Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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 | #66138 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#4083 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#4028 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×C5×#99 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #65244 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#3938 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #64747 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C24×D5 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×C5×D4 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×C22⋊D5 | — | 2 | 1 | no | — |
| 11 | C22×C22⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×D20 | — | 2 | 1 | no | — |
| 13 | C2×C5×C22⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C5×C22⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 15 | #4099 | — | 2 | 1 | no | — |
| 16 | C2×C22⋊Dic5 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C22⋊Dic5 | C22 | 1 | 1 | yes | characteristic |
| 18 | #4085 | — | 2 | 2 | no | — |
| 19 | #4083 | — | 2 | 2 | no | — |
| 20 | #4083 | — | 2 | 1 | no | — |
| 21 | #4083 | — | 2 | 2 | no | — |
| 22 | #4081 | — | 2 | 1 | no | — |
| 23 | #4075 | — | 2 | 1 | no | — |
| 24 | C2×#685 | — | 2 | 1 | no | — |
| 25 | C2×#685 | — | 2 | 1 | no | — |
| 26 | C2×#685 | — | 2 | 2 | no | — |
| 27 | #4028 | — | 2 | 2 | no | — |
| 28 | #4028 | — | 2 | 2 | no | — |
| 29 | C5×#99 | — | 2 | 2 | no | — |
| 30 | #3938 | — | 2 | 2 | no | — |
| 31 | #2021 | — | 5 | 1 | no | maximal, Sylow |
| 32 | C24×C5 | D4 | 1 | 1 | yes | characteristic, complemented |
| 33 | C24×C5 | C23 | 1 | 1 | yes | characteristic |
| 34 | C23×D5 | — | 2 | 1 | no | — |
| 35 | C23×D5 | — | 2 | 1 | no | — |
| 36 | C23×D5 | — | 2 | 1 | no | — |
| 37 | C23×D5 | — | 2 | 1 | no | — |
| 38 | C23×D5 | — | 2 | 1 | no | — |
| 39 | C23×D5 | — | 2 | 1 | no | — |
| 40 | C23×D5 | — | 4 | 4 | no | — |
| 41 | C23×D5 | D4 | 1 | 1 | yes | characteristic, complemented |
| 42 | C23×D5 | D4 | 1 | 2 | yes | complemented |
| 43 | C2×C5×D4 | — | 2 | 1 | no | — |
| 44 | C2×C5×D4 | — | 2 | 1 | no | — |
| 45 | C2×C5×D4 | — | 2 | 1 | no | — |
| 46 | C2×C5×D4 | — | 2 | 1 | no | — |
| 47 | C2×C5×D4 | — | 2 | 1 | no | — |
| 48 | C2×C5×D4 | — | 2 | 1 | no | — |
| 49 | C22×C4×C5 | — | 2 | 1 | no | — |
| 50 | C22×C4×C5 | — | 2 | 1 | no | — |
| 51 | C22×C4×C5 | D4 | 1 | 1 | yes | characteristic, complemented |
| 52 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 53 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 54 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 55 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 56 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 57 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 58 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 59 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 60 | C2×C22⋊D5 | — | 4 | 4 | no | — |
| 61 | C22×Dic5 | — | 2 | 1 | no | — |
| 62 | C22×Dic5 | D4 | 1 | 1 | yes | characteristic, complemented |
| 63 | C22×Dic5 | D4 | 1 | 2 | yes | complemented |
| 64 | C2×D20 | — | 2 | 4 | no | — |
| 65 | C2×D20 | — | 4 | 4 | no | — |
| 66 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 67 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 68 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 69 | C5×C22⋊C4 | D4 | 1 | 2 | yes | complemented |
| 70 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 71 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 72 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 73 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 74 | C22⋊Dic5 | D4 | 1 | 2 | yes | complemented |
| 75 | #685 | — | 2 | 4 | no | — |
| 76 | #685 | — | 2 | 4 | no | — |
| 77 | #685 | — | 2 | 2 | no | — |
| 78 | #685 | — | 4 | 4 | no | — |
| 79 | #683 | — | 2 | 2 | no | — |
| 80 | #534 | — | 5 | 1 | no | — |
| 81 | C2×#120 | — | 5 | 1 | no | — |
| 82 | C2×#120 | — | 5 | 1 | no | — |
| 83 | C2×#99 | — | 5 | 1 | no | — |
| 84 | C2×#99 | D5 | 1 | 1 | yes | characteristic, complemented |
| 85 | #379 | — | 5 | 1 | no | — |
| 86 | #342 | — | 5 | 1 | no | — |
| 87 | C23×C5 | — | 2 | 1 | no | — |
| 88 | C23×C5 | — | 2 | 1 | no | — |
| 89 | C23×C5 | — | 2 | 1 | no | — |
| 90 | C23×C5 | — | 4 | 2 | no | — |
| 91 | C23×C5 | — | 4 | 2 | no | — |
| 92 | C23×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C23×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | C23×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C23×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C23×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C23×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C23×C5 | #41 | 1 | 1 | yes | characteristic |
| 99 | C22×D5 | — | 2 | 4 | no | — |
| 100 | C22×D5 | — | 2 | 4 | no | — |
| 101 | C22×D5 | — | 2 | 4 | no | — |
| 102 | C22×D5 | — | 2 | 2 | no | — |
| 103 | C22×D5 | — | 2 | 2 | no | — |
| 104 | C22×D5 | — | 2 | 2 | no | — |
| 105 | C22×D5 | — | 2 | 1 | no | — |
| 106 | C22×D5 | — | 2 | 1 | no | — |
| 107 | C22×D5 | — | 2 | 1 | no | — |
| 108 | C22×D5 | — | 4 | 4 | no | — |
| 109 | C22×D5 | — | 4 | 4 | no | — |
| 110 | C22×D5 | — | 4 | 4 | no | — |
| 111 | C22×D5 | — | 4 | 4 | no | — |
| 112 | C22×D5 | — | 4 | 2 | no | — |
| 113 | C22×D5 | — | 4 | 2 | no | — |
| 114 | C22×D5 | — | 4 | 2 | no | — |
| 115 | C22×D5 | — | 4 | 1 | no | — |
| 116 | C22×D5 | — | 4 | 1 | no | — |
| 117 | C22×D5 | — | 4 | 1 | no | — |
| 118 | C22×D5 | — | 4 | 1 | no | — |
| 119 | C22×D5 | — | 4 | 2 | no | — |
| 120 | C5×D4 | — | 4 | 1 | no | — |
| 121 | C5×D4 | — | 4 | 1 | no | — |
| 122 | C5×D4 | — | 4 | 1 | no | — |
| 123 | C5×D4 | — | 4 | 1 | no | — |
| 124 | C2×C4×C5 | — | 2 | 1 | no | — |
| 125 | C2×C4×C5 | — | 2 | 1 | no | — |
| 126 | C2×C4×C5 | — | 2 | 2 | no | — |
| 127 | C2×C4×C5 | — | 2 | 1 | no | — |
| 128 | C2×C4×C5 | — | 4 | 2 | no | — |
| 129 | C2×C4×C5 | — | 4 | 2 | no | — |
| 130 | C2×C4×C5 | — | 4 | 1 | no | — |
| 131 | C22⋊D5 | — | 4 | 8 | no | — |
| 132 | C22⋊D5 | — | 4 | 1 | no | — |
| 133 | C22⋊D5 | — | 4 | 1 | no | — |
| 134 | C22⋊D5 | — | 4 | 1 | no | — |
| 135 | C22⋊D5 | — | 4 | 1 | no | — |
| 136 | C22⋊D5 | — | 8 | 2 | no | — |
| 137 | C2×Dic5 | — | 2 | 1 | no | — |
| 138 | C2×Dic5 | — | 2 | 2 | no | — |
| 139 | C2×Dic5 | — | 2 | 1 | no | — |
| 140 | C2×Dic5 | — | 2 | 2 | no | — |
| 141 | C2×Dic5 | — | 2 | 1 | no | — |
| 142 | C2×Dic5 | — | 4 | 2 | no | — |
| 143 | C2×Dic5 | — | 4 | 2 | no | — |
| 144 | D20 | — | 4 | 8 | no | — |
| 145 | C25 | — | 5 | 1 | no | — |
| 146 | C22×D4 | — | 5 | 1 | no | — |
| 147 | C22×D4 | — | 10 | 1 | no | — |
| 148 | C22×D4 | — | 10 | 1 | no | — |
| 149 | C22×D4 | C2×D5 | 1 | 1 | yes | characteristic |
| 150 | #123 | — | 10 | 1 | no | — |
| 151 | #123 | — | 10 | 1 | no | — |
| 152 | #121 | — | 10 | 2 | no | — |
| 153 | #120 | — | 10 | 2 | no | — |
| 154 | #120 | — | 10 | 2 | no | — |
| 155 | #120 | — | 10 | 2 | no | — |
| 156 | #120 | — | 10 | 1 | no | — |
| 157 | #120 | — | 10 | 1 | no | — |
| 158 | #120 | — | 10 | 2 | no | — |
| 159 | C2×C22⋊C4 | — | 5 | 1 | no | — |
| 160 | C2×C22⋊C4 | — | 5 | 1 | no | — |
| 161 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 162 | C2×C22⋊C4 | — | 10 | 1 | no | — |
| 163 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 164 | C2×C22⋊C4 | C2×D5 | 1 | 1 | yes | characteristic |
| 165 | C2×C22⋊C4 | C2×D5 | 1 | 1 | yes | characteristic |
| 166 | #99 | — | 2 | 2 | no | — |
| 167 | #99 | — | 10 | 2 | no | — |
| 168 | C22×C5 | — | 2 | 2 | no | — |
| 169 | C22×C5 | — | 2 | 2 | no | — |
| 170 | C22×C5 | — | 2 | 2 | no | — |
| 171 | C22×C5 | — | 4 | 1 | no | — |
| 172 | C22×C5 | — | 4 | 1 | no | — |
| 173 | C22×C5 | — | 4 | 1 | no | — |
| 174 | C22×C5 | — | 4 | 1 | no | — |
| 175 | C22×C5 | — | 4 | 2 | no | — |
| 176 | C22×C5 | — | 4 | 1 | no | — |
| 177 | C22×C5 | — | 4 | 2 | no | — |
| 178 | C22×C5 | — | 8 | 1 | no | — |
| 179 | C22×C5 | #120 | 1 | 1 | yes | characteristic |
| 180 | C22×C5 | #120 | 1 | 1 | yes | characteristic |
| 181 | C22×C5 | #120 | 1 | 1 | yes | characteristic |
| 182 | C22×C5 | #121 | 1 | 1 | yes | characteristic |
| 183 | C22×C5 | #121 | 1 | 1 | yes | characteristic |
| 184 | C22×C5 | #121 | 1 | 1 | yes | characteristic |
| 185 | C22×C5 | #127 | 1 | 1 | yes | characteristic |
| 186 | C2×D5 | — | 2 | 4 | no | — |
| 187 | C2×D5 | — | 2 | 4 | no | — |
| 188 | C2×D5 | — | 2 | 4 | no | — |
| 189 | C2×D5 | — | 4 | 2 | no | — |
| 190 | C2×D5 | — | 4 | 2 | no | — |
| 191 | C2×D5 | — | 4 | 4 | no | — |
| 192 | C2×D5 | — | 4 | 2 | no | — |
| 193 | C2×D5 | — | 4 | 4 | no | — |
| 194 | C2×D5 | — | 4 | 4 | no | — |
| 195 | C2×D5 | — | 4 | 2 | no | — |
| 196 | C2×D5 | — | 4 | 4 | no | — |
| 197 | C2×D5 | — | 4 | 2 | no | — |
| 198 | C2×D5 | — | 4 | 1 | no | — |
| 199 | C2×D5 | — | 4 | 2 | no | — |
| 200 | C2×D5 | — | 8 | 1 | no | — |
| 201 | C4×C5 | — | 4 | 2 | no | — |
| 202 | C4×C5 | — | 4 | 1 | no | — |
| 203 | C4×C5 | — | 8 | 1 | no | — |
| 204 | Dic5 | — | 4 | 2 | no | — |
| 205 | Dic5 | — | 4 | 1 | no | — |
| 206 | Dic5 | — | 4 | 2 | no | — |
| 207 | C24 | — | 5 | 2 | no | — |
| 208 | C24 | — | 5 | 1 | no | — |
| 209 | C24 | — | 10 | 1 | no | — |
| 210 | C24 | — | 10 | 1 | no | — |
| 211 | C24 | — | 10 | 1 | no | — |
| 212 | C24 | — | 10 | 1 | no | — |
| 213 | C24 | — | 10 | 1 | no | — |
| 214 | C24 | — | 10 | 1 | no | — |
| 215 | C24 | — | 20 | 4 | no | — |
| 216 | C24 | D20 | 1 | 1 | yes | characteristic, complemented |
| 217 | C24 | C22×D5 | 1 | 1 | yes | characteristic |
| 218 | C2×D4 | — | 2 | 1 | no | — |
| 219 | C2×D4 | — | 2 | 1 | no | — |
| 220 | C2×D4 | — | 2 | 1 | no | — |
| 221 | C2×D4 | — | 2 | 1 | no | — |
| 222 | C2×D4 | — | 2 | 1 | no | — |
| 223 | C2×D4 | — | 2 | 1 | no | — |
| 224 | C2×D4 | — | 10 | 4 | no | — |
| 225 | C2×D4 | — | 10 | 4 | no | — |
| 226 | C2×D4 | — | 10 | 1 | no | — |
| 227 | C2×D4 | — | 10 | 1 | no | — |
| 228 | C2×D4 | — | 10 | 1 | no | — |
| 229 | C2×D4 | — | 10 | 1 | no | — |
| 230 | C2×D4 | — | 10 | 1 | no | — |
| 231 | C2×D4 | — | 10 | 1 | no | — |
| 232 | C2×D4 | — | 10 | 2 | no | — |
| 233 | C2×D4 | — | 20 | 4 | no | — |
| 234 | C2×D4 | — | 20 | 4 | no | — |
| 235 | C22×C4 | — | 2 | 1 | no | — |
| 236 | C22×C4 | — | 2 | 1 | no | — |
| 237 | C22×C4 | — | 5 | 1 | no | — |
| 238 | C22×C4 | — | 5 | 2 | no | — |
| 239 | C22×C4 | — | 10 | 1 | no | — |
| 240 | C22×C4 | D20 | 1 | 1 | yes | characteristic, complemented |
| 241 | C4⋊C4 | — | 10 | 2 | no | — |
| 242 | C22⋊C4 | — | 2 | 1 | no | — |
| 243 | C22⋊C4 | — | 2 | 1 | no | — |
| 244 | C22⋊C4 | — | 2 | 1 | no | — |
| 245 | C22⋊C4 | — | 5 | 2 | no | — |
| 246 | C22⋊C4 | — | 10 | 4 | no | — |
| 247 | C22⋊C4 | — | 10 | 4 | no | — |
| 248 | C22⋊C4 | — | 10 | 2 | no | — |
| 249 | C22⋊C4 | — | 10 | 2 | no | — |
| 250 | C22⋊C4 | — | 10 | 1 | no | — |
| 251 | C22⋊C4 | — | 10 | 1 | no | — |
| 252 | C22⋊C4 | — | 10 | 1 | no | — |
| 253 | C22⋊C4 | — | 20 | 4 | no | — |
| 254 | C22⋊C4 | C22⋊D5 | 1 | 2 | yes | complemented |
| 255 | C2×C5 | — | 2 | 1 | no | — |
| 256 | C2×C5 | — | 2 | 1 | no | — |
| 257 | C2×C5 | — | 2 | 1 | no | — |
| 258 | C2×C5 | — | 2 | 1 | no | — |
| 259 | C2×C5 | — | 2 | 1 | no | — |
| 260 | C2×C5 | — | 2 | 1 | no | — |
| 261 | C2×C5 | — | 8 | 1 | no | — |
| 262 | C2×C5 | #392 | 1 | 1 | yes | characteristic |
| 263 | C2×C5 | B(4,𝔽2) | 1 | 2 | yes | — |
| 264 | D5 | — | 4 | 4 | no | — |
| 265 | D5 | — | 8 | 1 | no | — |
| 266 | C23 | — | 2 | 1 | no | — |
| 267 | C23 | — | 2 | 1 | no | — |
| 268 | C23 | — | 2 | 1 | no | — |
| 269 | C23 | — | 4 | 2 | no | — |
| 270 | C23 | — | 4 | 2 | no | — |
| 271 | C23 | — | 10 | 4 | no | — |
| 272 | C23 | — | 10 | 4 | no | — |
| 273 | C23 | — | 10 | 4 | no | — |
| 274 | C23 | — | 10 | 2 | no | — |
| 275 | C23 | — | 10 | 2 | no | — |
| 276 | C23 | — | 10 | 2 | no | — |
| 277 | C23 | — | 10 | 1 | no | — |
| 278 | C23 | — | 10 | 1 | no | — |
| 279 | C23 | — | 10 | 1 | no | — |
| 280 | C23 | — | 20 | 2 | no | — |
| 281 | C23 | — | 20 | 2 | no | — |
| 282 | C23 | — | 20 | 2 | no | — |
| 283 | C23 | — | 20 | 2 | no | — |
| 284 | C23 | — | 20 | 4 | no | — |
| 285 | C23 | — | 20 | 4 | no | — |
| 286 | C23 | — | 20 | 4 | no | — |
| 287 | C23 | — | 20 | 4 | no | — |
| 288 | C23 | — | 20 | 1 | no | — |
| 289 | C23 | — | 20 | 1 | no | — |
| 290 | C23 | — | 20 | 1 | no | — |
| 291 | C23 | — | 20 | 1 | no | — |
| 292 | C23 | C2×D20 | 1 | 1 | yes | characteristic |
| 293 | C23 | #709 | 1 | 1 | yes | characteristic |
| 294 | C23 | D4×D5 | 1 | 1 | yes | characteristic |
| 295 | C23 | D4×D5 | 1 | 1 | yes | characteristic |
| 296 | C23 | D4×D5 | 1 | 1 | yes | characteristic |
| 297 | C23 | D4×D5 | 1 | 1 | yes | characteristic |
| 298 | C23 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 299 | D4 | — | 4 | 1 | no | — |
| 300 | D4 | — | 4 | 1 | no | — |
| 301 | D4 | — | 4 | 1 | no | — |
| 302 | D4 | — | 4 | 1 | no | — |
| 303 | D4 | — | 20 | 8 | no | — |
| 304 | D4 | — | 20 | 8 | no | — |
| 305 | D4 | — | 20 | 1 | no | — |
| 306 | D4 | — | 20 | 1 | no | — |
| 307 | D4 | — | 20 | 1 | no | — |
| 308 | D4 | — | 20 | 1 | no | — |
| 309 | D4 | — | 40 | 2 | no | — |
| 310 | C2×C4 | — | 2 | 1 | no | — |
| 311 | C2×C4 | — | 2 | 1 | no | — |
| 312 | C2×C4 | — | 2 | 1 | no | — |
| 313 | C2×C4 | — | 2 | 2 | no | — |
| 314 | C2×C4 | — | 4 | 2 | no | — |
| 315 | C2×C4 | — | 4 | 2 | no | — |
| 316 | C2×C4 | — | 4 | 1 | no | — |
| 317 | C2×C4 | — | 10 | 2 | no | — |
| 318 | C2×C4 | — | 10 | 2 | no | — |
| 319 | C2×C4 | — | 10 | 1 | no | — |
| 320 | C2×C4 | — | 10 | 1 | no | — |
| 321 | C2×C4 | — | 10 | 1 | no | — |
| 322 | C2×C4 | — | 20 | 2 | no | — |
| 323 | C2×C4 | — | 20 | 2 | no | — |
| 324 | C5 | #2021 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 325 | C22 | — | 2 | 2 | no | — |
| 326 | C22 | — | 2 | 2 | no | — |
| 327 | C22 | — | 2 | 2 | no | — |
| 328 | C22 | — | 4 | 1 | no | — |
| 329 | C22 | — | 4 | 1 | no | — |
| 330 | C22 | — | 4 | 1 | no | — |
| 331 | C22 | — | 4 | 1 | no | — |
| 332 | C22 | — | 4 | 2 | no | — |
| 333 | C22 | — | 4 | 2 | no | — |
| 334 | C22 | — | 4 | 1 | no | — |
| 335 | C22 | — | 8 | 1 | no | — |
| 336 | C22 | — | 10 | 4 | no | — |
| 337 | C22 | — | 10 | 4 | no | — |
| 338 | C22 | — | 10 | 4 | no | — |
| 339 | C22 | — | 20 | 2 | no | — |
| 340 | C22 | — | 20 | 4 | no | — |
| 341 | C22 | — | 20 | 2 | no | — |
| 342 | C22 | — | 20 | 4 | no | — |
| 343 | C22 | — | 20 | 2 | no | — |
| 344 | C22 | — | 20 | 4 | no | — |
| 345 | C22 | — | 20 | 2 | no | — |
| 346 | C22 | — | 20 | 4 | no | — |
| 347 | C22 | — | 20 | 2 | no | — |
| 348 | C22 | — | 20 | 2 | no | — |
| 349 | C22 | — | 20 | 1 | no | — |
| 350 | C22 | — | 40 | 1 | no | — |
| 351 | C22 | #4028 | 1 | 1 | yes | characteristic |
| 352 | C22 | #4028 | 1 | 1 | yes | characteristic |
| 353 | C22 | #4030 | 1 | 1 | yes | characteristic |
| 354 | C22 | #4030 | 1 | 1 | yes | characteristic |
| 355 | C22 | #4076 | 1 | 1 | yes | characteristic |
| 356 | C22 | #4083 | 1 | 1 | yes | characteristic |
| 357 | C22 | #4086 | 1 | 1 | yes | characteristic |
| 358 | C4 | — | 4 | 2 | no | — |
| 359 | C4 | — | 4 | 1 | no | — |
| 360 | C4 | — | 8 | 1 | no | — |
| 361 | C4 | — | 20 | 2 | no | — |
| 362 | C4 | — | 20 | 2 | no | — |
| 363 | C4 | — | 20 | 1 | no | — |
| 364 | C2 | — | 2 | 1 | no | — |
| 365 | C2 | — | 2 | 1 | no | — |
| 366 | C2 | — | 2 | 1 | no | — |
| 367 | C2 | — | 2 | 1 | no | — |
| 368 | C2 | — | 2 | 1 | no | — |
| 369 | C2 | — | 2 | 1 | no | — |
| 370 | C2 | — | 8 | 1 | no | — |
| 371 | C2 | — | 20 | 4 | no | — |
| 372 | C2 | — | 40 | 1 | no | — |
| 373 | C2 | #65030 | 1 | 2 | yes | — |
| 374 | C2 | #65249 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #4028 |
| commutator, cosocle | C24×C5 | C23 |
| Frattini | C24 | C22×D5 |
| Fitting | C2×C5×#99 | C2 |
| socle | C22×C5 | #120 |
| hypercenter | C2×#99 | D5 |
| hypocenter | C5 | #2021 |
| LCS | G ▷ C24×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C2×#99 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #66138 | C2 | semidirect |
| 2. C2×#4083 | C2 | semidirect |
| 3. C2×#4028 | C2 | semidirect |
| 4. C2×C5×#99 | C2 | semidirect |
| 5. #65244 | C2 | semidirect |
| 6. C2×#3938 | C2 | semidirect |
| 7. #64747 | C2 | semidirect |
| 32. C24×C5 | D4 | semidirect |
| 41. C23×D5 | D4 | semidirect |
| 42. C23×D5 | D4 | semidirect |
| 51. C22×C4×C5 | D4 | semidirect |
| 62. C22×Dic5 | D4 | semidirect |
| 63. C22×Dic5 | D4 | semidirect |
| 69. C5×C22⋊C4 | D4 | semidirect |
| 74. C22⋊Dic5 | D4 | semidirect |
| 84. C2×#99 | D5 | semidirect |
| 216. C24 | D20 | semidirect |
| 240. C22×C4 | D20 | semidirect |
| 254. C22⋊C4 | C22⋊D5 | semidirect |
| 324. C5 | #2021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66138 | 2 |
| C2×#4083 | 2 |
| C2×#4028 | 2 |
| C2×C5×#99 | 2 |
| #65244 | 2 |
| C2×#3938 | 2 |
| #64747 | 2 |
| #2021 | 5 |