← #72223099
Subgroups — #72223099
Order 6400.
3416 conjugacy classes of subgroups.
The subgroup lattice has 444 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72223098 | C2 | 1 | 4 | yes | maximal |
| 2 | #72221180 | C2 | 1 | 2 | yes | maximal |
| 3 | C4⋊Q8×#1043 | C2 | 1 | 2 | yes | maximal |
| 4 | C5⋊D5×#498 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72220870 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C4×#11716860 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72220668 | C2 | 1 | 4 | yes | maximal |
| 8 | C2×Q8×#1043 | — | 2 | 2 | no | — |
| 9 | C4⋊Q8×C5⋊D5 | C22 | 1 | 2 | yes | — |
| 10 | #13104802 | — | 2 | 2 | no | — |
| 11 | C2×#11716862 | C22 | 1 | 4 | yes | — |
| 12 | C2×#11716860 | C22 | 1 | 2 | yes | — |
| 13 | C2×#11716860 | C22 | 1 | 2 | yes | — |
| 14 | #13104724 | — | 2 | 2 | no | — |
| 15 | #13104724 | C22 | 1 | 4 | yes | — |
| 16 | C4⋊C4×#1043 | — | 2 | 2 | no | — |
| 17 | C4⋊C4×#1043 | C22 | 1 | 4 | yes | — |
| 18 | #13104700 | C22 | 1 | 2 | yes | — |
| 19 | C42×#1043 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×#87855 | C22 | 1 | 1 | yes | characteristic |
| 21 | C52×#498 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #13102942 | C4 | 1 | 2 | yes | complemented |
| 23 | #106×C5⋊D5 | C22 | 1 | 4 | yes | — |
| 24 | #13102717 | C4 | 1 | 4 | yes | complemented |
| 25 | C4×C8×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 26 | #13102543 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #13100253 | C22 | 1 | 8 | yes | — |
| 28 | #13036904 | — | 5 | 6 | no | maximal |
| 29 | C2×Q8×C5⋊D5 | — | 2 | 2 | no | — |
| 30 | Q8×#1043 | — | 4 | 8 | no | — |
| 31 | C2×C4⋊#1043 | — | 2 | 4 | no | — |
| 32 | C2×C4⋊#1043 | — | 2 | 2 | no | — |
| 33 | C2×C4⋊#1043 | — | 2 | 2 | no | — |
| 34 | C2×C4⋊#1043 | C23 | 1 | 4 | yes | — |
| 35 | C2×C4×#1043 | — | 2 | 4 | no | — |
| 36 | C2×C4×#1043 | D4 | 1 | 2 | yes | — |
| 37 | C2×C4×#1043 | D4 | 1 | 2 | yes | — |
| 38 | C2×C4×#1043 | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×C4×#1043 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×#87855 | C23 | 1 | 2 | yes | — |
| 41 | C52×C4⋊Q8 | C2×C4 | 1 | 2 | yes | — |
| 42 | #11717264 | — | 2 | 2 | no | — |
| 43 | C2×C8×C5⋊D5 | C23 | 1 | 2 | yes | — |
| 44 | C4⋊C4×C5⋊D5 | — | 2 | 2 | no | — |
| 45 | C4⋊C4×C5⋊D5 | C23 | 1 | 4 | yes | — |
| 46 | #11717208 | — | 2 | 2 | no | — |
| 47 | #11717208 | C2×C4 | 1 | 4 | yes | — |
| 48 | C42×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 49 | #11717189 | C2×C4 | 1 | 2 | yes | — |
| 50 | #11716874 | — | 2 | 4 | no | — |
| 51 | #11716874 | — | 2 | 4 | no | — |
| 52 | C4×#6033 | — | 2 | 2 | no | — |
| 53 | #11716862 | — | 2 | 8 | no | — |
| 54 | #11716860 | — | 2 | 4 | no | — |
| 55 | #11716860 | Q8 | 1 | 8 | yes | complemented |
| 56 | C52×#106 | C2×C4 | 1 | 4 | yes | — |
| 57 | C4×C52×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | #11716684 | C2×C4 | 1 | 4 | yes | — |
| 59 | C8×#1039 | C2×C4 | 1 | 2 | yes | — |
| 60 | #11716675 | C2×C4 | 1 | 8 | yes | — |
| 61 | C4×#6029 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | AGL(1,𝔽5)×C4⋊Q8 | — | 5 | 12 | no | — |
| 63 | D5×#498 | — | 5 | 6 | no | — |
| 64 | #10604674 | — | 5 | 12 | no | — |
| 65 | #10604052 | — | 5 | 24 | no | — |
| 66 | #10604048 | — | 5 | 24 | no | — |
| 67 | #10603848 | — | 5 | 6 | no | — |
| 68 | C4×#3992 | — | 5 | 6 | no | — |
| 69 | C22×#1043 | — | 2 | 4 | no | — |
| 70 | C22×#1043 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C22×#1043 | C2×D4 | 1 | 1 | yes | characteristic |
| 72 | C22×#1043 | C2×D4 | 1 | 2 | yes | — |
| 73 | C2×C52×Q8 | — | 2 | 2 | no | — |
| 74 | Q8×C5⋊D5 | — | 4 | 4 | no | — |
| 75 | Q8×C5⋊D5 | — | 4 | 4 | no | — |
| 76 | C2×C4×C5⋊D5 | — | 2 | 4 | no | — |
| 77 | C2×C4×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 78 | C2×C4×C5⋊D5 | C24 | 1 | 1 | yes | characteristic |
| 79 | C2×#6045 | — | 2 | 2 | no | — |
| 80 | C2×#6045 | — | 2 | 4 | no | — |
| 81 | C2×#6033 | — | 2 | 2 | no | — |
| 82 | C4⋊#1043 | — | 2 | 8 | no | — |
| 83 | C4⋊#1043 | — | 4 | 8 | no | — |
| 84 | C4⋊#1043 | — | 4 | 4 | no | — |
| 85 | C4⋊#1043 | — | 4 | 4 | no | — |
| 86 | C4×#1043 | — | 2 | 4 | no | — |
| 87 | C4×#1043 | — | 2 | 4 | no | — |
| 88 | C4×#1043 | — | 2 | 2 | no | — |
| 89 | C4×#1043 | — | 4 | 8 | no | — |
| 90 | C4×#1043 | C2×Q8 | 1 | 4 | yes | — |
| 91 | #87855 | — | 2 | 2 | no | — |
| 92 | #87855 | C2×Q8 | 1 | 4 | yes | — |
| 93 | C2×C52×C8 | C22×C4 | 1 | 2 | yes | — |
| 94 | C52×C4⋊C4 | — | 2 | 2 | no | — |
| 95 | C52×C4⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 96 | C42×C52 | C22×C4 | 1 | 1 | yes | characteristic |
| 97 | C4⋊#1039 | — | 2 | 2 | no | — |
| 98 | C4⋊#1039 | C22×C4 | 1 | 4 | yes | — |
| 99 | #87806 | — | 2 | 4 | no | — |
| 100 | #87806 | — | 2 | 4 | no | — |
| 101 | C4×#1039 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | C4×#1039 | #41 | 1 | 2 | yes | — |
| 103 | C2×#6029 | C22×C4 | 1 | 2 | yes | — |
| 104 | C8×C5⋊D5 | C2×Q8 | 1 | 4 | yes | — |
| 105 | C8×C5⋊D5 | #41 | 1 | 4 | yes | — |
| 106 | C2×Q8×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 107 | D5×C4⋊Q8 | — | 5 | 12 | no | — |
| 108 | (C2×AGL(1,𝔽5))⋊Q8 | — | 10 | 12 | no | — |
| 109 | C2×#3994 | — | 5 | 24 | no | — |
| 110 | C2×#3992 | — | 5 | 12 | no | — |
| 111 | C2×#3992 | — | 5 | 12 | no | — |
| 112 | #65712 | — | 5 | 24 | no | — |
| 113 | #65712 | — | 10 | 12 | no | — |
| 114 | C4⋊C4×AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 115 | C4⋊C4×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 116 | #65688 | — | 5 | 12 | no | — |
| 117 | C42×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 118 | C4×D5⋊C8 | — | 5 | 6 | no | — |
| 119 | C5×#498 | AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 120 | #65368 | — | 5 | 12 | no | — |
| 121 | D5×#106 | — | 5 | 24 | no | — |
| 122 | #65144 | — | 5 | 24 | no | — |
| 123 | C4×C8×D5 | — | 5 | 6 | no | — |
| 124 | #64969 | — | 5 | 6 | no | — |
| 125 | #64874 | — | 5 | 48 | no | — |
| 126 | #21727 | — | 25 | 1 | no | Sylow |
| 127 | C22×C5⋊D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 128 | C2×#1043 | — | 2 | 2 | no | — |
| 129 | C2×#1043 | — | 2 | 2 | no | — |
| 130 | C2×#1043 | — | 2 | 1 | no | — |
| 131 | C2×#1043 | — | 2 | 1 | no | — |
| 132 | C2×#1043 | — | 2 | 2 | no | — |
| 133 | C2×#1043 | — | 2 | 2 | no | — |
| 134 | C2×#1043 | — | 4 | 4 | no | — |
| 135 | C2×#1043 | — | 4 | 4 | no | — |
| 136 | C2×#1043 | — | 4 | 4 | no | — |
| 137 | C2×#1043 | C4⋊Q8 | 1 | 4 | yes | — |
| 138 | C52×Q8 | — | 4 | 4 | no | — |
| 139 | C2×C4×C52 | — | 2 | 4 | no | — |
| 140 | C2×C4×C52 | C4×D4 | 1 | 2 | yes | — |
| 141 | C2×C4×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 142 | C2×#1039 | — | 2 | 4 | no | — |
| 143 | C2×#1039 | C4×D4 | 1 | 2 | yes | — |
| 144 | C2×#1039 | C2×#41 | 1 | 1 | yes | characteristic |
| 145 | C4×C5⋊D5 | — | 4 | 4 | no | — |
| 146 | C4×C5⋊D5 | — | 4 | 4 | no | — |
| 147 | C4×C5⋊D5 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 148 | C4×C5⋊D5 | #137 | 1 | 4 | yes | — |
| 149 | C4×C5⋊D5 | C22×Q8 | 1 | 2 | yes | — |
| 150 | C4×C5⋊D5 | C2×#41 | 1 | 2 | yes | — |
| 151 | #6045 | — | 4 | 4 | no | — |
| 152 | #6045 | — | 4 | 8 | no | — |
| 153 | #6033 | — | 2 | 4 | no | — |
| 154 | C52×C8 | C4×Q8 | 1 | 4 | yes | complemented |
| 155 | #6029 | C4×Q8 | 1 | 4 | yes | complemented |
| 156 | C2×Q8×D5 | — | 10 | 12 | no | — |
| 157 | Q8×AGL(1,𝔽5) | — | 20 | 48 | no | — |
| 158 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 159 | C2×C4⋊AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 160 | C2×C4⋊AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 161 | C2×C4⋊AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 162 | C2×C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 163 | C2×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 164 | C2×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 165 | C2×C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 166 | C2×C4×AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 167 | C2×D5⋊C8 | — | 5 | 12 | no | — |
| 168 | C5×C4⋊Q8 | C2×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 169 | #4090 | — | 10 | 12 | no | — |
| 170 | C2×C8×D5 | — | 5 | 12 | no | — |
| 171 | D5×C4⋊C4 | — | 5 | 24 | no | — |
| 172 | D5×C4⋊C4 | — | 10 | 12 | no | — |
| 173 | #4034 | — | 5 | 24 | no | — |
| 174 | #4034 | — | 10 | 12 | no | — |
| 175 | C42×D5 | — | 5 | 6 | no | — |
| 176 | #4015 | — | 5 | 12 | no | — |
| 177 | (C2×AGL(1,𝔽5))⋊C4 | — | 10 | 24 | no | — |
| 178 | (C2×AGL(1,𝔽5))⋊C4 | — | 10 | 24 | no | — |
| 179 | C4×#170 | — | 10 | 12 | no | — |
| 180 | #3994 | — | 10 | 48 | no | — |
| 181 | #3992 | — | 5 | 48 | no | — |
| 182 | #3992 | — | 10 | 24 | no | — |
| 183 | C5×#106 | C2×AGL(1,𝔽5) | 1 | 24 | yes | — |
| 184 | C4×C5×C8 | C2×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 185 | #3949 | — | 5 | 24 | no | — |
| 186 | C8×Dic5 | — | 5 | 12 | no | — |
| 187 | #3940 | — | 5 | 48 | no | — |
| 188 | C4×#168 | — | 5 | 6 | no | — |
| 189 | C2×#498 | — | 25 | 1 | no | — |
| 190 | C4×C4⋊Q8 | — | 25 | 2 | no | — |
| 191 | #1990 | — | 25 | 2 | no | — |
| 192 | #1944 | — | 25 | 4 | no | — |
| 193 | #1845 | — | 25 | 1 | no | — |
| 194 | #1776 | — | 25 | 4 | no | — |
| 195 | C4×#97 | — | 25 | 1 | no | — |
| 196 | C22×C52 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×C5⋊D5 | C2×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 198 | C2×C5⋊D5 | #532 | 1 | 1 | yes | characteristic |
| 199 | C2×C5⋊D5 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 200 | C2×C5⋊D5 | C2×#137 | 1 | 2 | yes | — |
| 201 | #1043 | — | 2 | 4 | no | — |
| 202 | #1043 | — | 4 | 1 | no | — |
| 203 | #1043 | — | 4 | 1 | no | — |
| 204 | #1043 | — | 8 | 4 | no | — |
| 205 | C4×C52 | — | 4 | 4 | no | — |
| 206 | C4×C52 | #440 | 1 | 4 | yes | — |
| 207 | C4×C52 | C2×C4×Q8 | 1 | 2 | yes | — |
| 208 | #1039 | — | 4 | 4 | no | — |
| 209 | #1039 | #440 | 1 | 4 | yes | — |
| 210 | #1039 | #533 | 1 | 2 | yes | — |
| 211 | C22×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 212 | C22×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 213 | C22×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 214 | C22×AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 215 | C2×C5×Q8 | — | 2 | 12 | no | — |
| 216 | Q8×D5 | — | 20 | 24 | no | — |
| 217 | Q8×D5 | — | 20 | 24 | no | — |
| 218 | C2×C4×D5 | — | 5 | 12 | no | — |
| 219 | C2×C4×D5 | — | 5 | 6 | no | — |
| 220 | C2×C4×D5 | — | 10 | 24 | no | — |
| 221 | C2×Dic10 | — | 10 | 24 | no | — |
| 222 | C2×Dic10 | — | 10 | 12 | no | — |
| 223 | C2×#170 | — | 10 | 12 | no | — |
| 224 | C4⋊AGL(1,𝔽5) | — | 10 | 48 | no | — |
| 225 | C4⋊AGL(1,𝔽5) | — | 20 | 24 | no | — |
| 226 | C4⋊AGL(1,𝔽5) | — | 20 | 24 | no | — |
| 227 | C4⋊AGL(1,𝔽5) | — | 20 | 48 | no | — |
| 228 | C4×AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 229 | C4×AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 230 | C4×AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 231 | C4×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 232 | C4×AGL(1,𝔽5) | — | 20 | 48 | no | — |
| 233 | D5⋊C8 | — | 5 | 24 | no | — |
| 234 | D5⋊C8 | — | 10 | 12 | no | — |
| 235 | C2×C5×C8 | C22×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 236 | C5×C4⋊C4 | — | 2 | 12 | no | — |
| 237 | C5×C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 24 | yes | — |
| 238 | C42×C5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 239 | C4⋊Dic5 | — | 5 | 24 | no | — |
| 240 | C4⋊Dic5 | — | 10 | 12 | no | — |
| 241 | #683 | — | 10 | 24 | no | — |
| 242 | #683 | — | 10 | 24 | no | — |
| 243 | C4×Dic5 | — | 5 | 12 | no | — |
| 244 | C4×Dic5 | — | 5 | 6 | no | — |
| 245 | C2×#168 | — | 5 | 12 | no | — |
| 246 | C8×D5 | — | 5 | 24 | no | — |
| 247 | C8×D5 | — | 5 | 24 | no | — |
| 248 | C2×C4⋊Q8 | — | 25 | 2 | no | — |
| 249 | C2×C4×Q8 | — | 50 | 2 | no | — |
| 250 | #498 | — | 25 | 2 | no | — |
| 251 | #498 | — | 25 | 4 | no | — |
| 252 | #498 | — | 25 | 1 | no | — |
| 253 | #498 | #1043 | 1 | 1 | yes | characteristic, complemented |
| 254 | C2×#107 | — | 25 | 4 | no | — |
| 255 | C2×#106 | — | 25 | 4 | no | — |
| 256 | C2×#97 | — | 25 | 2 | no | — |
| 257 | C2×#97 | — | 25 | 2 | no | — |
| 258 | C2×C4×C8 | — | 25 | 1 | no | — |
| 259 | C2×C4×C8 | — | 25 | 1 | no | — |
| 260 | #391 | — | 50 | 2 | no | — |
| 261 | #389 | — | 25 | 4 | no | — |
| 262 | #389 | — | 50 | 2 | no | — |
| 263 | #384 | — | 25 | 2 | no | — |
| 264 | C4×C4⋊C4 | — | 25 | 4 | no | — |
| 265 | C4×C4⋊C4 | — | 50 | 2 | no | — |
| 266 | C43 | — | 25 | 1 | no | — |
| 267 | #340 | — | 25 | 8 | no | — |
| 268 | C2×C52 | C4×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 269 | C2×C52 | C2×#440 | 1 | 2 | yes | — |
| 270 | C5⋊D5 | #3165 | 1 | 2 | yes | — |
| 271 | C5⋊D5 | #3184 | 1 | 1 | yes | characteristic |
| 272 | C5⋊D5 | #3185 | 1 | 1 | yes | characteristic |
| 273 | C22×D5 | — | 5 | 6 | no | — |
| 274 | C2×AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 275 | C2×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 276 | C2×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 277 | C2×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 278 | C2×AGL(1,𝔽5) | — | 10 | 6 | no | — |
| 279 | C2×AGL(1,𝔽5) | — | 10 | 6 | no | — |
| 280 | C2×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 281 | C2×AGL(1,𝔽5) | — | 20 | 24 | no | — |
| 282 | C2×AGL(1,𝔽5) | — | 20 | 24 | no | — |
| 283 | C2×AGL(1,𝔽5) | — | 20 | 24 | no | — |
| 284 | C5×Q8 | — | 4 | 24 | no | — |
| 285 | C2×C4×C5 | — | 2 | 24 | no | — |
| 286 | C2×C4×C5 | D4×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 287 | C2×C4×C5 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 288 | C2×Dic5 | — | 5 | 12 | no | — |
| 289 | C2×Dic5 | — | 5 | 6 | no | — |
| 290 | C2×Dic5 | — | 10 | 24 | no | — |
| 291 | C4×D5 | — | 5 | 24 | no | — |
| 292 | C4×D5 | — | 5 | 24 | no | — |
| 293 | C4×D5 | — | 5 | 12 | no | — |
| 294 | C4×D5 | — | 5 | 12 | no | — |
| 295 | C4×D5 | — | 20 | 24 | no | — |
| 296 | C4×D5 | — | 20 | 24 | no | — |
| 297 | Dic10 | — | 20 | 48 | no | — |
| 298 | Dic10 | — | 20 | 24 | no | — |
| 299 | #170 | — | 10 | 24 | no | — |
| 300 | C5×C8 | Q8×AGL(1,𝔽5) | 1 | 24 | yes | complemented |
| 301 | #168 | — | 5 | 24 | no | — |
| 302 | C22×Q8 | — | 50 | 2 | no | — |
| 303 | C22×C8 | — | 25 | 2 | no | — |
| 304 | C22×C8 | — | 25 | 2 | no | — |
| 305 | C4⋊Q8 | — | 25 | 4 | no | — |
| 306 | C4⋊Q8 | — | 25 | 2 | no | — |
| 307 | C4⋊Q8 | — | 50 | 2 | no | — |
| 308 | C4⋊Q8 | — | 50 | 2 | no | — |
| 309 | C4⋊Q8 | C2×#1043 | 1 | 2 | yes | — |
| 310 | C4×Q8 | — | 100 | 8 | no | — |
| 311 | C2×C4⋊C4 | — | 25 | 4 | no | — |
| 312 | C2×C4⋊C4 | — | 25 | 4 | no | — |
| 313 | C2×C4⋊C4 | — | 50 | 2 | no | — |
| 314 | C2×C4⋊C4 | — | 50 | 2 | no | — |
| 315 | C2×C4⋊C4 | — | 50 | 4 | no | — |
| 316 | C2×C4⋊C4 | — | 50 | 2 | no | — |
| 317 | C2×C42 | — | 25 | 1 | no | — |
| 318 | C2×C42 | — | 25 | 1 | no | — |
| 319 | C2×C42 | — | 25 | 2 | no | — |
| 320 | C2×C42 | — | 25 | 2 | no | — |
| 321 | C2×C42 | — | 25 | 1 | no | — |
| 322 | C2×C42 | — | 50 | 4 | no | — |
| 323 | #107 | — | 50 | 8 | no | — |
| 324 | #106 | — | 25 | 4 | no | — |
| 325 | #106 | — | 25 | 8 | no | — |
| 326 | #106 | C2×#1043 | 1 | 4 | yes | — |
| 327 | #97 | — | 25 | 8 | no | — |
| 328 | #97 | — | 50 | 4 | no | — |
| 329 | C4×C8 | — | 25 | 2 | no | — |
| 330 | C4×C8 | — | 25 | 1 | no | — |
| 331 | C4×C8 | — | 50 | 2 | no | — |
| 332 | C4×C8 | C2×#1043 | 1 | 1 | yes | characteristic |
| 333 | #95 | — | 50 | 4 | no | — |
| 334 | #95 | — | 50 | 4 | no | — |
| 335 | C52 | #21727 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 336 | C22×C5 | C2×D4×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 337 | C2×D5 | — | 5 | 6 | no | — |
| 338 | C2×D5 | — | 5 | 6 | no | — |
| 339 | C2×D5 | — | 5 | 12 | no | — |
| 340 | C2×D5 | — | 5 | 12 | no | — |
| 341 | AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 342 | AGL(1,𝔽5) | — | 20 | 6 | no | — |
| 343 | AGL(1,𝔽5) | — | 20 | 6 | no | — |
| 344 | AGL(1,𝔽5) | — | 40 | 24 | no | — |
| 345 | C4×C5 | — | 4 | 24 | no | — |
| 346 | C4×C5 | #65735 | 1 | 24 | yes | — |
| 347 | C4×C5 | C2×Q8×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 348 | Dic5 | — | 5 | 12 | no | — |
| 349 | Dic5 | — | 5 | 24 | no | — |
| 350 | Dic5 | — | 20 | 24 | no | — |
| 351 | C2×Q8 | — | 2 | 2 | no | — |
| 352 | C2×Q8 | — | 50 | 4 | no | — |
| 353 | C2×Q8 | — | 50 | 2 | no | — |
| 354 | C2×Q8 | — | 100 | 4 | no | — |
| 355 | C2×Q8 | — | 100 | 4 | no | — |
| 356 | C22×C4 | — | 25 | 2 | no | — |
| 357 | C22×C4 | — | 25 | 1 | no | — |
| 358 | C22×C4 | — | 25 | 2 | no | — |
| 359 | C22×C4 | — | 25 | 1 | no | — |
| 360 | C22×C4 | — | 25 | 1 | no | — |
| 361 | C22×C4 | — | 50 | 4 | no | — |
| 362 | C22×C4 | — | 50 | 4 | no | — |
| 363 | C2×C8 | — | 25 | 2 | no | — |
| 364 | C2×C8 | — | 25 | 4 | no | — |
| 365 | C2×C8 | — | 25 | 4 | no | — |
| 366 | C2×C8 | — | 25 | 4 | no | — |
| 367 | C2×C8 | — | 50 | 2 | no | — |
| 368 | C2×C8 | — | 50 | 2 | no | — |
| 369 | C2×C8 | C22×#1043 | 1 | 2 | yes | — |
| 370 | C4⋊C4 | — | 2 | 2 | no | — |
| 371 | C4⋊C4 | — | 25 | 4 | no | — |
| 372 | C4⋊C4 | — | 50 | 4 | no | — |
| 373 | C4⋊C4 | — | 50 | 4 | no | — |
| 374 | C4⋊C4 | — | 50 | 8 | no | — |
| 375 | C4⋊C4 | — | 50 | 2 | no | — |
| 376 | C4⋊C4 | — | 100 | 4 | no | — |
| 377 | C4⋊C4 | — | 100 | 4 | no | — |
| 378 | C4⋊C4 | — | 100 | 8 | no | — |
| 379 | C4⋊C4 | C22×#1043 | 1 | 4 | yes | — |
| 380 | C42 | — | 25 | 4 | no | — |
| 381 | C42 | — | 25 | 2 | no | — |
| 382 | C42 | — | 25 | 1 | no | — |
| 383 | C42 | — | 50 | 2 | no | — |
| 384 | C42 | — | 50 | 4 | no | — |
| 385 | C42 | — | 50 | 4 | no | — |
| 386 | C42 | — | 100 | 8 | no | — |
| 387 | C42 | C22×#1043 | 1 | 1 | yes | characteristic |
| 388 | C2×C5 | AGL(1,𝔽5)×C4⋊Q8 | 1 | 6 | yes | — |
| 389 | C2×C5 | C2×#65735 | 1 | 12 | yes | — |
| 390 | D5 | — | 5 | 12 | no | — |
| 391 | D5 | — | 5 | 6 | no | — |
| 392 | D5 | — | 5 | 6 | no | — |
| 393 | C23 | — | 25 | 1 | no | — |
| 394 | Q8 | — | 4 | 4 | no | — |
| 395 | Q8 | — | 100 | 8 | no | — |
| 396 | Q8 | — | 100 | 4 | no | — |
| 397 | C2×C4 | — | 2 | 4 | no | — |
| 398 | C2×C4 | — | 25 | 1 | no | — |
| 399 | C2×C4 | — | 25 | 2 | no | — |
| 400 | C2×C4 | — | 25 | 2 | no | — |
| 401 | C2×C4 | — | 25 | 2 | no | — |
| 402 | C2×C4 | — | 25 | 4 | no | — |
| 403 | C2×C4 | — | 25 | 4 | no | — |
| 404 | C2×C4 | — | 25 | 4 | no | — |
| 405 | C2×C4 | — | 50 | 2 | no | — |
| 406 | C2×C4 | — | 50 | 2 | no | — |
| 407 | C2×C4 | — | 50 | 2 | no | — |
| 408 | C2×C4 | — | 50 | 1 | no | — |
| 409 | C2×C4 | — | 50 | 1 | no | — |
| 410 | C2×C4 | — | 50 | 2 | no | — |
| 411 | C2×C4 | — | 50 | 4 | no | — |
| 412 | C2×C4 | — | 100 | 4 | no | — |
| 413 | C2×C4 | — | 100 | 4 | no | — |
| 414 | C2×C4 | — | 100 | 4 | no | — |
| 415 | C2×C4 | — | 100 | 4 | no | — |
| 416 | C2×C4 | — | 100 | 4 | no | — |
| 417 | C2×C4 | D4×#1043 | 1 | 2 | yes | — |
| 418 | C2×C4 | C23×#1043 | 1 | 1 | yes | characteristic |
| 419 | C8 | — | 25 | 4 | no | — |
| 420 | C8 | — | 50 | 4 | no | — |
| 421 | C8 | Q8×#1043 | 1 | 4 | yes | complemented |
| 422 | C5 | #13036904 | 1 | 6 | yes | complemented |
| 423 | C22 | — | 25 | 1 | no | — |
| 424 | C22 | — | 25 | 1 | no | — |
| 425 | C22 | — | 25 | 2 | no | — |
| 426 | C22 | — | 25 | 2 | no | — |
| 427 | C22 | C2×D4×#1043 | 1 | 1 | yes | characteristic |
| 428 | C4 | — | 4 | 4 | no | — |
| 429 | C4 | — | 25 | 2 | no | — |
| 430 | C4 | — | 25 | 4 | no | — |
| 431 | C4 | — | 50 | 4 | no | — |
| 432 | C4 | — | 100 | 1 | no | — |
| 433 | C4 | — | 100 | 1 | no | — |
| 434 | C4 | — | 100 | 4 | no | — |
| 435 | C4 | — | 200 | 4 | no | — |
| 436 | C4 | #13104747 | 1 | 4 | yes | — |
| 437 | C4 | C2×Q8×#1043 | 1 | 2 | yes | — |
| 438 | C2 | — | 25 | 2 | no | — |
| 439 | C2 | — | 25 | 1 | no | — |
| 440 | C2 | — | 25 | 1 | no | — |
| 441 | C2 | C2×#13104747 | 1 | 2 | yes | — |
| 442 | C2 | C4⋊Q8×#1043 | 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