← D5⋊#2171 #13043553
Subgroups — D5⋊#2171 #13043553
Order 1280.
654 conjugacy classes of subgroups.
The subgroup lattice has 380 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D5⋊#504 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | D5×#443 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10604862 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | D5⋊#350 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10604084 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10604000 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | D5⋊#364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10603823 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | D5×#135 | C4 | 1 | 1 | yes | characteristic |
| 10 | D5×#131 | C22 | 1 | 2 | yes | — |
| 11 | #65791 | C22 | 1 | 4 | yes | complemented |
| 12 | #65725 | — | 2 | 4 | no | — |
| 13 | #65725 | C22 | 1 | 4 | yes | complemented |
| 14 | D5⋊M32 | — | 2 | 2 | no | — |
| 15 | D5⋊M32 | C22 | 1 | 2 | yes | — |
| 16 | C2×D5⋊C16 | — | 2 | 2 | no | — |
| 17 | C2×D5⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×D5⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 19 | C5×#443 | C4 | 1 | 1 | yes | characteristic |
| 20 | #65485 | C22 | 1 | 1 | yes | characteristic |
| 21 | #65433 | C4 | 1 | 2 | yes | — |
| 22 | #65184 | C22 | 1 | 1 | yes | characteristic |
| 23 | D5×#108 | C4 | 1 | 1 | yes | characteristic |
| 24 | #65113 | C22 | 1 | 2 | yes | — |
| 25 | D5×#104 | C4 | 1 | 2 | yes | — |
| 26 | #64989 | C4 | 1 | 1 | yes | characteristic |
| 27 | C4×C8×D5 | C22 | 1 | 1 | yes | characteristic |
| 28 | #64932 | C22 | 1 | 4 | yes | complemented |
| 29 | #64898 | C22 | 1 | 4 | yes | complemented |
| 30 | #64889 | C22 | 1 | 2 | yes | complemented |
| 31 | #64886 | C22 | 1 | 2 | yes | complemented |
| 32 | #64861 | C22 | 1 | 2 | yes | complemented |
| 33 | #64859 | C22 | 1 | 2 | yes | complemented |
| 34 | C2×#2171 | — | 5 | 1 | no | maximal, Sylow |
| 35 | D5×#41 | C2×C4 | 1 | 2 | yes | — |
| 36 | C5×#135 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C5×#131 | C2×C4 | 1 | 2 | yes | — |
| 38 | #4096 | C2×C4 | 1 | 2 | yes | — |
| 39 | #4094 | C23 | 1 | 2 | yes | — |
| 40 | #4065 | C8 | 1 | 1 | yes | characteristic |
| 41 | D5×Q16 | C8 | 1 | 1 | yes | characteristic |
| 42 | #4062 | C8 | 1 | 2 | yes | — |
| 43 | D5×SD16 | C8 | 1 | 2 | yes | — |
| 44 | #4058 | C8 | 1 | 1 | yes | characteristic |
| 45 | D5×D8 | C8 | 1 | 1 | yes | characteristic |
| 46 | #4053 | — | 2 | 2 | no | — |
| 47 | #4053 | C23 | 1 | 2 | yes | — |
| 48 | D5×M16 | — | 2 | 2 | no | — |
| 49 | D5×M16 | C2×C4 | 1 | 2 | yes | — |
| 50 | #4050 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | #4047 | — | 2 | 2 | no | — |
| 52 | #4047 | C2×C4 | 1 | 2 | yes | — |
| 53 | C2×C8×D5 | — | 2 | 2 | no | — |
| 54 | C2×C8×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 56 | C42×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | #3998 | — | 2 | 4 | no | — |
| 58 | #3998 | C23 | 1 | 4 | yes | — |
| 59 | C2×#674 | — | 2 | 4 | no | — |
| 60 | C2×#674 | C23 | 1 | 2 | yes | — |
| 61 | C2×#674 | C23 | 1 | 2 | yes | — |
| 62 | #3990 | — | 2 | 2 | no | — |
| 63 | #3990 | — | 2 | 4 | no | — |
| 64 | D5⋊C16 | — | 2 | 2 | no | — |
| 65 | D5⋊C16 | — | 2 | 1 | no | — |
| 66 | D5⋊C16 | — | 2 | 1 | no | — |
| 67 | D5⋊C16 | — | 2 | 4 | no | — |
| 68 | D5⋊C16 | D4 | 1 | 2 | yes | — |
| 69 | D5⋊C16 | D4 | 1 | 2 | yes | — |
| 70 | C5×#108 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | C5×#104 | C2×C4 | 1 | 2 | yes | — |
| 72 | C4×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | #3969 | C2×C4 | 1 | 2 | yes | — |
| 74 | #3957 | C2×C4 | 1 | 2 | yes | — |
| 75 | #3954 | C2×C4 | 1 | 2 | yes | — |
| 76 | #3951 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | C8×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | C8×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 79 | #3937 | C2×C4 | 1 | 2 | yes | — |
| 80 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×#504 | — | 5 | 2 | no | — |
| 82 | C2×#443 | — | 5 | 1 | no | — |
| 83 | #2171 | — | 5 | 2 | no | — |
| 84 | #2171 | — | 5 | 2 | no | — |
| 85 | #2171 | — | 5 | 4 | no | — |
| 86 | C2×#364 | — | 5 | 1 | no | — |
| 87 | C2×#350 | — | 5 | 2 | no | — |
| 88 | C2×#346 | — | 5 | 1 | no | — |
| 89 | C5×#41 | C22×C4 | 1 | 2 | yes | — |
| 90 | #713 | C2×C8 | 1 | 2 | yes | — |
| 91 | Q8×D5 | C2×C8 | 1 | 2 | yes | — |
| 92 | #711 | — | 2 | 2 | no | — |
| 93 | #711 | C2×C8 | 1 | 2 | yes | — |
| 94 | D4×D5 | — | 2 | 2 | no | — |
| 95 | D4×D5 | C2×C8 | 1 | 2 | yes | — |
| 96 | #709 | — | 2 | 2 | no | — |
| 97 | #709 | C22×C4 | 1 | 2 | yes | — |
| 98 | C2×C4×D5 | — | 2 | 2 | no | — |
| 99 | C2×C4×D5 | — | 2 | 1 | no | — |
| 100 | C2×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | C5×Q16 | C2×C8 | 1 | 1 | yes | characteristic |
| 102 | C5×SD16 | C2×C8 | 1 | 2 | yes | — |
| 103 | C5×D8 | C2×C8 | 1 | 1 | yes | characteristic |
| 104 | C5×M16 | — | 2 | 2 | no | — |
| 105 | C5×M16 | C22×C4 | 1 | 2 | yes | — |
| 106 | C2×C5×C8 | — | 2 | 2 | no | — |
| 107 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 108 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 109 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 110 | #689 | C2×C8 | 1 | 2 | yes | — |
| 111 | #688 | C2×C8 | 1 | 2 | yes | — |
| 112 | #687 | C2×C8 | 1 | 2 | yes | — |
| 113 | #686 | C2×C8 | 1 | 2 | yes | — |
| 114 | C4×Dic5 | — | 2 | 1 | no | — |
| 115 | C4×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | #681 | — | 2 | 2 | no | — |
| 117 | #681 | C22×C4 | 1 | 2 | yes | — |
| 118 | C2×#168 | — | 2 | 2 | no | — |
| 119 | C2×#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 120 | C2×#168 | C24 | 1 | 1 | yes | characteristic |
| 121 | Dic20 | C2×C8 | 1 | 1 | yes | characteristic |
| 122 | D40 | C2×C8 | 1 | 1 | yes | characteristic |
| 123 | #677 | C2×C8 | 1 | 2 | yes | — |
| 124 | #676 | — | 2 | 2 | no | — |
| 125 | #676 | — | 2 | 2 | no | — |
| 126 | #676 | — | 2 | 2 | no | — |
| 127 | C8×D5 | — | 2 | 2 | no | — |
| 128 | C8×D5 | — | 2 | 2 | no | — |
| 129 | C8×D5 | — | 2 | 2 | no | — |
| 130 | C8×D5 | C2×C8 | 1 | 1 | yes | characteristic |
| 131 | C8×D5 | C2×C8 | 1 | 1 | yes | characteristic |
| 132 | C8×D5 | C2×C8 | 1 | 1 | yes | characteristic |
| 133 | C8×D5 | C2×C8 | 1 | 1 | yes | characteristic |
| 134 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C8×D5 | #41 | 1 | 1 | yes | characteristic |
| 137 | C8×D5 | #41 | 1 | 1 | yes | characteristic |
| 138 | #674 | — | 2 | 4 | no | — |
| 139 | #674 | — | 2 | 2 | no | — |
| 140 | #674 | C2×D4 | 1 | 4 | yes | — |
| 141 | C2×#135 | — | 5 | 1 | no | — |
| 142 | C2×#131 | — | 5 | 2 | no | — |
| 143 | #504 | — | 5 | 4 | no | — |
| 144 | #504 | — | 5 | 4 | no | — |
| 145 | #504 | — | 10 | 4 | no | — |
| 146 | C2×M32 | — | 5 | 2 | no | — |
| 147 | C2×M32 | — | 10 | 2 | no | — |
| 148 | C22×C16 | — | 5 | 1 | no | — |
| 149 | C22×C16 | — | 5 | 1 | no | — |
| 150 | C22×C16 | — | 10 | 2 | no | — |
| 151 | #443 | — | 5 | 1 | no | — |
| 152 | #443 | — | 5 | 2 | no | — |
| 153 | #443 | — | 5 | 1 | no | — |
| 154 | #443 | — | 5 | 2 | no | — |
| 155 | #443 | — | 5 | 1 | no | — |
| 156 | #443 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 157 | C2×#108 | — | 5 | 1 | no | — |
| 158 | C2×#104 | — | 5 | 2 | no | — |
| 159 | C2×C4×C8 | — | 5 | 1 | no | — |
| 160 | #364 | — | 5 | 2 | no | — |
| 161 | #364 | — | 5 | 2 | no | — |
| 162 | #350 | — | 5 | 4 | no | — |
| 163 | #350 | — | 5 | 4 | no | — |
| 164 | #346 | — | 5 | 2 | no | — |
| 165 | #346 | — | 5 | 2 | no | — |
| 166 | C22×D5 | — | 2 | 2 | no | — |
| 167 | C22×D5 | #131 | 1 | 1 | yes | characteristic |
| 168 | C5×Q8 | C22×C8 | 1 | 2 | yes | — |
| 169 | C5×D4 | — | 2 | 2 | no | — |
| 170 | C5×D4 | C22×C8 | 1 | 2 | yes | — |
| 171 | C2×C4×C5 | — | 2 | 2 | no | — |
| 172 | C2×C4×C5 | — | 2 | 1 | no | — |
| 173 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 174 | C22⋊D5 | — | 2 | 2 | no | — |
| 175 | C22⋊D5 | — | 2 | 2 | no | — |
| 176 | C22⋊D5 | — | 2 | 2 | no | — |
| 177 | C2×Dic5 | — | 2 | 2 | no | — |
| 178 | C2×Dic5 | — | 2 | 1 | no | — |
| 179 | C2×Dic5 | #131 | 1 | 1 | yes | characteristic |
| 180 | D20 | — | 2 | 2 | no | — |
| 181 | D20 | C22×C8 | 1 | 2 | yes | — |
| 182 | C4×D5 | — | 2 | 2 | no | — |
| 183 | C4×D5 | — | 2 | 2 | no | — |
| 184 | C4×D5 | — | 2 | 2 | no | — |
| 185 | C4×D5 | — | 4 | 2 | no | — |
| 186 | C4×D5 | C4×D4 | 1 | 1 | yes | characteristic |
| 187 | C4×D5 | C4×D4 | 1 | 1 | yes | characteristic |
| 188 | C4×D5 | C22×C8 | 1 | 1 | yes | characteristic |
| 189 | C4×D5 | C22×C8 | 1 | 1 | yes | characteristic |
| 190 | Dic10 | — | 2 | 2 | no | — |
| 191 | Dic10 | C22×C8 | 1 | 2 | yes | — |
| 192 | C5×C8 | — | 2 | 2 | no | — |
| 193 | C5×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 194 | C5×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 195 | C5×C8 | C22×C8 | 1 | 1 | yes | characteristic |
| 196 | C5×C8 | C22×C8 | 1 | 1 | yes | characteristic |
| 197 | #168 | — | 2 | 2 | no | — |
| 198 | #168 | C22×C8 | 1 | 1 | yes | characteristic |
| 199 | #168 | C22×C8 | 1 | 1 | yes | characteristic |
| 200 | #168 | C22×D4 | 1 | 1 | yes | characteristic |
| 201 | #168 | C2×#41 | 1 | 1 | yes | characteristic |
| 202 | C2×#41 | — | 5 | 2 | no | — |
| 203 | #135 | — | 5 | 2 | no | — |
| 204 | #135 | — | 5 | 1 | no | — |
| 205 | #135 | — | 5 | 2 | no | — |
| 206 | #135 | — | 5 | 1 | no | — |
| 207 | #135 | — | 5 | 1 | no | — |
| 208 | #135 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 209 | C2×Q16 | — | 5 | 1 | no | — |
| 210 | C2×SD16 | — | 5 | 2 | no | — |
| 211 | C2×D8 | — | 5 | 1 | no | — |
| 212 | #131 | — | 5 | 2 | no | — |
| 213 | #131 | — | 5 | 2 | no | — |
| 214 | #131 | — | 5 | 2 | no | — |
| 215 | #131 | — | 10 | 2 | no | — |
| 216 | #131 | — | 10 | 2 | no | — |
| 217 | #131 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 218 | C2×M16 | — | 5 | 2 | no | — |
| 219 | C2×M16 | — | 10 | 2 | no | — |
| 220 | C22×C8 | — | 5 | 1 | no | — |
| 221 | C22×C8 | — | 5 | 1 | no | — |
| 222 | C22×C8 | — | 10 | 2 | no | — |
| 223 | C2×C42 | — | 5 | 1 | no | — |
| 224 | M32 | — | 5 | 4 | no | — |
| 225 | M32 | — | 10 | 4 | no | — |
| 226 | M32 | — | 10 | 4 | no | — |
| 227 | M32 | — | 10 | 2 | no | — |
| 228 | C2×C16 | — | 5 | 2 | no | — |
| 229 | C2×C16 | — | 5 | 2 | no | — |
| 230 | C2×C16 | — | 5 | 2 | no | — |
| 231 | C2×C16 | — | 5 | 2 | no | — |
| 232 | C2×C16 | — | 10 | 4 | no | — |
| 233 | C2×C16 | — | 10 | 4 | no | — |
| 234 | C2×C16 | — | 10 | 1 | no | — |
| 235 | C2×C16 | — | 10 | 1 | no | — |
| 236 | C2×C16 | — | 10 | 2 | no | — |
| 237 | #108 | — | 5 | 2 | no | — |
| 238 | #108 | — | 5 | 1 | no | — |
| 239 | #108 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 240 | #104 | — | 5 | 2 | no | — |
| 241 | #104 | — | 5 | 2 | no | — |
| 242 | #104 | — | 5 | 2 | no | — |
| 243 | #104 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 244 | C4×C8 | — | 5 | 1 | no | — |
| 245 | C4×C8 | — | 5 | 1 | no | — |
| 246 | C4×C8 | — | 5 | 1 | no | — |
| 247 | C4×C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 248 | C22×C5 | — | 2 | 2 | no | — |
| 249 | C22×C5 | C2×#131 | 1 | 1 | yes | characteristic |
| 250 | C2×D5 | — | 2 | 2 | no | — |
| 251 | C2×D5 | — | 2 | 2 | no | — |
| 252 | C2×D5 | — | 4 | 4 | no | — |
| 253 | C2×D5 | C8×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×D5 | C8×D4 | 1 | 1 | yes | characteristic |
| 255 | C4×C5 | — | 2 | 2 | no | — |
| 256 | C4×C5 | — | 4 | 1 | no | — |
| 257 | C4×C5 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 258 | C4×C5 | C23×C8 | 1 | 1 | yes | characteristic |
| 259 | Dic5 | — | 2 | 2 | no | — |
| 260 | Dic5 | — | 4 | 1 | no | — |
| 261 | Dic5 | C8×D4 | 1 | 1 | yes | characteristic |
| 262 | Dic5 | C8×D4 | 1 | 1 | yes | characteristic |
| 263 | #41 | — | 5 | 2 | no | — |
| 264 | #41 | — | 5 | 2 | no | — |
| 265 | #41 | — | 5 | 2 | no | — |
| 266 | #41 | — | 10 | 2 | no | — |
| 267 | #41 | — | 10 | 2 | no | — |
| 268 | #41 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 269 | C2×Q8 | — | 5 | 2 | no | — |
| 270 | C2×D4 | — | 5 | 2 | no | — |
| 271 | C2×D4 | — | 10 | 2 | no | — |
| 272 | C22×C4 | — | 5 | 1 | no | — |
| 273 | C22×C4 | — | 10 | 2 | no | — |
| 274 | C22×C4 | — | 10 | 1 | no | — |
| 275 | Q16 | — | 5 | 2 | no | — |
| 276 | Q16 | — | 5 | 1 | no | — |
| 277 | Q16 | D5⋊C8 | 1 | 1 | yes | characteristic |
| 278 | SD16 | — | 5 | 2 | no | — |
| 279 | SD16 | — | 5 | 2 | no | — |
| 280 | SD16 | — | 5 | 2 | no | — |
| 281 | SD16 | D5⋊C8 | 1 | 2 | yes | — |
| 282 | D8 | — | 5 | 2 | no | — |
| 283 | D8 | — | 5 | 1 | no | — |
| 284 | D8 | D5⋊C8 | 1 | 1 | yes | characteristic |
| 285 | M16 | — | 2 | 2 | no | — |
| 286 | M16 | — | 5 | 2 | no | — |
| 287 | M16 | — | 10 | 2 | no | — |
| 288 | M16 | — | 10 | 2 | no | — |
| 289 | M16 | — | 10 | 2 | no | — |
| 290 | M16 | — | 10 | 2 | no | — |
| 291 | M16 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 292 | C2×C8 | — | 2 | 2 | no | — |
| 293 | C2×C8 | — | 5 | 1 | no | — |
| 294 | C2×C8 | — | 5 | 1 | no | — |
| 295 | C2×C8 | — | 5 | 1 | no | — |
| 296 | C2×C8 | — | 5 | 1 | no | — |
| 297 | C2×C8 | — | 5 | 1 | no | — |
| 298 | C2×C8 | — | 5 | 1 | no | — |
| 299 | C2×C8 | — | 5 | 1 | no | — |
| 300 | C2×C8 | — | 5 | 1 | no | — |
| 301 | C2×C8 | — | 5 | 1 | no | — |
| 302 | C2×C8 | — | 5 | 1 | no | — |
| 303 | C2×C8 | — | 10 | 2 | no | — |
| 304 | C2×C8 | — | 10 | 2 | no | — |
| 305 | C2×C8 | — | 10 | 2 | no | — |
| 306 | C2×C8 | — | 10 | 2 | no | — |
| 307 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 308 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 309 | C42 | — | 5 | 1 | no | — |
| 310 | C42 | — | 10 | 1 | no | — |
| 311 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 312 | C16 | — | 5 | 4 | no | — |
| 313 | C16 | — | 10 | 2 | no | — |
| 314 | C16 | — | 10 | 4 | no | — |
| 315 | C2×C5 | — | 2 | 1 | no | — |
| 316 | C2×C5 | — | 4 | 2 | no | — |
| 317 | C2×C5 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 318 | D5 | — | 2 | 1 | no | — |
| 319 | D5 | — | 4 | 2 | no | — |
| 320 | D5 | #2171 | 1 | 2 | yes | complemented |
| 321 | C23 | — | 5 | 1 | no | — |
| 322 | C23 | — | 10 | 2 | no | — |
| 323 | Q8 | — | 5 | 2 | no | — |
| 324 | Q8 | — | 10 | 2 | no | — |
| 325 | Q8 | C2×D5⋊C8 | 1 | 2 | yes | — |
| 326 | D4 | — | 2 | 2 | no | — |
| 327 | D4 | — | 5 | 2 | no | — |
| 328 | D4 | — | 10 | 2 | no | — |
| 329 | D4 | — | 10 | 2 | no | — |
| 330 | D4 | — | 10 | 2 | no | — |
| 331 | D4 | — | 10 | 2 | no | — |
| 332 | D4 | C2×D5⋊C8 | 1 | 2 | yes | — |
| 333 | C2×C4 | — | 2 | 2 | no | — |
| 334 | C2×C4 | — | 2 | 1 | no | — |
| 335 | C2×C4 | — | 5 | 1 | no | — |
| 336 | C2×C4 | — | 5 | 1 | no | — |
| 337 | C2×C4 | — | 5 | 1 | no | — |
| 338 | C2×C4 | — | 5 | 1 | no | — |
| 339 | C2×C4 | — | 5 | 1 | no | — |
| 340 | C2×C4 | — | 10 | 2 | no | — |
| 341 | C2×C4 | — | 10 | 2 | no | — |
| 342 | C2×C4 | — | 10 | 2 | no | — |
| 343 | C2×C4 | — | 10 | 2 | no | — |
| 344 | C2×C4 | — | 10 | 1 | no | — |
| 345 | C2×C4 | — | 20 | 2 | no | — |
| 346 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 347 | C8 | — | 2 | 2 | no | — |
| 348 | C8 | — | 5 | 1 | no | — |
| 349 | C8 | — | 5 | 1 | no | — |
| 350 | C8 | — | 5 | 1 | no | — |
| 351 | C8 | — | 5 | 1 | no | — |
| 352 | C8 | — | 10 | 2 | no | — |
| 353 | C8 | C2×D5⋊C8 | 1 | 1 | yes | characteristic |
| 354 | C8 | C2×D5⋊C8 | 1 | 1 | yes | characteristic |
| 355 | C8 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 356 | C8 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 357 | C5 | C2×#2171 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 358 | C22 | — | 2 | 2 | no | — |
| 359 | C22 | — | 5 | 1 | no | — |
| 360 | C22 | — | 5 | 1 | no | — |
| 361 | C22 | — | 10 | 2 | no | — |
| 362 | C22 | — | 10 | 2 | no | — |
| 363 | C22 | — | 20 | 4 | no | — |
| 364 | C22 | D5⋊#131 | 1 | 1 | yes | characteristic |
| 365 | C4 | — | 2 | 2 | no | — |
| 366 | C4 | — | 4 | 1 | no | — |
| 367 | C4 | — | 5 | 1 | no | — |
| 368 | C4 | — | 5 | 1 | no | — |
| 369 | C4 | — | 10 | 2 | no | — |
| 370 | C4 | — | 20 | 1 | no | — |
| 371 | C4 | C22×D5⋊C8 | 1 | 1 | yes | characteristic |
| 372 | C4 | C2×D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 373 | C2 | — | 2 | 1 | no | — |
| 374 | C2 | — | 4 | 2 | no | — |
| 375 | C2 | — | 5 | 2 | no | — |
| 376 | C2 | — | 10 | 1 | no | — |
| 377 | C2 | — | 20 | 2 | no | — |
| 378 | C2 | D4×D5⋊C8 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta