Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11753083 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11752048 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11752031 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11746735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#64864 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11746578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11746577 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10604460 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×#1201 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×#6780 | C22 | 1 | 1 | yes | characteristic |
| 11 | D3×#704 | — | 2 | 1 | no | — |
| 12 | #91923 | — | 2 | 1 | no | — |
| 13 | #91766 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | C5×#882 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×#4028 | C22 | 1 | 1 | yes | characteristic |
| 16 | #91568 | C22 | 1 | 1 | yes | characteristic |
| 17 | #91563 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #91464 | — | 2 | 1 | no | — |
| 19 | #91463 | — | 2 | 1 | no | — |
| 20 | #91453 | — | 2 | 1 | no | — |
| 21 | #91408 | — | 2 | 1 | no | — |
| 22 | #91242 | C22 | 1 | 1 | yes | characteristic |
| 23 | #91240 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#4013 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#4011 | C22 | 1 | 1 | yes | characteristic |
| 26 | #91175 | — | 2 | 1 | no | — |
| 27 | #91172 | — | 2 | 1 | no | — |
| 28 | #69137 | — | 5 | 1 | no | maximal, Hall |
| 29 | #65926 | — | 3 | 1 | no | — |
| 30 | #65777 | — | 3 | 1 | no | — |
| 31 | #65771 | — | 3 | 1 | no | — |
| 32 | #64934 | — | 3 | 1 | no | — |
| 33 | #64934 | — | 3 | 1 | no | — |
| 34 | #64864 | — | 3 | 1 | no | — |
| 35 | #64864 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C23×C5×D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C23×C3×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C22×Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C2×C5×#67 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C2×C5×D12 | — | 2 | 1 | no | — |
| 41 | C2×C3×C22⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×C3×D20 | — | 2 | 1 | no | — |
| 43 | C2×#1204 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×#1201 | — | 2 | 1 | no | — |
| 45 | C2×#1201 | — | 2 | 1 | no | — |
| 46 | C2×#1201 | — | 2 | 1 | no | — |
| 47 | C2×#1201 | — | 2 | 1 | no | — |
| 48 | C2×#1201 | — | 4 | 1 | no | — |
| 49 | C2×#1201 | — | 4 | 1 | no | — |
| 50 | C2×#1201 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×D3×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 52 | #6780 | — | 4 | 1 | no | — |
| 53 | #6780 | — | 4 | 1 | no | — |
| 54 | C2×D5×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 55 | #6763 | — | 2 | 1 | no | — |
| 56 | #6762 | — | 2 | 1 | no | — |
| 57 | C3×C22⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 58 | C3×#704 | — | 2 | 1 | no | — |
| 59 | #6739 | — | 4 | 1 | no | — |
| 60 | D3×#170 | — | 4 | 1 | no | — |
| 61 | Dic3⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 62 | Dic3×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 63 | C3×C5×C22⋊C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | #6719 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | #6712 | — | 2 | 1 | no | — |
| 66 | C4×Dic15 | — | 2 | 1 | no | — |
| 67 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 68 | C3×#685 | — | 2 | 1 | no | — |
| 69 | (C2×D3)⋊Dic5 | — | 2 | 1 | no | — |
| 70 | #6665 | — | 2 | 1 | no | — |
| 71 | #5592 | — | 5 | 1 | no | — |
| 72 | #4745 | — | 5 | 1 | no | — |
| 73 | #4740 | — | 5 | 1 | no | — |
| 74 | C3×AΣL(1,𝔽16) | — | 5 | 1 | no | — |
| 75 | #4536 | — | 5 | 1 | no | — |
| 76 | #4475 | — | 5 | 1 | no | — |
| 77 | #4471 | — | 5 | 1 | no | — |
| 78 | C22×C22⋊D5 | — | 3 | 1 | no | — |
| 79 | C2×#711 | — | 3 | 1 | no | — |
| 80 | C2×#704 | — | 6 | 1 | no | — |
| 81 | #4130 | — | 6 | 1 | no | — |
| 82 | C5×#120 | — | 3 | 1 | no | — |
| 83 | #4099 | — | 3 | 1 | no | — |
| 84 | #4086 | — | 6 | 1 | no | — |
| 85 | #4085 | — | 6 | 1 | no | — |
| 86 | #4083 | — | 3 | 1 | no | — |
| 87 | #4031 | — | 6 | 1 | no | — |
| 88 | #4030 | — | 6 | 1 | no | — |
| 89 | #4028 | C2×D3 | 1 | 1 | yes | characteristic |
| 90 | #4023 | — | 3 | 1 | no | — |
| 91 | #4013 | — | 3 | 1 | no | — |
| 92 | #4013 | C2×D3 | 1 | 1 | yes | characteristic |
| 93 | #4011 | — | 3 | 1 | no | — |
| 94 | #4011 | — | 6 | 1 | no | — |
| 95 | #4011 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | #4005 | — | 6 | 1 | no | — |
| 97 | #2122 | — | 15 | 1 | no | Sylow |
| 98 | C23×C3×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 99 | C22×C5×D3 | — | 2 | 1 | no | — |
| 100 | C22×C5×D3 | — | 4 | 1 | no | — |
| 101 | C22×C5×D3 | — | 8 | 1 | no | — |
| 102 | C22×C5×D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 103 | C22×C3×D5 | — | 2 | 1 | no | — |
| 104 | C22×C3×D5 | — | 4 | 1 | no | — |
| 105 | C22×C3×D5 | — | 8 | 1 | no | — |
| 106 | C22×C3×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C2×ΓL(1,𝔽16) | — | 4 | 1 | no | — |
| 108 | C2×C3×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 109 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 110 | C2×Dic15 | — | 2 | 1 | no | — |
| 111 | C2×Dic15 | — | 2 | 1 | no | — |
| 112 | C2×Dic15 | — | 2 | 1 | no | — |
| 113 | C2×Dic15 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 114 | C2×Dic15 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C5×#67 | — | 4 | 1 | no | — |
| 116 | C2×C5×Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 117 | C5×D12 | — | 8 | 1 | no | — |
| 118 | C3×C22⋊D5 | — | 4 | 1 | no | — |
| 119 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C3×D20 | — | 8 | 1 | no | — |
| 121 | #1204 | — | 4 | 1 | no | — |
| 122 | #1201 | — | 4 | 1 | no | — |
| 123 | #1201 | — | 4 | 2 | no | — |
| 124 | #1201 | — | 4 | 1 | no | — |
| 125 | #1201 | — | 4 | 1 | no | — |
| 126 | #1201 | — | 8 | 1 | no | — |
| 127 | #1201 | — | 8 | 1 | no | — |
| 128 | D3×Dic5 | — | 2 | 1 | no | — |
| 129 | D3×Dic5 | — | 2 | 1 | no | — |
| 130 | D5×Dic3 | — | 2 | 1 | no | — |
| 131 | D5×Dic3 | — | 2 | 1 | no | — |
| 132 | C3⋊#170 | — | 4 | 1 | no | — |
| 133 | C3×#170 | — | 4 | 1 | no | — |
| 134 | C22×#67 | — | 5 | 1 | no | — |
| 135 | C2×#237 | — | 5 | 1 | no | — |
| 136 | C3×#120 | — | 5 | 1 | no | — |
| 137 | #953 | — | 5 | 1 | no | — |
| 138 | #940 | — | 10 | 1 | no | — |
| 139 | #939 | — | 10 | 1 | no | — |
| 140 | #937 | — | 5 | 1 | no | — |
| 141 | D3×M16 | — | 10 | 1 | no | — |
| 142 | #885 | — | 10 | 1 | no | — |
| 143 | #884 | — | 10 | 1 | no | — |
| 144 | #882 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 145 | #877 | — | 5 | 1 | no | — |
| 146 | #877 | — | 10 | 1 | no | — |
| 147 | C3×#100 | — | 5 | 1 | no | — |
| 148 | C3×#99 | — | 5 | 1 | no | — |
| 149 | #834 | — | 5 | 1 | no | — |
| 150 | #833 | — | 5 | 1 | no | — |
| 151 | #824 | — | 10 | 1 | no | — |
| 152 | #806 | — | 10 | 1 | no | — |
| 153 | C24×C5 | — | 3 | 1 | no | — |
| 154 | C23×D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 155 | C2×C5×D4 | — | 3 | 1 | no | — |
| 156 | C2×C5×D4 | — | 6 | 1 | no | — |
| 157 | C2×C22⋊D5 | — | 3 | 1 | no | — |
| 158 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 159 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 160 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 161 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 162 | C2×C22⋊D5 | — | 12 | 1 | no | — |
| 163 | C2×C22⋊D5 | — | 12 | 1 | no | — |
| 164 | C2×C22⋊D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 165 | C22×Dic5 | — | 3 | 1 | no | — |
| 166 | C22×Dic5 | — | 3 | 1 | no | — |
| 167 | #711 | — | 12 | 1 | no | — |
| 168 | #711 | — | 12 | 1 | no | — |
| 169 | C2×D20 | — | 2 | 1 | no | — |
| 170 | C2×C4×D5 | — | 3 | 1 | no | — |
| 171 | C2×Dic10 | — | 3 | 1 | no | — |
| 172 | C22⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 173 | C22⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 174 | #704 | — | 2 | 1 | no | — |
| 175 | #704 | — | 6 | 1 | no | — |
| 176 | #704 | — | 12 | 1 | no | — |
| 177 | C2×#170 | — | 12 | 1 | no | — |
| 178 | C4⋊AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 179 | C4×AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 180 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 181 | C5×C22⋊C4 | C4×D3 | 1 | 1 | yes | characteristic |
| 182 | C22⋊Dic5 | — | 3 | 1 | no | — |
| 183 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 184 | #685 | — | 2 | 1 | no | — |
| 185 | #685 | — | 6 | 1 | no | — |
| 186 | #683 | — | 6 | 1 | no | — |
| 187 | C4×Dic5 | — | 6 | 1 | no | — |
| 188 | #535 | — | 15 | 1 | no | — |
| 189 | #413 | — | 15 | 1 | no | — |
| 190 | #410 | — | 15 | 1 | no | — |
| 191 | AΣL(1,𝔽16) | — | 5 | 1 | no | — |
| 192 | AΣL(1,𝔽16) | — | 15 | 1 | no | — |
| 193 | AΣL(1,𝔽16) | — | 15 | 1 | no | — |
| 194 | AΣL(1,𝔽16) | — | 15 | 1 | no | — |
| 195 | C22×C3×C5 | — | 2 | 1 | no | — |
| 196 | C22×C3×C5 | — | 4 | 1 | no | — |
| 197 | C22×C3×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 198 | C2×C5×D3 | — | 2 | 1 | no | — |
| 199 | C2×C5×D3 | — | 4 | 1 | no | — |
| 200 | C2×C5×D3 | — | 4 | 1 | no | — |
| 201 | C2×C5×D3 | — | 4 | 1 | no | — |
| 202 | C2×C5×D3 | — | 4 | 1 | no | — |
| 203 | C2×C5×D3 | — | 8 | 2 | no | — |
| 204 | C2×C3×D5 | — | 2 | 1 | no | — |
| 205 | C2×C3×D5 | — | 4 | 1 | no | — |
| 206 | C2×C3×D5 | — | 4 | 1 | no | — |
| 207 | C2×C3×D5 | — | 4 | 1 | no | — |
| 208 | C2×C3×D5 | — | 4 | 1 | no | — |
| 209 | C2×C3×D5 | — | 8 | 2 | no | — |
| 210 | ΓL(1,𝔽16) | — | 8 | 1 | no | — |
| 211 | C3×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 212 | C3×C4×C5 | — | 4 | 1 | no | — |
| 213 | Dic15 | — | 2 | 1 | no | — |
| 214 | Dic15 | — | 4 | 1 | no | — |
| 215 | Dic15 | #99 | 1 | 1 | yes | characteristic |
| 216 | Dic15 | #99 | 1 | 1 | yes | characteristic |
| 217 | C3×Dic5 | — | 2 | 1 | no | — |
| 218 | C5×Dic3 | — | 2 | 1 | no | — |
| 219 | C24×C3 | — | 5 | 1 | no | — |
| 220 | C23×D3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 221 | C2×C3×D4 | — | 5 | 1 | no | — |
| 222 | C2×C3×D4 | — | 10 | 1 | no | — |
| 223 | C2×#67 | — | 5 | 1 | no | — |
| 224 | C2×#67 | — | 10 | 1 | no | — |
| 225 | C2×#67 | — | 10 | 1 | no | — |
| 226 | C2×#67 | — | 10 | 1 | no | — |
| 227 | C2×#67 | — | 10 | 1 | no | — |
| 228 | C2×#67 | — | 20 | 1 | no | — |
| 229 | C2×#67 | — | 20 | 1 | no | — |
| 230 | C2×#67 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 231 | C22×Dic3 | — | 5 | 1 | no | — |
| 232 | C22×Dic3 | — | 5 | 1 | no | — |
| 233 | #237 | — | 20 | 1 | no | — |
| 234 | #237 | — | 20 | 1 | no | — |
| 235 | C2×D12 | — | 2 | 1 | no | — |
| 236 | C2×C4×D3 | — | 5 | 1 | no | — |
| 237 | C2×Dic6 | — | 5 | 1 | no | — |
| 238 | C3×M16 | — | 10 | 1 | no | — |
| 239 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 240 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 241 | C3×C22⋊C4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 242 | #217 | — | 5 | 1 | no | — |
| 243 | #217 | — | 10 | 1 | no | — |
| 244 | #217 | — | 10 | 1 | no | — |
| 245 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 246 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 247 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 248 | Dic3⋊C4 | — | 20 | 1 | no | — |
| 249 | C4×Dic3 | — | 10 | 1 | no | — |
| 250 | C4×Dic3 | — | 20 | 1 | no | — |
| 251 | #208 | — | 10 | 1 | no | — |
| 252 | ΓL(1,𝔽25) | — | 20 | 1 | no | — |
| 253 | D3×C8 | — | 20 | 1 | no | — |
| 254 | C23×C5 | — | 3 | 1 | no | — |
| 255 | C23×C5 | — | 6 | 1 | no | — |
| 256 | C23×C5 | — | 12 | 1 | no | — |
| 257 | C23×C5 | — | 24 | 1 | no | — |
| 258 | C23×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 259 | C22×D5 | — | 2 | 1 | no | — |
| 260 | C22×D5 | — | 4 | 1 | no | — |
| 261 | C22×D5 | — | 8 | 1 | no | — |
| 262 | C22×D5 | D3×D4 | 1 | 1 | yes | characteristic |
| 263 | C2×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 264 | C2×AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 265 | C5×D4 | — | 12 | 1 | no | — |
| 266 | C5×D4 | — | 24 | 1 | no | — |
| 267 | C2×C4×C5 | — | 2 | 1 | no | — |
| 268 | C2×C4×C5 | — | 3 | 1 | no | — |
| 269 | C22⋊D5 | — | 4 | 1 | no | — |
| 270 | C22⋊D5 | — | 12 | 1 | no | — |
| 271 | C22⋊D5 | — | 12 | 1 | no | — |
| 272 | C22⋊D5 | — | 12 | 1 | no | — |
| 273 | C22⋊D5 | — | 12 | 2 | no | — |
| 274 | C22⋊D5 | — | 24 | 1 | no | — |
| 275 | C22⋊D5 | — | 24 | 1 | no | — |
| 276 | C2×Dic5 | — | 3 | 1 | no | — |
| 277 | C2×Dic5 | — | 3 | 1 | no | — |
| 278 | C2×Dic5 | — | 6 | 1 | no | — |
| 279 | C2×Dic5 | — | 6 | 1 | no | — |
| 280 | C2×Dic5 | — | 6 | 1 | no | — |
| 281 | C2×Dic5 | — | 6 | 1 | no | — |
| 282 | C2×Dic5 | — | 6 | 1 | no | — |
| 283 | C2×Dic5 | D3×D4 | 1 | 1 | yes | characteristic |
| 284 | D20 | — | 8 | 1 | no | — |
| 285 | C4×D5 | — | 6 | 1 | no | — |
| 286 | C4×D5 | — | 6 | 1 | no | — |
| 287 | Dic10 | — | 12 | 1 | no | — |
| 288 | #170 | — | 4 | 1 | no | — |
| 289 | #170 | — | 12 | 1 | no | — |
| 290 | C2×#41 | — | 15 | 1 | no | — |
| 291 | C22×D4 | — | 15 | 1 | no | — |
| 292 | C2×M16 | — | 30 | 1 | no | — |
| 293 | #127 | — | 30 | 1 | no | — |
| 294 | #124 | — | 30 | 1 | no | — |
| 295 | #121 | — | 30 | 1 | no | — |
| 296 | #121 | — | 30 | 1 | no | — |
| 297 | #120 | — | 3 | 1 | no | — |
| 298 | #120 | — | 5 | 1 | no | — |
| 299 | #120 | — | 15 | 1 | no | — |
| 300 | #120 | — | 15 | 1 | no | — |
| 301 | #117 | — | 15 | 1 | no | — |
| 302 | #117 | — | 30 | 1 | no | — |
| 303 | #101 | — | 30 | 1 | no | — |
| 304 | #100 | — | 5 | 1 | no | — |
| 305 | #100 | — | 15 | 1 | no | — |
| 306 | #99 | — | 5 | 1 | no | — |
| 307 | #99 | — | 15 | 1 | no | — |
| 308 | #99 | — | 30 | 1 | no | — |
| 309 | C2×C3×C5 | — | 2 | 1 | no | — |
| 310 | C2×C3×C5 | — | 4 | 1 | no | — |
| 311 | C2×C3×C5 | C2×#99 | 1 | 1 | yes | characteristic |
| 312 | C3×D5 | — | 4 | 1 | no | — |
| 313 | C3×D5 | — | 8 | 1 | no | — |
| 314 | C5×D3 | — | 4 | 1 | no | — |
| 315 | C5×D3 | — | 8 | 1 | no | — |
| 316 | C23×C3 | — | 5 | 1 | no | — |
| 317 | C23×C3 | — | 10 | 1 | no | — |
| 318 | C23×C3 | — | 20 | 1 | no | — |
| 319 | C23×C3 | — | 40 | 1 | no | — |
| 320 | C23×C3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 321 | C22×D3 | — | 2 | 1 | no | — |
| 322 | C22×D3 | — | 4 | 1 | no | — |
| 323 | C22×D3 | — | 8 | 1 | no | — |
| 324 | C22×D3 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 325 | C3×D4 | — | 20 | 1 | no | — |
| 326 | C3×D4 | — | 40 | 1 | no | — |
| 327 | C2×C3×C4 | — | 2 | 1 | no | — |
| 328 | C2×C3×C4 | — | 5 | 1 | no | — |
| 329 | C2×C3×C4 | — | 20 | 1 | no | — |
| 330 | #67 | — | 4 | 1 | no | — |
| 331 | #67 | — | 20 | 1 | no | — |
| 332 | #67 | — | 20 | 1 | no | — |
| 333 | #67 | — | 20 | 1 | no | — |
| 334 | #67 | — | 20 | 2 | no | — |
| 335 | #67 | — | 40 | 1 | no | — |
| 336 | #67 | — | 40 | 1 | no | — |
| 337 | C2×Dic3 | — | 5 | 1 | no | — |
| 338 | C2×Dic3 | — | 5 | 1 | no | — |
| 339 | C2×Dic3 | — | 10 | 1 | no | — |
| 340 | C2×Dic3 | — | 10 | 1 | no | — |
| 341 | C2×Dic3 | — | 10 | 1 | no | — |
| 342 | C2×Dic3 | — | 10 | 1 | no | — |
| 343 | C2×Dic3 | — | 10 | 1 | no | — |
| 344 | C2×Dic3 | — | 20 | 1 | no | — |
| 345 | C2×Dic3 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 346 | D12 | — | 8 | 1 | no | — |
| 347 | C4×D3 | — | 10 | 1 | no | — |
| 348 | C4×D3 | — | 10 | 1 | no | — |
| 349 | Dic6 | — | 20 | 1 | no | — |
| 350 | C3×C8 | — | 20 | 1 | no | — |
| 351 | C3⋊C8 | — | 20 | 1 | no | — |
| 352 | C22×C5 | — | 2 | 1 | no | — |
| 353 | C22×C5 | — | 4 | 1 | no | — |
| 354 | C22×C5 | — | 6 | 1 | no | — |
| 355 | C22×C5 | — | 12 | 1 | no | — |
| 356 | C22×C5 | — | 12 | 1 | no | — |
| 357 | C22×C5 | — | 12 | 1 | no | — |
| 358 | C22×C5 | — | 12 | 1 | no | — |
| 359 | C22×C5 | — | 24 | 2 | no | — |
| 360 | C22×C5 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 361 | C2×D5 | — | 2 | 1 | no | — |
| 362 | C2×D5 | — | 4 | 1 | no | — |
| 363 | C2×D5 | — | 4 | 1 | no | — |
| 364 | C2×D5 | — | 4 | 1 | no | — |
| 365 | C2×D5 | — | 4 | 1 | no | — |
| 366 | C2×D5 | — | 8 | 2 | no | — |
| 367 | AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 368 | AGL(1,𝔽5) | — | 24 | 1 | no | — |
| 369 | C4×C5 | — | 4 | 1 | no | — |
| 370 | C4×C5 | — | 6 | 1 | no | — |
| 371 | Dic5 | — | 2 | 1 | no | — |
| 372 | Dic5 | — | 3 | 1 | no | — |
| 373 | Dic5 | — | 3 | 1 | no | — |
| 374 | Dic5 | — | 6 | 1 | no | — |
| 375 | Dic5 | — | 12 | 1 | no | — |
| 376 | C24 | — | 3 | 1 | no | — |
| 377 | C24 | — | 5 | 1 | no | — |
| 378 | #41 | — | 60 | 1 | no | — |
| 379 | #41 | — | 60 | 1 | no | — |
| 380 | C2×Q8 | — | 15 | 1 | no | — |
| 381 | C2×D4 | — | 3 | 1 | no | — |
| 382 | C2×D4 | — | 5 | 1 | no | — |
| 383 | C2×D4 | — | 6 | 1 | no | — |
| 384 | C2×D4 | — | 10 | 1 | no | — |
| 385 | C2×D4 | — | 15 | 1 | no | — |
| 386 | C2×D4 | — | 30 | 1 | no | — |
| 387 | C2×D4 | — | 30 | 1 | no | — |
| 388 | C2×D4 | — | 30 | 1 | no | — |
| 389 | C2×D4 | — | 30 | 1 | no | — |
| 390 | C2×D4 | — | 60 | 1 | no | — |
| 391 | C2×D4 | — | 60 | 1 | no | — |
| 392 | C22×C4 | — | 15 | 1 | no | — |
| 393 | C22×C4 | — | 15 | 1 | no | — |
| 394 | C22×C4 | — | 15 | 1 | no | — |
| 395 | M16 | — | 10 | 1 | no | — |
| 396 | M16 | — | 30 | 1 | no | — |
| 397 | M16 | — | 60 | 1 | no | — |
| 398 | C2×C8 | — | 60 | 1 | no | — |
| 399 | C4⋊C4 | — | 30 | 1 | no | — |
| 400 | C4⋊C4 | — | 60 | 1 | no | — |
| 401 | C22⋊C4 | — | 6 | 1 | no | — |
| 402 | C22⋊C4 | — | 10 | 1 | no | — |
| 403 | C22⋊C4 | — | 10 | 1 | no | — |
| 404 | C22⋊C4 | — | 15 | 1 | no | — |
| 405 | C22⋊C4 | — | 30 | 1 | no | — |
| 406 | C22⋊C4 | — | 30 | 1 | no | — |
| 407 | C22⋊C4 | — | 30 | 1 | no | — |
| 408 | C22⋊C4 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 409 | C42 | — | 30 | 1 | no | — |
| 410 | C42 | — | 60 | 1 | no | — |
| 411 | C3×C5 | #2122 | 1 | 1 | yes | characteristic, complemented, Hall |
| 412 | C22×C3 | — | 2 | 1 | no | — |
| 413 | C22×C3 | — | 4 | 1 | no | — |
| 414 | C22×C3 | — | 10 | 1 | no | — |
| 415 | C22×C3 | — | 20 | 1 | no | — |
| 416 | C22×C3 | — | 20 | 1 | no | — |
| 417 | C22×C3 | — | 20 | 1 | no | — |
| 418 | C22×C3 | — | 20 | 1 | no | — |
| 419 | C22×C3 | — | 40 | 2 | no | — |
| 420 | C22×C3 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 421 | C2×D3 | — | 2 | 1 | no | — |
| 422 | C2×D3 | — | 4 | 1 | no | — |
| 423 | C2×D3 | — | 4 | 1 | no | — |
| 424 | C2×D3 | — | 4 | 1 | no | — |
| 425 | C2×D3 | — | 4 | 1 | no | — |
| 426 | C2×D3 | — | 8 | 2 | no | — |
| 427 | C3×C4 | — | 4 | 1 | no | — |
| 428 | C3×C4 | — | 10 | 1 | no | — |
| 429 | C3×C4 | — | 40 | 1 | no | — |
| 430 | Dic3 | — | 2 | 1 | no | — |
| 431 | Dic3 | — | 5 | 1 | no | — |
| 432 | Dic3 | — | 5 | 1 | no | — |
| 433 | Dic3 | — | 10 | 1 | no | — |
| 434 | Dic3 | — | 20 | 1 | no | — |
| 435 | Dic3 | — | 40 | 1 | no | — |
| 436 | C2×C5 | — | 2 | 1 | no | — |
| 437 | C2×C5 | — | 4 | 1 | no | — |
| 438 | C2×C5 | — | 12 | 1 | no | — |
| 439 | C2×C5 | — | 24 | 1 | no | — |
| 440 | C2×C5 | D3×#99 | 1 | 1 | yes | characteristic |
| 441 | D5 | — | 4 | 1 | no | — |
| 442 | D5 | — | 8 | 1 | no | — |
| 443 | C23 | — | 3 | 1 | no | — |
| 444 | C23 | — | 5 | 1 | no | — |
| 445 | C23 | — | 6 | 1 | no | — |
| 446 | C23 | — | 10 | 1 | no | — |
| 447 | C23 | — | 12 | 1 | no | — |
| 448 | C23 | — | 20 | 1 | no | — |
| 449 | C23 | — | 24 | 1 | no | — |
| 450 | C23 | — | 40 | 1 | no | — |
| 451 | C23 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 452 | Q8 | — | 60 | 1 | no | — |
| 453 | D4 | — | 12 | 1 | no | — |
| 454 | D4 | — | 20 | 1 | no | — |
| 455 | D4 | — | 24 | 1 | no | — |
| 456 | D4 | — | 40 | 1 | no | — |
| 457 | D4 | — | 60 | 1 | no | — |
| 458 | D4 | — | 60 | 1 | no | — |
| 459 | D4 | — | 60 | 1 | no | — |
| 460 | D4 | — | 60 | 2 | no | — |
| 461 | D4 | — | 120 | 1 | no | — |
| 462 | D4 | — | 120 | 1 | no | — |
| 463 | C2×C4 | — | 2 | 1 | no | — |
| 464 | C2×C4 | — | 3 | 1 | no | — |
| 465 | C2×C4 | — | 5 | 1 | no | — |
| 466 | C2×C4 | — | 15 | 1 | no | — |
| 467 | C2×C4 | — | 15 | 1 | no | — |
| 468 | C2×C4 | — | 20 | 1 | no | — |
| 469 | C2×C4 | — | 30 | 1 | no | — |
| 470 | C2×C4 | — | 30 | 1 | no | — |
| 471 | C2×C4 | — | 30 | 1 | no | — |
| 472 | C2×C4 | — | 30 | 1 | no | — |
| 473 | C2×C4 | — | 30 | 1 | no | — |
| 474 | C2×C4 | — | 30 | 1 | no | — |
| 475 | C2×C4 | — | 30 | 1 | no | — |
| 476 | C2×C4 | — | 60 | 1 | no | — |
| 477 | C8 | — | 20 | 1 | no | — |
| 478 | C8 | — | 60 | 1 | no | — |
| 479 | C2×C3 | — | 2 | 1 | no | — |
| 480 | C2×C3 | — | 4 | 1 | no | — |
| 481 | C2×C3 | — | 20 | 1 | no | — |
| 482 | C2×C3 | — | 40 | 1 | no | — |
| 483 | C2×C3 | D5⋊#99 | 1 | 1 | yes | characteristic |
| 484 | D3 | — | 4 | 1 | no | — |
| 485 | D3 | — | 8 | 1 | no | — |
| 486 | C5 | #69137 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 487 | C22 | — | 2 | 1 | no | — |
| 488 | C22 | — | 4 | 1 | no | — |
| 489 | C22 | — | 6 | 1 | no | — |
| 490 | C22 | — | 10 | 1 | no | — |
| 491 | C22 | — | 12 | 1 | no | — |
| 492 | C22 | — | 12 | 1 | no | — |
| 493 | C22 | — | 12 | 1 | no | — |
| 494 | C22 | — | 12 | 1 | no | — |
| 495 | C22 | — | 20 | 1 | no | — |
| 496 | C22 | — | 20 | 1 | no | — |
| 497 | C22 | — | 20 | 1 | no | — |
| 498 | C22 | — | 20 | 1 | no | — |
| 499 | C22 | — | 24 | 2 | no | — |
| 500 | C22 | — | 40 | 2 | no | — |
| 501 | C22 | D3×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 502 | C4 | — | 4 | 1 | no | — |
| 503 | C4 | — | 6 | 1 | no | — |
| 504 | C4 | — | 10 | 1 | no | — |
| 505 | C4 | — | 15 | 1 | no | — |
| 506 | C4 | — | 15 | 1 | no | — |
| 507 | C4 | — | 30 | 1 | no | — |
| 508 | C4 | — | 40 | 1 | no | — |
| 509 | C4 | — | 60 | 1 | no | — |
| 510 | C4 | — | 120 | 1 | no | — |
| 511 | C3 | #10604460 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 512 | C2 | — | 2 | 1 | no | — |
| 513 | C2 | — | 4 | 1 | no | — |
| 514 | C2 | — | 12 | 1 | no | — |
| 515 | C2 | — | 20 | 1 | no | — |
| 516 | C2 | — | 24 | 1 | no | — |
| 517 | C2 | — | 40 | 1 | no | — |
| 518 | C2 | #11751852 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11752048 | C2 | semidirect |
| 3. #11752031 | C2 | semidirect |
| 4. #11746735 | C2 | semidirect |
| 5. C3×#64864 | C2 | semidirect |
| 6. #11746578 | C2 | semidirect |
| 7. #11746577 | C2 | semidirect |
| 9. C22×#1201 | C4 | semidirect |
| 13. #91766 | C4 | semidirect |
| 14. C5×#882 | C4 | semidirect |
| 17. #91563 | C4 | semidirect |
| 35. #64864 | D3 | semidirect |
| 144. #882 | AGL(1,𝔽5) | semidirect |
| 411. C3×C5 | #2122 | semidirect |
| 486. C5 | #69137 | semidirect |
| 511. C3 | #10604460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753083 | 2 |
| #11752048 | 2 |
| #11752031 | 2 |
| #11746735 | 2 |
| C3×#64864 | 2 |
| #11746578 | 2 |
| #11746577 | 2 |
| #10604460 | 3 |
| #69137 | 5 |