Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
694 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #13107550 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13104814 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13103930 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13103906 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13100574 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #13100240 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13099909 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11717471 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#87862 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#87862 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11717438 | C22 | 1 | 1 | yes | characteristic |
| 12 | #11717435 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11717373 | — | 2 | 2 | no | — |
| 14 | #11717361 | — | 2 | 1 | no | — |
| 15 | #11717360 | C4 | 1 | 4 | yes | complemented |
| 16 | D5⋊(D5⋊C8) | — | 2 | 1 | no | — |
| 17 | C42×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 18 | #11716936 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11716895 | — | 2 | 2 | no | — |
| 20 | #11716767 | C4 | 1 | 2 | yes | complemented |
| 21 | #11716765 | C4 | 1 | 2 | yes | complemented |
| 22 | #11716763 | — | 2 | 1 | no | — |
| 23 | #11716761 | — | 2 | 1 | no | — |
| 24 | C5×#3937 | C4 | 1 | 2 | yes | complemented |
| 25 | #11716609 | C4 | 1 | 2 | yes | complemented |
| 26 | #10604006 | — | 5 | 2 | no | maximal |
| 27 | C2×C4×C5⋊D5 | — | 2 | 1 | no | — |
| 28 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 29 | C5×#709 | C2×C4 | 1 | 2 | yes | — |
| 30 | #87886 | — | 2 | 1 | no | — |
| 31 | #87880 | — | 2 | 1 | no | — |
| 32 | #87877 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C4×D52 | — | 2 | 1 | no | — |
| 34 | #87873 | — | 2 | 1 | no | — |
| 35 | #87872 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | #87871 | C2×C4 | 1 | 2 | yes | — |
| 37 | C2×#6034 | — | 2 | 1 | no | — |
| 38 | C2×#6034 | D4 | 1 | 2 | yes | — |
| 39 | #87862 | — | 2 | 1 | no | — |
| 40 | #87862 | C2×C4 | 1 | 2 | yes | — |
| 41 | #87862 | C2×C4 | 1 | 2 | yes | — |
| 42 | #87862 | D4 | 1 | 1 | yes | characteristic |
| 43 | #87862 | D4 | 1 | 1 | yes | characteristic |
| 44 | C22⋊#1043 | — | 2 | 1 | no | — |
| 45 | #87860 | — | 2 | 1 | no | — |
| 46 | C4⋊#1043 | C2×C4 | 1 | 2 | yes | — |
| 47 | C4×#1043 | — | 2 | 1 | no | — |
| 48 | #87856 | C2×C4 | 1 | 2 | yes | — |
| 49 | #87855 | — | 2 | 1 | no | — |
| 50 | #87834 | — | 2 | 4 | no | — |
| 51 | D5⋊#170 | — | 2 | 4 | no | — |
| 52 | C42×C52 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C4×#1039 | — | 2 | 1 | no | — |
| 54 | C4×#1039 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C5×#681 | C2×C4 | 1 | 2 | yes | — |
| 56 | #87769 | — | 2 | 1 | no | — |
| 57 | #87767 | — | 2 | 1 | no | — |
| 58 | D5⋊#131 | — | 5 | 2 | no | — |
| 59 | #65794 | — | 5 | 2 | no | — |
| 60 | #65728 | — | 5 | 2 | no | — |
| 61 | #65676 | — | 5 | 2 | no | — |
| 62 | D5×#104 | — | 5 | 2 | no | — |
| 63 | #64901 | — | 5 | 2 | no | — |
| 64 | #64862 | — | 5 | 2 | no | — |
| 65 | #64862 | — | 10 | 2 | no | — |
| 66 | C22×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 67 | C2×D52 | — | 2 | 1 | no | — |
| 68 | C2×#1043 | — | 2 | 2 | no | — |
| 69 | C2×C4×C52 | — | 2 | 1 | no | — |
| 70 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 71 | C2×#1039 | — | 2 | 1 | no | — |
| 72 | C2×#1039 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C4×C5⋊D5 | — | 4 | 2 | no | — |
| 74 | C4×C5⋊D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 75 | C4×C5⋊D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 76 | C4×C5⋊D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C4×C5⋊D5 | #41 | 1 | 1 | yes | characteristic |
| 78 | C5×C22⋊D5 | — | 2 | 2 | no | — |
| 79 | C5×D20 | C42 | 1 | 2 | yes | — |
| 80 | C4×C5×D5 | — | 2 | 2 | no | — |
| 81 | C5×Dic10 | C42 | 1 | 2 | yes | — |
| 82 | #6039 | — | 2 | 1 | no | — |
| 83 | #6038 | — | 2 | 2 | no | — |
| 84 | #6037 | — | 2 | 1 | no | — |
| 85 | #6036 | — | 2 | 1 | no | — |
| 86 | D5×Dic5 | — | 2 | 2 | no | — |
| 87 | #6034 | — | 2 | 2 | no | — |
| 88 | #6034 | C22⋊C4 | 1 | 2 | yes | — |
| 89 | #6034 | C22⋊C4 | 1 | 2 | yes | — |
| 90 | #6033 | — | 2 | 2 | no | — |
| 91 | C5×#168 | — | 2 | 2 | no | — |
| 92 | D5×#41 | — | 5 | 2 | no | — |
| 93 | #4133 | — | 5 | 4 | no | — |
| 94 | #4131 | — | 5 | 4 | no | — |
| 95 | #4131 | — | 10 | 4 | no | — |
| 96 | #4130 | — | 5 | 2 | no | — |
| 97 | #4130 | — | 10 | 2 | no | — |
| 98 | D5⋊M16 | — | 5 | 2 | no | — |
| 99 | D5⋊M16 | — | 10 | 2 | no | — |
| 100 | D5⋊M16 | — | 10 | 2 | no | — |
| 101 | C2×D5⋊C8 | — | 5 | 2 | no | — |
| 102 | C2×D5⋊C8 | — | 5 | 2 | no | — |
| 103 | C2×D5⋊C8 | — | 10 | 2 | no | — |
| 104 | D5×M16 | — | 5 | 2 | no | — |
| 105 | C42×D5 | — | 5 | 2 | no | — |
| 106 | C42×D5 | — | 10 | 2 | no | — |
| 107 | #4009 | — | 5 | 4 | no | — |
| 108 | #4007 | — | 5 | 4 | no | — |
| 109 | #4002 | — | 10 | 4 | no | — |
| 110 | #3992 | — | 10 | 2 | no | — |
| 111 | C8×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 112 | C5×#104 | — | 5 | 2 | no | — |
| 113 | #3969 | — | 5 | 2 | no | — |
| 114 | #3957 | — | 5 | 2 | no | — |
| 115 | #3937 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 116 | #1765 | — | 25 | 1 | no | Sylow |
| 117 | C22×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×C5⋊D5 | — | 2 | 2 | no | — |
| 119 | C2×C5⋊D5 | #117 | 1 | 1 | yes | characteristic |
| 120 | C2×C5⋊D5 | C4×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C5×D5 | — | 2 | 2 | no | — |
| 122 | D52 | — | 4 | 2 | no | — |
| 123 | #1043 | — | 4 | 2 | no | — |
| 124 | C4×C52 | — | 4 | 1 | no | — |
| 125 | C4×C52 | C2×C42 | 1 | 1 | yes | characteristic |
| 126 | C4×C52 | C4×D4 | 1 | 1 | yes | characteristic |
| 127 | #1039 | — | 4 | 1 | no | — |
| 128 | #1039 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 129 | #1039 | C4×D4 | 1 | 1 | yes | characteristic |
| 130 | C5×Dic5 | — | 2 | 2 | no | — |
| 131 | C5×#41 | — | 5 | 2 | no | — |
| 132 | #713 | — | 5 | 2 | no | — |
| 133 | Q8×D5 | — | 5 | 2 | no | — |
| 134 | #711 | — | 5 | 2 | no | — |
| 135 | #711 | — | 10 | 2 | no | — |
| 136 | D4×D5 | — | 5 | 2 | no | — |
| 137 | D4×D5 | — | 10 | 2 | no | — |
| 138 | #709 | — | 10 | 2 | no | — |
| 139 | #709 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 140 | C2×C4×D5 | — | 5 | 2 | no | — |
| 141 | C2×C4×D5 | — | 10 | 2 | no | — |
| 142 | C2×C4×D5 | — | 10 | 2 | no | — |
| 143 | C2×C4×D5 | — | 10 | 2 | no | — |
| 144 | C2×C4×D5 | — | 20 | 2 | no | — |
| 145 | C22⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 146 | C22⋊AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 147 | #704 | — | 10 | 4 | no | — |
| 148 | #704 | — | 10 | 2 | no | — |
| 149 | #704 | — | 20 | 2 | no | — |
| 150 | C2×#170 | — | 5 | 4 | no | — |
| 151 | C2×#170 | — | 10 | 4 | no | — |
| 152 | C2×#170 | — | 10 | 2 | no | — |
| 153 | C4⋊AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 154 | C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 155 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 156 | C4×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 157 | #700 | — | 5 | 4 | no | — |
| 158 | #700 | — | 10 | 4 | no | — |
| 159 | #700 | — | 10 | 4 | no | — |
| 160 | D5⋊C8 | — | 5 | 2 | no | — |
| 161 | D5⋊C8 | — | 5 | 2 | no | — |
| 162 | D5⋊C8 | — | 5 | 4 | no | — |
| 163 | D5⋊C8 | — | 5 | 4 | no | — |
| 164 | D5⋊C8 | — | 10 | 4 | no | — |
| 165 | D5⋊C8 | — | 10 | 2 | no | — |
| 166 | D5⋊C8 | — | 10 | 2 | no | — |
| 167 | D5⋊C8 | — | 20 | 2 | no | — |
| 168 | C5×M16 | — | 5 | 2 | no | — |
| 169 | C42×C5 | — | 2 | 2 | no | — |
| 170 | C42×C5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 171 | C4×Dic5 | — | 5 | 2 | no | — |
| 172 | C4×Dic5 | — | 10 | 2 | no | — |
| 173 | C4×Dic5 | — | 10 | 2 | no | — |
| 174 | C4×Dic5 | — | 20 | 2 | no | — |
| 175 | #681 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 176 | #676 | — | 10 | 2 | no | — |
| 177 | C8×D5 | — | 10 | 2 | no | — |
| 178 | C2×#131 | — | 25 | 1 | no | — |
| 179 | C2×#104 | — | 25 | 1 | no | — |
| 180 | #416 | — | 25 | 1 | no | — |
| 181 | #405 | — | 25 | 1 | no | — |
| 182 | C2×#97 | — | 25 | 1 | no | — |
| 183 | #341 | — | 25 | 1 | no | — |
| 184 | #339 | — | 25 | 1 | no | — |
| 185 | C2×C52 | — | 2 | 1 | no | — |
| 186 | C2×C52 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 187 | C5⋊D5 | — | 2 | 1 | no | — |
| 188 | C5⋊D5 | #444 | 1 | 2 | yes | — |
| 189 | C5×D5 | — | 4 | 2 | no | — |
| 190 | C22×D5 | — | 5 | 2 | no | — |
| 191 | C22×D5 | — | 10 | 2 | no | — |
| 192 | C22×D5 | — | 10 | 2 | no | — |
| 193 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 194 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 195 | C5×Q8 | — | 5 | 2 | no | — |
| 196 | C5×D4 | — | 5 | 2 | no | — |
| 197 | C5×D4 | — | 10 | 2 | no | — |
| 198 | C2×C4×C5 | — | 2 | 2 | no | — |
| 199 | C2×C4×C5 | — | 2 | 2 | no | — |
| 200 | C2×C4×C5 | — | 4 | 2 | no | — |
| 201 | C2×C4×C5 | — | 10 | 2 | no | — |
| 202 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 203 | C22⋊D5 | — | 2 | 2 | no | — |
| 204 | C22⋊D5 | — | 10 | 2 | no | — |
| 205 | C22⋊D5 | — | 10 | 2 | no | — |
| 206 | C2×Dic5 | — | 5 | 2 | no | — |
| 207 | C2×Dic5 | — | 10 | 2 | no | — |
| 208 | C2×Dic5 | — | 10 | 2 | no | — |
| 209 | C2×Dic5 | — | 10 | 2 | no | — |
| 210 | C2×Dic5 | — | 20 | 2 | no | — |
| 211 | D20 | — | 10 | 2 | no | — |
| 212 | D20 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 213 | C4×D5 | — | 2 | 2 | no | — |
| 214 | C4×D5 | — | 5 | 2 | no | — |
| 215 | C4×D5 | — | 5 | 2 | no | — |
| 216 | C4×D5 | — | 5 | 2 | no | — |
| 217 | C4×D5 | — | 5 | 2 | no | — |
| 218 | C4×D5 | — | 10 | 2 | no | — |
| 219 | C4×D5 | — | 10 | 2 | no | — |
| 220 | C4×D5 | — | 10 | 2 | no | — |
| 221 | C4×D5 | — | 10 | 2 | no | — |
| 222 | C4×D5 | — | 10 | 2 | no | — |
| 223 | C4×D5 | — | 10 | 2 | no | — |
| 224 | C4×D5 | — | 20 | 4 | no | — |
| 225 | C4×D5 | — | 20 | 8 | no | — |
| 226 | Dic10 | — | 10 | 2 | no | — |
| 227 | Dic10 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 228 | #170 | — | 5 | 4 | no | — |
| 229 | #170 | — | 5 | 4 | no | — |
| 230 | #170 | — | 10 | 4 | no | — |
| 231 | #170 | — | 10 | 4 | no | — |
| 232 | #170 | — | 20 | 4 | no | — |
| 233 | C5×C8 | — | 10 | 2 | no | — |
| 234 | #168 | — | 2 | 2 | no | — |
| 235 | C2×#41 | — | 25 | 1 | no | — |
| 236 | #131 | — | 25 | 4 | no | — |
| 237 | #131 | — | 50 | 2 | no | — |
| 238 | C2×M16 | — | 25 | 1 | no | — |
| 239 | C2×M16 | — | 25 | 1 | no | — |
| 240 | C2×M16 | — | 50 | 1 | no | — |
| 241 | C22×C8 | — | 25 | 1 | no | — |
| 242 | C22×C8 | — | 25 | 1 | no | — |
| 243 | C22×C8 | — | 50 | 1 | no | — |
| 244 | #117 | — | 25 | 1 | no | — |
| 245 | C2×C42 | — | 25 | 1 | no | — |
| 246 | #104 | — | 5 | 2 | no | — |
| 247 | #104 | — | 25 | 2 | no | — |
| 248 | #103 | — | 25 | 2 | no | — |
| 249 | #102 | — | 25 | 2 | no | — |
| 250 | #97 | — | 50 | 2 | no | — |
| 251 | #97 | — | 50 | 1 | no | — |
| 252 | C4×C8 | — | 50 | 1 | no | — |
| 253 | C52 | #1765 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 254 | C22×C5 | — | 2 | 2 | no | — |
| 255 | C22×C5 | — | 10 | 2 | no | — |
| 256 | C22×C5 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 257 | C2×D5 | — | 2 | 2 | no | — |
| 258 | C2×D5 | — | 5 | 2 | no | — |
| 259 | C2×D5 | — | 5 | 2 | no | — |
| 260 | C2×D5 | — | 10 | 2 | no | — |
| 261 | C2×D5 | — | 10 | 2 | no | — |
| 262 | C2×D5 | — | 10 | 4 | no | — |
| 263 | C2×D5 | — | 20 | 4 | no | — |
| 264 | C2×D5 | — | 20 | 4 | no | — |
| 265 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 266 | AGL(1,𝔽5) | — | 40 | 4 | no | — |
| 267 | C4×C5 | — | 2 | 2 | no | — |
| 268 | C4×C5 | — | 2 | 2 | no | — |
| 269 | C4×C5 | — | 4 | 2 | no | — |
| 270 | C4×C5 | — | 4 | 4 | no | — |
| 271 | C4×C5 | — | 10 | 2 | no | — |
| 272 | C4×C5 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 273 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 274 | Dic5 | — | 2 | 2 | no | — |
| 275 | Dic5 | — | 5 | 2 | no | — |
| 276 | Dic5 | — | 5 | 2 | no | — |
| 277 | Dic5 | — | 10 | 2 | no | — |
| 278 | Dic5 | — | 10 | 2 | no | — |
| 279 | Dic5 | — | 20 | 2 | no | — |
| 280 | Dic5 | — | 20 | 4 | no | — |
| 281 | #41 | — | 5 | 2 | no | — |
| 282 | #41 | — | 25 | 2 | no | — |
| 283 | #41 | — | 50 | 1 | no | — |
| 284 | #41 | — | 50 | 1 | no | — |
| 285 | C2×Q8 | — | 25 | 1 | no | — |
| 286 | C2×D4 | — | 25 | 1 | no | — |
| 287 | C2×D4 | — | 50 | 1 | no | — |
| 288 | C22×C4 | — | 25 | 1 | no | — |
| 289 | C22×C4 | — | 50 | 1 | no | — |
| 290 | C22×C4 | — | 50 | 1 | no | — |
| 291 | M16 | — | 5 | 2 | no | — |
| 292 | M16 | — | 25 | 2 | no | — |
| 293 | M16 | — | 50 | 1 | no | — |
| 294 | M16 | — | 50 | 4 | no | — |
| 295 | M16 | — | 50 | 1 | no | — |
| 296 | C2×C8 | — | 25 | 1 | no | — |
| 297 | C2×C8 | — | 25 | 1 | no | — |
| 298 | C2×C8 | — | 25 | 2 | no | — |
| 299 | C2×C8 | — | 25 | 2 | no | — |
| 300 | C2×C8 | — | 25 | 2 | no | — |
| 301 | C2×C8 | — | 50 | 1 | no | — |
| 302 | C2×C8 | — | 50 | 4 | no | — |
| 303 | C2×C8 | — | 50 | 1 | no | — |
| 304 | C2×C8 | — | 50 | 1 | no | — |
| 305 | C2×C8 | — | 50 | 1 | no | — |
| 306 | C4⋊C4 | — | 25 | 2 | no | — |
| 307 | C22⋊C4 | — | 50 | 1 | no | — |
| 308 | C42 | — | 25 | 1 | no | — |
| 309 | C42 | — | 50 | 1 | no | — |
| 310 | C42 | — | 50 | 1 | no | — |
| 311 | C42 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 312 | C2×C5 | — | 2 | 2 | no | — |
| 313 | C2×C5 | — | 2 | 2 | no | — |
| 314 | C2×C5 | — | 4 | 2 | no | — |
| 315 | C2×C5 | — | 20 | 2 | no | — |
| 316 | C2×C5 | C22⋊C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 317 | D5 | — | 4 | 2 | no | — |
| 318 | D5 | — | 5 | 4 | no | — |
| 319 | D5 | — | 10 | 4 | no | — |
| 320 | D5 | — | 10 | 2 | no | — |
| 321 | D5 | — | 20 | 2 | no | — |
| 322 | C23 | — | 25 | 1 | no | — |
| 323 | C23 | — | 50 | 1 | no | — |
| 324 | Q8 | — | 5 | 2 | no | — |
| 325 | Q8 | — | 50 | 1 | no | — |
| 326 | D4 | — | 5 | 2 | no | — |
| 327 | D4 | — | 10 | 2 | no | — |
| 328 | D4 | — | 50 | 2 | no | — |
| 329 | D4 | — | 50 | 1 | no | — |
| 330 | C2×C4 | — | 2 | 1 | no | — |
| 331 | C2×C4 | — | 10 | 2 | no | — |
| 332 | C2×C4 | — | 25 | 1 | no | — |
| 333 | C2×C4 | — | 25 | 1 | no | — |
| 334 | C2×C4 | — | 25 | 1 | no | — |
| 335 | C2×C4 | — | 25 | 1 | no | — |
| 336 | C2×C4 | — | 25 | 1 | no | — |
| 337 | C2×C4 | — | 50 | 1 | no | — |
| 338 | C2×C4 | — | 50 | 2 | no | — |
| 339 | C2×C4 | — | 50 | 2 | no | — |
| 340 | C2×C4 | — | 50 | 1 | no | — |
| 341 | C2×C4 | — | 100 | 2 | no | — |
| 342 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 343 | C8 | — | 10 | 2 | no | — |
| 344 | C8 | — | 25 | 2 | no | — |
| 345 | C8 | — | 25 | 2 | no | — |
| 346 | C8 | — | 50 | 2 | no | — |
| 347 | C8 | — | 50 | 2 | no | — |
| 348 | C5 | — | 2 | 2 | no | — |
| 349 | C5 | #10604006 | 1 | 2 | yes | complemented |
| 350 | C22 | — | 10 | 2 | no | — |
| 351 | C22 | — | 25 | 1 | no | — |
| 352 | C22 | — | 25 | 1 | no | — |
| 353 | C22 | — | 50 | 2 | no | — |
| 354 | C22 | — | 100 | 2 | no | — |
| 355 | C22 | #11717377 | 1 | 1 | yes | characteristic |
| 356 | C4 | — | 4 | 1 | no | — |
| 357 | C4 | — | 10 | 2 | no | — |
| 358 | C4 | — | 25 | 1 | no | — |
| 359 | C4 | — | 25 | 1 | no | — |
| 360 | C4 | — | 100 | 1 | no | — |
| 361 | C4 | — | 100 | 2 | no | — |
| 362 | C4 | C4×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 363 | C4 | #11717365 | 1 | 1 | yes | characteristic |
| 364 | C2 | — | 2 | 1 | no | — |
| 365 | C2 | — | 20 | 2 | no | — |
| 366 | C2 | — | 25 | 2 | no | — |
| 367 | C2 | — | 50 | 1 | no | — |
| 368 | C2 | #13104047 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13104814 | C2 | semidirect |
| 4. #13103906 | C2 | semidirect |
| 6. #13100240 | C2 | semidirect |
| 7. #13099909 | C2 | semidirect |
| 15. #11717360 | C4 | semidirect |
| 20. #11716767 | C4 | semidirect |
| 21. #11716765 | C4 | semidirect |
| 24. C5×#3937 | C4 | semidirect |
| 25. #11716609 | C4 | semidirect |
| 115. #3937 | AGL(1,𝔽5) | semidirect |
| 253. C52 | #1765 | semidirect |
| 349. C5 | #10604006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107550 | 2 |
| #13104814 | 2 |
| #13103930 | 2 |
| #13103906 | 2 |
| #13100574 | 2 |
| #13100240 | 2 |
| #13099909 | 2 |
| #10604006 | 5 |