Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
472 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 62 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 | #11755199 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#65041 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11749384 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11749383 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11746298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C5×#4477 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11746015 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10599954 | — | 3 | 1 | no | maximal, Hall |
| 9 | C3×#4147 | C22 | 1 | 1 | yes | characteristic |
| 10 | #91836 | C22 | 1 | 1 | yes | characteristic |
| 11 | C5×#947 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#4090 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#4055 | — | 2 | 1 | no | — |
| 14 | #91420 | — | 2 | 1 | no | — |
| 15 | #91416 | — | 2 | 1 | no | — |
| 16 | #91405 | — | 2 | 1 | no | — |
| 17 | #91403 | — | 2 | 1 | no | — |
| 18 | #91400 | — | 2 | 1 | no | — |
| 19 | #91326 | — | 2 | 1 | no | — |
| 20 | #91301 | — | 2 | 1 | no | — |
| 21 | #91299 | — | 2 | 1 | no | — |
| 22 | C3×C5×#101 | C22 | 1 | 1 | yes | characteristic |
| 23 | #91120 | C22 | 1 | 1 | yes | characteristic |
| 24 | C5×#836 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#3957 | — | 2 | 1 | no | — |
| 26 | #90977 | — | 2 | 1 | no | — |
| 27 | #90976 | — | 2 | 1 | no | — |
| 28 | #70994 | — | 5 | 1 | no | maximal, Hall |
| 29 | #66004 | — | 3 | 1 | no | — |
| 30 | #65351 | — | 3 | 1 | no | — |
| 31 | #65042 | — | 3 | 1 | no | — |
| 32 | #65041 | D3 | 1 | 1 | yes | characteristic, complemented |
| 33 | C5×#355 | — | 3 | 1 | no | — |
| 34 | #64698 | — | 3 | 1 | no | — |
| 35 | #64697 | — | 3 | 1 | no | — |
| 36 | C2×C3×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 37 | C2×D60 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×C5×D12 | D4 | 1 | 1 | yes | characteristic |
| 39 | C3×#713 | — | 4 | 1 | no | — |
| 40 | C3×Q8×D5 | — | 4 | 1 | no | — |
| 41 | C3×#709 | — | 2 | 1 | no | — |
| 42 | C3×#709 | — | 2 | 1 | no | — |
| 43 | C3×#709 | — | 2 | 1 | no | — |
| 44 | C2×C3×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×#1203 | — | 2 | 1 | no | — |
| 46 | C2×#1203 | — | 2 | 1 | no | — |
| 47 | C2×#1200 | — | 2 | 1 | no | — |
| 48 | C2×D3×Dic5 | — | 2 | 1 | no | — |
| 49 | C3×C5×M16 | — | 2 | 1 | no | — |
| 50 | #6714 | — | 2 | 1 | no | — |
| 51 | #6714 | — | 2 | 1 | no | — |
| 52 | C4×Dic15 | D4 | 1 | 1 | yes | characteristic |
| 53 | #6710 | — | 2 | 1 | no | — |
| 54 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 55 | C5×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 56 | C4×C5×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 57 | C5×#208 | — | 2 | 1 | no | — |
| 58 | C3×#683 | — | 2 | 1 | no | — |
| 59 | C3×#683 | — | 2 | 1 | no | — |
| 60 | C3×C4×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 61 | C3×Dic20 | — | 4 | 1 | no | — |
| 62 | C3×#677 | — | 4 | 1 | no | — |
| 63 | #6668 | — | 2 | 1 | no | — |
| 64 | #6667 | — | 2 | 1 | no | — |
| 65 | (C2×D3)⋊Dic5 | — | 2 | 1 | no | — |
| 66 | Dic3×Dic5 | — | 2 | 1 | no | — |
| 67 | #6658 | — | 4 | 1 | no | — |
| 68 | #6656 | — | 4 | 1 | no | — |
| 69 | #6653 | — | 4 | 1 | no | — |
| 70 | #6652 | — | 4 | 1 | no | — |
| 71 | #5734 | — | 5 | 1 | no | — |
| 72 | C3×#456 | — | 5 | 1 | no | — |
| 73 | #5245 | — | 5 | 1 | no | — |
| 74 | #5245 | — | 5 | 1 | no | — |
| 75 | #4548 | — | 5 | 1 | no | — |
| 76 | #4477 | — | 5 | 1 | no | — |
| 77 | #4477 | D5 | 1 | 1 | yes | characteristic, complemented |
| 78 | #4147 | C2×D3 | 1 | 1 | yes | characteristic |
| 79 | C5×#124 | — | 3 | 1 | no | — |
| 80 | #4093 | — | 3 | 1 | no | — |
| 81 | #4090 | C2×D3 | 1 | 1 | yes | characteristic |
| 82 | #4085 | — | 6 | 1 | no | — |
| 83 | #4078 | — | 6 | 1 | no | — |
| 84 | #4055 | — | 2 | 1 | no | — |
| 85 | #4054 | — | 6 | 1 | no | — |
| 86 | #4031 | — | 6 | 1 | no | — |
| 87 | #4030 | — | 6 | 1 | no | — |
| 88 | #4027 | — | 6 | 1 | no | — |
| 89 | #4023 | — | 6 | 1 | no | — |
| 90 | #4018 | — | 6 | 1 | no | — |
| 91 | C5×#101 | — | 3 | 1 | no | — |
| 92 | C5×#101 | C2×D3 | 1 | 1 | yes | characteristic |
| 93 | #3968 | — | 3 | 1 | no | — |
| 94 | #3957 | — | 2 | 1 | no | — |
| 95 | #3957 | — | 6 | 1 | no | — |
| 96 | #3937 | — | 6 | 1 | no | — |
| 97 | #2204 | — | 15 | 1 | no | Sylow |
| 98 | C22×D15 | — | 2 | 1 | no | — |
| 99 | C22×C5×D3 | — | 2 | 1 | no | — |
| 100 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 101 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×Dic15 | — | 2 | 1 | no | — |
| 105 | D60 | — | 4 | 1 | no | — |
| 106 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 107 | C5×D12 | — | 4 | 1 | no | — |
| 108 | C3×C22⋊D5 | — | 4 | 1 | no | — |
| 109 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 110 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 111 | C3×D20 | — | 2 | 1 | no | — |
| 112 | C3×D20 | — | 2 | 1 | no | — |
| 113 | C3×D20 | — | 2 | 1 | no | — |
| 114 | C3×C4×D5 | — | 4 | 1 | no | — |
| 115 | C3×C4×D5 | — | 4 | 1 | no | — |
| 116 | C3×C4×D5 | — | 4 | 1 | no | — |
| 117 | C3×Dic10 | — | 2 | 1 | no | — |
| 118 | C3×Dic10 | — | 2 | 1 | no | — |
| 119 | C3×Dic10 | — | 2 | 1 | no | — |
| 120 | C3×Dic10 | — | 4 | 1 | no | — |
| 121 | #1203 | — | 4 | 2 | no | — |
| 122 | #1203 | — | 8 | 1 | no | — |
| 123 | #1200 | — | 4 | 2 | no | — |
| 124 | D3×Dic5 | — | 4 | 2 | no | — |
| 125 | C3×C5×C8 | — | 4 | 1 | no | — |
| 126 | C3⋊#168 | — | 4 | 1 | no | — |
| 127 | C5×C3⋊C8 | — | 4 | 1 | no | — |
| 128 | C3×2−1+4 | — | 5 | 1 | no | — |
| 129 | C3×#137 | — | 10 | 1 | no | — |
| 130 | C3×C4⋊Q8 | — | 5 | 1 | no | — |
| 131 | #949 | — | 10 | 1 | no | — |
| 132 | #949 | — | 10 | 1 | no | — |
| 133 | #947 | — | 5 | 1 | no | — |
| 134 | #947 | — | 10 | 1 | no | — |
| 135 | #947 | C2×D5 | 1 | 1 | yes | characteristic |
| 136 | #895 | — | 10 | 1 | no | — |
| 137 | #895 | — | 10 | 1 | no | — |
| 138 | #892 | — | 10 | 1 | no | — |
| 139 | #892 | — | 10 | 1 | no | — |
| 140 | C4×D12 | — | 10 | 1 | no | — |
| 141 | C3×#104 | — | 10 | 1 | no | — |
| 142 | C3×#101 | C2×D5 | 1 | 1 | yes | characteristic |
| 143 | #837 | — | 10 | 1 | no | — |
| 144 | #837 | — | 10 | 1 | no | — |
| 145 | #836 | — | 5 | 1 | no | — |
| 146 | #836 | C2×D5 | 1 | 1 | yes | characteristic |
| 147 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 148 | C2×C5×D4 | — | 3 | 1 | no | — |
| 149 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 150 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 151 | C22×Dic5 | — | 6 | 1 | no | — |
| 152 | #713 | — | 4 | 1 | no | — |
| 153 | Q8×D5 | — | 4 | 1 | no | — |
| 154 | #709 | — | 2 | 1 | no | — |
| 155 | #709 | — | 2 | 1 | no | — |
| 156 | #709 | — | 2 | 1 | no | — |
| 157 | C2×D20 | — | 3 | 1 | no | — |
| 158 | C2×C4×D5 | — | 6 | 1 | no | — |
| 159 | C2×Dic10 | #67 | 1 | 1 | yes | characteristic |
| 160 | C5×M16 | — | 2 | 1 | no | — |
| 161 | C5×M16 | — | 6 | 1 | no | — |
| 162 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 163 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 164 | C42×C5 | — | 3 | 1 | no | — |
| 165 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 166 | #687 | — | 12 | 1 | no | — |
| 167 | #686 | — | 12 | 1 | no | — |
| 168 | #685 | — | 6 | 1 | no | — |
| 169 | #685 | — | 6 | 1 | no | — |
| 170 | #685 | — | 6 | 1 | no | — |
| 171 | #683 | — | 2 | 1 | no | — |
| 172 | #683 | — | 2 | 1 | no | — |
| 173 | #683 | — | 6 | 1 | no | — |
| 174 | C4×Dic5 | — | 3 | 1 | no | — |
| 175 | C4×Dic5 | — | 6 | 1 | no | — |
| 176 | C4×Dic5 | #67 | 1 | 1 | yes | characteristic |
| 177 | #681 | — | 6 | 1 | no | — |
| 178 | Dic20 | — | 4 | 1 | no | — |
| 179 | D40 | — | 12 | 1 | no | — |
| 180 | #677 | — | 4 | 1 | no | — |
| 181 | #677 | — | 12 | 1 | no | — |
| 182 | #555 | — | 15 | 1 | no | — |
| 183 | #456 | — | 5 | 1 | no | — |
| 184 | #454 | — | 15 | 1 | no | — |
| 185 | #454 | — | 15 | 1 | no | — |
| 186 | #356 | — | 15 | 1 | no | — |
| 187 | #355 | — | 3 | 1 | no | — |
| 188 | #355 | — | 15 | 1 | no | — |
| 189 | C22×C3×C5 | #120 | 1 | 1 | yes | characteristic |
| 190 | C2×D15 | — | 4 | 1 | no | — |
| 191 | C2×D15 | — | 4 | 1 | no | — |
| 192 | C2×D15 | — | 4 | 1 | no | — |
| 193 | C2×C5×D3 | — | 4 | 1 | no | — |
| 194 | C2×C5×D3 | — | 4 | 1 | no | — |
| 195 | C2×C5×D3 | — | 4 | 1 | no | — |
| 196 | C2×C3×D5 | — | 4 | 1 | no | — |
| 197 | C3×C4×C5 | — | 2 | 1 | no | — |
| 198 | C3×C4×C5 | — | 2 | 1 | no | — |
| 199 | C3×C4×C5 | — | 2 | 1 | no | — |
| 200 | Dic15 | — | 4 | 1 | no | — |
| 201 | C3×Dic5 | — | 2 | 2 | no | — |
| 202 | C3×Dic5 | — | 4 | 1 | no | — |
| 203 | C3×Dic5 | — | 4 | 1 | no | — |
| 204 | C5×Dic3 | — | 4 | 1 | no | — |
| 205 | C3×#41 | — | 10 | 1 | no | — |
| 206 | C3×#41 | — | 10 | 1 | no | — |
| 207 | C3×#41 | — | 10 | 1 | no | — |
| 208 | C3×#41 | — | 20 | 1 | no | — |
| 209 | C2×C3×Q8 | — | 5 | 1 | no | — |
| 210 | C2×C3×Q8 | — | 20 | 1 | no | — |
| 211 | C2×C3×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 212 | C2×D12 | — | 5 | 1 | no | — |
| 213 | C2×D12 | — | 10 | 1 | no | — |
| 214 | C2×D12 | — | 10 | 1 | no | — |
| 215 | C2×D12 | D20 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×D3 | — | 10 | 1 | no | — |
| 217 | C2×C4×D3 | — | 10 | 1 | no | — |
| 218 | C3×Q16 | — | 20 | 1 | no | — |
| 219 | C3×SD16 | — | 20 | 1 | no | — |
| 220 | C3×M16 | — | 2 | 1 | no | — |
| 221 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 222 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 223 | C3×C42 | — | 5 | 1 | no | — |
| 224 | #215 | — | 20 | 1 | no | — |
| 225 | #215 | — | 20 | 1 | no | — |
| 226 | #213 | — | 20 | 1 | no | — |
| 227 | #213 | — | 20 | 1 | no | — |
| 228 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 229 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 230 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 231 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 232 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 233 | (C2×D3)⋊C4 | — | 10 | 1 | no | — |
| 234 | C4⋊Dic3 | — | 10 | 1 | no | — |
| 235 | C4×Dic3 | — | 5 | 1 | no | — |
| 236 | C4×Dic3 | — | 10 | 1 | no | — |
| 237 | C4×Dic3 | D20 | 1 | 1 | yes | characteristic |
| 238 | #208 | — | 2 | 1 | no | — |
| 239 | #208 | — | 10 | 1 | no | — |
| 240 | C23×C5 | — | 6 | 1 | no | — |
| 241 | C22×D5 | — | 6 | 1 | no | — |
| 242 | C5×Q8 | — | 4 | 1 | no | — |
| 243 | C5×D4 | — | 12 | 1 | no | — |
| 244 | C2×C4×C5 | — | 6 | 1 | no | — |
| 245 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 246 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 247 | C2×C4×C5 | C2×#67 | 1 | 1 | yes | characteristic |
| 248 | C22⋊D5 | — | 4 | 1 | no | — |
| 249 | C22⋊D5 | — | 12 | 2 | no | — |
| 250 | C22⋊D5 | — | 24 | 1 | no | — |
| 251 | C2×Dic5 | — | 2 | 1 | no | — |
| 252 | C2×Dic5 | — | 2 | 1 | no | — |
| 253 | C2×Dic5 | — | 6 | 1 | no | — |
| 254 | C2×Dic5 | — | 12 | 2 | no | — |
| 255 | D20 | — | 2 | 1 | no | — |
| 256 | D20 | — | 2 | 1 | no | — |
| 257 | D20 | — | 2 | 1 | no | — |
| 258 | D20 | — | 12 | 1 | no | — |
| 259 | C4×D5 | — | 4 | 1 | no | — |
| 260 | C4×D5 | — | 4 | 1 | no | — |
| 261 | C4×D5 | — | 4 | 1 | no | — |
| 262 | C4×D5 | — | 12 | 2 | no | — |
| 263 | Dic10 | — | 2 | 1 | no | — |
| 264 | Dic10 | — | 2 | 1 | no | — |
| 265 | Dic10 | — | 2 | 1 | no | — |
| 266 | Dic10 | — | 4 | 1 | no | — |
| 267 | C5×C8 | — | 4 | 1 | no | — |
| 268 | C5×C8 | — | 12 | 1 | no | — |
| 269 | #168 | — | 12 | 1 | no | — |
| 270 | 2−1+4 | — | 5 | 1 | no | — |
| 271 | #137 | — | 10 | 1 | no | — |
| 272 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 273 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 274 | C4⋊Q8 | — | 5 | 1 | no | — |
| 275 | #124 | — | 3 | 1 | no | — |
| 276 | #124 | — | 15 | 1 | no | — |
| 277 | #124 | — | 30 | 1 | no | — |
| 278 | #121 | — | 30 | 1 | no | — |
| 279 | #121 | — | 30 | 1 | no | — |
| 280 | C4×D4 | — | 30 | 1 | no | — |
| 281 | #117 | — | 30 | 1 | no | — |
| 282 | #117 | — | 30 | 1 | no | — |
| 283 | #104 | — | 10 | 1 | no | — |
| 284 | #104 | — | 30 | 1 | no | — |
| 285 | #104 | — | 30 | 1 | no | — |
| 286 | #101 | — | 3 | 1 | no | — |
| 287 | #101 | — | 15 | 1 | no | — |
| 288 | #101 | D3×D5 | 1 | 1 | yes | characteristic |
| 289 | C2×C3×C5 | — | 2 | 1 | no | — |
| 290 | C2×C3×C5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 291 | D15 | — | 8 | 1 | no | — |
| 292 | C3×D5 | — | 8 | 1 | no | — |
| 293 | C5×D3 | — | 8 | 1 | no | — |
| 294 | C22×D3 | — | 2 | 1 | no | — |
| 295 | C22×D3 | — | 10 | 1 | no | — |
| 296 | C3×Q8 | — | 4 | 1 | no | — |
| 297 | C3×Q8 | — | 10 | 1 | no | — |
| 298 | C3×Q8 | — | 10 | 1 | no | — |
| 299 | C3×Q8 | — | 10 | 1 | no | — |
| 300 | C3×Q8 | — | 20 | 1 | no | — |
| 301 | C3×D4 | — | 10 | 1 | no | — |
| 302 | C3×D4 | — | 10 | 1 | no | — |
| 303 | C3×D4 | — | 10 | 1 | no | — |
| 304 | C3×D4 | — | 20 | 1 | no | — |
| 305 | C2×C3×C4 | — | 10 | 1 | no | — |
| 306 | C2×C3×C4 | — | 10 | 1 | no | — |
| 307 | C2×C3×C4 | — | 20 | 1 | no | — |
| 308 | C2×C3×C4 | — | 20 | 1 | no | — |
| 309 | C2×C3×C4 | — | 20 | 1 | no | — |
| 310 | C2×C3×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 311 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 312 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 313 | C2×Dic3 | — | 2 | 1 | no | — |
| 314 | C2×Dic3 | — | 10 | 1 | no | — |
| 315 | D12 | — | 4 | 1 | no | — |
| 316 | D12 | — | 20 | 1 | no | — |
| 317 | D12 | — | 20 | 2 | no | — |
| 318 | D12 | — | 40 | 1 | no | — |
| 319 | C4×D3 | — | 20 | 2 | no | — |
| 320 | C4×D3 | — | 20 | 2 | no | — |
| 321 | C3×C8 | — | 4 | 1 | no | — |
| 322 | C3⋊C8 | — | 4 | 1 | no | — |
| 323 | C3⋊C8 | — | 20 | 1 | no | — |
| 324 | C22×C5 | — | 12 | 1 | no | — |
| 325 | C22×C5 | — | 12 | 1 | no | — |
| 326 | C22×C5 | — | 12 | 1 | no | — |
| 327 | C22×C5 | #937 | 1 | 1 | yes | characteristic |
| 328 | C2×D5 | — | 4 | 1 | no | — |
| 329 | C2×D5 | — | 12 | 1 | no | — |
| 330 | C2×D5 | — | 12 | 1 | no | — |
| 331 | C2×D5 | — | 12 | 1 | no | — |
| 332 | C4×C5 | — | 2 | 1 | no | — |
| 333 | C4×C5 | — | 2 | 1 | no | — |
| 334 | C4×C5 | — | 2 | 1 | no | — |
| 335 | C4×C5 | — | 12 | 1 | no | — |
| 336 | Dic5 | — | 2 | 2 | no | — |
| 337 | Dic5 | — | 4 | 1 | no | — |
| 338 | Dic5 | — | 4 | 1 | no | — |
| 339 | Dic5 | — | 12 | 1 | no | — |
| 340 | #41 | — | 10 | 1 | no | — |
| 341 | #41 | — | 10 | 1 | no | — |
| 342 | #41 | — | 10 | 1 | no | — |
| 343 | #41 | — | 20 | 1 | no | — |
| 344 | C2×Q8 | — | 5 | 1 | no | — |
| 345 | C2×Q8 | — | 20 | 1 | no | — |
| 346 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 347 | C2×D4 | — | 3 | 1 | no | — |
| 348 | C2×D4 | — | 15 | 1 | no | — |
| 349 | C2×D4 | — | 30 | 1 | no | — |
| 350 | C2×D4 | — | 30 | 1 | no | — |
| 351 | C22×C4 | — | 30 | 1 | no | — |
| 352 | C22×C4 | — | 30 | 1 | no | — |
| 353 | Q16 | — | 20 | 1 | no | — |
| 354 | SD16 | — | 20 | 1 | no | — |
| 355 | SD16 | — | 60 | 1 | no | — |
| 356 | SD16 | — | 60 | 1 | no | — |
| 357 | D8 | — | 60 | 1 | no | — |
| 358 | D8 | — | 60 | 1 | no | — |
| 359 | M16 | — | 2 | 1 | no | — |
| 360 | M16 | — | 6 | 1 | no | — |
| 361 | M16 | — | 30 | 1 | no | — |
| 362 | C4⋊C4 | — | 10 | 1 | no | — |
| 363 | C4⋊C4 | — | 10 | 1 | no | — |
| 364 | C4⋊C4 | — | 30 | 1 | no | — |
| 365 | C22⋊C4 | — | 6 | 1 | no | — |
| 366 | C22⋊C4 | — | 6 | 1 | no | — |
| 367 | C22⋊C4 | — | 30 | 1 | no | — |
| 368 | C22⋊C4 | — | 30 | 1 | no | — |
| 369 | C22⋊C4 | — | 30 | 1 | no | — |
| 370 | C22⋊C4 | — | 30 | 1 | no | — |
| 371 | C42 | — | 3 | 1 | no | — |
| 372 | C42 | — | 5 | 1 | no | — |
| 373 | C42 | — | 15 | 1 | no | — |
| 374 | C42 | — | 30 | 1 | no | — |
| 375 | C3×C5 | #2204 | 1 | 1 | yes | characteristic, complemented, Hall |
| 376 | C22×C3 | — | 20 | 1 | no | — |
| 377 | C22×C3 | #4028 | 1 | 1 | yes | characteristic |
| 378 | C2×D3 | — | 4 | 1 | no | — |
| 379 | C2×D3 | — | 4 | 1 | no | — |
| 380 | C2×D3 | — | 4 | 1 | no | — |
| 381 | C2×D3 | — | 20 | 1 | no | — |
| 382 | C2×D3 | — | 20 | 1 | no | — |
| 383 | C2×D3 | — | 20 | 1 | no | — |
| 384 | C3×C4 | — | 2 | 1 | no | — |
| 385 | C3×C4 | — | 2 | 1 | no | — |
| 386 | C3×C4 | — | 2 | 1 | no | — |
| 387 | C3×C4 | — | 10 | 2 | no | — |
| 388 | C3×C4 | — | 20 | 1 | no | — |
| 389 | C3×C4 | — | 20 | 1 | no | — |
| 390 | Dic3 | — | 4 | 1 | no | — |
| 391 | Dic3 | — | 20 | 1 | no | — |
| 392 | C2×C5 | — | 2 | 1 | no | — |
| 393 | C2×C5 | — | 24 | 1 | no | — |
| 394 | C2×C5 | #5032 | 1 | 1 | yes | characteristic |
| 395 | D5 | — | 8 | 1 | no | — |
| 396 | D5 | — | 24 | 1 | no | — |
| 397 | C23 | — | 6 | 1 | no | — |
| 398 | C23 | — | 30 | 1 | no | — |
| 399 | Q8 | — | 4 | 1 | no | — |
| 400 | Q8 | — | 10 | 1 | no | — |
| 401 | Q8 | — | 10 | 1 | no | — |
| 402 | Q8 | — | 10 | 1 | no | — |
| 403 | Q8 | — | 20 | 1 | no | — |
| 404 | D4 | — | 10 | 1 | no | — |
| 405 | D4 | — | 10 | 1 | no | — |
| 406 | D4 | — | 10 | 1 | no | — |
| 407 | D4 | — | 12 | 1 | no | — |
| 408 | D4 | — | 20 | 1 | no | — |
| 409 | D4 | — | 60 | 1 | no | — |
| 410 | D4 | — | 60 | 2 | no | — |
| 411 | D4 | — | 120 | 1 | no | — |
| 412 | C2×C4 | — | 6 | 1 | no | — |
| 413 | C2×C4 | — | 10 | 1 | no | — |
| 414 | C2×C4 | — | 10 | 1 | no | — |
| 415 | C2×C4 | — | 20 | 1 | no | — |
| 416 | C2×C4 | — | 20 | 1 | no | — |
| 417 | C2×C4 | — | 20 | 1 | no | — |
| 418 | C2×C4 | — | 30 | 1 | no | — |
| 419 | C2×C4 | — | 60 | 2 | no | — |
| 420 | C2×C4 | — | 60 | 2 | no | — |
| 421 | C2×C4 | D3×D20 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | #6777 | 1 | 1 | yes | characteristic |
| 423 | C2×C4 | D5×#67 | 1 | 1 | yes | characteristic |
| 424 | C8 | — | 4 | 1 | no | — |
| 425 | C8 | — | 12 | 1 | no | — |
| 426 | C8 | — | 60 | 1 | no | — |
| 427 | C2×C3 | — | 2 | 1 | no | — |
| 428 | C2×C3 | — | 40 | 1 | no | — |
| 429 | C2×C3 | #65030 | 1 | 1 | yes | characteristic |
| 430 | D3 | — | 8 | 1 | no | — |
| 431 | D3 | — | 40 | 1 | no | — |
| 432 | C5 | #70994 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 433 | C22 | — | 12 | 1 | no | — |
| 434 | C22 | — | 12 | 1 | no | — |
| 435 | C22 | — | 12 | 1 | no | — |
| 436 | C22 | — | 20 | 1 | no | — |
| 437 | C22 | — | 60 | 1 | no | — |
| 438 | C22 | — | 60 | 1 | no | — |
| 439 | C22 | — | 60 | 1 | no | — |
| 440 | C22 | #91474 | 1 | 1 | yes | characteristic |
| 441 | C4 | — | 2 | 1 | no | — |
| 442 | C4 | — | 2 | 1 | no | — |
| 443 | C4 | — | 2 | 1 | no | — |
| 444 | C4 | — | 10 | 2 | no | — |
| 445 | C4 | — | 12 | 1 | no | — |
| 446 | C4 | — | 20 | 1 | no | — |
| 447 | C4 | — | 20 | 1 | no | — |
| 448 | C4 | — | 60 | 1 | no | — |
| 449 | C3 | #10599954 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 450 | C2 | — | 2 | 1 | no | — |
| 451 | C2 | — | 24 | 1 | no | — |
| 452 | C2 | — | 40 | 1 | no | — |
| 453 | C2 | — | 120 | 1 | no | — |
| 454 | C2 | #11747132 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11755199 | C2 | semidirect |
| 2. C3×#65041 | C2 | semidirect |
| 3. #11749384 | C2 | semidirect |
| 4. #11749383 | C2 | semidirect |
| 5. #11746298 | C2 | semidirect |
| 6. C5×#4477 | C2 | semidirect |
| 7. #11746015 | C2 | semidirect |
| 32. #65041 | D3 | semidirect |
| 77. #4477 | D5 | semidirect |
| 375. C3×C5 | #2204 | semidirect |
| 432. C5 | #70994 | semidirect |
| 449. C3 | #10599954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11755199 | 2 |
| C3×#65041 | 2 |
| #11749384 | 2 |
| #11749383 | 2 |
| #11746298 | 2 |
| C5×#4477 | 2 |
| #11746015 | 2 |
| #10599954 | 3 |
| #70994 | 5 |