Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
910 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 910 conjugacy classes of subgroups — too many to draw. Only its 89 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 | #13107775 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13106549 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13104804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13103991 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13103932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13099913 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13099900 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #41×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#87877 | C22 | 1 | 1 | yes | characteristic |
| 10 | Q8×#1044 | — | 2 | 1 | no | — |
| 11 | D4×#1044 | — | 2 | 2 | no | — |
| 12 | D4×#1044 | — | 2 | 1 | no | — |
| 13 | #11717451 | — | 2 | 1 | no | — |
| 14 | #11717451 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C4⋊#1044 | — | 2 | 1 | no | — |
| 16 | C2×C4⋊#1044 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4×#1043 | C22 | 1 | 1 | yes | characteristic |
| 18 | #11717435 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#87831 | — | 2 | 2 | no | — |
| 20 | C5×#4095 | C4 | 1 | 2 | yes | complemented |
| 21 | #11717059 | — | 2 | 1 | no | — |
| 22 | #11717058 | — | 2 | 1 | no | — |
| 23 | #11717045 | — | 2 | 1 | no | — |
| 24 | #11717044 | — | 2 | 1 | no | — |
| 25 | #11716948 | C4 | 1 | 2 | yes | complemented |
| 26 | #11716936 | C22 | 1 | 1 | yes | characteristic |
| 27 | #11716878 | — | 2 | 1 | no | — |
| 28 | #11716876 | — | 2 | 1 | no | — |
| 29 | #11716766 | — | 2 | 1 | no | — |
| 30 | #11716766 | — | 2 | 1 | no | — |
| 31 | #10604863 | — | 5 | 2 | no | maximal |
| 32 | C22×D52 | — | 2 | 1 | no | — |
| 33 | C22×#1044 | — | 2 | 2 | no | — |
| 34 | C22×#1044 | D4 | 1 | 2 | yes | — |
| 35 | C22×#1043 | — | 2 | 1 | no | — |
| 36 | C52×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | #87904 | D4 | 1 | 1 | yes | characteristic |
| 38 | Q8×C5⋊D5 | D4 | 1 | 1 | yes | characteristic |
| 39 | #87902 | — | 2 | 1 | no | — |
| 40 | #87902 | D4 | 1 | 1 | yes | characteristic |
| 41 | D4×C5⋊D5 | — | 2 | 1 | no | — |
| 42 | D4×C5⋊D5 | D4 | 1 | 1 | yes | characteristic |
| 43 | #87900 | — | 2 | 1 | no | — |
| 44 | #87900 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 46 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×C5×D20 | C2×C4 | 1 | 2 | yes | complemented |
| 48 | C2×#6037 | — | 2 | 1 | no | — |
| 49 | #87877 | — | 2 | 1 | no | — |
| 50 | #87877 | — | 2 | 1 | no | — |
| 51 | #87877 | — | 2 | 1 | no | — |
| 52 | #87877 | — | 2 | 1 | no | — |
| 53 | C22⋊#1044 | — | 2 | 2 | no | — |
| 54 | C22⋊#1044 | — | 2 | 1 | no | — |
| 55 | C4⋊#1044 | — | 2 | 2 | no | — |
| 56 | C4⋊#1044 | — | 2 | 1 | no | — |
| 57 | C4⋊#1044 | — | 2 | 1 | no | — |
| 58 | C4⋊#1044 | D4 | 1 | 1 | yes | characteristic |
| 59 | C4⋊#1044 | D4 | 1 | 1 | yes | characteristic |
| 60 | C4×#1044 | — | 2 | 2 | no | — |
| 61 | C4×#1044 | — | 2 | 1 | no | — |
| 62 | #87860 | — | 2 | 1 | no | — |
| 63 | C4×#1043 | — | 2 | 1 | no | — |
| 64 | C4×#1043 | — | 2 | 1 | no | — |
| 65 | #87856 | — | 2 | 1 | no | — |
| 66 | #87855 | — | 2 | 1 | no | — |
| 67 | #87831 | — | 4 | 4 | no | — |
| 68 | C5×#688 | — | 2 | 2 | no | — |
| 69 | C5×#686 | — | 2 | 2 | no | — |
| 70 | C5×#681 | C2×C4 | 1 | 2 | yes | complemented |
| 71 | #87773 | — | 2 | 2 | no | — |
| 72 | #87771 | — | 2 | 2 | no | — |
| 73 | #87769 | — | 2 | 1 | no | — |
| 74 | #87767 | — | 2 | 1 | no | — |
| 75 | #66266 | — | 5 | 2 | no | — |
| 76 | D5×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 77 | D5⋊#104 | — | 5 | 2 | no | — |
| 78 | D5⋊#104 | — | 10 | 2 | no | — |
| 79 | #65780 | — | 5 | 2 | no | — |
| 80 | #65767 | — | 5 | 2 | no | — |
| 81 | #64900 | — | 5 | 2 | no | — |
| 82 | #64899 | — | 5 | 2 | no | — |
| 83 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 84 | C22×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C22×C5×D5 | — | 2 | 2 | no | — |
| 86 | C2×D52 | — | 4 | 2 | no | — |
| 87 | C2×D52 | — | 4 | 2 | no | — |
| 88 | C2×D52 | — | 4 | 1 | no | — |
| 89 | C2×D52 | — | 4 | 1 | no | — |
| 90 | C2×#1044 | — | 2 | 1 | no | — |
| 91 | C2×#1044 | — | 2 | 2 | no | — |
| 92 | C2×#1044 | — | 2 | 1 | no | — |
| 93 | C2×#1044 | — | 4 | 2 | no | — |
| 94 | C2×#1044 | — | 8 | 2 | no | — |
| 95 | C2×#1043 | — | 2 | 2 | no | — |
| 96 | C2×#1043 | — | 4 | 1 | no | — |
| 97 | C2×#1043 | — | 4 | 1 | no | — |
| 98 | C52×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 99 | C52×D4 | — | 2 | 1 | no | — |
| 100 | C52×D4 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 101 | C2×C4×C52 | — | 2 | 1 | no | — |
| 102 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 103 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 104 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 105 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 106 | C2×#1039 | — | 2 | 1 | no | — |
| 107 | C2×#1039 | #41 | 1 | 1 | yes | characteristic |
| 108 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 109 | C4⋊(C5⋊D5) | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 110 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 111 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 112 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 113 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C4×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 117 | #6045 | — | 2 | 1 | no | — |
| 118 | #6045 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 119 | C5×D20 | — | 2 | 2 | no | — |
| 120 | C5×D20 | — | 2 | 2 | no | — |
| 121 | #6037 | — | 4 | 1 | no | — |
| 122 | #6037 | — | 4 | 1 | no | — |
| 123 | #6033 | — | 4 | 1 | no | — |
| 124 | C5×#168 | — | 2 | 2 | no | — |
| 125 | D5×#41 | — | 5 | 2 | no | — |
| 126 | D5×#41 | — | 10 | 2 | no | — |
| 127 | C2×D4×D5 | — | 5 | 2 | no | — |
| 128 | C2×C22⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 129 | Q8×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 130 | D4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 131 | D4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 132 | #4130 | — | 5 | 2 | no | — |
| 133 | #4130 | — | 10 | 2 | no | — |
| 134 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 135 | C2×C4⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 136 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 137 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 138 | D5⋊M16 | — | 5 | 2 | no | — |
| 139 | D5⋊M16 | — | 10 | 2 | no | — |
| 140 | C5×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 141 | #4095 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 142 | #4078 | — | 5 | 2 | no | — |
| 143 | #4060 | — | 10 | 2 | no | — |
| 144 | D5×SD16 | — | 10 | 2 | no | — |
| 145 | #4057 | — | 10 | 2 | no | — |
| 146 | D5×D8 | — | 10 | 2 | no | — |
| 147 | #4054 | — | 5 | 2 | no | — |
| 148 | D5×M16 | — | 5 | 2 | no | — |
| 149 | #4010 | — | 10 | 2 | no | — |
| 150 | #4010 | — | 10 | 4 | no | — |
| 151 | #4008 | — | 10 | 2 | no | — |
| 152 | #4008 | — | 10 | 4 | no | — |
| 153 | #4007 | — | 10 | 2 | no | — |
| 154 | #4007 | — | 10 | 2 | no | — |
| 155 | #1883 | — | 25 | 1 | no | Sylow |
| 156 | C22×C52 | — | 2 | 1 | no | — |
| 157 | C22×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 159 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 160 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 161 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 162 | C2×C5⋊D5 | — | 4 | 1 | no | — |
| 163 | C2×C5⋊D5 | #120 | 1 | 1 | yes | characteristic |
| 164 | C2×C5⋊D5 | #121 | 1 | 1 | yes | characteristic |
| 165 | C2×C5×D5 | — | 4 | 4 | no | — |
| 166 | C2×C5×D5 | — | 4 | 2 | no | — |
| 167 | D52 | — | 8 | 2 | no | — |
| 168 | D52 | — | 8 | 1 | no | — |
| 169 | D52 | — | 8 | 1 | no | — |
| 170 | #1044 | — | 4 | 2 | no | — |
| 171 | #1044 | — | 4 | 1 | no | — |
| 172 | #1044 | — | 4 | 1 | no | — |
| 173 | #1043 | — | 4 | 2 | no | — |
| 174 | C4×C52 | — | 2 | 1 | no | — |
| 175 | C4×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 176 | C4×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 177 | #1039 | — | 2 | 1 | no | — |
| 178 | #1039 | #121 | 1 | 1 | yes | characteristic |
| 179 | #1039 | #123 | 1 | 1 | yes | characteristic |
| 180 | C23×D5 | — | 10 | 2 | no | — |
| 181 | C22×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 182 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 183 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 184 | C22×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 185 | C5×#41 | — | 2 | 2 | no | — |
| 186 | C5×#41 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 187 | C2×C5×D4 | — | 5 | 2 | no | — |
| 188 | C2×C22⋊D5 | — | 10 | 2 | no | — |
| 189 | #713 | — | 5 | 2 | no | — |
| 190 | #713 | — | 10 | 2 | no | — |
| 191 | Q8×D5 | — | 5 | 2 | no | — |
| 192 | Q8×D5 | — | 10 | 2 | no | — |
| 193 | #711 | — | 5 | 2 | no | — |
| 194 | #711 | — | 10 | 2 | no | — |
| 195 | #711 | — | 10 | 2 | no | — |
| 196 | #711 | — | 20 | 2 | no | — |
| 197 | D4×D5 | — | 5 | 2 | no | — |
| 198 | D4×D5 | — | 10 | 2 | no | — |
| 199 | D4×D5 | — | 10 | 2 | no | — |
| 200 | D4×D5 | — | 10 | 2 | no | — |
| 201 | D4×D5 | — | 10 | 2 | no | — |
| 202 | D4×D5 | — | 10 | 2 | no | — |
| 203 | D4×D5 | — | 10 | 2 | no | — |
| 204 | D4×D5 | — | 20 | 2 | no | — |
| 205 | #709 | — | 5 | 2 | no | — |
| 206 | #709 | — | 10 | 2 | no | — |
| 207 | #709 | — | 10 | 2 | no | — |
| 208 | #709 | — | 20 | 2 | no | — |
| 209 | C2×D20 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 210 | C2×C4×D5 | — | 5 | 2 | no | — |
| 211 | C2×C4×D5 | — | 10 | 2 | no | — |
| 212 | C2×C4×D5 | — | 10 | 2 | no | — |
| 213 | C2×C4×D5 | — | 20 | 2 | no | — |
| 214 | C22⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 215 | C22⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 216 | C22⋊AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 217 | #704 | — | 10 | 2 | no | — |
| 218 | #704 | — | 20 | 2 | no | — |
| 219 | C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 220 | C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 221 | C4⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 222 | C4⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 223 | C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 224 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 225 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 226 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 227 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 228 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 229 | C4×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 230 | #700 | — | 10 | 2 | no | — |
| 231 | #700 | — | 10 | 4 | no | — |
| 232 | D5⋊C8 | — | 10 | 2 | no | — |
| 233 | D5⋊C8 | — | 20 | 2 | no | — |
| 234 | C5×SD16 | — | 10 | 2 | no | — |
| 235 | C5×D8 | — | 10 | 2 | no | — |
| 236 | C5×M16 | — | 5 | 2 | no | — |
| 237 | #688 | — | 2 | 2 | no | — |
| 238 | #687 | — | 10 | 2 | no | — |
| 239 | #686 | — | 2 | 2 | no | — |
| 240 | #686 | — | 10 | 2 | no | — |
| 241 | #681 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 242 | D40 | — | 10 | 2 | no | — |
| 243 | #677 | — | 10 | 2 | no | — |
| 244 | #676 | — | 10 | 2 | no | — |
| 245 | C8×D5 | — | 10 | 2 | no | — |
| 246 | C2×AGL(1,ℤ/8) | — | 25 | 1 | no | — |
| 247 | #520 | — | 25 | 1 | no | — |
| 248 | C2×#104 | — | 25 | 1 | no | — |
| 249 | #418 | — | 25 | 1 | no | — |
| 250 | #390 | — | 25 | 1 | no | — |
| 251 | #343 | — | 25 | 1 | no | — |
| 252 | #339 | — | 25 | 1 | no | — |
| 253 | C2×C52 | — | 2 | 1 | no | — |
| 254 | C2×C52 | — | 4 | 1 | no | — |
| 255 | C2×C52 | #386 | 1 | 1 | yes | characteristic |
| 256 | C5⋊D5 | — | 2 | 1 | no | — |
| 257 | C5⋊D5 | — | 4 | 1 | no | — |
| 258 | C5⋊D5 | #453 | 1 | 1 | yes | characteristic |
| 259 | C5⋊D5 | #454 | 1 | 1 | yes | characteristic |
| 260 | C5×D5 | — | 8 | 2 | no | — |
| 261 | C23×C5 | — | 10 | 2 | no | — |
| 262 | C22×D5 | — | 2 | 2 | no | — |
| 263 | C22×D5 | — | 5 | 2 | no | — |
| 264 | C22×D5 | — | 10 | 2 | no | — |
| 265 | C22×D5 | — | 10 | 2 | no | — |
| 266 | C22×D5 | — | 20 | 2 | no | — |
| 267 | C22×D5 | — | 20 | 2 | no | — |
| 268 | C22×D5 | — | 20 | 2 | no | — |
| 269 | C22×D5 | — | 20 | 4 | no | — |
| 270 | C22×D5 | — | 20 | 4 | no | — |
| 271 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 272 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 273 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 274 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 275 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 276 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 277 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 278 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 279 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 280 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 281 | C2×AGL(1,𝔽5) | — | 40 | 4 | no | — |
| 282 | C5×Q8 | — | 2 | 2 | no | — |
| 283 | C5×Q8 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 284 | C5×D4 | — | 2 | 2 | no | — |
| 285 | C5×D4 | — | 2 | 2 | no | — |
| 286 | C5×D4 | — | 4 | 2 | no | — |
| 287 | C5×D4 | — | 10 | 2 | no | — |
| 288 | C5×D4 | — | 10 | 2 | no | — |
| 289 | C5×D4 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 290 | C2×C4×C5 | — | 2 | 2 | no | — |
| 291 | C2×C4×C5 | — | 2 | 2 | no | — |
| 292 | C2×C4×C5 | — | 4 | 2 | no | — |
| 293 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 294 | C22⋊D5 | — | 10 | 2 | no | — |
| 295 | C22⋊D5 | — | 10 | 2 | no | — |
| 296 | C22⋊D5 | — | 10 | 2 | no | — |
| 297 | C22⋊D5 | — | 20 | 2 | no | — |
| 298 | C22⋊D5 | — | 20 | 2 | no | — |
| 299 | C22⋊D5 | — | 20 | 2 | no | — |
| 300 | C22⋊D5 | — | 20 | 2 | no | — |
| 301 | C22⋊D5 | — | 20 | 2 | no | — |
| 302 | C2×Dic5 | — | 5 | 2 | no | — |
| 303 | C2×Dic5 | — | 10 | 2 | no | — |
| 304 | C2×Dic5 | — | 10 | 2 | no | — |
| 305 | C2×Dic5 | — | 20 | 2 | no | — |
| 306 | D20 | — | 2 | 2 | no | — |
| 307 | D20 | — | 2 | 2 | no | — |
| 308 | D20 | — | 5 | 2 | no | — |
| 309 | D20 | — | 10 | 2 | no | — |
| 310 | D20 | — | 10 | 2 | no | — |
| 311 | D20 | — | 20 | 2 | no | — |
| 312 | C4×D5 | — | 5 | 2 | no | — |
| 313 | C4×D5 | — | 5 | 2 | no | — |
| 314 | C4×D5 | — | 5 | 2 | no | — |
| 315 | C4×D5 | — | 5 | 2 | no | — |
| 316 | C4×D5 | — | 10 | 2 | no | — |
| 317 | C4×D5 | — | 10 | 2 | no | — |
| 318 | C4×D5 | — | 10 | 2 | no | — |
| 319 | C4×D5 | — | 10 | 2 | no | — |
| 320 | C4×D5 | — | 10 | 2 | no | — |
| 321 | C4×D5 | — | 10 | 2 | no | — |
| 322 | C4×D5 | — | 10 | 2 | no | — |
| 323 | C4×D5 | — | 20 | 2 | no | — |
| 324 | C4×D5 | — | 20 | 2 | no | — |
| 325 | C4×D5 | — | 20 | 2 | no | — |
| 326 | Dic10 | — | 5 | 2 | no | — |
| 327 | Dic10 | — | 10 | 2 | no | — |
| 328 | Dic10 | — | 10 | 2 | no | — |
| 329 | Dic10 | — | 20 | 2 | no | — |
| 330 | #170 | — | 20 | 2 | no | — |
| 331 | #170 | — | 20 | 4 | no | — |
| 332 | C5×C8 | — | 10 | 2 | no | — |
| 333 | #168 | — | 2 | 2 | no | — |
| 334 | C2×#41 | — | 25 | 1 | no | — |
| 335 | C22×D4 | — | 25 | 1 | no | — |
| 336 | AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 337 | AGL(1,ℤ/8) | — | 25 | 2 | no | — |
| 338 | AGL(1,ℤ/8) | — | 50 | 1 | no | — |
| 339 | AGL(1,ℤ/8) | — | 50 | 1 | no | — |
| 340 | C2×SD16 | — | 50 | 1 | no | — |
| 341 | C2×D8 | — | 50 | 1 | no | — |
| 342 | C2×M16 | — | 25 | 1 | no | — |
| 343 | C2×M16 | — | 25 | 1 | no | — |
| 344 | C4×Q8 | — | 50 | 1 | no | — |
| 345 | C4×D4 | — | 50 | 2 | no | — |
| 346 | C4×D4 | — | 50 | 1 | no | — |
| 347 | #117 | — | 25 | 1 | no | — |
| 348 | #117 | — | 50 | 1 | no | — |
| 349 | C2×C4⋊C4 | — | 25 | 1 | no | — |
| 350 | C2×C4⋊C4 | — | 50 | 1 | no | — |
| 351 | C2×C22⋊C4 | — | 50 | 2 | no | — |
| 352 | C2×C42 | — | 25 | 1 | no | — |
| 353 | #104 | — | 50 | 1 | no | — |
| 354 | #104 | — | 50 | 1 | no | — |
| 355 | #102 | — | 50 | 1 | no | — |
| 356 | #102 | — | 50 | 1 | no | — |
| 357 | C52 | #1883 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 358 | C22×C5 | — | 2 | 2 | no | — |
| 359 | C22×C5 | — | 2 | 2 | no | — |
| 360 | C22×C5 | — | 4 | 2 | no | — |
| 361 | C22×C5 | — | 20 | 4 | no | — |
| 362 | C22×C5 | — | 20 | 2 | no | — |
| 363 | C22×C5 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 364 | C2×D5 | — | 4 | 4 | no | — |
| 365 | C2×D5 | — | 4 | 2 | no | — |
| 366 | C2×D5 | — | 5 | 2 | no | — |
| 367 | C2×D5 | — | 5 | 2 | no | — |
| 368 | C2×D5 | — | 10 | 2 | no | — |
| 369 | C2×D5 | — | 10 | 2 | no | — |
| 370 | C2×D5 | — | 10 | 2 | no | — |
| 371 | C2×D5 | — | 10 | 2 | no | — |
| 372 | C2×D5 | — | 10 | 2 | no | — |
| 373 | C2×D5 | — | 20 | 2 | no | — |
| 374 | C2×D5 | — | 20 | 2 | no | — |
| 375 | C2×D5 | — | 20 | 2 | no | — |
| 376 | C2×D5 | — | 20 | 2 | no | — |
| 377 | C2×D5 | — | 20 | 2 | no | — |
| 378 | C2×D5 | — | 40 | 2 | no | — |
| 379 | C2×D5 | — | 40 | 2 | no | — |
| 380 | C2×D5 | — | 40 | 2 | no | — |
| 381 | C2×D5 | — | 40 | 2 | no | — |
| 382 | C2×D5 | — | 40 | 4 | no | — |
| 383 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 384 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 385 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 386 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 387 | AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 388 | C4×C5 | — | 2 | 2 | no | — |
| 389 | C4×C5 | — | 2 | 2 | no | — |
| 390 | C4×C5 | — | 2 | 2 | no | — |
| 391 | C4×C5 | — | 4 | 2 | no | — |
| 392 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 393 | C4×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 394 | Dic5 | — | 5 | 2 | no | — |
| 395 | Dic5 | — | 5 | 2 | no | — |
| 396 | Dic5 | — | 10 | 2 | no | — |
| 397 | Dic5 | — | 10 | 2 | no | — |
| 398 | Dic5 | — | 10 | 2 | no | — |
| 399 | Dic5 | — | 20 | 2 | no | — |
| 400 | C24 | — | 50 | 1 | no | — |
| 401 | #41 | — | 25 | 1 | no | — |
| 402 | #41 | — | 25 | 1 | no | — |
| 403 | #41 | — | 25 | 1 | no | — |
| 404 | #41 | — | 50 | 1 | no | — |
| 405 | #41 | — | 50 | 1 | no | — |
| 406 | #41 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 407 | C2×Q8 | — | 25 | 1 | no | — |
| 408 | C2×D4 | — | 5 | 2 | no | — |
| 409 | C2×D4 | — | 25 | 1 | no | — |
| 410 | C2×D4 | — | 50 | 1 | no | — |
| 411 | C2×D4 | — | 50 | 1 | no | — |
| 412 | C2×D4 | — | 50 | 1 | no | — |
| 413 | C2×D4 | — | 50 | 1 | no | — |
| 414 | C2×D4 | — | 50 | 1 | no | — |
| 415 | C2×D4 | — | 50 | 1 | no | — |
| 416 | C22×C4 | — | 25 | 1 | no | — |
| 417 | C22×C4 | — | 25 | 2 | no | — |
| 418 | C22×C4 | — | 50 | 1 | no | — |
| 419 | C22×C4 | — | 50 | 1 | no | — |
| 420 | C22×C4 | — | 50 | 2 | no | — |
| 421 | SD16 | — | 10 | 2 | no | — |
| 422 | SD16 | — | 50 | 2 | no | — |
| 423 | D8 | — | 10 | 2 | no | — |
| 424 | D8 | — | 50 | 2 | no | — |
| 425 | M16 | — | 5 | 2 | no | — |
| 426 | M16 | — | 50 | 1 | no | — |
| 427 | M16 | — | 50 | 1 | no | — |
| 428 | M16 | — | 50 | 1 | no | — |
| 429 | C2×C8 | — | 50 | 1 | no | — |
| 430 | C2×C8 | — | 50 | 1 | no | — |
| 431 | C4⋊C4 | — | 25 | 1 | no | — |
| 432 | C4⋊C4 | — | 25 | 1 | no | — |
| 433 | C4⋊C4 | — | 50 | 1 | no | — |
| 434 | C4⋊C4 | — | 50 | 1 | no | — |
| 435 | C4⋊C4 | — | 50 | 2 | no | — |
| 436 | C22⋊C4 | — | 50 | 1 | no | — |
| 437 | C22⋊C4 | — | 50 | 2 | no | — |
| 438 | C22⋊C4 | — | 100 | 4 | no | — |
| 439 | C42 | — | 50 | 1 | no | — |
| 440 | C42 | — | 50 | 1 | no | — |
| 441 | C42 | — | 50 | 1 | no | — |
| 442 | C42 | — | 50 | 2 | no | — |
| 443 | C2×C5 | — | 2 | 2 | no | — |
| 444 | C2×C5 | — | 2 | 2 | no | — |
| 445 | C2×C5 | — | 4 | 2 | no | — |
| 446 | C2×C5 | — | 4 | 2 | no | — |
| 447 | C2×C5 | — | 8 | 2 | no | — |
| 448 | C2×C5 | — | 40 | 2 | no | — |
| 449 | C2×C5 | #65779 | 1 | 2 | yes | — |
| 450 | D5 | — | 5 | 2 | no | — |
| 451 | D5 | — | 5 | 2 | no | — |
| 452 | D5 | — | 8 | 2 | no | — |
| 453 | D5 | — | 10 | 2 | no | — |
| 454 | D5 | — | 10 | 2 | no | — |
| 455 | D5 | — | 10 | 2 | no | — |
| 456 | D5 | — | 20 | 2 | no | — |
| 457 | D5 | — | 20 | 2 | no | — |
| 458 | D5 | — | 40 | 2 | no | — |
| 459 | C23 | — | 10 | 2 | no | — |
| 460 | C23 | — | 25 | 1 | no | — |
| 461 | C23 | — | 50 | 1 | no | — |
| 462 | C23 | — | 100 | 1 | no | — |
| 463 | C23 | — | 100 | 1 | no | — |
| 464 | C23 | — | 100 | 2 | no | — |
| 465 | C23 | — | 100 | 2 | no | — |
| 466 | Q8 | — | 25 | 1 | no | — |
| 467 | Q8 | — | 50 | 1 | no | — |
| 468 | Q8 | #87831 | 1 | 1 | yes | characteristic, complemented |
| 469 | D4 | — | 2 | 1 | no | — |
| 470 | D4 | — | 10 | 2 | no | — |
| 471 | D4 | — | 10 | 2 | no | — |
| 472 | D4 | — | 25 | 1 | no | — |
| 473 | D4 | — | 50 | 1 | no | — |
| 474 | D4 | — | 50 | 1 | no | — |
| 475 | D4 | — | 50 | 1 | no | — |
| 476 | D4 | — | 50 | 1 | no | — |
| 477 | D4 | — | 100 | 1 | no | — |
| 478 | D4 | — | 100 | 1 | no | — |
| 479 | D4 | #87831 | 1 | 1 | yes | characteristic, complemented |
| 480 | C2×C4 | — | 2 | 1 | no | — |
| 481 | C2×C4 | — | 25 | 1 | no | — |
| 482 | C2×C4 | — | 25 | 1 | no | — |
| 483 | C2×C4 | — | 25 | 1 | no | — |
| 484 | C2×C4 | — | 25 | 1 | no | — |
| 485 | C2×C4 | — | 25 | 1 | no | — |
| 486 | C2×C4 | — | 50 | 1 | no | — |
| 487 | C2×C4 | — | 50 | 1 | no | — |
| 488 | C2×C4 | — | 50 | 1 | no | — |
| 489 | C2×C4 | — | 50 | 1 | no | — |
| 490 | C2×C4 | — | 50 | 1 | no | — |
| 491 | C2×C4 | — | 50 | 1 | no | — |
| 492 | C2×C4 | — | 50 | 2 | no | — |
| 493 | C2×C4 | — | 50 | 2 | no | — |
| 494 | C2×C4 | — | 100 | 1 | no | — |
| 495 | C2×C4 | — | 100 | 1 | no | — |
| 496 | C2×C4 | — | 100 | 2 | no | — |
| 497 | C2×C4 | — | 200 | 2 | no | — |
| 498 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 499 | C8 | — | 10 | 2 | no | — |
| 500 | C8 | — | 100 | 1 | no | — |
| 501 | C5 | — | 2 | 2 | no | — |
| 502 | C5 | #10604863 | 1 | 2 | yes | complemented |
| 503 | C22 | — | 2 | 1 | no | — |
| 504 | C22 | — | 20 | 4 | no | — |
| 505 | C22 | — | 20 | 2 | no | — |
| 506 | C22 | — | 25 | 1 | no | — |
| 507 | C22 | — | 25 | 1 | no | — |
| 508 | C22 | — | 50 | 1 | no | — |
| 509 | C22 | — | 50 | 1 | no | — |
| 510 | C22 | — | 50 | 1 | no | — |
| 511 | C22 | — | 100 | 1 | no | — |
| 512 | C22 | — | 100 | 1 | no | — |
| 513 | C22 | — | 200 | 1 | no | — |
| 514 | C22 | — | 200 | 1 | no | — |
| 515 | C22 | — | 200 | 2 | no | — |
| 516 | C22 | #11717377 | 1 | 1 | yes | characteristic |
| 517 | C4 | — | 2 | 1 | no | — |
| 518 | C4 | — | 25 | 1 | no | — |
| 519 | C4 | — | 25 | 1 | no | — |
| 520 | C4 | — | 50 | 1 | no | — |
| 521 | C4 | — | 100 | 2 | no | — |
| 522 | C4 | — | 100 | 1 | no | — |
| 523 | C4 | — | 100 | 1 | no | — |
| 524 | C4 | — | 100 | 2 | no | — |
| 525 | C4 | C2×#87831 | 1 | 1 | yes | characteristic |
| 526 | C4 | #11717377 | 1 | 1 | yes | characteristic |
| 527 | C2 | — | 2 | 1 | no | — |
| 528 | C2 | — | 4 | 1 | no | — |
| 529 | C2 | — | 25 | 1 | no | — |
| 530 | C2 | — | 25 | 1 | no | — |
| 531 | C2 | — | 40 | 2 | no | — |
| 532 | C2 | — | 50 | 1 | no | — |
| 533 | C2 | — | 100 | 1 | no | — |
| 534 | C2 | #13104118 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107775 | C2 | semidirect |
| 3. #13104804 | C2 | semidirect |
| 4. #13103991 | C2 | semidirect |
| 5. #13103932 | C2 | semidirect |
| 6. #13099913 | C2 | semidirect |
| 7. #13099900 | C2 | semidirect |
| 20. C5×#4095 | C4 | semidirect |
| 25. #11716948 | C4 | semidirect |
| 47. C2×C5×D20 | C2×C4 | semidirect |
| 70. C5×#681 | C2×C4 | semidirect |
| 98. C52×Q8 | C22⋊C4 | semidirect |
| 100. C52×D4 | C22⋊C4 | semidirect |
| 109. C4⋊(C5⋊D5) | C22⋊C4 | semidirect |
| 118. #6045 | C22⋊C4 | semidirect |
| 141. #4095 | AGL(1,𝔽5) | semidirect |
| 209. C2×D20 | C2×AGL(1,𝔽5) | semidirect |
| 241. #681 | C2×AGL(1,𝔽5) | semidirect |
| 283. C5×Q8 | C22⋊AGL(1,𝔽5) | semidirect |
| 289. C5×D4 | C22⋊AGL(1,𝔽5) | semidirect |
| 357. C52 | #1883 | semidirect |
| 468. Q8 | #87831 | semidirect |
| 479. D4 | #87831 | semidirect |
| 502. C5 | #10604863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107775 | 2 |
| #13106549 | 2 |
| #13104804 | 2 |
| #13103991 | 2 |
| #13103932 | 2 |
| #13099913 | 2 |
| #13099900 | 2 |
| #10604863 | 5 |