← #14417609
Subgroups — #14417609
Order 1920.
912 conjugacy classes of subgroups.
The subgroup lattice has 404 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11756812 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×D5×Dic12 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11752380 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×#65718 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11751712 | C2 | 1 | 2 | yes | maximal |
| 6 | #11751668 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | AGL(1,𝔽5)×Dic12 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10617434 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×D5×Dic6 | C22 | 1 | 2 | yes | — |
| 10 | #91989 | C22 | 1 | 2 | yes | — |
| 11 | C3×#4130 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×D5⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 13 | #91923 | — | 2 | 4 | no | — |
| 14 | ΓL(1,𝔽16)⋊Q8 | — | 2 | 4 | no | — |
| 15 | AGL(1,𝔽5)×Dic6 | C22 | 1 | 8 | yes | — |
| 16 | C2×Dic60 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×C5×Dic12 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×C3×C8×D5 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#6663 | C4 | 1 | 2 | yes | complemented |
| 20 | D5×Dic12 | C4 | 1 | 2 | yes | complemented |
| 21 | D5×Dic12 | C4 | 1 | 2 | yes | complemented |
| 22 | D5×Dic12 | C22 | 1 | 2 | yes | — |
| 23 | D5×Dic12 | C22 | 1 | 2 | yes | — |
| 24 | #91223 | C22 | 1 | 2 | yes | — |
| 25 | #91222 | C22 | 1 | 2 | yes | — |
| 26 | C3×#3992 | C22 | 1 | 2 | yes | — |
| 27 | C3×C8×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 28 | #91154 | C22 | 1 | 8 | yes | — |
| 29 | #78573 | — | 5 | 1 | no | maximal, Hall |
| 30 | #66262 | — | 3 | 2 | no | — |
| 31 | C2×D5×Q16 | — | 3 | 1 | no | — |
| 32 | #65782 | — | 3 | 2 | no | — |
| 33 | #65739 | — | 3 | 4 | no | — |
| 34 | Q16×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 35 | #65721 | — | 3 | 1 | no | — |
| 36 | #65718 | D3 | 1 | 1 | yes | characteristic |
| 37 | C2×Dic30 | C2×C4 | 1 | 2 | yes | — |
| 38 | C2×C5×Dic6 | C2×C4 | 1 | 2 | yes | — |
| 39 | C2×C3×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×#1204 | — | 2 | 2 | no | — |
| 41 | C2×D5×Dic3 | — | 2 | 2 | no | — |
| 42 | D5×Dic6 | — | 2 | 2 | no | — |
| 43 | D5×Dic6 | — | 2 | 2 | no | — |
| 44 | D5×Dic6 | C2×C4 | 1 | 4 | yes | — |
| 45 | D5×Dic6 | C23 | 1 | 4 | yes | — |
| 46 | #6763 | — | 2 | 2 | no | — |
| 47 | C4⋊ΓL(1,𝔽16) | C23 | 1 | 4 | yes | — |
| 48 | C4×ΓL(1,𝔽16) | — | 2 | 2 | no | — |
| 49 | C3×C22⋊AGL(1,𝔽5) | D4 | 1 | 2 | yes | — |
| 50 | C3×#704 | — | 2 | 1 | no | — |
| 51 | C3×C4⋊AGL(1,𝔽5) | D4 | 1 | 2 | yes | — |
| 52 | C3×C4×AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 53 | C3×#700 | — | 2 | 1 | no | — |
| 54 | C3×D5⋊C8 | C23 | 1 | 2 | yes | — |
| 55 | Dic3⋊AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 56 | Dic3×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 57 | C2×C3×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | Dic60 | C2×C4 | 1 | 2 | yes | — |
| 59 | Dic60 | C2×C4 | 1 | 2 | yes | — |
| 60 | C5×Dic12 | C2×C4 | 1 | 2 | yes | — |
| 61 | C5×Dic12 | C2×C4 | 1 | 2 | yes | — |
| 62 | C2×C3×#168 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C3×C8×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | C3×C8×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C3×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 66 | C3×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 67 | #6663 | C2×C4 | 1 | 4 | yes | — |
| 68 | #6663 | C2×C4 | 1 | 4 | yes | — |
| 69 | C22×Dic12 | — | 5 | 1 | no | — |
| 70 | #5516 | — | 5 | 2 | no | — |
| 71 | C3×#405 | — | 5 | 1 | no | — |
| 72 | #5120 | — | 5 | 2 | no | — |
| 73 | #5106 | — | 5 | 1 | no | — |
| 74 | #4716 | — | 5 | 4 | no | — |
| 75 | C4×Dic12 | — | 5 | 4 | no | — |
| 76 | C2×Q8×D5 | — | 3 | 2 | no | — |
| 77 | Q8×AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 78 | Q8×AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 79 | #4130 | — | 3 | 2 | no | — |
| 80 | #4130 | — | 6 | 4 | no | — |
| 81 | #4130 | C2×D3 | 1 | 1 | yes | characteristic |
| 82 | D5⋊M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 83 | C2×C5×Q16 | — | 3 | 1 | no | — |
| 84 | C2×#689 | — | 3 | 2 | no | — |
| 85 | D5×Q16 | — | 3 | 2 | no | — |
| 86 | D5×Q16 | — | 3 | 2 | no | — |
| 87 | D5×Q16 | — | 3 | 2 | no | — |
| 88 | D5×Q16 | — | 3 | 2 | no | — |
| 89 | C2×Dic20 | — | 3 | 1 | no | — |
| 90 | C2×C8×D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 91 | #4009 | — | 3 | 8 | no | — |
| 92 | #3994 | — | 3 | 2 | no | — |
| 93 | #3993 | — | 3 | 2 | no | — |
| 94 | #3992 | C2×D3 | 1 | 2 | yes | — |
| 95 | C8×AGL(1,𝔽5) | C2×D3 | 1 | 2 | yes | — |
| 96 | #2950 | — | 15 | 1 | no | Sylow |
| 97 | C22×C3×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×ΓL(1,𝔽16) | — | 2 | 4 | no | — |
| 99 | C2×C3×AGL(1,𝔽5) | C2×D4 | 1 | 4 | yes | — |
| 100 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | C2×Dic15 | — | 2 | 2 | no | — |
| 102 | Dic30 | — | 2 | 2 | no | — |
| 103 | Dic30 | C22×C4 | 1 | 4 | yes | — |
| 104 | C2×C5×Dic3 | — | 2 | 2 | no | — |
| 105 | C5×Dic6 | — | 2 | 2 | no | — |
| 106 | C5×Dic6 | C22×C4 | 1 | 4 | yes | — |
| 107 | C2×C3×Dic5 | #41 | 1 | 1 | yes | characteristic |
| 108 | C3×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 109 | C3×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C3×C4×D5 | #41 | 1 | 1 | yes | characteristic |
| 111 | C3×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 112 | #1204 | — | 2 | 4 | no | — |
| 113 | #1204 | — | 2 | 4 | no | — |
| 114 | D5×Dic3 | — | 2 | 4 | no | — |
| 115 | D5×Dic3 | — | 2 | 4 | no | — |
| 116 | C3×#170 | — | 2 | 2 | no | — |
| 117 | C3×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 118 | C3×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 119 | C3×#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 120 | C3×#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 121 | C22×Dic6 | — | 5 | 2 | no | — |
| 122 | C2×C3×M16 | — | 5 | 1 | no | — |
| 123 | C22×C3×C8 | — | 5 | 1 | no | — |
| 124 | C3×#117 | — | 5 | 1 | no | — |
| 125 | #926 | — | 5 | 2 | no | — |
| 126 | C2×Dic12 | — | 5 | 2 | no | — |
| 127 | C2×Dic12 | — | 5 | 1 | no | — |
| 128 | C2×Dic12 | — | 5 | 2 | no | — |
| 129 | C2×Dic12 | — | 5 | 2 | no | — |
| 130 | C2×Dic12 | — | 5 | 2 | no | — |
| 131 | C2×Dic12 | — | 5 | 2 | no | — |
| 132 | C2×Dic12 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 133 | #887 | — | 10 | 4 | no | — |
| 134 | #877 | — | 10 | 4 | no | — |
| 135 | C4×Dic6 | — | 5 | 8 | no | — |
| 136 | C3×#97 | — | 5 | 2 | no | — |
| 137 | C3×C4×C8 | — | 5 | 2 | no | — |
| 138 | #818 | — | 5 | 2 | no | — |
| 139 | #817 | — | 5 | 2 | no | — |
| 140 | #816 | — | 5 | 8 | no | — |
| 141 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 142 | Q8×D5 | — | 3 | 4 | no | — |
| 143 | Q8×D5 | — | 3 | 4 | no | — |
| 144 | Q8×D5 | — | 6 | 2 | no | — |
| 145 | Q8×D5 | — | 6 | 2 | no | — |
| 146 | C2×C4×D5 | — | 6 | 2 | no | — |
| 147 | C2×C4×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 148 | C2×Dic10 | — | 3 | 2 | no | — |
| 149 | C2×Dic10 | — | 6 | 2 | no | — |
| 150 | C22⋊AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 151 | C22⋊AGL(1,𝔽5) | D12 | 1 | 2 | yes | — |
| 152 | #704 | — | 2 | 1 | no | — |
| 153 | C4⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 154 | C4⋊AGL(1,𝔽5) | — | 6 | 8 | no | — |
| 155 | C4⋊AGL(1,𝔽5) | D12 | 1 | 2 | yes | — |
| 156 | C4×AGL(1,𝔽5) | — | 6 | 8 | no | — |
| 157 | C4×AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 158 | C4×AGL(1,𝔽5) | C22×D3 | 1 | 2 | yes | — |
| 159 | #700 | — | 2 | 1 | no | — |
| 160 | D5⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 161 | C5×Q16 | — | 3 | 2 | no | — |
| 162 | C5×Q16 | — | 3 | 2 | no | — |
| 163 | C2×C5×C8 | C4×D3 | 1 | 1 | yes | characteristic |
| 164 | #689 | — | 3 | 4 | no | — |
| 165 | #689 | — | 3 | 4 | no | — |
| 166 | C2×#168 | C4×D3 | 1 | 1 | yes | characteristic |
| 167 | Dic20 | — | 3 | 2 | no | — |
| 168 | Dic20 | — | 3 | 2 | no | — |
| 169 | C8×D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 170 | C8×D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 171 | C8×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 172 | C8×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 173 | C22×Q16 | — | 15 | 1 | no | — |
| 174 | #519 | — | 15 | 2 | no | — |
| 175 | #441 | — | 15 | 4 | no | — |
| 176 | C4×Q16 | — | 15 | 4 | no | — |
| 177 | #427 | — | 15 | 1 | no | — |
| 178 | #419 | — | 15 | 2 | no | — |
| 179 | #405 | — | 5 | 1 | no | — |
| 180 | C22×C3×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×C3×D5 | — | 2 | 2 | no | — |
| 182 | C2×C3×D5 | C4×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C3×D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 184 | ΓL(1,𝔽16) | — | 4 | 4 | no | — |
| 185 | C3×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 186 | C3×C4×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 187 | C3×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 188 | Dic15 | — | 2 | 4 | no | — |
| 189 | C3×Dic5 | C4×D4 | 1 | 1 | yes | characteristic |
| 190 | C3×Dic5 | C2×#41 | 1 | 1 | yes | characteristic |
| 191 | C5×Dic3 | — | 2 | 4 | no | — |
| 192 | C22×C3×C4 | — | 5 | 1 | no | — |
| 193 | C22×Dic3 | — | 10 | 2 | no | — |
| 194 | C2×Dic6 | — | 5 | 2 | no | — |
| 195 | C2×Dic6 | — | 5 | 4 | no | — |
| 196 | C2×Dic6 | — | 5 | 4 | no | — |
| 197 | C2×Dic6 | — | 10 | 2 | no | — |
| 198 | C2×Dic6 | — | 10 | 2 | no | — |
| 199 | C2×Dic6 | — | 10 | 2 | no | — |
| 200 | C2×Dic6 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 201 | C3×M16 | — | 10 | 1 | no | — |
| 202 | C3×M16 | — | 10 | 1 | no | — |
| 203 | C2×C3×C8 | — | 5 | 1 | no | — |
| 204 | C2×C3×C8 | — | 5 | 1 | no | — |
| 205 | C2×C3×C8 | — | 5 | 1 | no | — |
| 206 | C2×C3×C8 | — | 5 | 1 | no | — |
| 207 | C2×C3×C8 | — | 5 | 1 | no | — |
| 208 | C2×C3×C8 | — | 5 | 2 | no | — |
| 209 | C2×C3×C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 210 | C3×C4⋊C4 | — | 5 | 2 | no | — |
| 211 | C3×C22⋊C4 | — | 5 | 2 | no | — |
| 212 | C3×C42 | — | 5 | 2 | no | — |
| 213 | #217 | — | 10 | 2 | no | — |
| 214 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 215 | Dic3⋊C4 | — | 10 | 8 | no | — |
| 216 | C4×Dic3 | — | 10 | 8 | no | — |
| 217 | C4×Dic3 | — | 10 | 2 | no | — |
| 218 | Dic12 | — | 5 | 4 | no | — |
| 219 | Dic12 | — | 5 | 4 | no | — |
| 220 | Dic12 | — | 5 | 2 | no | — |
| 221 | Dic12 | — | 5 | 2 | no | — |
| 222 | Dic12 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 223 | Dic12 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 224 | C22×D5 | C2×D12 | 1 | 1 | yes | characteristic |
| 225 | C2×AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 226 | C2×AGL(1,𝔽5) | C2×D12 | 1 | 4 | yes | — |
| 227 | C5×Q8 | — | 3 | 4 | no | — |
| 228 | C5×Q8 | — | 6 | 2 | no | — |
| 229 | C2×C4×C5 | — | 6 | 2 | no | — |
| 230 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 231 | C2×Dic5 | — | 6 | 2 | no | — |
| 232 | C2×Dic5 | #235 | 1 | 1 | yes | characteristic |
| 233 | C4×D5 | — | 6 | 4 | no | — |
| 234 | C4×D5 | — | 6 | 4 | no | — |
| 235 | C4×D5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 236 | C4×D5 | C2×D12 | 1 | 1 | yes | characteristic |
| 237 | C4×D5 | #235 | 1 | 1 | yes | characteristic |
| 238 | C4×D5 | C23×D3 | 1 | 1 | yes | characteristic |
| 239 | Dic10 | — | 3 | 4 | no | — |
| 240 | Dic10 | — | 6 | 2 | no | — |
| 241 | Dic10 | — | 6 | 4 | no | — |
| 242 | Dic10 | — | 6 | 4 | no | — |
| 243 | #170 | — | 2 | 2 | no | — |
| 244 | C5×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 245 | C5×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 246 | #168 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 247 | #168 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 248 | C22×Q8 | — | 15 | 2 | no | — |
| 249 | C2×Q16 | — | 3 | 1 | no | — |
| 250 | C2×Q16 | — | 15 | 2 | no | — |
| 251 | C2×Q16 | — | 15 | 2 | no | — |
| 252 | C2×Q16 | — | 15 | 2 | no | — |
| 253 | C2×Q16 | — | 15 | 2 | no | — |
| 254 | C2×Q16 | — | 15 | 2 | no | — |
| 255 | C2×Q16 | — | 15 | 1 | no | — |
| 256 | C2×M16 | — | 5 | 1 | no | — |
| 257 | C22×C8 | — | 5 | 1 | no | — |
| 258 | C4×Q8 | — | 15 | 8 | no | — |
| 259 | C4×Q8 | — | 30 | 4 | no | — |
| 260 | #117 | — | 5 | 1 | no | — |
| 261 | #117 | — | 15 | 2 | no | — |
| 262 | #117 | — | 30 | 4 | no | — |
| 263 | #107 | — | 15 | 2 | no | — |
| 264 | #106 | — | 15 | 2 | no | — |
| 265 | #103 | — | 15 | 8 | no | — |
| 266 | #97 | — | 5 | 2 | no | — |
| 267 | C4×C8 | — | 5 | 2 | no | — |
| 268 | C2×C3×C5 | — | 2 | 1 | no | — |
| 269 | C2×C3×C5 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 270 | C3×D5 | — | 2 | 1 | no | — |
| 271 | C3×D5 | #578 | 1 | 2 | yes | — |
| 272 | C23×C3 | — | 5 | 1 | no | — |
| 273 | C2×C3×C4 | — | 5 | 1 | no | — |
| 274 | C2×C3×C4 | — | 5 | 1 | no | — |
| 275 | C2×C3×C4 | — | 5 | 1 | no | — |
| 276 | C2×C3×C4 | — | 5 | 1 | no | — |
| 277 | C2×C3×C4 | — | 5 | 1 | no | — |
| 278 | C2×C3×C4 | — | 5 | 4 | no | — |
| 279 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 280 | C2×Dic3 | — | 2 | 2 | no | — |
| 281 | C2×Dic3 | — | 10 | 4 | no | — |
| 282 | C2×Dic3 | — | 10 | 4 | no | — |
| 283 | C2×Dic3 | — | 10 | 2 | no | — |
| 284 | C2×Dic3 | — | 10 | 4 | no | — |
| 285 | Dic6 | — | 2 | 2 | no | — |
| 286 | Dic6 | — | 5 | 4 | no | — |
| 287 | Dic6 | — | 10 | 4 | no | — |
| 288 | Dic6 | — | 10 | 4 | no | — |
| 289 | Dic6 | — | 10 | 2 | no | — |
| 290 | Dic6 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 291 | C3×C8 | — | 5 | 1 | no | — |
| 292 | C3×C8 | — | 5 | 1 | no | — |
| 293 | C3×C8 | — | 10 | 2 | no | — |
| 294 | C3×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 295 | C3×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 296 | C22×C5 | C4×D12 | 1 | 1 | yes | characteristic |
| 297 | C2×D5 | — | 2 | 2 | no | — |
| 298 | C2×D5 | C4×D12 | 1 | 1 | yes | characteristic |
| 299 | C2×D5 | C22×D12 | 1 | 1 | yes | characteristic |
| 300 | AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 301 | AGL(1,𝔽5) | — | 12 | 4 | no | — |
| 302 | C4×C5 | — | 6 | 4 | no | — |
| 303 | C4×C5 | C4×D12 | 1 | 1 | yes | characteristic |
| 304 | C4×C5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 305 | Dic5 | — | 6 | 4 | no | — |
| 306 | Dic5 | C4×D12 | 1 | 1 | yes | characteristic |
| 307 | Dic5 | C2×#235 | 1 | 1 | yes | characteristic |
| 308 | C2×Q8 | — | 3 | 2 | no | — |
| 309 | C2×Q8 | — | 15 | 4 | no | — |
| 310 | C2×Q8 | — | 15 | 4 | no | — |
| 311 | C2×Q8 | — | 15 | 2 | no | — |
| 312 | C2×Q8 | — | 30 | 2 | no | — |
| 313 | C2×Q8 | — | 30 | 2 | no | — |
| 314 | C2×Q8 | — | 30 | 2 | no | — |
| 315 | C22×C4 | — | 5 | 1 | no | — |
| 316 | C22×C4 | — | 30 | 2 | no | — |
| 317 | Q16 | — | 3 | 2 | no | — |
| 318 | Q16 | — | 3 | 2 | no | — |
| 319 | Q16 | — | 15 | 4 | no | — |
| 320 | Q16 | — | 15 | 4 | no | — |
| 321 | Q16 | — | 15 | 2 | no | — |
| 322 | Q16 | — | 15 | 2 | no | — |
| 323 | M16 | — | 10 | 1 | no | — |
| 324 | M16 | — | 10 | 1 | no | — |
| 325 | C2×C8 | — | 5 | 1 | no | — |
| 326 | C2×C8 | — | 5 | 1 | no | — |
| 327 | C2×C8 | — | 5 | 1 | no | — |
| 328 | C2×C8 | — | 5 | 1 | no | — |
| 329 | C2×C8 | — | 5 | 1 | no | — |
| 330 | C2×C8 | — | 5 | 2 | no | — |
| 331 | C2×C8 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 332 | C4⋊C4 | — | 5 | 2 | no | — |
| 333 | C4⋊C4 | — | 15 | 4 | no | — |
| 334 | C4⋊C4 | — | 30 | 8 | no | — |
| 335 | C22⋊C4 | — | 5 | 2 | no | — |
| 336 | C22⋊C4 | — | 30 | 2 | no | — |
| 337 | C42 | — | 5 | 2 | no | — |
| 338 | C42 | — | 30 | 2 | no | — |
| 339 | C42 | — | 30 | 8 | no | — |
| 340 | C3×C5 | #2950 | 1 | 1 | yes | characteristic, complemented, Hall |
| 341 | C22×C3 | — | 5 | 1 | no | — |
| 342 | C22×C3 | — | 5 | 1 | no | — |
| 343 | C22×C3 | — | 10 | 2 | no | — |
| 344 | C22×C3 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 345 | C3×C4 | — | 5 | 1 | no | — |
| 346 | C3×C4 | — | 5 | 1 | no | — |
| 347 | C3×C4 | — | 10 | 4 | no | — |
| 348 | C3×C4 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 349 | C3×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 350 | Dic3 | — | 2 | 4 | no | — |
| 351 | Dic3 | — | 10 | 4 | no | — |
| 352 | Dic3 | — | 20 | 4 | no | — |
| 353 | C2×C5 | — | 2 | 1 | no | — |
| 354 | C2×C5 | C2×C4×D12 | 1 | 1 | yes | characteristic |
| 355 | D5 | — | 2 | 1 | no | — |
| 356 | D5 | #5753 | 1 | 2 | yes | — |
| 357 | C23 | — | 5 | 1 | no | — |
| 358 | Q8 | — | 3 | 4 | no | — |
| 359 | Q8 | — | 6 | 2 | no | — |
| 360 | Q8 | — | 15 | 4 | no | — |
| 361 | Q8 | — | 30 | 4 | no | — |
| 362 | Q8 | — | 30 | 4 | no | — |
| 363 | Q8 | — | 30 | 2 | no | — |
| 364 | C2×C4 | — | 5 | 1 | no | — |
| 365 | C2×C4 | — | 5 | 1 | no | — |
| 366 | C2×C4 | — | 5 | 1 | no | — |
| 367 | C2×C4 | — | 5 | 1 | no | — |
| 368 | C2×C4 | — | 5 | 1 | no | — |
| 369 | C2×C4 | — | 5 | 4 | no | — |
| 370 | C2×C4 | — | 6 | 2 | no | — |
| 371 | C2×C4 | — | 30 | 4 | no | — |
| 372 | C2×C4 | — | 30 | 4 | no | — |
| 373 | C2×C4 | — | 30 | 2 | no | — |
| 374 | C2×C4 | — | 30 | 4 | no | — |
| 375 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 376 | C8 | — | 5 | 1 | no | — |
| 377 | C8 | — | 5 | 1 | no | — |
| 378 | C8 | — | 10 | 2 | no | — |
| 379 | C8 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 380 | C8 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 381 | C2×C3 | — | 2 | 1 | no | — |
| 382 | C2×C3 | — | 5 | 2 | no | — |
| 383 | C2×C3 | — | 10 | 1 | no | — |
| 384 | C2×C3 | C2×D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 385 | C5 | #78573 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 386 | C22 | — | 5 | 1 | no | — |
| 387 | C22 | — | 5 | 1 | no | — |
| 388 | C22 | — | 10 | 2 | no | — |
| 389 | C22 | AGL(1,𝔽5)×D12 | 1 | 1 | yes | characteristic |
| 390 | C4 | — | 5 | 1 | no | — |
| 391 | C4 | — | 5 | 1 | no | — |
| 392 | C4 | — | 6 | 4 | no | — |
| 393 | C4 | — | 10 | 4 | no | — |
| 394 | C4 | — | 30 | 4 | no | — |
| 395 | C4 | — | 60 | 4 | no | — |
| 396 | C4 | AGL(1,𝔽5)×D12 | 1 | 1 | yes | characteristic |
| 397 | C4 | C22×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 398 | C3 | #10617434 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 399 | C2 | — | 2 | 1 | no | — |
| 400 | C2 | — | 5 | 2 | no | — |
| 401 | C2 | — | 10 | 1 | no | — |
| 402 | C2 | C2×AGL(1,𝔽5)×D12 | 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