← D5⋊#4828 #14418459
Subgroups — D5⋊#4828 #14418459
Order 1920.
800 conjugacy classes of subgroups.
The subgroup lattice has 568 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C4×D5×Dic6 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11752335 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×D5⋊(C4⋊C8) | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | D5⋊(Dic3⋊C8) | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | D5⋊(Dic3⋊C8) | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11751788 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #11751775 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11751771 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11751766 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11751765 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | Dic3×D5⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | D5⋊#446 | — | 3 | 1 | no | maximal, Hall |
| 13 | C2×D5×Dic6 | C4 | 1 | 1 | yes | characteristic |
| 14 | C2×D5⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×D5⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C3×D5⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C3×D5⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 18 | C4×Dic30 | C4 | 1 | 1 | yes | characteristic |
| 19 | C4×C5×Dic6 | C4 | 1 | 1 | yes | characteristic |
| 20 | C3×C42×D5 | C22 | 1 | 1 | yes | characteristic |
| 21 | C4×#1204 | C4 | 1 | 1 | yes | characteristic |
| 22 | C4×#1204 | C4 | 1 | 1 | yes | characteristic |
| 23 | D5×C4⋊Dic3 | C4 | 1 | 1 | yes | characteristic |
| 24 | D5×Dic3⋊C4 | C4 | 1 | 1 | yes | characteristic |
| 25 | D5×Dic3⋊C4 | C4 | 1 | 1 | yes | characteristic |
| 26 | C4×D5×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×D5×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 28 | #91333 | C22 | 1 | 1 | yes | characteristic |
| 29 | Dic5×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 30 | #91323 | C22 | 1 | 1 | yes | characteristic |
| 31 | #91323 | C22 | 1 | 1 | yes | characteristic |
| 32 | #91231 | C22 | 1 | 2 | yes | — |
| 33 | #91231 | C22 | 1 | 2 | yes | — |
| 34 | C3×#4004 | C22 | 1 | 2 | yes | — |
| 35 | C3×C4⋊#170 | C22 | 1 | 2 | yes | — |
| 36 | #91177 | C22 | 1 | 2 | yes | — |
| 37 | #91177 | C22 | 1 | 2 | yes | — |
| 38 | Dic3⋊#170 | C22 | 1 | 2 | yes | — |
| 39 | Dic3⋊#170 | C22 | 1 | 2 | yes | — |
| 40 | #91169 | C22 | 1 | 2 | yes | — |
| 41 | #91169 | C22 | 1 | 2 | yes | — |
| 42 | Dic3×#170 | C22 | 1 | 2 | yes | — |
| 43 | Dic3×#170 | C22 | 1 | 2 | yes | — |
| 44 | C2×#4828 | — | 5 | 1 | no | maximal, Hall |
| 45 | C4×Q8×D5 | — | 3 | 1 | no | — |
| 46 | #65788 | — | 3 | 2 | no | — |
| 47 | #65709 | — | 3 | 2 | no | — |
| 48 | #65707 | — | 3 | 2 | no | — |
| 49 | #65707 | — | 3 | 2 | no | — |
| 50 | D5⋊(C4⋊C8) | — | 3 | 1 | no | — |
| 51 | D5⋊(C4⋊C8) | — | 3 | 1 | no | — |
| 52 | D5⋊(C4⋊C8) | D3 | 1 | 1 | yes | characteristic |
| 53 | #65676 | — | 3 | 1 | no | — |
| 54 | #65676 | — | 3 | 1 | no | — |
| 55 | C4×D5⋊C8 | — | 3 | 1 | no | — |
| 56 | C2×Dic30 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×C5×Dic6 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C2×C3×C4×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C2×C3×C4×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C2×C3×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×#1204 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | C2×#1204 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C2×D5×Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | C2×D5×Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C2×D5×Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C2×D5×Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | D5×Dic6 | — | 2 | 4 | no | — |
| 68 | C2×C3⋊#170 | C23 | 1 | 2 | yes | — |
| 69 | C2×C3⋊#170 | C23 | 1 | 2 | yes | — |
| 70 | D5⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 71 | D5⋊(C3⋊C8) | Q8 | 1 | 4 | yes | complemented |
| 72 | C2×C3×#170 | C23 | 1 | 2 | yes | — |
| 73 | C2×C3×#170 | C23 | 1 | 2 | yes | — |
| 74 | C3×D5⋊C8 | — | 2 | 2 | no | — |
| 75 | C3×D5⋊C8 | — | 2 | 2 | no | — |
| 76 | C3×C42×C5 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | C4⋊Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | #6712 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | #6712 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | C4×Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | C4×Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 82 | C5×C4⋊Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C5×Dic3⋊C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C5×Dic3⋊C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C4×C5×Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | C4×C5×Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | C3×C4×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | C3×C4×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 89 | C3×C4×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 90 | Dic3⋊Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 91 | Dic3⋊Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 92 | #6669 | C2×C4 | 1 | 1 | yes | characteristic |
| 93 | #6669 | C2×C4 | 1 | 1 | yes | characteristic |
| 94 | #6668 | C2×C4 | 1 | 1 | yes | characteristic |
| 95 | #6668 | C2×C4 | 1 | 1 | yes | characteristic |
| 96 | Dic3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 97 | Dic3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 98 | Dic3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 99 | Dic3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×C4×Dic6 | — | 5 | 1 | no | — |
| 101 | C2×C3×C4⋊C8 | — | 5 | 1 | no | — |
| 102 | C2×#815 | — | 5 | 1 | no | — |
| 103 | C2×Dic3⋊C8 | — | 5 | 1 | no | — |
| 104 | C2×Dic3⋊C8 | — | 5 | 1 | no | — |
| 105 | C2×C8×Dic3 | — | 5 | 1 | no | — |
| 106 | C2×#803 | — | 5 | 1 | no | — |
| 107 | #4828 | — | 5 | 2 | no | — |
| 108 | #4828 | — | 5 | 2 | no | — |
| 109 | #4828 | — | 5 | 2 | no | — |
| 110 | #4828 | — | 5 | 2 | no | — |
| 111 | C2×Q8×D5 | — | 3 | 1 | no | — |
| 112 | C2×D5⋊C8 | — | 3 | 1 | no | — |
| 113 | C2×D5⋊C8 | — | 3 | 1 | no | — |
| 114 | C2×D5⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 115 | C2×D5⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 116 | C4×C5×Q8 | — | 3 | 1 | no | — |
| 117 | Q8×Dic5 | — | 3 | 1 | no | — |
| 118 | D5×C4⋊C4 | — | 3 | 1 | no | — |
| 119 | D5×C4⋊C4 | — | 3 | 1 | no | — |
| 120 | D5×C4⋊C4 | — | 3 | 1 | no | — |
| 121 | #4033 | — | 3 | 1 | no | — |
| 122 | #4033 | — | 3 | 1 | no | — |
| 123 | #4033 | — | 3 | 1 | no | — |
| 124 | C42×D5 | — | 3 | 1 | no | — |
| 125 | C42×D5 | — | 3 | 1 | no | — |
| 126 | C42×D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 127 | C4×Dic10 | — | 3 | 1 | no | — |
| 128 | C4×Dic10 | — | 3 | 1 | no | — |
| 129 | C4×Dic10 | — | 3 | 1 | no | — |
| 130 | #4004 | — | 3 | 2 | no | — |
| 131 | #4004 | — | 3 | 2 | no | — |
| 132 | #4004 | C2×D3 | 1 | 2 | yes | — |
| 133 | #4002 | — | 3 | 2 | no | — |
| 134 | #4002 | — | 3 | 2 | no | — |
| 135 | #4002 | — | 3 | 2 | no | — |
| 136 | #4002 | — | 3 | 2 | no | — |
| 137 | C4⋊#170 | — | 3 | 2 | no | — |
| 138 | C4⋊#170 | — | 3 | 2 | no | — |
| 139 | C4⋊#170 | C2×D3 | 1 | 2 | yes | — |
| 140 | C4×#170 | — | 3 | 2 | no | — |
| 141 | C4×#170 | — | 3 | 2 | no | — |
| 142 | C2×#446 | — | 15 | 1 | no | Sylow |
| 143 | C22×C3×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 144 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 145 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 146 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 147 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 148 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 149 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 150 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 151 | Dic30 | — | 2 | 2 | no | — |
| 152 | C2×C5×Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 153 | C2×C5×Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 154 | C2×C5×Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 155 | C2×C5×Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 156 | C5×Dic6 | — | 2 | 2 | no | — |
| 157 | C2×C3×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 158 | C2×C3×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 159 | C2×C3×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 160 | C3×C4×D5 | — | 2 | 2 | no | — |
| 161 | C3×C4×D5 | — | 2 | 2 | no | — |
| 162 | C3×C4×D5 | C2×Q8 | 1 | 2 | yes | — |
| 163 | C3×C4×D5 | #41 | 1 | 2 | yes | — |
| 164 | #1204 | — | 2 | 2 | no | — |
| 165 | #1204 | — | 2 | 2 | no | — |
| 166 | D5×Dic3 | — | 2 | 2 | no | — |
| 167 | D5×Dic3 | — | 2 | 2 | no | — |
| 168 | D5×Dic3 | — | 2 | 2 | no | — |
| 169 | D5×Dic3 | M16 | 1 | 4 | yes | — |
| 170 | C3⋊#170 | — | 2 | 2 | no | — |
| 171 | C3⋊#170 | C2×Q8 | 1 | 4 | yes | complemented |
| 172 | C3×#170 | — | 2 | 2 | no | — |
| 173 | C3×#170 | — | 2 | 2 | no | — |
| 174 | C22×Dic6 | — | 5 | 1 | no | — |
| 175 | C22×C3×C8 | — | 5 | 1 | no | — |
| 176 | C22×C3×C8 | — | 5 | 1 | no | — |
| 177 | C2×C3×C42 | — | 5 | 1 | no | — |
| 178 | C2×C4⋊Dic3 | — | 5 | 1 | no | — |
| 179 | C2×Dic3⋊C4 | — | 5 | 1 | no | — |
| 180 | C2×Dic3⋊C4 | — | 5 | 1 | no | — |
| 181 | C2×C4×Dic3 | — | 5 | 1 | no | — |
| 182 | C2×C4×Dic3 | — | 5 | 1 | no | — |
| 183 | C22×C3⋊C8 | — | 5 | 1 | no | — |
| 184 | C22×C3⋊C8 | — | 5 | 1 | no | — |
| 185 | C4×Dic6 | — | 5 | 1 | no | — |
| 186 | C4×Dic6 | — | 5 | 1 | no | — |
| 187 | C4×Dic6 | — | 5 | 1 | no | — |
| 188 | C4×Dic6 | — | 5 | 1 | no | — |
| 189 | C4×Dic6 | — | 5 | 1 | no | — |
| 190 | C4×Dic6 | — | 5 | 1 | no | — |
| 191 | C4×Dic6 | — | 5 | 1 | no | — |
| 192 | C4×Dic6 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 193 | C3×C4⋊C8 | — | 5 | 2 | no | — |
| 194 | C3×C4⋊C8 | — | 5 | 2 | no | — |
| 195 | #815 | — | 5 | 2 | no | — |
| 196 | #815 | — | 5 | 2 | no | — |
| 197 | Dic3⋊C8 | — | 5 | 2 | no | — |
| 198 | Dic3⋊C8 | — | 5 | 2 | no | — |
| 199 | Dic3⋊C8 | — | 5 | 2 | no | — |
| 200 | Dic3⋊C8 | — | 5 | 2 | no | — |
| 201 | C8×Dic3 | — | 5 | 2 | no | — |
| 202 | C8×Dic3 | — | 5 | 2 | no | — |
| 203 | #803 | — | 5 | 2 | no | — |
| 204 | #803 | — | 5 | 2 | no | — |
| 205 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 206 | Q8×D5 | — | 6 | 4 | no | — |
| 207 | C2×C4×D5 | — | 3 | 1 | no | — |
| 208 | C2×C4×D5 | — | 3 | 1 | no | — |
| 209 | C2×C4×D5 | — | 3 | 1 | no | — |
| 210 | C2×C4×D5 | — | 3 | 1 | no | — |
| 211 | C2×C4×D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 212 | C2×C4×D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 214 | C2×Dic10 | — | 3 | 1 | no | — |
| 215 | C2×Dic10 | — | 3 | 1 | no | — |
| 216 | C2×Dic10 | — | 3 | 1 | no | — |
| 217 | C2×#170 | — | 3 | 2 | no | — |
| 218 | C2×#170 | — | 3 | 2 | no | — |
| 219 | C2×#170 | C22×D3 | 1 | 2 | yes | — |
| 220 | C2×#170 | C22×D3 | 1 | 2 | yes | — |
| 221 | D5⋊C8 | — | 2 | 2 | no | — |
| 222 | D5⋊C8 | — | 2 | 2 | no | — |
| 223 | D5⋊C8 | — | 3 | 4 | no | — |
| 224 | D5⋊C8 | — | 6 | 2 | no | — |
| 225 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 226 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 227 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 228 | C42×C5 | — | 3 | 1 | no | — |
| 229 | C42×C5 | — | 3 | 1 | no | — |
| 230 | C42×C5 | C4×D3 | 1 | 1 | yes | characteristic |
| 231 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 232 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 233 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 234 | #683 | — | 3 | 1 | no | — |
| 235 | #683 | — | 3 | 1 | no | — |
| 236 | #683 | — | 3 | 1 | no | — |
| 237 | #683 | — | 3 | 1 | no | — |
| 238 | #683 | — | 3 | 1 | no | — |
| 239 | #683 | — | 3 | 1 | no | — |
| 240 | C4×Dic5 | — | 3 | 1 | no | — |
| 241 | C4×Dic5 | — | 3 | 1 | no | — |
| 242 | C4×Dic5 | — | 3 | 1 | no | — |
| 243 | C4×Dic5 | — | 3 | 1 | no | — |
| 244 | C4×Dic5 | — | 3 | 1 | no | — |
| 245 | C4×Dic5 | — | 3 | 1 | no | — |
| 246 | C4×Dic5 | C4×D3 | 1 | 1 | yes | characteristic |
| 247 | C4×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 248 | C4×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 249 | C2×C4×Q8 | — | 15 | 1 | no | — |
| 250 | #446 | — | 15 | 2 | no | — |
| 251 | #446 | — | 15 | 2 | no | — |
| 252 | #446 | — | 15 | 2 | no | — |
| 253 | #446 | — | 15 | 2 | no | — |
| 254 | C2×C4⋊C8 | — | 5 | 1 | no | — |
| 255 | C2×C4⋊C8 | — | 15 | 1 | no | — |
| 256 | C2×C4⋊C8 | — | 15 | 1 | no | — |
| 257 | C2×#97 | — | 15 | 1 | no | — |
| 258 | C2×#97 | — | 15 | 1 | no | — |
| 259 | C2×C4×C8 | — | 15 | 1 | no | — |
| 260 | C22×C3×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 261 | C2×C3×D5 | C4×Q8 | 1 | 2 | yes | — |
| 262 | C2×C3×D5 | C2×M16 | 1 | 2 | yes | — |
| 263 | C2×C3×D5 | #131 | 1 | 2 | yes | — |
| 264 | C3×C4×C5 | — | 2 | 1 | no | — |
| 265 | C3×C4×C5 | — | 2 | 1 | no | — |
| 266 | C3×C4×C5 | C4×Q8 | 1 | 2 | yes | — |
| 267 | Dic15 | — | 2 | 1 | no | — |
| 268 | Dic15 | — | 2 | 1 | no | — |
| 269 | Dic15 | — | 2 | 1 | no | — |
| 270 | Dic15 | C2×M16 | 1 | 2 | yes | — |
| 271 | C3×Dic5 | — | 2 | 1 | no | — |
| 272 | C3×Dic5 | — | 2 | 1 | no | — |
| 273 | C3×Dic5 | C22×Q8 | 1 | 1 | yes | characteristic |
| 274 | C3×Dic5 | C2×#41 | 1 | 1 | yes | characteristic |
| 275 | C5×Dic3 | — | 2 | 1 | no | — |
| 276 | C5×Dic3 | — | 2 | 1 | no | — |
| 277 | C5×Dic3 | — | 2 | 1 | no | — |
| 278 | C5×Dic3 | C2×M16 | 1 | 2 | yes | — |
| 279 | C22×C3×C4 | — | 5 | 1 | no | — |
| 280 | C22×C3×C4 | — | 5 | 1 | no | — |
| 281 | C22×C3×C4 | — | 5 | 1 | no | — |
| 282 | C22×Dic3 | — | 5 | 1 | no | — |
| 283 | C22×Dic3 | — | 5 | 1 | no | — |
| 284 | C22×Dic3 | — | 5 | 1 | no | — |
| 285 | C22×Dic3 | — | 5 | 1 | no | — |
| 286 | C2×Dic6 | — | 5 | 1 | no | — |
| 287 | C2×Dic6 | — | 5 | 1 | no | — |
| 288 | C2×Dic6 | — | 5 | 1 | no | — |
| 289 | C2×Dic6 | — | 10 | 4 | no | — |
| 290 | C2×Dic6 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 291 | C2×C3×C8 | — | 5 | 2 | no | — |
| 292 | C2×C3×C8 | — | 5 | 2 | no | — |
| 293 | C2×C3×C8 | — | 10 | 2 | no | — |
| 294 | C2×C3×C8 | — | 10 | 2 | no | — |
| 295 | C3×C42 | — | 5 | 1 | no | — |
| 296 | C3×C42 | — | 5 | 1 | no | — |
| 297 | C3×C42 | — | 5 | 1 | no | — |
| 298 | C3×C42 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 299 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 300 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 301 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 302 | C4⋊Dic3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 303 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 304 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 305 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 306 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 307 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 308 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 309 | Dic3⋊C4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 310 | Dic3⋊C4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 311 | C4×Dic3 | — | 5 | 1 | no | — |
| 312 | C4×Dic3 | — | 5 | 1 | no | — |
| 313 | C4×Dic3 | — | 5 | 1 | no | — |
| 314 | C4×Dic3 | — | 5 | 1 | no | — |
| 315 | C4×Dic3 | — | 5 | 1 | no | — |
| 316 | C4×Dic3 | — | 5 | 1 | no | — |
| 317 | C4×Dic3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 318 | C4×Dic3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 319 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 320 | C2×C3⋊C8 | — | 5 | 4 | no | — |
| 321 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 322 | C2×C3⋊C8 | — | 10 | 2 | no | — |
| 323 | C22×D5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 324 | C5×Q8 | — | 6 | 2 | no | — |
| 325 | C2×C4×C5 | — | 3 | 1 | no | — |
| 326 | C2×C4×C5 | — | 3 | 1 | no | — |
| 327 | C2×C4×C5 | — | 3 | 1 | no | — |
| 328 | C2×C4×C5 | — | 3 | 1 | no | — |
| 329 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 330 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 331 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 332 | C2×Dic5 | — | 3 | 1 | no | — |
| 333 | C2×Dic5 | — | 3 | 1 | no | — |
| 334 | C2×Dic5 | — | 3 | 1 | no | — |
| 335 | C2×Dic5 | — | 3 | 1 | no | — |
| 336 | C2×Dic5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 337 | C2×Dic5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 338 | C2×Dic5 | C23×D3 | 1 | 1 | yes | characteristic |
| 339 | C4×D5 | — | 2 | 2 | no | — |
| 340 | C4×D5 | — | 2 | 2 | no | — |
| 341 | C4×D5 | — | 3 | 4 | no | — |
| 342 | C4×D5 | — | 6 | 2 | no | — |
| 343 | C4×D5 | — | 6 | 2 | no | — |
| 344 | C4×D5 | — | 6 | 2 | no | — |
| 345 | C4×D5 | #237 | 1 | 2 | yes | — |
| 346 | C4×D5 | D3×Q8 | 1 | 2 | yes | — |
| 347 | Dic10 | — | 6 | 2 | no | — |
| 348 | Dic10 | — | 6 | 2 | no | — |
| 349 | Dic10 | — | 6 | 2 | no | — |
| 350 | #170 | — | 2 | 2 | no | — |
| 351 | #170 | — | 2 | 2 | no | — |
| 352 | #170 | — | 3 | 4 | no | — |
| 353 | #170 | — | 6 | 2 | no | — |
| 354 | C22×Q8 | — | 15 | 1 | no | — |
| 355 | C22×C8 | — | 5 | 1 | no | — |
| 356 | C22×C8 | — | 5 | 1 | no | — |
| 357 | C22×C8 | — | 15 | 1 | no | — |
| 358 | C22×C8 | — | 15 | 1 | no | — |
| 359 | C4×Q8 | — | 3 | 1 | no | — |
| 360 | C4×Q8 | — | 15 | 1 | no | — |
| 361 | C4×Q8 | — | 15 | 1 | no | — |
| 362 | C4×Q8 | — | 15 | 1 | no | — |
| 363 | C4×Q8 | — | 15 | 1 | no | — |
| 364 | C4×Q8 | — | 15 | 1 | no | — |
| 365 | C4×Q8 | — | 15 | 1 | no | — |
| 366 | C4×Q8 | — | 15 | 1 | no | — |
| 367 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 368 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 369 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 370 | C2×C42 | — | 5 | 1 | no | — |
| 371 | C2×C42 | — | 15 | 1 | no | — |
| 372 | C2×C42 | — | 15 | 1 | no | — |
| 373 | C4⋊C8 | — | 5 | 2 | no | — |
| 374 | C4⋊C8 | — | 5 | 2 | no | — |
| 375 | C4⋊C8 | — | 15 | 2 | no | — |
| 376 | C4⋊C8 | — | 15 | 2 | no | — |
| 377 | C4⋊C8 | — | 15 | 2 | no | — |
| 378 | C4⋊C8 | — | 15 | 2 | no | — |
| 379 | #97 | — | 15 | 2 | no | — |
| 380 | #97 | — | 15 | 2 | no | — |
| 381 | #97 | — | 15 | 2 | no | — |
| 382 | #97 | — | 15 | 2 | no | — |
| 383 | C4×C8 | — | 15 | 2 | no | — |
| 384 | C4×C8 | — | 15 | 2 | no | — |
| 385 | C2×C3×C5 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 386 | C2×C3×C5 | C22×M16 | 1 | 1 | yes | characteristic |
| 387 | C2×C3×C5 | C2×#131 | 1 | 1 | yes | characteristic |
| 388 | C3×D5 | #446 | 1 | 4 | yes | complemented |
| 389 | C23×C3 | — | 5 | 1 | no | — |
| 390 | C2×C3×C4 | — | 5 | 1 | no | — |
| 391 | C2×C3×C4 | — | 5 | 2 | no | — |
| 392 | C2×C3×C4 | — | 5 | 2 | no | — |
| 393 | C2×C3×C4 | — | 5 | 1 | no | — |
| 394 | C2×C3×C4 | — | 5 | 1 | no | — |
| 395 | C2×C3×C4 | — | 10 | 2 | no | — |
| 396 | C2×C3×C4 | — | 10 | 2 | no | — |
| 397 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 398 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 399 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 400 | C2×Dic3 | — | 5 | 1 | no | — |
| 401 | C2×Dic3 | — | 5 | 4 | no | — |
| 402 | C2×Dic3 | — | 5 | 1 | no | — |
| 403 | C2×Dic3 | — | 5 | 1 | no | — |
| 404 | C2×Dic3 | — | 5 | 1 | no | — |
| 405 | C2×Dic3 | — | 10 | 2 | no | — |
| 406 | C2×Dic3 | — | 10 | 2 | no | — |
| 407 | C2×Dic3 | — | 10 | 2 | no | — |
| 408 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 409 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 410 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 411 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 412 | Dic6 | — | 2 | 2 | no | — |
| 413 | Dic6 | — | 10 | 2 | no | — |
| 414 | Dic6 | — | 10 | 2 | no | — |
| 415 | Dic6 | — | 10 | 2 | no | — |
| 416 | C3×C8 | — | 10 | 2 | no | — |
| 417 | C3×C8 | — | 10 | 2 | no | — |
| 418 | C3⋊C8 | — | 5 | 4 | no | — |
| 419 | C3⋊C8 | — | 10 | 2 | no | — |
| 420 | C22×C5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 421 | C2×D5 | #887 | 1 | 2 | yes | — |
| 422 | C2×D5 | #901 | 1 | 2 | yes | — |
| 423 | C2×D5 | D3×M16 | 1 | 2 | yes | — |
| 424 | C4×C5 | — | 2 | 1 | no | — |
| 425 | C4×C5 | — | 2 | 1 | no | — |
| 426 | C4×C5 | — | 3 | 2 | no | — |
| 427 | C4×C5 | — | 6 | 1 | no | — |
| 428 | C4×C5 | — | 6 | 1 | no | — |
| 429 | C4×C5 | — | 6 | 1 | no | — |
| 430 | C4×C5 | #887 | 1 | 2 | yes | — |
| 431 | Dic5 | — | 2 | 1 | no | — |
| 432 | Dic5 | — | 2 | 1 | no | — |
| 433 | Dic5 | — | 3 | 2 | no | — |
| 434 | Dic5 | — | 6 | 1 | no | — |
| 435 | Dic5 | — | 6 | 1 | no | — |
| 436 | Dic5 | — | 6 | 1 | no | — |
| 437 | Dic5 | C2×#237 | 1 | 1 | yes | characteristic |
| 438 | Dic5 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 439 | C2×Q8 | — | 3 | 1 | no | — |
| 440 | C2×Q8 | — | 15 | 1 | no | — |
| 441 | C2×Q8 | — | 15 | 1 | no | — |
| 442 | C2×Q8 | — | 15 | 1 | no | — |
| 443 | C2×Q8 | — | 30 | 4 | no | — |
| 444 | C22×C4 | — | 5 | 1 | no | — |
| 445 | C22×C4 | — | 5 | 1 | no | — |
| 446 | C22×C4 | — | 5 | 1 | no | — |
| 447 | C22×C4 | — | 15 | 1 | no | — |
| 448 | C22×C4 | — | 15 | 1 | no | — |
| 449 | C22×C4 | — | 15 | 1 | no | — |
| 450 | C22×C4 | — | 15 | 1 | no | — |
| 451 | C2×C8 | — | 5 | 2 | no | — |
| 452 | C2×C8 | — | 5 | 2 | no | — |
| 453 | C2×C8 | — | 10 | 2 | no | — |
| 454 | C2×C8 | — | 10 | 2 | no | — |
| 455 | C2×C8 | — | 15 | 2 | no | — |
| 456 | C2×C8 | — | 15 | 4 | no | — |
| 457 | C2×C8 | — | 15 | 2 | no | — |
| 458 | C2×C8 | — | 30 | 2 | no | — |
| 459 | C4⋊C4 | — | 3 | 1 | no | — |
| 460 | C4⋊C4 | — | 3 | 1 | no | — |
| 461 | C4⋊C4 | — | 3 | 1 | no | — |
| 462 | C4⋊C4 | — | 15 | 1 | no | — |
| 463 | C4⋊C4 | — | 15 | 1 | no | — |
| 464 | C4⋊C4 | — | 15 | 1 | no | — |
| 465 | C4⋊C4 | — | 15 | 1 | no | — |
| 466 | C4⋊C4 | — | 15 | 1 | no | — |
| 467 | C4⋊C4 | — | 15 | 1 | no | — |
| 468 | C4⋊C4 | — | 15 | 1 | no | — |
| 469 | C4⋊C4 | — | 15 | 1 | no | — |
| 470 | C4⋊C4 | — | 15 | 1 | no | — |
| 471 | C42 | — | 3 | 1 | no | — |
| 472 | C42 | — | 3 | 1 | no | — |
| 473 | C42 | — | 5 | 1 | no | — |
| 474 | C42 | — | 5 | 1 | no | — |
| 475 | C42 | — | 5 | 1 | no | — |
| 476 | C42 | — | 15 | 1 | no | — |
| 477 | C42 | — | 15 | 1 | no | — |
| 478 | C42 | — | 15 | 1 | no | — |
| 479 | C42 | — | 15 | 1 | no | — |
| 480 | C42 | — | 15 | 1 | no | — |
| 481 | C42 | — | 15 | 1 | no | — |
| 482 | C42 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 483 | C3×C5 | C2×#446 | 1 | 1 | yes | characteristic, complemented, Hall |
| 484 | C22×C3 | — | 5 | 2 | no | — |
| 485 | C22×C3 | — | 5 | 2 | no | — |
| 486 | C22×C3 | — | 5 | 2 | no | — |
| 487 | C22×C3 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 488 | C3×C4 | — | 2 | 1 | no | — |
| 489 | C3×C4 | — | 2 | 1 | no | — |
| 490 | C3×C4 | — | 5 | 1 | no | — |
| 491 | C3×C4 | — | 5 | 1 | no | — |
| 492 | C3×C4 | — | 10 | 1 | no | — |
| 493 | C3×C4 | — | 10 | 1 | no | — |
| 494 | C3×C4 | Q8×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 495 | Dic3 | — | 2 | 1 | no | — |
| 496 | Dic3 | — | 2 | 1 | no | — |
| 497 | Dic3 | — | 2 | 1 | no | — |
| 498 | Dic3 | — | 5 | 2 | no | — |
| 499 | Dic3 | — | 10 | 1 | no | — |
| 500 | Dic3 | — | 10 | 1 | no | — |
| 501 | Dic3 | — | 10 | 1 | no | — |
| 502 | Dic3 | D5⋊M16 | 1 | 2 | yes | — |
| 503 | C2×C5 | C2×#887 | 1 | 1 | yes | characteristic |
| 504 | C2×C5 | C2×#901 | 1 | 1 | yes | characteristic |
| 505 | C2×C5 | C2×D3×M16 | 1 | 1 | yes | characteristic |
| 506 | D5 | #4828 | 1 | 4 | yes | complemented |
| 507 | C23 | — | 5 | 1 | no | — |
| 508 | Q8 | — | 6 | 2 | no | — |
| 509 | Q8 | — | 30 | 2 | no | — |
| 510 | Q8 | — | 30 | 2 | no | — |
| 511 | Q8 | — | 30 | 2 | no | — |
| 512 | C2×C4 | — | 3 | 1 | no | — |
| 513 | C2×C4 | — | 3 | 1 | no | — |
| 514 | C2×C4 | — | 3 | 1 | no | — |
| 515 | C2×C4 | — | 3 | 1 | no | — |
| 516 | C2×C4 | — | 5 | 1 | no | — |
| 517 | C2×C4 | — | 5 | 2 | no | — |
| 518 | C2×C4 | — | 5 | 2 | no | — |
| 519 | C2×C4 | — | 5 | 1 | no | — |
| 520 | C2×C4 | — | 5 | 1 | no | — |
| 521 | C2×C4 | — | 10 | 2 | no | — |
| 522 | C2×C4 | — | 10 | 2 | no | — |
| 523 | C2×C4 | — | 15 | 4 | no | — |
| 524 | C2×C4 | — | 15 | 1 | no | — |
| 525 | C2×C4 | — | 15 | 1 | no | — |
| 526 | C2×C4 | — | 15 | 1 | no | — |
| 527 | C2×C4 | — | 15 | 1 | no | — |
| 528 | C2×C4 | — | 30 | 2 | no | — |
| 529 | C2×C4 | — | 30 | 2 | no | — |
| 530 | C2×C4 | — | 30 | 2 | no | — |
| 531 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 532 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 533 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 534 | C8 | — | 10 | 2 | no | — |
| 535 | C8 | — | 10 | 2 | no | — |
| 536 | C8 | — | 15 | 4 | no | — |
| 537 | C8 | — | 30 | 2 | no | — |
| 538 | C2×C3 | — | 5 | 4 | no | — |
| 539 | C2×C3 | C2×D5⋊M16 | 1 | 1 | yes | characteristic |
| 540 | C2×C3 | C2×Q8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 541 | C2×C3 | D5⋊#131 | 1 | 1 | yes | characteristic |
| 542 | C5 | C2×#4828 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 543 | C22 | — | 5 | 2 | no | — |
| 544 | C22 | — | 5 | 2 | no | — |
| 545 | C22 | — | 5 | 2 | no | — |
| 546 | C22 | C22×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 547 | C4 | — | 2 | 1 | no | — |
| 548 | C4 | — | 2 | 1 | no | — |
| 549 | C4 | — | 3 | 2 | no | — |
| 550 | C4 | — | 5 | 1 | no | — |
| 551 | C4 | — | 5 | 1 | no | — |
| 552 | C4 | — | 6 | 1 | no | — |
| 553 | C4 | — | 6 | 1 | no | — |
| 554 | C4 | — | 6 | 1 | no | — |
| 555 | C4 | — | 10 | 1 | no | — |
| 556 | C4 | — | 10 | 1 | no | — |
| 557 | C4 | — | 15 | 2 | no | — |
| 558 | C4 | — | 30 | 1 | no | — |
| 559 | C4 | — | 30 | 1 | no | — |
| 560 | C4 | — | 30 | 1 | no | — |
| 561 | C4 | ΓL(1,𝔽16)⋊Q8 | 1 | 2 | yes | — |
| 562 | C3 | D5⋊#446 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 563 | C2 | — | 5 | 4 | no | — |
| 564 | C2 | C2×ΓL(1,𝔽16)⋊Q8 | 1 | 1 | yes | characteristic |
| 565 | C2 | D5⋊#901 | 1 | 1 | yes | characteristic |
| 566 | C2 | D3×D5⋊M16 | 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