← #72221793
Subgroups — #72221793
Order 3200.
3278 conjugacy classes of subgroups.
The subgroup lattice has 564 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13107840 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #41×#1044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13107754 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | Q8×D5⋊AGL(1,𝔽5) | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13107571 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13107570 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #13107568 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #13107562 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #13107561 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #13107542 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×#11717355 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #41×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 13 | C5×#4150 | C4 | 1 | 2 | yes | complemented |
| 14 | Q8×D52 | C22 | 1 | 2 | yes | — |
| 15 | #11717481 | C4 | 1 | 2 | yes | complemented |
| 16 | #11717477 | C22 | 1 | 6 | yes | — |
| 17 | #11717474 | C4 | 1 | 6 | yes | complemented |
| 18 | #11717471 | C22 | 1 | 3 | yes | — |
| 19 | C2×#87872 | C22 | 1 | 3 | yes | — |
| 20 | #11717462 | C4 | 1 | 6 | yes | complemented |
| 21 | Q8×#1044 | C22 | 1 | 1 | yes | characteristic |
| 22 | Q8×#1044 | C22 | 1 | 1 | yes | characteristic |
| 23 | D4×#1044 | C22 | 1 | 3 | yes | — |
| 24 | D4×#1044 | C22 | 1 | 3 | yes | — |
| 25 | #11717451 | C22 | 1 | 3 | yes | — |
| 26 | C2×C4×#1044 | C22 | 1 | 3 | yes | — |
| 27 | Q8×#1043 | C22 | 1 | 2 | yes | — |
| 28 | D4×#1043 | C22 | 1 | 6 | yes | — |
| 29 | #11717438 | C22 | 1 | 3 | yes | — |
| 30 | C2×C4⋊#1043 | C22 | 1 | 3 | yes | — |
| 31 | #11717377 | C22 | 1 | 6 | yes | — |
| 32 | #11717377 | C22 | 1 | 6 | yes | — |
| 33 | #11717375 | C22 | 1 | 12 | yes | — |
| 34 | C2×#87832 | C22 | 1 | 6 | yes | — |
| 35 | #11717367 | C22 | 1 | 12 | yes | — |
| 36 | C2×#87830 | C22 | 1 | 6 | yes | — |
| 37 | #11717365 | C22 | 1 | 1 | yes | characteristic |
| 38 | #11717365 | C22 | 1 | 3 | yes | — |
| 39 | D5⋊(C4⋊AGL(1,𝔽5)) | C22 | 1 | 6 | yes | — |
| 40 | C4×D5⋊AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 41 | #11717356 | C22 | 1 | 6 | yes | — |
| 42 | #11717355 | C22 | 1 | 3 | yes | — |
| 43 | #11717355 | C22 | 1 | 6 | yes | — |
| 44 | #11717355 | C22 | 1 | 6 | yes | — |
| 45 | #11717355 | C22 | 1 | 6 | yes | — |
| 46 | #11717355 | C22 | 1 | 3 | yes | — |
| 47 | #11717354 | C22 | 1 | 6 | yes | — |
| 48 | #11717353 | C22 | 1 | 6 | yes | — |
| 49 | #11717353 | C22 | 1 | 6 | yes | — |
| 50 | AGL(1,𝔽5)×2−1+4 | — | 5 | 2 | no | maximal |
| 51 | C22×#1044 | C23 | 1 | 3 | yes | — |
| 52 | C22×#1044 | C23 | 1 | 3 | yes | — |
| 53 | C22×#1043 | C23 | 1 | 6 | yes | — |
| 54 | C2×D5⋊AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 55 | C2×D5⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 56 | C52×#41 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 57 | #87904 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 58 | Q8×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 59 | #87902 | C2×C4 | 1 | 3 | yes | complemented |
| 60 | D4×C5⋊D5 | C23 | 1 | 3 | yes | — |
| 61 | #87900 | C2×C4 | 1 | 3 | yes | complemented |
| 62 | C2×C4×C5⋊D5 | C23 | 1 | 3 | yes | — |
| 63 | C5×Q8×D5 | C2×C4 | 1 | 4 | yes | complemented |
| 64 | C5×#711 | C2×C4 | 1 | 12 | yes | complemented |
| 65 | C5×#709 | C2×C4 | 1 | 6 | yes | complemented |
| 66 | C2×C5×Dic10 | C2×C4 | 1 | 6 | yes | complemented |
| 67 | #87886 | C23 | 1 | 6 | yes | — |
| 68 | C2×#6039 | C2×C4 | 1 | 6 | yes | complemented |
| 69 | C2×#6036 | C23 | 1 | 6 | yes | — |
| 70 | #87880 | C2×C4 | 1 | 6 | yes | complemented |
| 71 | #87879 | C2×C4 | 1 | 24 | yes | complemented |
| 72 | #87877 | C23 | 1 | 1 | yes | characteristic |
| 73 | C4×D52 | C23 | 1 | 6 | yes | — |
| 74 | #87874 | C2×C4 | 1 | 12 | yes | complemented |
| 75 | #87873 | C2×C4 | 1 | 6 | yes | complemented |
| 76 | #87872 | C2×C4 | 1 | 6 | yes | complemented |
| 77 | #87872 | C2×C4 | 1 | 6 | yes | complemented |
| 78 | #87872 | C23 | 1 | 3 | yes | — |
| 79 | #87872 | C23 | 1 | 6 | yes | — |
| 80 | #87871 | C2×C4 | 1 | 6 | yes | complemented |
| 81 | D5×Dic10 | C2×C4 | 1 | 12 | yes | complemented |
| 82 | C22⋊#1044 | C23 | 1 | 6 | yes | — |
| 83 | C4⋊#1044 | C23 | 1 | 3 | yes | — |
| 84 | C4⋊#1044 | C23 | 1 | 3 | yes | — |
| 85 | C4×#1044 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4×#1044 | C23 | 1 | 3 | yes | — |
| 87 | C4×#1044 | C23 | 1 | 3 | yes | — |
| 88 | C4×#1044 | C23 | 1 | 3 | yes | — |
| 89 | C22⋊#1043 | C23 | 1 | 6 | yes | — |
| 90 | C4⋊#1043 | C23 | 1 | 3 | yes | — |
| 91 | C4⋊#1043 | C23 | 1 | 6 | yes | — |
| 92 | C4⋊#1043 | C23 | 1 | 1 | yes | characteristic |
| 93 | C4×#1043 | C23 | 1 | 6 | yes | — |
| 94 | #87832 | C23 | 1 | 6 | yes | — |
| 95 | #87832 | C23 | 1 | 6 | yes | — |
| 96 | #87832 | C23 | 1 | 12 | yes | — |
| 97 | #87831 | C23 | 1 | 2 | yes | — |
| 98 | #87831 | C23 | 1 | 6 | yes | — |
| 99 | #87830 | C23 | 1 | 6 | yes | — |
| 100 | #87830 | C23 | 1 | 6 | yes | — |
| 101 | #87830 | C23 | 1 | 12 | yes | — |
| 102 | D5×2−1+4 | — | 5 | 2 | no | — |
| 103 | #66266 | — | 5 | 2 | no | — |
| 104 | #66266 | — | 5 | 6 | no | — |
| 105 | #66266 | — | 5 | 12 | no | — |
| 106 | #66266 | — | 10 | 2 | no | — |
| 107 | #41×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 108 | #41×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 109 | #41×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 110 | #66262 | — | 5 | 6 | no | — |
| 111 | #66262 | — | 5 | 4 | no | — |
| 112 | C2×Q8×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 113 | C2×Q8×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 114 | C22×C5⋊D5 | C24 | 1 | 3 | yes | — |
| 115 | C2×D52 | C24 | 1 | 2 | yes | — |
| 116 | C2×#1044 | — | 2 | 6 | no | — |
| 117 | C2×#1044 | — | 4 | 3 | no | — |
| 118 | C2×#1044 | C24 | 1 | 3 | yes | — |
| 119 | C2×#1044 | C24 | 1 | 3 | yes | — |
| 120 | C2×#1044 | C24 | 1 | 1 | yes | characteristic |
| 121 | C2×#1044 | C24 | 1 | 1 | yes | characteristic |
| 122 | C2×#1043 | — | 4 | 6 | no | — |
| 123 | C2×#1043 | C24 | 1 | 2 | yes | — |
| 124 | C2×#1043 | C24 | 1 | 6 | yes | — |
| 125 | D5⋊AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 126 | D5⋊AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 127 | C52×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 128 | C52×D4 | C22×C4 | 1 | 3 | yes | — |
| 129 | C2×C4×C52 | C22×C4 | 1 | 3 | yes | — |
| 130 | C22⋊(C5⋊D5) | C22×C4 | 1 | 6 | yes | — |
| 131 | C2×#1039 | C22×C4 | 1 | 3 | yes | — |
| 132 | C4⋊(C5⋊D5) | C22×C4 | 1 | 3 | yes | — |
| 133 | C4×C5⋊D5 | C22×C4 | 1 | 3 | yes | — |
| 134 | C4×C5⋊D5 | C22×C4 | 1 | 3 | yes | — |
| 135 | C4×C5⋊D5 | C24 | 1 | 3 | yes | — |
| 136 | C4×C5⋊D5 | C24 | 1 | 1 | yes | characteristic |
| 137 | #6045 | C22×C4 | 1 | 3 | yes | — |
| 138 | C5×C22⋊D5 | C22×C4 | 1 | 12 | yes | — |
| 139 | C2×C5×Dic5 | C22×C4 | 1 | 12 | yes | — |
| 140 | C5×D20 | C22×C4 | 1 | 2 | yes | — |
| 141 | C4×C5×D5 | C22×C4 | 1 | 12 | yes | — |
| 142 | C5×Dic10 | C22×C4 | 1 | 12 | yes | — |
| 143 | C5×Dic10 | C22×C4 | 1 | 6 | yes | — |
| 144 | #6039 | C22×C4 | 1 | 12 | yes | — |
| 145 | #6039 | C22×C4 | 1 | 6 | yes | — |
| 146 | #6038 | C22×C4 | 1 | 12 | yes | — |
| 147 | #6037 | C22×C4 | 1 | 2 | yes | — |
| 148 | #6036 | C22×C4 | 1 | 12 | yes | — |
| 149 | #6036 | C24 | 1 | 6 | yes | — |
| 150 | D5×Dic5 | C22×C4 | 1 | 12 | yes | — |
| 151 | C5×2−1+4 | — | 5 | 2 | no | — |
| 152 | #4150 | — | 5 | 12 | no | — |
| 153 | #4150 | — | 5 | 6 | no | — |
| 154 | #4150 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 155 | D5×#41 | — | 5 | 2 | no | — |
| 156 | D5×#41 | — | 5 | 12 | no | — |
| 157 | D5×#41 | — | 5 | 6 | no | — |
| 158 | D5×#41 | — | 10 | 2 | no | — |
| 159 | #4147 | — | 5 | 4 | no | — |
| 160 | #4147 | — | 5 | 6 | no | — |
| 161 | C2×Q8×D5 | — | 5 | 4 | no | — |
| 162 | C2×Q8×D5 | — | 5 | 6 | no | — |
| 163 | Q8×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 164 | Q8×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 165 | Q8×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 166 | Q8×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 167 | Q8×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 168 | Q8×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 169 | Q8×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 170 | Q8×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 171 | Q8×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 172 | Q8×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 173 | Q8×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 174 | D4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 175 | D4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 176 | D4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 177 | D4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 178 | D4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 179 | D4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 180 | D4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 181 | D4×AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 182 | D4×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 183 | #4130 | — | 5 | 6 | no | — |
| 184 | #4130 | — | 5 | 6 | no | — |
| 185 | #4130 | — | 5 | 12 | no | — |
| 186 | #4130 | — | 5 | 12 | no | — |
| 187 | #4130 | — | 5 | 24 | no | — |
| 188 | #4130 | — | 10 | 6 | no | — |
| 189 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 190 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 191 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 192 | C2×C4⋊AGL(1,𝔽5) | — | 10 | 6 | no | — |
| 193 | C2×C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 194 | C2×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 195 | C2×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 196 | C4×2−1+4 | — | 25 | 1 | no | Sylow |
| 197 | C22×C52 | C23×C4 | 1 | 3 | yes | — |
| 198 | C2×C5⋊D5 | — | 2 | 3 | no | — |
| 199 | C2×C5⋊D5 | — | 2 | 3 | no | — |
| 200 | C2×C5⋊D5 | C23×C4 | 1 | 3 | yes | — |
| 201 | C2×C5⋊D5 | C25 | 1 | 1 | yes | characteristic |
| 202 | C2×C5×D5 | C23×C4 | 1 | 4 | yes | — |
| 203 | D52 | — | 2 | 2 | no | — |
| 204 | D52 | — | 2 | 2 | no | — |
| 205 | #1044 | — | 2 | 3 | no | — |
| 206 | #1044 | — | 2 | 3 | no | — |
| 207 | #1044 | — | 2 | 1 | no | — |
| 208 | #1044 | 2−1+4 | 1 | 2 | yes | complemented |
| 209 | #1043 | — | 2 | 2 | no | — |
| 210 | #1043 | — | 2 | 6 | no | — |
| 211 | C4×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 212 | C4×C52 | C23×C4 | 1 | 3 | yes | — |
| 213 | #1039 | C23×C4 | 1 | 3 | yes | — |
| 214 | #1039 | C23×C4 | 1 | 1 | yes | characteristic |
| 215 | C5×Dic5 | C23×C4 | 1 | 12 | yes | — |
| 216 | C22×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 217 | C22×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 218 | C22×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 219 | C22×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 220 | C22×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 221 | C22×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 222 | C5×#41 | — | 2 | 2 | no | — |
| 223 | C5×#41 | — | 5 | 12 | no | — |
| 224 | C5×#41 | — | 5 | 6 | no | — |
| 225 | C5×#41 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 226 | C2×C5×Q8 | — | 5 | 4 | no | — |
| 227 | C2×C5×Q8 | — | 5 | 6 | no | — |
| 228 | #713 | — | 5 | 2 | no | — |
| 229 | #713 | — | 5 | 6 | no | — |
| 230 | #713 | — | 5 | 12 | no | — |
| 231 | #713 | — | 10 | 2 | no | — |
| 232 | Q8×D5 | — | 5 | 2 | no | — |
| 233 | Q8×D5 | — | 5 | 12 | no | — |
| 234 | Q8×D5 | — | 5 | 12 | no | — |
| 235 | Q8×D5 | — | 5 | 6 | no | — |
| 236 | Q8×D5 | — | 5 | 12 | no | — |
| 237 | Q8×D5 | — | 5 | 12 | no | — |
| 238 | Q8×D5 | — | 10 | 2 | no | — |
| 239 | Q8×D5 | C2×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 240 | #711 | — | 5 | 6 | no | — |
| 241 | #711 | — | 5 | 12 | no | — |
| 242 | #711 | — | 5 | 24 | no | — |
| 243 | #711 | — | 5 | 6 | no | — |
| 244 | #711 | — | 10 | 6 | no | — |
| 245 | #711 | C2×AGL(1,𝔽5) | 1 | 12 | yes | complemented |
| 246 | D4×D5 | — | 5 | 6 | no | — |
| 247 | D4×D5 | — | 5 | 12 | no | — |
| 248 | D4×D5 | — | 5 | 2 | no | — |
| 249 | D4×D5 | — | 10 | 6 | no | — |
| 250 | #709 | — | 5 | 6 | no | — |
| 251 | #709 | — | 5 | 24 | no | — |
| 252 | #709 | — | 5 | 12 | no | — |
| 253 | #709 | — | 5 | 12 | no | — |
| 254 | #709 | — | 10 | 6 | no | — |
| 255 | #709 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 256 | C2×C4×D5 | — | 5 | 6 | no | — |
| 257 | C2×C4×D5 | — | 5 | 12 | no | — |
| 258 | C2×C4×D5 | — | 5 | 12 | no | — |
| 259 | C2×C4×D5 | — | 10 | 6 | no | — |
| 260 | C2×Dic10 | — | 5 | 12 | no | — |
| 261 | C2×Dic10 | — | 5 | 12 | no | — |
| 262 | C2×Dic10 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 263 | C22⋊AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 264 | C22⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 265 | C22⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 266 | C22⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 267 | C22⋊AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 268 | C4⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 269 | C4⋊AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 270 | C4⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 271 | C4⋊AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 272 | C4⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 273 | C4⋊AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 274 | C4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 275 | C4⋊AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 276 | C4⋊AGL(1,𝔽5) | — | 10 | 6 | no | — |
| 277 | C4⋊AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 278 | C4⋊AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 279 | C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 280 | C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 281 | C4×AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 282 | C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 283 | C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 284 | C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 285 | C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 286 | C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 287 | C4×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 288 | C2×2−1+4 | — | 25 | 1 | no | — |
| 289 | #520 | — | 25 | 6 | no | — |
| 290 | #520 | — | 25 | 3 | no | — |
| 291 | #520 | — | 25 | 1 | no | — |
| 292 | #519 | — | 25 | 2 | no | — |
| 293 | #519 | — | 25 | 3 | no | — |
| 294 | C4×#41 | — | 25 | 1 | no | — |
| 295 | C4×#41 | — | 25 | 6 | no | — |
| 296 | C4×#41 | — | 25 | 3 | no | — |
| 297 | C2×C4×Q8 | — | 25 | 2 | no | — |
| 298 | C2×C4×Q8 | — | 25 | 3 | no | — |
| 299 | C2×C52 | — | 2 | 3 | no | — |
| 300 | C2×C52 | C24×C4 | 1 | 1 | yes | characteristic |
| 301 | C5⋊D5 | — | 2 | 3 | no | — |
| 302 | C5⋊D5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 303 | C5⋊D5 | #585 | 1 | 1 | yes | characteristic |
| 304 | C5×D5 | — | 2 | 4 | no | — |
| 305 | C22×D5 | — | 5 | 6 | no | — |
| 306 | C22×D5 | — | 5 | 4 | no | — |
| 307 | C22×D5 | — | 10 | 6 | no | — |
| 308 | C2×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 309 | C2×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 310 | C2×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 311 | C2×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 312 | C2×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 313 | C2×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 314 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 315 | C2×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 316 | C2×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 317 | C2×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 318 | C2×AGL(1,𝔽5) | — | 20 | 12 | no | — |
| 319 | C2×AGL(1,𝔽5) | — | 20 | 12 | no | — |
| 320 | C2×AGL(1,𝔽5) | — | 20 | 6 | no | — |
| 321 | C2×AGL(1,𝔽5) | — | 40 | 12 | no | — |
| 322 | C5×Q8 | — | 2 | 2 | no | — |
| 323 | C5×Q8 | — | 5 | 12 | no | — |
| 324 | C5×Q8 | — | 5 | 6 | no | — |
| 325 | C5×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 326 | C5×D4 | — | 2 | 6 | no | — |
| 327 | C5×D4 | — | 5 | 12 | no | — |
| 328 | C5×D4 | — | 5 | 2 | no | — |
| 329 | C5×D4 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 330 | C2×C4×C5 | — | 2 | 6 | no | — |
| 331 | C2×C4×C5 | — | 5 | 12 | no | — |
| 332 | C2×C4×C5 | — | 5 | 12 | no | — |
| 333 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 334 | C22⋊D5 | — | 5 | 12 | no | — |
| 335 | C22⋊D5 | — | 5 | 4 | no | — |
| 336 | C22⋊D5 | — | 5 | 12 | no | — |
| 337 | C22⋊D5 | — | 10 | 12 | no | — |
| 338 | C22⋊D5 | C22×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 339 | C2×Dic5 | — | 5 | 6 | no | — |
| 340 | C2×Dic5 | — | 5 | 12 | no | — |
| 341 | C2×Dic5 | — | 10 | 6 | no | — |
| 342 | C2×Dic5 | C22×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 343 | D20 | — | 5 | 12 | no | — |
| 344 | D20 | — | 5 | 6 | no | — |
| 345 | D20 | — | 10 | 6 | no | — |
| 346 | D20 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 347 | C4×D5 | — | 5 | 12 | no | — |
| 348 | C4×D5 | — | 5 | 6 | no | — |
| 349 | C4×D5 | — | 5 | 6 | no | — |
| 350 | C4×D5 | — | 5 | 6 | no | — |
| 351 | C4×D5 | — | 5 | 2 | no | — |
| 352 | C4×D5 | — | 5 | 24 | no | — |
| 353 | C4×D5 | — | 5 | 12 | no | — |
| 354 | C4×D5 | — | 10 | 6 | no | — |
| 355 | C4×D5 | — | 10 | 6 | no | — |
| 356 | C4×D5 | — | 10 | 6 | no | — |
| 357 | C4×D5 | — | 10 | 2 | no | — |
| 358 | C4×D5 | C22×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 359 | Dic10 | — | 5 | 6 | no | — |
| 360 | Dic10 | — | 5 | 24 | no | — |
| 361 | Dic10 | — | 5 | 12 | no | — |
| 362 | Dic10 | — | 10 | 6 | no | — |
| 363 | Dic10 | C22×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 364 | Dic10 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 365 | 2−1+4 | — | 5 | 2 | no | — |
| 366 | 2−1+4 | — | 25 | 2 | no | — |
| 367 | 2−1+4 | — | 25 | 6 | no | — |
| 368 | 2−1+4 | — | 25 | 6 | no | — |
| 369 | C2×#41 | — | 25 | 6 | no | — |
| 370 | C2×#41 | — | 25 | 3 | no | — |
| 371 | C2×#41 | — | 25 | 1 | no | — |
| 372 | C22×Q8 | — | 25 | 2 | no | — |
| 373 | C22×Q8 | — | 25 | 3 | no | — |
| 374 | C4×Q8 | — | 25 | 1 | no | — |
| 375 | C4×Q8 | — | 25 | 6 | no | — |
| 376 | C4×Q8 | — | 25 | 3 | no | — |
| 377 | C4×Q8 | — | 25 | 6 | no | — |
| 378 | C4×Q8 | — | 25 | 6 | no | — |
| 379 | C4×Q8 | — | 25 | 6 | no | — |
| 380 | C4×Q8 | — | 25 | 2 | no | — |
| 381 | C4×Q8 | — | 25 | 1 | no | — |
| 382 | C4×Q8 | — | 25 | 3 | no | — |
| 383 | C4×Q8 | — | 25 | 6 | no | — |
| 384 | C4×D4 | — | 25 | 3 | no | — |
| 385 | C4×D4 | — | 25 | 1 | no | — |
| 386 | C4×D4 | — | 25 | 6 | no | — |
| 387 | C4×D4 | — | 25 | 3 | no | — |
| 388 | C4×D4 | — | 25 | 12 | no | — |
| 389 | C4×D4 | — | 25 | 3 | no | — |
| 390 | C4×D4 | — | 25 | 6 | no | — |
| 391 | C4×D4 | — | 25 | 6 | no | — |
| 392 | #117 | — | 25 | 3 | no | — |
| 393 | #117 | — | 25 | 6 | no | — |
| 394 | #117 | — | 25 | 12 | no | — |
| 395 | #117 | — | 25 | 6 | no | — |
| 396 | #117 | — | 25 | 3 | no | — |
| 397 | C2×C4⋊C4 | — | 25 | 6 | no | — |
| 398 | C2×C4⋊C4 | — | 25 | 6 | no | — |
| 399 | C2×C4⋊C4 | — | 25 | 3 | no | — |
| 400 | C2×C42 | — | 25 | 6 | no | — |
| 401 | C2×C42 | — | 25 | 3 | no | — |
| 402 | C2×C42 | — | 25 | 6 | no | — |
| 403 | C52 | C4×2−1+4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 404 | C22×C5 | — | 2 | 6 | no | — |
| 405 | C22×C5 | — | 5 | 4 | no | — |
| 406 | C22×C5 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 407 | C2×D5 | — | 5 | 2 | no | — |
| 408 | C2×D5 | — | 5 | 6 | no | — |
| 409 | C2×D5 | — | 10 | 2 | no | — |
| 410 | C2×D5 | — | 10 | 6 | no | — |
| 411 | C2×D5 | — | 10 | 4 | no | — |
| 412 | C2×D5 | — | 10 | 4 | no | — |
| 413 | C2×D5 | — | 10 | 6 | no | — |
| 414 | C2×D5 | — | 10 | 6 | no | — |
| 415 | C2×D5 | — | 20 | 6 | no | — |
| 416 | C2×D5 | — | 20 | 6 | no | — |
| 417 | C2×D5 | C23×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 418 | AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 419 | AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 420 | AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 421 | AGL(1,𝔽5) | — | 10 | 6 | no | — |
| 422 | AGL(1,𝔽5) | — | 10 | 6 | no | — |
| 423 | AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 424 | AGL(1,𝔽5) | — | 20 | 4 | no | — |
| 425 | AGL(1,𝔽5) | — | 20 | 12 | no | — |
| 426 | C4×C5 | — | 2 | 6 | no | — |
| 427 | C4×C5 | — | 2 | 2 | no | — |
| 428 | C4×C5 | — | 5 | 12 | no | — |
| 429 | C4×C5 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 430 | C4×C5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 431 | Dic5 | — | 5 | 6 | no | — |
| 432 | Dic5 | — | 5 | 2 | no | — |
| 433 | Dic5 | — | 10 | 6 | no | — |
| 434 | Dic5 | — | 10 | 2 | no | — |
| 435 | Dic5 | C23×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 436 | #41 | — | 5 | 12 | no | — |
| 437 | #41 | — | 5 | 6 | no | — |
| 438 | #41 | — | 25 | 6 | no | — |
| 439 | #41 | — | 25 | 24 | no | — |
| 440 | #41 | — | 25 | 12 | no | — |
| 441 | #41 | — | 25 | 6 | no | — |
| 442 | #41 | — | 25 | 6 | no | — |
| 443 | #41 | — | 25 | 1 | no | — |
| 444 | #41 | — | 25 | 3 | no | — |
| 445 | #41 | — | 25 | 3 | no | — |
| 446 | #41 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 447 | C2×Q8 | — | 5 | 4 | no | — |
| 448 | C2×Q8 | — | 5 | 6 | no | — |
| 449 | C2×Q8 | — | 25 | 6 | no | — |
| 450 | C2×Q8 | — | 25 | 12 | no | — |
| 451 | C2×Q8 | — | 25 | 6 | no | — |
| 452 | C2×Q8 | — | 25 | 3 | no | — |
| 453 | C2×Q8 | — | 25 | 6 | no | — |
| 454 | C2×Q8 | — | 25 | 6 | no | — |
| 455 | C2×Q8 | — | 25 | 1 | no | — |
| 456 | C2×D4 | — | 25 | 6 | no | — |
| 457 | C2×D4 | — | 25 | 1 | no | — |
| 458 | C2×D4 | — | 25 | 3 | no | — |
| 459 | C22×C4 | — | 25 | 6 | no | — |
| 460 | C22×C4 | — | 25 | 6 | no | — |
| 461 | C22×C4 | — | 25 | 3 | no | — |
| 462 | C22×C4 | — | 25 | 3 | no | — |
| 463 | C22×C4 | — | 25 | 2 | no | — |
| 464 | C22×C4 | — | 25 | 3 | no | — |
| 465 | C22×C4 | — | 25 | 6 | no | — |
| 466 | C22×C4 | — | 25 | 6 | no | — |
| 467 | C4⋊C4 | — | 25 | 6 | no | — |
| 468 | C4⋊C4 | — | 25 | 12 | no | — |
| 469 | C4⋊C4 | — | 25 | 3 | no | — |
| 470 | C4⋊C4 | — | 25 | 6 | no | — |
| 471 | C4⋊C4 | — | 25 | 3 | no | — |
| 472 | C4⋊C4 | — | 25 | 6 | no | — |
| 473 | C4⋊C4 | — | 25 | 3 | no | — |
| 474 | C4⋊C4 | — | 25 | 1 | no | — |
| 475 | C22⋊C4 | — | 25 | 6 | no | — |
| 476 | C22⋊C4 | — | 25 | 6 | no | — |
| 477 | C22⋊C4 | — | 25 | 2 | no | — |
| 478 | C22⋊C4 | — | 25 | 6 | no | — |
| 479 | C42 | — | 25 | 6 | no | — |
| 480 | C42 | — | 25 | 3 | no | — |
| 481 | C42 | — | 25 | 1 | no | — |
| 482 | C42 | — | 25 | 12 | no | — |
| 483 | C42 | — | 25 | 6 | no | — |
| 484 | C42 | — | 25 | 3 | no | — |
| 485 | C42 | — | 25 | 3 | no | — |
| 486 | C42 | — | 25 | 6 | no | — |
| 487 | C2×C5 | — | 2 | 6 | no | — |
| 488 | C2×C5 | — | 2 | 2 | no | — |
| 489 | C2×C5 | — | 4 | 6 | no | — |
| 490 | C2×C5 | — | 10 | 4 | no | — |
| 491 | C2×C5 | C24×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 492 | D5 | — | 2 | 4 | no | — |
| 493 | D5 | — | 5 | 2 | no | — |
| 494 | D5 | — | 5 | 2 | no | — |
| 495 | D5 | — | 10 | 2 | no | — |
| 496 | D5 | — | 10 | 2 | no | — |
| 497 | D5 | — | 10 | 6 | no | — |
| 498 | D5 | — | 20 | 6 | no | — |
| 499 | C23 | — | 25 | 2 | no | — |
| 500 | C23 | — | 25 | 3 | no | — |
| 501 | Q8 | — | 5 | 12 | no | — |
| 502 | Q8 | — | 5 | 6 | no | — |
| 503 | Q8 | — | 25 | 6 | no | — |
| 504 | Q8 | — | 25 | 12 | no | — |
| 505 | Q8 | — | 25 | 3 | no | — |
| 506 | Q8 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 507 | D4 | — | 5 | 12 | no | — |
| 508 | D4 | — | 5 | 2 | no | — |
| 509 | D4 | — | 25 | 12 | no | — |
| 510 | D4 | — | 25 | 2 | no | — |
| 511 | D4 | — | 25 | 6 | no | — |
| 512 | D4 | — | 25 | 3 | no | — |
| 513 | D4 | C2×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 514 | C2×C4 | — | 5 | 12 | no | — |
| 515 | C2×C4 | — | 5 | 12 | no | — |
| 516 | C2×C4 | — | 25 | 6 | no | — |
| 517 | C2×C4 | — | 25 | 12 | no | — |
| 518 | C2×C4 | — | 25 | 12 | no | — |
| 519 | C2×C4 | — | 25 | 1 | no | — |
| 520 | C2×C4 | — | 25 | 3 | no | — |
| 521 | C2×C4 | — | 25 | 3 | no | — |
| 522 | C2×C4 | — | 25 | 1 | no | — |
| 523 | C2×C4 | — | 25 | 3 | no | — |
| 524 | C2×C4 | — | 25 | 3 | no | — |
| 525 | C2×C4 | — | 25 | 3 | no | — |
| 526 | C2×C4 | — | 25 | 2 | no | — |
| 527 | C2×C4 | — | 25 | 3 | no | — |
| 528 | C2×C4 | — | 25 | 1 | no | — |
| 529 | C2×C4 | — | 25 | 6 | no | — |
| 530 | C2×C4 | — | 50 | 6 | no | — |
| 531 | C2×C4 | — | 50 | 4 | no | — |
| 532 | C2×C4 | — | 100 | 3 | no | — |
| 533 | C2×C4 | — | 100 | 6 | no | — |
| 534 | C2×C4 | — | 100 | 6 | no | — |
| 535 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 536 | C5 | — | 2 | 2 | no | — |
| 537 | C5 | AGL(1,𝔽5)×2−1+4 | 1 | 2 | yes | complemented |
| 538 | C22 | — | 5 | 4 | no | — |
| 539 | C22 | — | 25 | 1 | no | — |
| 540 | C22 | — | 25 | 3 | no | — |
| 541 | C22 | — | 50 | 3 | no | — |
| 542 | C22 | — | 50 | 3 | no | — |
| 543 | C22 | — | 50 | 2 | no | — |
| 544 | C22 | — | 50 | 2 | no | — |
| 545 | C22 | C22×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 546 | C4 | — | 5 | 12 | no | — |
| 547 | C4 | — | 25 | 2 | no | — |
| 548 | C4 | — | 25 | 3 | no | — |
| 549 | C4 | — | 25 | 1 | no | — |
| 550 | C4 | — | 50 | 3 | no | — |
| 551 | C4 | — | 50 | 2 | no | — |
| 552 | C4 | — | 50 | 1 | no | — |
| 553 | C4 | — | 50 | 3 | no | — |
| 554 | C4 | — | 50 | 6 | no | — |
| 555 | C4 | C22×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 556 | C4 | C22×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 557 | C2 | — | 2 | 3 | no | — |
| 558 | C2 | — | 10 | 4 | no | — |
| 559 | C2 | — | 25 | 1 | no | — |
| 560 | C2 | — | 25 | 1 | no | — |
| 561 | C2 | — | 50 | 3 | no | — |
| 562 | C2 | C23×D5⋊AGL(1,𝔽5) | 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