 | C2 | semidirect |
| 9. #13100574 | C2 | semidirect |
| 10. C2×Q8×C5⋊D5 | C22 | semidirect |
| 20. C52×#124 | C22 | semidirect |
| 21. #11717267 | C22 | semidirect |
| 22. #11717256 | C22 | semidirect |
| 25. #11717195 | C22 | semidirect |
| 26. C42×C5⋊D5 | C22 | semidirect |
| 27. C5×#4088 | C22 | semidirect |
| 31. #11716949 | C22 | semidirect |
| 32. #11716936 | C22 | semidirect |
| 33. C5×#3965 | C22 | semidirect |
| 34. C5×#3937 | C22 | semidirect |
| 35. #11716609 | C22 | semidirect |
| 36. #11716600 | C22 | semidirect |
| 40. C2×C52×Q8 | C23 | semidirect |
| 52. C2×#6045 | C23 | semidirect |
| 74. C42×C52 | C23 | semidirect |
| 79. C4×#1039 | C23 | semidirect |
| 82. C5×#681 | C23 | semidirect |
| 94. #65350 | D5 | semidirect |
| 156. C5×#124 | C2×D5 | semidirect |
| 160. #4088 | C2×D5 | semidirect |
| 180. #3965 | C2×D5 | semidirect |
| 183. #3937 | C2×D5 | semidirect |
| 212. C2×C5×Q8 | C22×D5 | semidirect |
| 271. C42×C5 | C22×D5 | semidirect |
| 286. #681 | C22×D5 | semidirect |
| 305. C5⋊D5 | #455 | semidirect |
| 402. #124 | D52 | semidirect |
| 409. C52 | C2×#455 | semidirect |
| 464. C2×Q8 | C2×D52 | semidirect |
| 498. C42 | C2×D52 | semidirect |
| 555. C5 | D5×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107821 | 2 |
| #124×C5⋊D5 | 2 |
| #13106467 | 2 |
| C5×#65350 | 2 |
| #13101839 | 2 |
| #13101703 | 2 |
| #13101682 | 2 |
| #13100578 | 2 |
| #13100574 | 2 |
| D5×#455 | 5 |