← #72242619
Subgroups — #72242619
Order 3200.
1282 conjugacy classes of subgroups.
The subgroup lattice has 558 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11717356 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#11717355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13105723 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C4⋊C4×#1044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13104724 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13104006 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13103995 | C2 | 1 | 2 | yes | maximal |
| 8 | #13103994 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #13103990 | C2 | 1 | 2 | yes | maximal |
| 10 | #13103979 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #13103880 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×C4×D52 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#87872 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C4⋊#1044 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C4×#1044 | C22 | 1 | 2 | yes | — |
| 16 | C2×C4×#1044 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4⋊#1043 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C4⋊#1043 | C22 | 1 | 2 | yes | — |
| 19 | C2×C4×#1043 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#87832 | C22 | 1 | 2 | yes | — |
| 21 | C2×#87832 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#87832 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#87831 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#87831 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#87831 | C22 | 1 | 2 | yes | — |
| 26 | C2×#87830 | C22 | 1 | 2 | yes | — |
| 27 | #11717356 | — | 2 | 4 | no | — |
| 28 | #11717355 | — | 2 | 4 | no | — |
| 29 | C4⋊C4×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 30 | C5×#4043 | C4 | 1 | 2 | yes | complemented |
| 31 | #11717039 | C22 | 1 | 2 | yes | — |
| 32 | #11717018 | C22 | 1 | 2 | yes | — |
| 33 | #11717014 | C4 | 1 | 4 | yes | complemented |
| 34 | #11716974 | C4 | 1 | 2 | yes | complemented |
| 35 | #11716899 | C22 | 1 | 2 | yes | — |
| 36 | #11716874 | C22 | 1 | 2 | yes | — |
| 37 | #11716776 | C22 | 1 | 2 | yes | — |
| 38 | #11716776 | C22 | 1 | 2 | yes | — |
| 39 | #11716776 | C22 | 1 | 2 | yes | — |
| 40 | #10617282 | — | 5 | 2 | no | maximal |
| 41 | C22×D52 | C23 | 1 | 1 | yes | characteristic |
| 42 | C22×#1044 | C23 | 1 | 2 | yes | — |
| 43 | C22×#1044 | C23 | 1 | 1 | yes | characteristic |
| 44 | C22×#1044 | C23 | 1 | 1 | yes | characteristic |
| 45 | C22×#1043 | C23 | 1 | 1 | yes | characteristic |
| 46 | C22×#1043 | C23 | 1 | 2 | yes | — |
| 47 | C22×#1043 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×C4×C5⋊D5 | C23 | 1 | 2 | yes | — |
| 49 | C2×C4×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C4×C5×D5 | C2×C4 | 1 | 2 | yes | — |
| 51 | C2×C5×Dic10 | C2×C4 | 1 | 2 | yes | — |
| 52 | C2×#6039 | C2×C4 | 1 | 2 | yes | — |
| 53 | C2×#6036 | C23 | 1 | 2 | yes | — |
| 54 | C2×#6036 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×D5×Dic5 | C2×C4 | 1 | 2 | yes | — |
| 56 | C4×D52 | — | 2 | 2 | no | — |
| 57 | C4×D52 | — | 2 | 2 | no | — |
| 58 | #87872 | — | 2 | 2 | no | — |
| 59 | #87872 | — | 2 | 2 | no | — |
| 60 | C4⋊#1044 | — | 2 | 2 | no | — |
| 61 | C4×#1044 | — | 4 | 2 | no | — |
| 62 | C4×#1044 | D4 | 1 | 4 | yes | — |
| 63 | C4⋊#1043 | — | 2 | 2 | no | — |
| 64 | C4⋊#1043 | — | 4 | 2 | no | — |
| 65 | C4×#1043 | — | 2 | 2 | no | — |
| 66 | #87832 | — | 2 | 4 | no | — |
| 67 | #87832 | — | 2 | 2 | no | — |
| 68 | #87832 | — | 2 | 2 | no | — |
| 69 | #87831 | — | 2 | 2 | no | — |
| 70 | #87831 | — | 2 | 2 | no | — |
| 71 | #87831 | — | 4 | 2 | no | — |
| 72 | #87830 | — | 2 | 4 | no | — |
| 73 | C52×C4⋊C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | C4⋊#1039 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | #87806 | C2×C4 | 1 | 2 | yes | — |
| 76 | C5×#685 | C2×C4 | 1 | 4 | yes | — |
| 77 | C5×C4⋊Dic5 | C2×C4 | 1 | 4 | yes | — |
| 78 | #87781 | C2×C4 | 1 | 4 | yes | — |
| 79 | #87778 | C2×C4 | 1 | 4 | yes | — |
| 80 | C2×Q8×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 81 | C2×#4130 | — | 5 | 2 | no | — |
| 82 | D5×C22⋊Q8 | — | 5 | 2 | no | — |
| 83 | (C2×AGL(1,𝔽5))⋊Q8 | — | 5 | 2 | no | — |
| 84 | #65765 | — | 5 | 2 | no | — |
| 85 | #65712 | — | 5 | 2 | no | — |
| 86 | #65712 | — | 5 | 4 | no | — |
| 87 | #65712 | — | 10 | 2 | no | — |
| 88 | #65711 | — | 5 | 4 | no | — |
| 89 | C4⋊C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 90 | #65700 | — | 5 | 4 | no | — |
| 91 | #65700 | — | 5 | 4 | no | — |
| 92 | C22×C5⋊D5 | C24 | 1 | 1 | yes | characteristic |
| 93 | C22×C5×D5 | C22×C4 | 1 | 2 | yes | — |
| 94 | C2×D52 | — | 2 | 1 | no | — |
| 95 | C2×D52 | — | 2 | 1 | no | — |
| 96 | C2×D52 | — | 2 | 1 | no | — |
| 97 | C2×D52 | — | 2 | 1 | no | — |
| 98 | C2×D52 | — | 2 | 1 | no | — |
| 99 | C2×D52 | — | 2 | 1 | no | — |
| 100 | C2×#1044 | — | 2 | 1 | no | — |
| 101 | C2×#1044 | — | 2 | 1 | no | — |
| 102 | C2×#1044 | — | 2 | 1 | no | — |
| 103 | C2×#1044 | — | 2 | 1 | no | — |
| 104 | C2×#1044 | — | 2 | 2 | no | — |
| 105 | C2×#1044 | — | 2 | 2 | no | — |
| 106 | C2×#1044 | — | 2 | 2 | no | — |
| 107 | C2×#1044 | C2×D4 | 1 | 2 | yes | — |
| 108 | C2×#1044 | C2×D4 | 1 | 2 | yes | — |
| 109 | C2×#1043 | — | 2 | 2 | no | — |
| 110 | C2×#1043 | — | 2 | 1 | no | — |
| 111 | C2×#1043 | — | 2 | 1 | no | — |
| 112 | C2×#1043 | — | 2 | 1 | no | — |
| 113 | C2×#1043 | — | 2 | 2 | no | — |
| 114 | C2×#1043 | — | 2 | 1 | no | — |
| 115 | C2×#1043 | — | 2 | 1 | no | — |
| 116 | C2×#1043 | — | 2 | 1 | no | — |
| 117 | C2×#1043 | — | 2 | 2 | no | — |
| 118 | C2×C4×C52 | C22×C4 | 1 | 2 | yes | — |
| 119 | C2×C4×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 120 | C2×#1039 | C22×C4 | 1 | 2 | yes | — |
| 121 | C2×#1039 | C22×C4 | 1 | 1 | yes | characteristic |
| 122 | C4×C5⋊D5 | — | 2 | 2 | no | — |
| 123 | C4×C5⋊D5 | — | 2 | 2 | no | — |
| 124 | C4×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 125 | C4×C5⋊D5 | #41 | 1 | 2 | yes | — |
| 126 | C2×C5×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 127 | C2×C5×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 128 | C4×C5×D5 | — | 2 | 4 | no | — |
| 129 | C5×Dic10 | — | 2 | 4 | no | — |
| 130 | #6039 | — | 2 | 4 | no | — |
| 131 | #6036 | — | 2 | 2 | no | — |
| 132 | #6036 | — | 2 | 1 | no | — |
| 133 | #6036 | — | 2 | 2 | no | — |
| 134 | #6036 | — | 2 | 1 | no | — |
| 135 | D5×Dic5 | — | 2 | 4 | no | — |
| 136 | C2×Q8×D5 | — | 5 | 2 | no | — |
| 137 | C22×C4×D5 | — | 5 | 2 | no | — |
| 138 | C2×C22⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 139 | C2×C22⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 140 | C2×C22⋊AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 141 | Q8×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 142 | #4130 | — | 10 | 8 | no | — |
| 143 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 144 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 145 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 146 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 147 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 148 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 149 | C2×C4⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 150 | C2×C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 151 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 152 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 153 | C2×C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 154 | C2×C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 155 | C2×C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 156 | C5×C22⋊Q8 | — | 5 | 2 | no | — |
| 157 | #4092 | — | 5 | 2 | no | — |
| 158 | #4070 | — | 5 | 2 | no | — |
| 159 | #4043 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 160 | #4042 | — | 5 | 4 | no | — |
| 161 | D5×C4⋊C4 | — | 5 | 2 | no | — |
| 162 | D5×C4⋊C4 | — | 5 | 4 | no | — |
| 163 | D5×C4⋊C4 | — | 10 | 2 | no | — |
| 164 | D5×C22⋊C4 | — | 5 | 4 | no | — |
| 165 | #4024 | — | 5 | 4 | no | — |
| 166 | (C2×AGL(1,𝔽5))⋊C4 | — | 5 | 4 | no | — |
| 167 | (C2×AGL(1,𝔽5))⋊C4 | — | 5 | 4 | no | — |
| 168 | (C2×AGL(1,𝔽5))⋊C4 | — | 5 | 4 | no | — |
| 169 | (C2×AGL(1,𝔽5))⋊C4 | — | 5 | 4 | no | — |
| 170 | (C2×AGL(1,𝔽5))⋊C4 | — | 5 | 4 | no | — |
| 171 | (C2×AGL(1,𝔽5))⋊C4 | — | 10 | 4 | no | — |
| 172 | #2323 | — | 25 | 1 | no | Sylow |
| 173 | C22×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 174 | C2×C5⋊D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C5⋊D5 | C2×#41 | 1 | 1 | yes | characteristic |
| 176 | C2×C5⋊D5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 177 | C2×C5⋊D5 | 2−1+4 | 1 | 1 | yes | characteristic |
| 178 | C2×C5⋊D5 | 2−1+4 | 1 | 1 | yes | characteristic |
| 179 | C2×C5⋊D5 | 2−1+4 | 1 | 1 | yes | characteristic |
| 180 | C2×C5×D5 | — | 2 | 2 | no | — |
| 181 | C2×C5×D5 | — | 2 | 2 | no | — |
| 182 | C2×C5×D5 | — | 2 | 2 | no | — |
| 183 | D52 | — | 4 | 1 | no | — |
| 184 | D52 | — | 4 | 1 | no | — |
| 185 | D52 | — | 4 | 1 | no | — |
| 186 | D52 | — | 4 | 1 | no | — |
| 187 | #1044 | — | 2 | 2 | no | — |
| 188 | #1044 | — | 2 | 2 | no | — |
| 189 | #1044 | — | 4 | 2 | no | — |
| 190 | #1043 | — | 4 | 1 | no | — |
| 191 | #1043 | — | 4 | 1 | no | — |
| 192 | #1043 | — | 4 | 2 | no | — |
| 193 | C4×C52 | — | 2 | 2 | no | — |
| 194 | C4×C52 | C4×D4 | 1 | 2 | yes | — |
| 195 | #1039 | — | 2 | 2 | no | — |
| 196 | #1039 | C4×D4 | 1 | 2 | yes | — |
| 197 | C5×Dic5 | — | 2 | 2 | no | — |
| 198 | C5×Dic5 | — | 2 | 4 | no | — |
| 199 | C23×D5 | — | 5 | 2 | no | — |
| 200 | C22×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 201 | C22×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 202 | C22×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 203 | C22×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 204 | C22×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 205 | C22×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 206 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 207 | C22×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 208 | C22×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 209 | C2×C5×Q8 | — | 5 | 2 | no | — |
| 210 | C22×C4×C5 | — | 5 | 2 | no | — |
| 211 | C22×Dic5 | — | 5 | 2 | no | — |
| 212 | Q8×D5 | — | 10 | 4 | no | — |
| 213 | Q8×D5 | — | 10 | 4 | no | — |
| 214 | C2×C4×D5 | — | 5 | 2 | no | — |
| 215 | C2×C4×D5 | — | 5 | 2 | no | — |
| 216 | C2×C4×D5 | — | 5 | 4 | no | — |
| 217 | C2×C4×D5 | — | 5 | 4 | no | — |
| 218 | C2×C4×D5 | — | 5 | 2 | no | — |
| 219 | C2×C4×D5 | — | 10 | 2 | no | — |
| 220 | C2×C4×D5 | — | 10 | 4 | no | — |
| 221 | C2×C4×D5 | — | 10 | 4 | no | — |
| 222 | C2×C4×D5 | — | 10 | 4 | no | — |
| 223 | C2×C4×D5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 224 | C2×Dic10 | — | 5 | 4 | no | — |
| 225 | C2×Dic10 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 226 | C22⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 227 | C22⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 228 | C22⋊AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 229 | C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 230 | C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 231 | C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 232 | C4⋊AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 233 | C4⋊AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 234 | C4⋊AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 235 | C4⋊AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 236 | C4⋊AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 237 | C4⋊AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 238 | C4×AGL(1,𝔽5) | — | 5 | 8 | no | — |
| 239 | C4×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 240 | C4×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 241 | C4×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 242 | C4×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 243 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 244 | C5×C4⋊C4 | — | 5 | 4 | no | — |
| 245 | C5×C4⋊C4 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 246 | C5×C22⋊C4 | — | 5 | 4 | no | — |
| 247 | C22⋊Dic5 | — | 5 | 4 | no | — |
| 248 | #685 | — | 5 | 4 | no | — |
| 249 | #685 | C2×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 250 | C4⋊Dic5 | — | 5 | 2 | no | — |
| 251 | C4⋊Dic5 | — | 10 | 2 | no | — |
| 252 | C4⋊Dic5 | C2×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 253 | #683 | — | 5 | 4 | no | — |
| 254 | #683 | — | 5 | 4 | no | — |
| 255 | #683 | — | 5 | 4 | no | — |
| 256 | #683 | — | 10 | 4 | no | — |
| 257 | C2×C22⋊Q8 | — | 25 | 1 | no | — |
| 258 | C2×C4×Q8 | — | 25 | 1 | no | — |
| 259 | C2×#117 | — | 25 | 1 | no | — |
| 260 | #391 | — | 25 | 1 | no | — |
| 261 | #389 | — | 25 | 2 | no | — |
| 262 | #389 | — | 25 | 1 | no | — |
| 263 | #388 | — | 25 | 2 | no | — |
| 264 | #388 | — | 25 | 2 | no | — |
| 265 | #387 | — | 25 | 2 | no | — |
| 266 | #380 | — | 25 | 1 | no | — |
| 267 | C4×C4⋊C4 | — | 25 | 1 | no | — |
| 268 | C2×C52 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 269 | C2×C52 | #519 | 1 | 1 | yes | characteristic |
| 270 | C2×C52 | #520 | 1 | 1 | yes | characteristic |
| 271 | C5⋊D5 | #536 | 1 | 1 | yes | characteristic |
| 272 | C5⋊D5 | #537 | 1 | 1 | yes | characteristic |
| 273 | C5⋊D5 | #541 | 1 | 1 | yes | characteristic |
| 274 | C5⋊D5 | #542 | 1 | 1 | yes | characteristic |
| 275 | C5×D5 | — | 4 | 2 | no | — |
| 276 | C23×C5 | — | 5 | 2 | no | — |
| 277 | C22×D5 | — | 5 | 2 | no | — |
| 278 | C22×D5 | — | 10 | 2 | no | — |
| 279 | C22×D5 | — | 10 | 2 | no | — |
| 280 | C22×D5 | — | 10 | 2 | no | — |
| 281 | C22×D5 | — | 10 | 2 | no | — |
| 282 | C22×D5 | — | 10 | 2 | no | — |
| 283 | C22×D5 | — | 10 | 2 | no | — |
| 284 | C22×D5 | — | 10 | 2 | no | — |
| 285 | C22×D5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 286 | C2×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 287 | C2×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 288 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 289 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 290 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 291 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 292 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 293 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 294 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 295 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 296 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 297 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 298 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 299 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 300 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 301 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 302 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 303 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 304 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 305 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 306 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 307 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 308 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 309 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 310 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 311 | C2×AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 312 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 313 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 314 | C2×AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 315 | C5×Q8 | — | 10 | 4 | no | — |
| 316 | C2×C4×C5 | — | 2 | 2 | no | — |
| 317 | C2×C4×C5 | — | 2 | 4 | no | — |
| 318 | C2×C4×C5 | — | 5 | 2 | no | — |
| 319 | C2×C4×C5 | — | 5 | 4 | no | — |
| 320 | C2×C4×C5 | — | 10 | 4 | no | — |
| 321 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 322 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 323 | C2×Dic5 | — | 5 | 2 | no | — |
| 324 | C2×Dic5 | — | 5 | 4 | no | — |
| 325 | C2×Dic5 | — | 10 | 2 | no | — |
| 326 | C2×Dic5 | — | 10 | 4 | no | — |
| 327 | C2×Dic5 | — | 10 | 4 | no | — |
| 328 | C2×Dic5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 329 | C2×Dic5 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 330 | C4×D5 | — | 2 | 4 | no | — |
| 331 | C4×D5 | — | 5 | 4 | no | — |
| 332 | C4×D5 | — | 5 | 4 | no | — |
| 333 | C4×D5 | — | 10 | 4 | no | — |
| 334 | C4×D5 | — | 10 | 4 | no | — |
| 335 | C4×D5 | — | 10 | 4 | no | — |
| 336 | C4×D5 | — | 10 | 2 | no | — |
| 337 | C4×D5 | — | 10 | 2 | no | — |
| 338 | C4×D5 | — | 10 | 4 | no | — |
| 339 | C4×D5 | — | 10 | 4 | no | — |
| 340 | C4×D5 | — | 10 | 4 | no | — |
| 341 | C4×D5 | — | 10 | 4 | no | — |
| 342 | C4×D5 | — | 20 | 4 | no | — |
| 343 | C4×D5 | — | 20 | 4 | no | — |
| 344 | Dic10 | — | 2 | 4 | no | — |
| 345 | Dic10 | — | 10 | 8 | no | — |
| 346 | C22×Q8 | — | 25 | 1 | no | — |
| 347 | C23×C4 | — | 25 | 1 | no | — |
| 348 | C22⋊Q8 | — | 5 | 2 | no | — |
| 349 | C22⋊Q8 | — | 25 | 4 | no | — |
| 350 | C22⋊Q8 | — | 25 | 2 | no | — |
| 351 | C4×Q8 | — | 50 | 4 | no | — |
| 352 | #117 | — | 50 | 4 | no | — |
| 353 | C2×C4⋊C4 | — | 25 | 2 | no | — |
| 354 | C2×C4⋊C4 | — | 25 | 1 | no | — |
| 355 | C2×C4⋊C4 | — | 25 | 1 | no | — |
| 356 | C2×C4⋊C4 | — | 25 | 1 | no | — |
| 357 | C2×C4⋊C4 | — | 25 | 1 | no | — |
| 358 | C2×C4⋊C4 | — | 25 | 2 | no | — |
| 359 | C2×C4⋊C4 | — | 25 | 1 | no | — |
| 360 | C2×C4⋊C4 | — | 25 | 2 | no | — |
| 361 | C2×C22⋊C4 | — | 25 | 2 | no | — |
| 362 | C2×C22⋊C4 | — | 25 | 1 | no | — |
| 363 | C2×C22⋊C4 | — | 25 | 1 | no | — |
| 364 | C2×C22⋊C4 | — | 25 | 2 | no | — |
| 365 | C2×C42 | — | 25 | 1 | no | — |
| 366 | C2×C42 | — | 25 | 1 | no | — |
| 367 | C2×C42 | — | 25 | 2 | no | — |
| 368 | C2×C42 | — | 25 | 2 | no | — |
| 369 | #95 | — | 25 | 2 | no | — |
| 370 | #95 | — | 25 | 2 | no | — |
| 371 | #95 | — | 25 | 2 | no | — |
| 372 | #95 | — | 25 | 2 | no | — |
| 373 | #95 | — | 25 | 2 | no | — |
| 374 | C52 | #2323 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 375 | C22×C5 | — | 2 | 2 | no | — |
| 376 | C22×C5 | — | 10 | 2 | no | — |
| 377 | C22×C5 | — | 10 | 2 | no | — |
| 378 | C22×C5 | — | 10 | 2 | no | — |
| 379 | C22×C5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 380 | C2×D5 | — | 2 | 2 | no | — |
| 381 | C2×D5 | — | 2 | 2 | no | — |
| 382 | C2×D5 | — | 2 | 2 | no | — |
| 383 | C2×D5 | — | 5 | 2 | no | — |
| 384 | C2×D5 | — | 5 | 2 | no | — |
| 385 | C2×D5 | — | 5 | 2 | no | — |
| 386 | C2×D5 | — | 5 | 2 | no | — |
| 387 | C2×D5 | — | 5 | 2 | no | — |
| 388 | C2×D5 | — | 5 | 2 | no | — |
| 389 | C2×D5 | — | 10 | 2 | no | — |
| 390 | C2×D5 | — | 10 | 2 | no | — |
| 391 | C2×D5 | — | 10 | 2 | no | — |
| 392 | C2×D5 | — | 10 | 2 | no | — |
| 393 | C2×D5 | — | 10 | 2 | no | — |
| 394 | C2×D5 | — | 10 | 2 | no | — |
| 395 | C2×D5 | — | 20 | 2 | no | — |
| 396 | C2×D5 | — | 20 | 2 | no | — |
| 397 | C2×D5 | — | 20 | 2 | no | — |
| 398 | C2×D5 | — | 20 | 2 | no | — |
| 399 | AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 400 | AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 401 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 402 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 403 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 404 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 405 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 406 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 407 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 408 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 409 | AGL(1,𝔽5) | — | 40 | 4 | no | — |
| 410 | C4×C5 | — | 2 | 4 | no | — |
| 411 | C4×C5 | — | 2 | 4 | no | — |
| 412 | C4×C5 | — | 4 | 4 | no | — |
| 413 | C4×C5 | — | 10 | 4 | no | — |
| 414 | C4×C5 | — | 10 | 2 | no | — |
| 415 | C4×C5 | D4×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 416 | Dic5 | — | 2 | 4 | no | — |
| 417 | Dic5 | — | 2 | 2 | no | — |
| 418 | Dic5 | — | 5 | 4 | no | — |
| 419 | Dic5 | — | 10 | 4 | no | — |
| 420 | Dic5 | — | 10 | 4 | no | — |
| 421 | Dic5 | — | 20 | 4 | no | — |
| 422 | C24 | — | 25 | 1 | no | — |
| 423 | C2×Q8 | — | 5 | 2 | no | — |
| 424 | C2×Q8 | — | 25 | 2 | no | — |
| 425 | C2×Q8 | — | 50 | 2 | no | — |
| 426 | C2×Q8 | — | 50 | 2 | no | — |
| 427 | C22×C4 | — | 5 | 2 | no | — |
| 428 | C22×C4 | — | 25 | 2 | no | — |
| 429 | C22×C4 | — | 25 | 1 | no | — |
| 430 | C22×C4 | — | 25 | 2 | no | — |
| 431 | C22×C4 | — | 25 | 1 | no | — |
| 432 | C22×C4 | — | 25 | 1 | no | — |
| 433 | C22×C4 | — | 25 | 1 | no | — |
| 434 | C22×C4 | — | 25 | 2 | no | — |
| 435 | C22×C4 | — | 25 | 2 | no | — |
| 436 | C22×C4 | — | 25 | 1 | no | — |
| 437 | C22×C4 | — | 25 | 1 | no | — |
| 438 | C22×C4 | — | 25 | 2 | no | — |
| 439 | C22×C4 | — | 50 | 2 | no | — |
| 440 | C22×C4 | — | 50 | 2 | no | — |
| 441 | C4⋊C4 | — | 5 | 4 | no | — |
| 442 | C4⋊C4 | — | 25 | 4 | no | — |
| 443 | C4⋊C4 | — | 25 | 2 | no | — |
| 444 | C4⋊C4 | — | 25 | 1 | no | — |
| 445 | C4⋊C4 | — | 50 | 2 | no | — |
| 446 | C4⋊C4 | — | 50 | 2 | no | — |
| 447 | C4⋊C4 | — | 50 | 4 | no | — |
| 448 | C4⋊C4 | — | 50 | 2 | no | — |
| 449 | C4⋊C4 | — | 50 | 2 | no | — |
| 450 | C4⋊C4 | — | 100 | 2 | no | — |
| 451 | C4⋊C4 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 452 | C22⋊C4 | — | 5 | 4 | no | — |
| 453 | C22⋊C4 | — | 25 | 4 | no | — |
| 454 | C22⋊C4 | — | 50 | 2 | no | — |
| 455 | C22⋊C4 | — | 50 | 2 | no | — |
| 456 | C22⋊C4 | — | 100 | 2 | no | — |
| 457 | C42 | — | 25 | 4 | no | — |
| 458 | C42 | — | 50 | 2 | no | — |
| 459 | C42 | — | 50 | 4 | no | — |
| 460 | C42 | — | 100 | 2 | no | — |
| 461 | C2×C5 | — | 2 | 2 | no | — |
| 462 | C2×C5 | — | 2 | 2 | no | — |
| 463 | C2×C5 | — | 2 | 2 | no | — |
| 464 | C2×C5 | — | 20 | 2 | no | — |
| 465 | C2×C5 | C2×D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 466 | C2×C5 | #66262 | 1 | 2 | yes | — |
| 467 | C2×C5 | #66266 | 1 | 2 | yes | — |
| 468 | D5 | — | 4 | 2 | no | — |
| 469 | D5 | — | 5 | 2 | no | — |
| 470 | D5 | — | 5 | 2 | no | — |
| 471 | D5 | — | 5 | 2 | no | — |
| 472 | D5 | — | 5 | 2 | no | — |
| 473 | D5 | — | 10 | 2 | no | — |
| 474 | D5 | — | 10 | 2 | no | — |
| 475 | D5 | — | 10 | 2 | no | — |
| 476 | D5 | — | 10 | 2 | no | — |
| 477 | C23 | — | 5 | 2 | no | — |
| 478 | C23 | — | 25 | 1 | no | — |
| 479 | C23 | — | 50 | 1 | no | — |
| 480 | C23 | — | 50 | 1 | no | — |
| 481 | C23 | — | 50 | 1 | no | — |
| 482 | C23 | — | 50 | 1 | no | — |
| 483 | C23 | — | 50 | 1 | no | — |
| 484 | C23 | — | 50 | 1 | no | — |
| 485 | Q8 | — | 10 | 4 | no | — |
| 486 | Q8 | — | 50 | 4 | no | — |
| 487 | C2×C4 | — | 5 | 4 | no | — |
| 488 | C2×C4 | — | 5 | 2 | no | — |
| 489 | C2×C4 | — | 10 | 4 | no | — |
| 490 | C2×C4 | — | 25 | 1 | no | — |
| 491 | C2×C4 | — | 25 | 2 | no | — |
| 492 | C2×C4 | — | 25 | 2 | no | — |
| 493 | C2×C4 | — | 25 | 2 | no | — |
| 494 | C2×C4 | — | 25 | 2 | no | — |
| 495 | C2×C4 | — | 25 | 2 | no | — |
| 496 | C2×C4 | — | 50 | 2 | no | — |
| 497 | C2×C4 | — | 50 | 2 | no | — |
| 498 | C2×C4 | — | 50 | 2 | no | — |
| 499 | C2×C4 | — | 50 | 1 | no | — |
| 500 | C2×C4 | — | 50 | 1 | no | — |
| 501 | C2×C4 | — | 50 | 2 | no | — |
| 502 | C2×C4 | — | 50 | 4 | no | — |
| 503 | C2×C4 | — | 50 | 1 | no | — |
| 504 | C2×C4 | — | 50 | 1 | no | — |
| 505 | C2×C4 | — | 50 | 1 | no | — |
| 506 | C2×C4 | — | 50 | 1 | no | — |
| 507 | C2×C4 | — | 50 | 1 | no | — |
| 508 | C2×C4 | — | 50 | 1 | no | — |
| 509 | C2×C4 | — | 50 | 2 | no | — |
| 510 | C2×C4 | — | 50 | 2 | no | — |
| 511 | C2×C4 | — | 50 | 2 | no | — |
| 512 | C2×C4 | — | 50 | 2 | no | — |
| 513 | C2×C4 | — | 50 | 1 | no | — |
| 514 | C2×C4 | — | 50 | 2 | no | — |
| 515 | C2×C4 | — | 50 | 1 | no | — |
| 516 | C2×C4 | — | 50 | 1 | no | — |
| 517 | C2×C4 | — | 50 | 1 | no | — |
| 518 | C2×C4 | — | 50 | 2 | no | — |
| 519 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 520 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 521 | C5 | — | 2 | 2 | no | — |
| 522 | C5 | #10617282 | 1 | 2 | yes | complemented |
| 523 | C22 | — | 10 | 2 | no | — |
| 524 | C22 | — | 10 | 2 | no | — |
| 525 | C22 | — | 10 | 2 | no | — |
| 526 | C22 | — | 25 | 1 | no | — |
| 527 | C22 | — | 25 | 1 | no | — |
| 528 | C22 | — | 25 | 1 | no | — |
| 529 | C22 | — | 25 | 1 | no | — |
| 530 | C22 | — | 25 | 1 | no | — |
| 531 | C22 | — | 25 | 1 | no | — |
| 532 | C22 | — | 100 | 1 | no | — |
| 533 | C22 | — | 100 | 1 | no | — |
| 534 | C22 | — | 100 | 1 | no | — |
| 535 | C22 | — | 100 | 1 | no | — |
| 536 | C22 | C22×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 537 | C4 | — | 2 | 2 | no | — |
| 538 | C4 | — | 10 | 2 | no | — |
| 539 | C4 | — | 10 | 4 | no | — |
| 540 | C4 | — | 25 | 2 | no | — |
| 541 | C4 | — | 50 | 2 | no | — |
| 542 | C4 | — | 50 | 2 | no | — |
| 543 | C4 | — | 50 | 2 | no | — |
| 544 | C4 | — | 100 | 2 | no | — |
| 545 | C4 | — | 100 | 1 | no | — |
| 546 | C4 | — | 100 | 1 | no | — |
| 547 | C4 | — | 100 | 2 | no | — |
| 548 | C4 | #11717365 | 1 | 2 | yes | — |
| 549 | C2 | — | 20 | 2 | no | — |
| 550 | C2 | — | 25 | 1 | no | — |
| 551 | C2 | — | 25 | 1 | no | — |
| 552 | C2 | — | 25 | 1 | no | — |
| 553 | C2 | — | 25 | 1 | no | — |
| 554 | C2 | C2×#11717365 | 1 | 1 | yes | characteristic |
| 555 | C2 | #13107570 | 1 | 1 | yes | characteristic |
| 556 | C2 | #13107571 | 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