Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
770 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 113 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 | #13106533 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13104933 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13104804 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13103909 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#11716761 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13099909 | 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 | #11717451 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#87862 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C4×#1043 | C22 | 1 | 1 | yes | characteristic |
| 12 | #11717435 | C22 | 1 | 1 | yes | characteristic |
| 13 | C5×#4094 | C4 | 1 | 2 | yes | complemented |
| 14 | #11716936 | — | 2 | 1 | no | — |
| 15 | #11716936 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11716935 | — | 2 | 2 | no | — |
| 17 | #11716935 | C4 | 1 | 2 | yes | complemented |
| 18 | C2×#87767 | — | 2 | 1 | no | — |
| 19 | C2×#87767 | C22 | 1 | 1 | yes | characteristic |
| 20 | #11716902 | C4 | 1 | 2 | yes | complemented |
| 21 | #11716900 | C4 | 1 | 2 | yes | complemented |
| 22 | #11716878 | C4 | 1 | 2 | yes | complemented |
| 23 | #11716876 | C4 | 1 | 2 | yes | complemented |
| 24 | #11716764 | — | 2 | 1 | no | — |
| 25 | #11716762 | — | 2 | 1 | no | — |
| 26 | #11716761 | — | 2 | 2 | no | — |
| 27 | #10604777 | — | 5 | 2 | no | maximal |
| 28 | C22×#1043 | — | 2 | 1 | no | — |
| 29 | C52×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | #87904 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | Q8×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | #87902 | — | 2 | 1 | no | — |
| 33 | #87902 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | D4×C5⋊D5 | — | 2 | 1 | no | — |
| 35 | D4×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | #87900 | — | 2 | 1 | no | — |
| 37 | #87900 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 39 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 40 | C22⋊#1044 | — | 2 | 1 | no | — |
| 41 | C2×#6034 | — | 2 | 1 | no | — |
| 42 | C4⋊#1044 | C2×C4 | 1 | 2 | yes | — |
| 43 | C4×#1044 | — | 2 | 1 | no | — |
| 44 | #87862 | — | 2 | 1 | no | — |
| 45 | #87862 | C2×C4 | 1 | 2 | yes | — |
| 46 | #87860 | — | 2 | 1 | no | — |
| 47 | C4×#1043 | — | 2 | 1 | no | — |
| 48 | C4×#1043 | C2×C4 | 1 | 2 | yes | — |
| 49 | #87856 | C2×C4 | 1 | 2 | yes | — |
| 50 | #87855 | — | 2 | 1 | no | — |
| 51 | C5×#681 | — | 2 | 2 | no | — |
| 52 | C5×#681 | C2×C4 | 1 | 2 | yes | — |
| 53 | C2×C5×#168 | — | 2 | 2 | no | — |
| 54 | C2×C5×#168 | C2×C4 | 1 | 2 | yes | — |
| 55 | #87769 | — | 2 | 1 | no | — |
| 56 | #87769 | — | 2 | 2 | no | — |
| 57 | #87767 | — | 2 | 1 | no | — |
| 58 | #87767 | — | 2 | 2 | no | — |
| 59 | #87767 | D4 | 1 | 1 | yes | characteristic |
| 60 | #87767 | D4 | 1 | 2 | yes | — |
| 61 | #87767 | D4 | 1 | 1 | yes | characteristic |
| 62 | D5×#131 | — | 5 | 2 | no | — |
| 63 | #65794 | — | 5 | 2 | no | — |
| 64 | D5⋊#104 | — | 5 | 2 | no | — |
| 65 | D5⋊#104 | — | 10 | 2 | no | — |
| 66 | #65718 | — | 5 | 2 | no | — |
| 67 | C2×C8×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 68 | #64901 | — | 5 | 2 | no | — |
| 69 | #64900 | — | 5 | 2 | no | — |
| 70 | C22×C5⋊D5 | — | 2 | 1 | no | — |
| 71 | C22×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 72 | C2×#1044 | — | 2 | 2 | no | — |
| 73 | C2×#1043 | — | 2 | 4 | no | — |
| 74 | C2×#1043 | — | 2 | 2 | no | — |
| 75 | C52×Q8 | C42 | 1 | 1 | yes | characteristic |
| 76 | C52×D4 | — | 2 | 1 | no | — |
| 77 | C52×D4 | C42 | 1 | 1 | yes | characteristic |
| 78 | C2×C4×C52 | — | 2 | 1 | no | — |
| 79 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 80 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 81 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 82 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 83 | C2×#1039 | — | 2 | 1 | no | — |
| 84 | C2×#1039 | #41 | 1 | 1 | yes | characteristic |
| 85 | C4⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 86 | C4⋊(C5⋊D5) | C42 | 1 | 1 | yes | characteristic |
| 87 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 88 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 89 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 90 | C4×C5⋊D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | C4×C5⋊D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 92 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | #6045 | — | 2 | 1 | no | — |
| 95 | #6045 | C42 | 1 | 1 | yes | characteristic |
| 96 | #6034 | — | 2 | 2 | no | — |
| 97 | #6033 | — | 2 | 2 | no | — |
| 98 | C5×#168 | — | 2 | 2 | no | — |
| 99 | C5×#168 | C22⋊C4 | 1 | 2 | yes | — |
| 100 | C5×#168 | C22⋊C4 | 1 | 2 | yes | — |
| 101 | D5×#41 | — | 5 | 2 | no | — |
| 102 | D5×#41 | — | 10 | 2 | no | — |
| 103 | #4130 | — | 5 | 2 | no | — |
| 104 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 105 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 106 | D5⋊M16 | — | 5 | 2 | no | — |
| 107 | D5⋊M16 | — | 10 | 2 | no | — |
| 108 | C2×D5⋊C8 | — | 5 | 2 | no | — |
| 109 | C5×#131 | — | 5 | 2 | no | — |
| 110 | #4094 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 111 | #4053 | — | 5 | 2 | no | — |
| 112 | #4053 | — | 10 | 2 | no | — |
| 113 | D5×M16 | — | 5 | 2 | no | — |
| 114 | D5×M16 | — | 10 | 2 | no | — |
| 115 | #4047 | — | 5 | 2 | no | — |
| 116 | #4047 | — | 10 | 2 | no | — |
| 117 | C2×C8×D5 | — | 5 | 2 | no | — |
| 118 | C2×C8×D5 | — | 10 | 2 | no | — |
| 119 | #4010 | — | 5 | 4 | no | — |
| 120 | #4010 | — | 10 | 4 | no | — |
| 121 | #4009 | — | 5 | 4 | no | — |
| 122 | #4008 | — | 5 | 4 | no | — |
| 123 | #4008 | — | 10 | 4 | no | — |
| 124 | #4007 | — | 5 | 4 | no | — |
| 125 | #3992 | — | 10 | 2 | no | — |
| 126 | C8×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 127 | C8×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 128 | C8×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 129 | #1764 | — | 25 | 1 | no | Sylow |
| 130 | C22×C52 | — | 2 | 1 | no | — |
| 131 | C22×C52 | #117 | 1 | 1 | yes | characteristic |
| 132 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 133 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 134 | C2×C5⋊D5 | — | 4 | 2 | no | — |
| 135 | C2×C5⋊D5 | C4×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×C5⋊D5 | C4×D4 | 1 | 1 | yes | characteristic |
| 137 | #1044 | — | 4 | 2 | no | — |
| 138 | #1043 | — | 2 | 4 | no | — |
| 139 | C4×C52 | — | 2 | 1 | no | — |
| 140 | C4×C52 | C2×C42 | 1 | 1 | yes | characteristic |
| 141 | C4×C52 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 142 | #1039 | — | 2 | 1 | no | — |
| 143 | #1039 | C4×D4 | 1 | 1 | yes | characteristic |
| 144 | #1039 | C4×D4 | 1 | 1 | yes | characteristic |
| 145 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 146 | C22×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 147 | C5×#41 | — | 2 | 2 | no | — |
| 148 | C5×#41 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 149 | #713 | — | 5 | 2 | no | — |
| 150 | #713 | — | 10 | 2 | no | — |
| 151 | Q8×D5 | — | 5 | 2 | no | — |
| 152 | Q8×D5 | — | 10 | 2 | no | — |
| 153 | #711 | — | 5 | 2 | no | — |
| 154 | #711 | — | 10 | 2 | no | — |
| 155 | #711 | — | 10 | 2 | no | — |
| 156 | #711 | — | 20 | 2 | no | — |
| 157 | D4×D5 | — | 5 | 2 | no | — |
| 158 | D4×D5 | — | 10 | 2 | no | — |
| 159 | D4×D5 | — | 10 | 2 | no | — |
| 160 | D4×D5 | — | 20 | 2 | no | — |
| 161 | #709 | — | 5 | 2 | no | — |
| 162 | #709 | — | 10 | 2 | no | — |
| 163 | #709 | — | 10 | 2 | no | — |
| 164 | #709 | — | 20 | 2 | no | — |
| 165 | C2×C4×D5 | — | 5 | 2 | no | — |
| 166 | C2×C4×D5 | — | 10 | 2 | no | — |
| 167 | C2×C4×D5 | — | 10 | 2 | no | — |
| 168 | C2×C4×D5 | — | 20 | 2 | no | — |
| 169 | C22⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 170 | #704 | — | 10 | 2 | no | — |
| 171 | #704 | — | 20 | 2 | no | — |
| 172 | C2×#170 | — | 10 | 2 | no | — |
| 173 | C4⋊AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 174 | C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 175 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 176 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 177 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 178 | C4×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 179 | #700 | — | 5 | 4 | no | — |
| 180 | #700 | — | 10 | 4 | no | — |
| 181 | D5⋊C8 | — | 5 | 4 | no | — |
| 182 | D5⋊C8 | — | 10 | 2 | no | — |
| 183 | D5⋊C8 | — | 10 | 2 | no | — |
| 184 | D5⋊C8 | — | 20 | 2 | no | — |
| 185 | C5×M16 | — | 5 | 2 | no | — |
| 186 | C5×M16 | — | 10 | 2 | no | — |
| 187 | C2×C5×C8 | — | 5 | 2 | no | — |
| 188 | C2×C5×C8 | — | 10 | 2 | no | — |
| 189 | #681 | — | 2 | 2 | no | — |
| 190 | #681 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 191 | C2×#168 | — | 2 | 2 | no | — |
| 192 | C2×#168 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 193 | #676 | — | 10 | 2 | no | — |
| 194 | #676 | — | 10 | 2 | no | — |
| 195 | #676 | — | 10 | 2 | no | — |
| 196 | C8×D5 | — | 5 | 2 | no | — |
| 197 | C8×D5 | — | 5 | 2 | no | — |
| 198 | C8×D5 | — | 5 | 2 | no | — |
| 199 | C8×D5 | — | 5 | 2 | no | — |
| 200 | C8×D5 | — | 10 | 2 | no | — |
| 201 | C8×D5 | — | 10 | 2 | no | — |
| 202 | C8×D5 | — | 10 | 2 | no | — |
| 203 | C2×#131 | — | 25 | 1 | no | — |
| 204 | C2×#104 | — | 25 | 1 | no | — |
| 205 | #416 | — | 25 | 1 | no | — |
| 206 | #405 | — | 25 | 1 | no | — |
| 207 | C2×C4×C8 | — | 25 | 1 | no | — |
| 208 | #341 | — | 25 | 1 | no | — |
| 209 | #339 | — | 25 | 1 | no | — |
| 210 | C2×C52 | — | 2 | 1 | no | — |
| 211 | C2×C52 | — | 4 | 1 | no | — |
| 212 | C2×C52 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 213 | C5⋊D5 | — | 2 | 1 | no | — |
| 214 | C5⋊D5 | — | 4 | 1 | no | — |
| 215 | C5⋊D5 | #443 | 1 | 2 | yes | — |
| 216 | C22×D5 | — | 5 | 2 | no | — |
| 217 | C22×D5 | — | 10 | 2 | no | — |
| 218 | C22×D5 | — | 10 | 2 | no | — |
| 219 | C22×D5 | — | 20 | 2 | no | — |
| 220 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 221 | C2×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 222 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 223 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 224 | C2×AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 225 | C5×Q8 | — | 2 | 2 | no | — |
| 226 | C5×Q8 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 227 | C5×D4 | — | 2 | 2 | no | — |
| 228 | C5×D4 | — | 2 | 2 | no | — |
| 229 | C5×D4 | — | 4 | 2 | no | — |
| 230 | C5×D4 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 231 | C2×C4×C5 | — | 2 | 2 | no | — |
| 232 | C2×C4×C5 | — | 2 | 2 | no | — |
| 233 | C2×C4×C5 | — | 4 | 2 | no | — |
| 234 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 235 | C22⋊D5 | — | 10 | 2 | no | — |
| 236 | C22⋊D5 | — | 10 | 2 | no | — |
| 237 | C22⋊D5 | — | 10 | 2 | no | — |
| 238 | C22⋊D5 | — | 20 | 2 | no | — |
| 239 | C22⋊D5 | — | 20 | 2 | no | — |
| 240 | C22⋊D5 | — | 20 | 2 | no | — |
| 241 | C2×Dic5 | — | 5 | 2 | no | — |
| 242 | C2×Dic5 | — | 10 | 2 | no | — |
| 243 | C2×Dic5 | — | 10 | 2 | no | — |
| 244 | C2×Dic5 | — | 20 | 2 | no | — |
| 245 | D20 | — | 5 | 2 | no | — |
| 246 | D20 | — | 10 | 2 | no | — |
| 247 | D20 | — | 10 | 2 | no | — |
| 248 | D20 | — | 20 | 2 | no | — |
| 249 | C4×D5 | — | 5 | 2 | no | — |
| 250 | C4×D5 | — | 5 | 2 | no | — |
| 251 | C4×D5 | — | 5 | 2 | no | — |
| 252 | C4×D5 | — | 5 | 2 | no | — |
| 253 | C4×D5 | — | 10 | 2 | no | — |
| 254 | C4×D5 | — | 10 | 2 | no | — |
| 255 | C4×D5 | — | 10 | 2 | no | — |
| 256 | C4×D5 | — | 10 | 2 | no | — |
| 257 | C4×D5 | — | 10 | 2 | no | — |
| 258 | C4×D5 | — | 10 | 2 | no | — |
| 259 | C4×D5 | — | 10 | 2 | no | — |
| 260 | C4×D5 | — | 20 | 2 | no | — |
| 261 | C4×D5 | — | 20 | 2 | no | — |
| 262 | C4×D5 | — | 20 | 2 | no | — |
| 263 | Dic10 | — | 5 | 2 | no | — |
| 264 | Dic10 | — | 10 | 2 | no | — |
| 265 | Dic10 | — | 10 | 2 | no | — |
| 266 | Dic10 | — | 20 | 2 | no | — |
| 267 | #170 | — | 10 | 4 | no | — |
| 268 | #170 | — | 10 | 4 | no | — |
| 269 | #170 | — | 20 | 4 | no | — |
| 270 | C5×C8 | — | 5 | 2 | no | — |
| 271 | C5×C8 | — | 5 | 2 | no | — |
| 272 | C5×C8 | — | 10 | 2 | no | — |
| 273 | #168 | — | 2 | 2 | no | — |
| 274 | #168 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 275 | #168 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 276 | C2×#41 | — | 25 | 1 | no | — |
| 277 | #131 | — | 5 | 2 | no | — |
| 278 | #131 | — | 25 | 2 | no | — |
| 279 | #131 | — | 50 | 2 | no | — |
| 280 | C2×M16 | — | 25 | 1 | no | — |
| 281 | C2×M16 | — | 25 | 1 | no | — |
| 282 | C2×M16 | — | 50 | 1 | no | — |
| 283 | C22×C8 | — | 25 | 1 | no | — |
| 284 | C22×C8 | — | 25 | 1 | no | — |
| 285 | C22×C8 | — | 50 | 1 | no | — |
| 286 | #117 | — | 25 | 1 | no | — |
| 287 | C2×C42 | — | 25 | 1 | no | — |
| 288 | #104 | — | 25 | 2 | no | — |
| 289 | #104 | — | 25 | 2 | no | — |
| 290 | #103 | — | 25 | 2 | no | — |
| 291 | #102 | — | 25 | 2 | no | — |
| 292 | #97 | — | 50 | 1 | no | — |
| 293 | C4×C8 | — | 50 | 2 | no | — |
| 294 | C4×C8 | — | 50 | 1 | no | — |
| 295 | C52 | #1764 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 296 | C22×C5 | — | 2 | 2 | no | — |
| 297 | C22×C5 | — | 2 | 2 | no | — |
| 298 | C22×C5 | — | 4 | 2 | no | — |
| 299 | C22×C5 | #4130 | 1 | 2 | yes | — |
| 300 | C2×D5 | — | 5 | 2 | no | — |
| 301 | C2×D5 | — | 5 | 2 | no | — |
| 302 | C2×D5 | — | 10 | 2 | no | — |
| 303 | C2×D5 | — | 10 | 2 | no | — |
| 304 | C2×D5 | — | 10 | 4 | no | — |
| 305 | C2×D5 | — | 10 | 2 | no | — |
| 306 | C2×D5 | — | 20 | 4 | no | — |
| 307 | C2×D5 | — | 20 | 2 | no | — |
| 308 | C2×D5 | — | 20 | 4 | no | — |
| 309 | C2×D5 | — | 40 | 4 | no | — |
| 310 | AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 311 | AGL(1,𝔽5) | — | 20 | 8 | no | — |
| 312 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 313 | C4×C5 | — | 2 | 2 | no | — |
| 314 | C4×C5 | — | 2 | 2 | no | — |
| 315 | C4×C5 | — | 2 | 2 | no | — |
| 316 | C4×C5 | — | 4 | 2 | no | — |
| 317 | C4×C5 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 318 | C4×C5 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 319 | Dic5 | — | 5 | 2 | no | — |
| 320 | Dic5 | — | 5 | 2 | no | — |
| 321 | Dic5 | — | 10 | 2 | no | — |
| 322 | Dic5 | — | 10 | 2 | no | — |
| 323 | Dic5 | — | 10 | 2 | no | — |
| 324 | Dic5 | — | 20 | 2 | no | — |
| 325 | #41 | — | 25 | 1 | no | — |
| 326 | #41 | — | 25 | 1 | no | — |
| 327 | #41 | — | 25 | 1 | no | — |
| 328 | #41 | — | 50 | 1 | no | — |
| 329 | #41 | — | 50 | 1 | no | — |
| 330 | #41 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 331 | C2×Q8 | — | 25 | 1 | no | — |
| 332 | C2×D4 | — | 25 | 1 | no | — |
| 333 | C2×D4 | — | 50 | 1 | no | — |
| 334 | C22×C4 | — | 25 | 1 | no | — |
| 335 | C22×C4 | — | 50 | 1 | no | — |
| 336 | C22×C4 | — | 50 | 1 | no | — |
| 337 | M16 | — | 5 | 2 | no | — |
| 338 | M16 | — | 10 | 2 | no | — |
| 339 | M16 | — | 25 | 2 | no | — |
| 340 | M16 | — | 50 | 2 | no | — |
| 341 | M16 | — | 50 | 1 | no | — |
| 342 | M16 | — | 50 | 1 | no | — |
| 343 | C2×C8 | — | 5 | 2 | no | — |
| 344 | C2×C8 | — | 10 | 2 | no | — |
| 345 | C2×C8 | — | 25 | 1 | no | — |
| 346 | C2×C8 | — | 25 | 2 | no | — |
| 347 | C2×C8 | — | 25 | 1 | no | — |
| 348 | C2×C8 | — | 25 | 2 | no | — |
| 349 | C2×C8 | — | 50 | 2 | no | — |
| 350 | C2×C8 | — | 50 | 1 | no | — |
| 351 | C2×C8 | — | 50 | 1 | no | — |
| 352 | C2×C8 | — | 50 | 1 | no | — |
| 353 | C2×C8 | — | 50 | 1 | no | — |
| 354 | C4⋊C4 | — | 25 | 2 | no | — |
| 355 | C22⋊C4 | — | 50 | 1 | no | — |
| 356 | C42 | — | 25 | 2 | no | — |
| 357 | C42 | — | 50 | 1 | no | — |
| 358 | C42 | — | 50 | 1 | no | — |
| 359 | C2×C5 | — | 2 | 2 | no | — |
| 360 | C2×C5 | — | 2 | 2 | no | — |
| 361 | C2×C5 | — | 4 | 2 | no | — |
| 362 | C2×C5 | — | 4 | 2 | no | — |
| 363 | C2×C5 | — | 8 | 2 | no | — |
| 364 | C2×C5 | C4×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 365 | D5 | — | 5 | 4 | no | — |
| 366 | D5 | — | 10 | 4 | no | — |
| 367 | D5 | — | 10 | 2 | no | — |
| 368 | D5 | — | 20 | 2 | no | — |
| 369 | D5 | — | 20 | 2 | no | — |
| 370 | D5 | — | 40 | 2 | no | — |
| 371 | C23 | — | 25 | 1 | no | — |
| 372 | C23 | — | 50 | 1 | no | — |
| 373 | Q8 | — | 25 | 1 | no | — |
| 374 | Q8 | — | 50 | 1 | no | — |
| 375 | Q8 | #87830 | 1 | 1 | yes | characteristic |
| 376 | D4 | — | 2 | 1 | no | — |
| 377 | D4 | — | 25 | 1 | no | — |
| 378 | D4 | — | 50 | 1 | no | — |
| 379 | D4 | — | 50 | 1 | no | — |
| 380 | D4 | — | 50 | 1 | no | — |
| 381 | D4 | — | 50 | 1 | no | — |
| 382 | D4 | #87830 | 1 | 1 | yes | characteristic |
| 383 | C2×C4 | — | 2 | 1 | no | — |
| 384 | C2×C4 | — | 25 | 1 | no | — |
| 385 | C2×C4 | — | 25 | 1 | no | — |
| 386 | C2×C4 | — | 25 | 1 | no | — |
| 387 | C2×C4 | — | 25 | 1 | no | — |
| 388 | C2×C4 | — | 25 | 1 | no | — |
| 389 | C2×C4 | — | 50 | 1 | no | — |
| 390 | C2×C4 | — | 50 | 1 | no | — |
| 391 | C2×C4 | — | 50 | 1 | no | — |
| 392 | C2×C4 | — | 50 | 2 | no | — |
| 393 | C2×C4 | — | 50 | 4 | no | — |
| 394 | C2×C4 | — | 50 | 1 | no | — |
| 395 | C2×C4 | — | 50 | 2 | no | — |
| 396 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 397 | C8 | — | 5 | 2 | no | — |
| 398 | C8 | — | 5 | 2 | no | — |
| 399 | C8 | — | 10 | 2 | no | — |
| 400 | C8 | — | 50 | 2 | no | — |
| 401 | C8 | — | 50 | 2 | no | — |
| 402 | C5 | — | 2 | 2 | no | — |
| 403 | C5 | #10604777 | 1 | 2 | yes | complemented |
| 404 | C22 | — | 2 | 1 | no | — |
| 405 | C22 | — | 25 | 1 | no | — |
| 406 | C22 | — | 25 | 1 | no | — |
| 407 | C22 | — | 50 | 2 | no | — |
| 408 | C22 | — | 50 | 1 | no | — |
| 409 | C22 | — | 100 | 2 | no | — |
| 410 | C22 | #11717367 | 1 | 1 | yes | characteristic |
| 411 | C4 | — | 2 | 1 | no | — |
| 412 | C4 | — | 25 | 1 | no | — |
| 413 | C4 | — | 25 | 1 | no | — |
| 414 | C4 | — | 50 | 4 | no | — |
| 415 | C4 | — | 50 | 1 | no | — |
| 416 | C4 | — | 100 | 2 | no | — |
| 417 | C4 | C2×#87830 | 1 | 1 | yes | characteristic |
| 418 | C4 | D5⋊(C22⋊AGL(1,𝔽5)) | 1 | 1 | yes | characteristic |
| 419 | C2 | — | 2 | 1 | no | — |
| 420 | C2 | — | 4 | 1 | no | — |
| 421 | C2 | — | 25 | 2 | no | — |
| 422 | C2 | — | 50 | 1 | no | — |
| 423 | C2 | — | 100 | 1 | no | — |
| 424 | C2 | #13104111 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #13103909 | C2 | semidirect |
| 5. C2×#11716761 | C2 | semidirect |
| 6. #13099909 | C2 | semidirect |
| 7. #13099900 | C2 | semidirect |
| 13. C5×#4094 | C4 | semidirect |
| 17. #11716935 | C4 | semidirect |
| 20. #11716902 | C4 | semidirect |
| 21. #11716900 | C4 | semidirect |
| 22. #11716878 | C4 | semidirect |
| 23. #11716876 | C4 | semidirect |
| 110. #4094 | AGL(1,𝔽5) | semidirect |
| 295. C52 | #1764 | semidirect |
| 403. C5 | #10604777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13106533 | 2 |
| #13104933 | 2 |
| #13104804 | 2 |
| #13103909 | 2 |
| C2×#11716761 | 2 |
| #13099909 | 2 |
| #13099900 | 2 |
| #10604777 | 5 |