Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2740 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 2740 conjugacy classes of subgroups — too many to draw. Only its 255 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 | C5×A4×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | A4×#713 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | D4×D5×A4 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | A4×#709 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×A4×D20 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C22×#4149 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 7 | C22×D5×A4 | C22 | 1 | 6 | yes | complemented |
| 8 | C3×#4149 | — | 4 | 1 | no | maximal |
| 9 | C5×Q8×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C5×D4×A4 | C22 | 1 | 3 | yes | complemented |
| 11 | C2×C4×C5×A4 | C22 | 1 | 3 | yes | complemented |
| 12 | A4×C22⋊D5 | C22 | 1 | 6 | yes | complemented |
| 13 | A4×D20 | C22 | 1 | 3 | yes | complemented |
| 14 | A4×D20 | C22 | 1 | 6 | yes | complemented |
| 15 | C4×D5×A4 | C22 | 1 | 6 | yes | complemented |
| 16 | A4×Dic10 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | A4×H(5,𝔽2) | — | 5 | 1 | no | maximal, Hall |
| 18 | C22×C5×#41 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#4149 | — | 3 | 1 | no | — |
| 20 | C2×#4149 | — | 3 | 3 | no | — |
| 21 | C2×#4149 | — | 3 | 3 | no | — |
| 22 | C2×#4149 | — | 3 | 6 | no | — |
| 23 | C2×#4149 | — | 3 | 2 | no | — |
| 24 | C2×#4149 | — | 3 | 1 | no | — |
| 25 | C22×#713 | C2×C3 | 1 | 2 | yes | complemented |
| 26 | C22×D4×D5 | C2×C3 | 1 | 6 | yes | complemented |
| 27 | C22×#709 | C2×C3 | 1 | 3 | yes | complemented |
| 28 | C23×D20 | C2×C3 | 1 | 3 | yes | complemented |
| 29 | C22×C5×A4 | C23 | 1 | 3 | yes | — |
| 30 | C2×D5×A4 | — | 4 | 6 | no | — |
| 31 | C2×D5×A4 | C23 | 1 | 6 | yes | — |
| 32 | C3×C5×#41 | — | 4 | 1 | no | — |
| 33 | C3×#713 | — | 4 | 2 | no | — |
| 34 | C3×D4×D5 | — | 4 | 6 | no | — |
| 35 | C3×#709 | — | 4 | 3 | no | — |
| 36 | C2×C3×D20 | — | 4 | 3 | no | — |
| 37 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 38 | C4×C5×A4 | C23 | 1 | 3 | yes | — |
| 39 | A4×Dic5 | C23 | 1 | 2 | yes | — |
| 40 | A4×#41 | — | 5 | 2 | no | — |
| 41 | A4×#41 | — | 5 | 3 | no | — |
| 42 | A4×#41 | D5 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×D4×A4 | — | 5 | 6 | no | — |
| 44 | C2×D4×A4 | — | 5 | 3 | no | — |
| 45 | C24×D5 | C22×C3 | 1 | 6 | yes | complemented |
| 46 | C2×C5×#41 | — | 3 | 3 | no | — |
| 47 | C2×C5×#41 | — | 3 | 3 | no | — |
| 48 | C2×C5×#41 | — | 3 | 1 | no | — |
| 49 | C2×C5×#41 | — | 3 | 1 | no | — |
| 50 | C22×C5×Q8 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 51 | C22×C5×D4 | C22×C3 | 1 | 3 | yes | complemented |
| 52 | C23×C4×C5 | C22×C3 | 1 | 3 | yes | complemented |
| 53 | C22×C22⋊D5 | C22×C3 | 1 | 6 | yes | complemented |
| 54 | #4149 | — | 3 | 2 | no | — |
| 55 | #4149 | — | 3 | 6 | no | — |
| 56 | #4149 | — | 3 | 12 | no | — |
| 57 | #4149 | — | 3 | 12 | no | — |
| 58 | #4149 | — | 3 | 2 | no | — |
| 59 | #4149 | — | 3 | 12 | no | — |
| 60 | #4149 | — | 3 | 6 | no | — |
| 61 | #4149 | — | 3 | 12 | no | — |
| 62 | #4149 | — | 3 | 6 | no | — |
| 63 | #4149 | — | 3 | 1 | no | — |
| 64 | #4149 | — | 3 | 2 | no | — |
| 65 | #4149 | — | 3 | 6 | no | — |
| 66 | #4149 | — | 3 | 3 | no | — |
| 67 | #4149 | — | 3 | 3 | no | — |
| 68 | #4149 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 69 | C2×#713 | — | 3 | 2 | no | — |
| 70 | C2×#713 | — | 3 | 6 | no | — |
| 71 | C2×#713 | — | 3 | 6 | no | — |
| 72 | C2×#713 | — | 3 | 2 | no | — |
| 73 | C2×D4×D5 | — | 3 | 6 | no | — |
| 74 | C2×D4×D5 | — | 3 | 6 | no | — |
| 75 | C2×D4×D5 | — | 3 | 6 | no | — |
| 76 | C2×D4×D5 | — | 3 | 12 | no | — |
| 77 | C2×D4×D5 | — | 3 | 6 | no | — |
| 78 | C2×D4×D5 | — | 3 | 12 | no | — |
| 79 | C2×#709 | — | 3 | 3 | no | — |
| 80 | C2×#709 | — | 3 | 3 | no | — |
| 81 | C2×#709 | — | 3 | 6 | no | — |
| 82 | C2×#709 | — | 3 | 3 | no | — |
| 83 | C2×#709 | — | 3 | 3 | no | — |
| 84 | C2×#709 | — | 3 | 6 | no | — |
| 85 | C22×D20 | — | 3 | 3 | no | — |
| 86 | C22×D20 | — | 3 | 6 | no | — |
| 87 | C22×D20 | — | 3 | 3 | no | — |
| 88 | C22×D20 | — | 3 | 6 | no | — |
| 89 | C22×D20 | — | 3 | 6 | no | — |
| 90 | C22×D20 | C22×C3 | 1 | 3 | yes | complemented |
| 91 | C22×D20 | C22×C3 | 1 | 6 | yes | complemented |
| 92 | C22×C4×D5 | C22×C3 | 1 | 6 | yes | complemented |
| 93 | C22×Dic10 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 94 | C22×H(5,𝔽2) | — | 5 | 1 | no | Sylow |
| 95 | C22×C3×D5 | — | 4 | 6 | no | — |
| 96 | C2×C5×A4 | — | 2 | 3 | no | — |
| 97 | C2×C5×A4 | C24 | 1 | 1 | yes | characteristic |
| 98 | D5×A4 | — | 2 | 6 | no | — |
| 99 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 100 | C3×C5×D4 | — | 4 | 3 | no | — |
| 101 | C2×C3×C4×C5 | — | 4 | 3 | no | — |
| 102 | C3×C22⋊D5 | — | 4 | 6 | no | — |
| 103 | C3×D20 | — | 4 | 3 | no | — |
| 104 | C3×D20 | — | 4 | 6 | no | — |
| 105 | C3×C4×D5 | — | 4 | 6 | no | — |
| 106 | C3×Dic10 | — | 4 | 1 | no | — |
| 107 | C23×A4 | — | 5 | 6 | no | — |
| 108 | C3×H(5,𝔽2) | — | 20 | 1 | no | — |
| 109 | Q8×A4 | — | 5 | 1 | no | — |
| 110 | Q8×A4 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 111 | D4×A4 | — | 5 | 6 | no | — |
| 112 | D4×A4 | — | 5 | 6 | no | — |
| 113 | D4×A4 | — | 5 | 3 | no | — |
| 114 | D4×A4 | C2×D5 | 1 | 3 | yes | complemented |
| 115 | C2×C4×A4 | — | 5 | 6 | no | — |
| 116 | C2×C4×A4 | C2×D5 | 1 | 3 | yes | complemented |
| 117 | C24×C5 | C23×C3 | 1 | 3 | yes | — |
| 118 | C23×D5 | — | 3 | 6 | no | — |
| 119 | C23×D5 | — | 3 | 6 | no | — |
| 120 | C23×D5 | — | 3 | 12 | no | — |
| 121 | C23×D5 | — | 4 | 6 | no | — |
| 122 | C23×D5 | — | 12 | 6 | no | — |
| 123 | C23×D5 | C23×C3 | 1 | 6 | yes | — |
| 124 | C5×#41 | — | 3 | 6 | no | — |
| 125 | C5×#41 | — | 3 | 6 | no | — |
| 126 | C5×#41 | — | 3 | 2 | no | — |
| 127 | C5×#41 | — | 3 | 1 | no | — |
| 128 | C5×#41 | — | 3 | 3 | no | — |
| 129 | C5×#41 | — | 3 | 3 | no | — |
| 130 | C5×#41 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 131 | C2×C5×Q8 | — | 3 | 3 | no | — |
| 132 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 133 | C2×C5×D4 | — | 3 | 3 | no | — |
| 134 | C2×C5×D4 | — | 3 | 3 | no | — |
| 135 | C2×C5×D4 | — | 3 | 6 | no | — |
| 136 | C22×C4×C5 | — | 3 | 3 | no | — |
| 137 | C22×C4×C5 | — | 3 | 3 | no | — |
| 138 | C22×C4×C5 | — | 3 | 3 | no | — |
| 139 | C22×C4×C5 | — | 3 | 3 | no | — |
| 140 | C22×C4×C5 | C23×C3 | 1 | 1 | yes | characteristic |
| 141 | C22×C4×C5 | C23×C3 | 1 | 3 | yes | — |
| 142 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 143 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 144 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 145 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 146 | C22×Dic5 | C23×C3 | 1 | 2 | yes | — |
| 147 | #713 | — | 3 | 12 | no | — |
| 148 | #713 | — | 3 | 12 | no | — |
| 149 | #713 | — | 3 | 4 | no | — |
| 150 | #713 | — | 3 | 2 | no | — |
| 151 | #713 | — | 3 | 6 | no | — |
| 152 | #713 | — | 3 | 6 | no | — |
| 153 | #713 | C2×A4 | 1 | 2 | yes | complemented |
| 154 | D4×D5 | — | 3 | 24 | no | — |
| 155 | D4×D5 | — | 3 | 24 | no | — |
| 156 | D4×D5 | — | 3 | 12 | no | — |
| 157 | D4×D5 | — | 3 | 12 | no | — |
| 158 | D4×D5 | — | 3 | 12 | no | — |
| 159 | D4×D5 | — | 3 | 12 | no | — |
| 160 | D4×D5 | — | 3 | 6 | no | — |
| 161 | D4×D5 | — | 3 | 12 | no | — |
| 162 | D4×D5 | — | 3 | 6 | no | — |
| 163 | D4×D5 | — | 3 | 6 | no | — |
| 164 | D4×D5 | C2×A4 | 1 | 6 | yes | complemented |
| 165 | #709 | — | 3 | 6 | no | — |
| 166 | #709 | — | 3 | 12 | no | — |
| 167 | #709 | — | 3 | 6 | no | — |
| 168 | #709 | — | 3 | 6 | no | — |
| 169 | #709 | — | 3 | 12 | no | — |
| 170 | #709 | — | 3 | 3 | no | — |
| 171 | #709 | — | 3 | 6 | no | — |
| 172 | #709 | — | 3 | 3 | no | — |
| 173 | #709 | — | 3 | 6 | no | — |
| 174 | #709 | — | 3 | 3 | no | — |
| 175 | #709 | C2×A4 | 1 | 3 | yes | complemented |
| 176 | C2×D20 | — | 3 | 6 | no | — |
| 177 | C2×D20 | — | 3 | 6 | no | — |
| 178 | C2×D20 | — | 3 | 24 | no | — |
| 179 | C2×D20 | — | 3 | 6 | no | — |
| 180 | C2×D20 | — | 3 | 6 | no | — |
| 181 | C2×D20 | — | 3 | 3 | no | — |
| 182 | C2×D20 | — | 3 | 3 | no | — |
| 183 | C2×D20 | — | 3 | 6 | no | — |
| 184 | C2×D20 | — | 3 | 6 | no | — |
| 185 | C2×D20 | — | 3 | 6 | no | — |
| 186 | C2×D20 | — | 3 | 6 | no | — |
| 187 | C2×D20 | — | 3 | 3 | no | — |
| 188 | C2×D20 | — | 3 | 12 | no | — |
| 189 | C2×D20 | — | 3 | 6 | no | — |
| 190 | C2×D20 | C2×A4 | 1 | 3 | yes | complemented |
| 191 | C2×C4×D5 | — | 3 | 6 | no | — |
| 192 | C2×C4×D5 | — | 3 | 6 | no | — |
| 193 | C2×C4×D5 | — | 3 | 6 | no | — |
| 194 | C2×C4×D5 | — | 3 | 6 | no | — |
| 195 | C2×Dic10 | — | 3 | 1 | no | — |
| 196 | C2×Dic10 | — | 3 | 1 | no | — |
| 197 | C2×Dic10 | — | 3 | 2 | no | — |
| 198 | C2×H(5,𝔽2) | — | 15 | 1 | no | — |
| 199 | C2×H(5,𝔽2) | — | 15 | 3 | no | — |
| 200 | C2×H(5,𝔽2) | — | 15 | 6 | no | — |
| 201 | C2×H(5,𝔽2) | — | 15 | 3 | no | — |
| 202 | C2×H(5,𝔽2) | — | 15 | 2 | no | — |
| 203 | C2×H(5,𝔽2) | — | 15 | 1 | no | — |
| 204 | C22×#41 | — | 5 | 2 | no | — |
| 205 | C22×#41 | — | 5 | 3 | no | — |
| 206 | C22×#41 | C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 207 | C23×D4 | — | 5 | 6 | no | — |
| 208 | C23×D4 | — | 5 | 3 | no | — |
| 209 | C22×C3×C5 | — | 4 | 3 | no | — |
| 210 | C2×C3×D5 | — | 4 | 6 | no | — |
| 211 | C2×C3×D5 | — | 16 | 6 | no | — |
| 212 | C5×A4 | H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 213 | C3×C4×C5 | — | 4 | 1 | no | — |
| 214 | C3×C4×C5 | — | 4 | 3 | no | — |
| 215 | C3×Dic5 | — | 4 | 2 | no | — |
| 216 | C22×A4 | — | 5 | 6 | no | — |
| 217 | C22×A4 | — | 20 | 6 | no | — |
| 218 | C22×A4 | C22×D5 | 1 | 3 | yes | — |
| 219 | C3×#41 | — | 4 | 1 | no | — |
| 220 | C3×#41 | — | 20 | 3 | no | — |
| 221 | C3×#41 | — | 20 | 2 | no | — |
| 222 | C2×C3×D4 | — | 20 | 3 | no | — |
| 223 | C2×C3×D4 | — | 20 | 6 | no | — |
| 224 | C4×A4 | — | 5 | 2 | no | — |
| 225 | C4×A4 | C22×D5 | 1 | 3 | yes | — |
| 226 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 227 | C23×C5 | — | 2 | 3 | no | — |
| 228 | C23×C5 | — | 3 | 3 | no | — |
| 229 | C23×C5 | — | 3 | 3 | no | — |
| 230 | C23×C5 | — | 6 | 3 | no | — |
| 231 | C23×C5 | C24×C3 | 1 | 1 | yes | characteristic |
| 232 | C22×D5 | — | 2 | 6 | no | — |
| 233 | C22×D5 | — | 3 | 12 | no | — |
| 234 | C22×D5 | — | 3 | 6 | no | — |
| 235 | C22×D5 | — | 3 | 6 | no | — |
| 236 | C22×D5 | — | 3 | 6 | no | — |
| 237 | C22×D5 | — | 3 | 12 | no | — |
| 238 | C22×D5 | — | 6 | 6 | no | — |
| 239 | C22×D5 | — | 12 | 6 | no | — |
| 240 | C22×D5 | — | 12 | 6 | no | — |
| 241 | C22×D5 | — | 12 | 12 | no | — |
| 242 | C22×D5 | — | 12 | 6 | no | — |
| 243 | C22×D5 | — | 12 | 12 | no | — |
| 244 | C22×D5 | — | 12 | 6 | no | — |
| 245 | C22×D5 | C22×A4 | 1 | 6 | yes | complemented |
| 246 | C5×Q8 | — | 3 | 2 | no | — |
| 247 | C5×Q8 | — | 3 | 3 | no | — |
| 248 | C5×Q8 | C22×A4 | 1 | 1 | yes | characteristic, complemented |
| 249 | C5×D4 | — | 3 | 6 | no | — |
| 250 | C5×D4 | — | 3 | 6 | no | — |
| 251 | C5×D4 | — | 3 | 3 | no | — |
| 252 | C5×D4 | C22×A4 | 1 | 3 | yes | complemented |
| 253 | C2×C4×C5 | — | 3 | 6 | no | — |
| 254 | C2×C4×C5 | — | 3 | 3 | no | — |
| 255 | C2×C4×C5 | — | 3 | 1 | no | — |
| 256 | C2×C4×C5 | — | 3 | 3 | no | — |
| 257 | C2×C4×C5 | — | 3 | 3 | no | — |
| 258 | C2×C4×C5 | — | 3 | 3 | no | — |
| 259 | C2×C4×C5 | — | 3 | 1 | no | — |
| 260 | C2×C4×C5 | — | 3 | 3 | no | — |
| 261 | C2×C4×C5 | C22×A4 | 1 | 3 | yes | complemented |
| 262 | C22⋊D5 | — | 3 | 12 | no | — |
| 263 | C22⋊D5 | — | 3 | 6 | no | — |
| 264 | C22⋊D5 | — | 3 | 6 | no | — |
| 265 | C22⋊D5 | — | 3 | 6 | no | — |
| 266 | C22⋊D5 | C22×A4 | 1 | 6 | yes | complemented |
| 267 | C2×Dic5 | — | 3 | 2 | no | — |
| 268 | C2×Dic5 | — | 3 | 2 | no | — |
| 269 | D20 | — | 3 | 6 | no | — |
| 270 | D20 | — | 3 | 12 | no | — |
| 271 | D20 | — | 3 | 6 | no | — |
| 272 | D20 | — | 3 | 12 | no | — |
| 273 | D20 | — | 3 | 3 | no | — |
| 274 | D20 | — | 3 | 6 | no | — |
| 275 | D20 | C22×A4 | 1 | 3 | yes | complemented |
| 276 | D20 | C22×A4 | 1 | 6 | yes | complemented |
| 277 | C4×D5 | — | 3 | 12 | no | — |
| 278 | C4×D5 | — | 3 | 6 | no | — |
| 279 | C4×D5 | — | 3 | 6 | no | — |
| 280 | C4×D5 | — | 3 | 6 | no | — |
| 281 | C4×D5 | C22×A4 | 1 | 6 | yes | complemented |
| 282 | Dic10 | — | 3 | 2 | no | — |
| 283 | Dic10 | — | 3 | 1 | no | — |
| 284 | Dic10 | — | 3 | 2 | no | — |
| 285 | Dic10 | C22×A4 | 1 | 1 | yes | characteristic, complemented |
| 286 | C25 | — | 5 | 6 | no | — |
| 287 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 288 | H(5,𝔽2) | — | 15 | 6 | no | — |
| 289 | H(5,𝔽2) | — | 15 | 3 | no | — |
| 290 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 291 | H(5,𝔽2) | — | 15 | 3 | no | — |
| 292 | H(5,𝔽2) | — | 15 | 6 | no | — |
| 293 | H(5,𝔽2) | — | 15 | 12 | no | — |
| 294 | H(5,𝔽2) | — | 15 | 12 | no | — |
| 295 | H(5,𝔽2) | — | 15 | 12 | no | — |
| 296 | H(5,𝔽2) | — | 15 | 12 | no | — |
| 297 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 298 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 299 | H(5,𝔽2) | — | 15 | 6 | no | — |
| 300 | H(5,𝔽2) | — | 15 | 6 | no | — |
| 301 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 302 | C2×#41 | — | 3 | 3 | no | — |
| 303 | C2×#41 | — | 3 | 3 | no | — |
| 304 | C2×#41 | — | 3 | 1 | no | — |
| 305 | C2×#41 | — | 3 | 1 | no | — |
| 306 | C2×#41 | — | 15 | 3 | no | — |
| 307 | C2×#41 | — | 15 | 3 | no | — |
| 308 | C2×#41 | — | 15 | 6 | no | — |
| 309 | C2×#41 | — | 15 | 3 | no | — |
| 310 | C2×#41 | — | 15 | 6 | no | — |
| 311 | C2×#41 | — | 15 | 3 | no | — |
| 312 | C2×#41 | — | 15 | 2 | no | — |
| 313 | C2×#41 | — | 15 | 6 | no | — |
| 314 | C2×#41 | — | 15 | 6 | no | — |
| 315 | C2×#41 | — | 15 | 2 | no | — |
| 316 | C22×Q8 | — | 5 | 1 | no | — |
| 317 | C22×Q8 | C2×C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 318 | C22×D4 | — | 5 | 6 | no | — |
| 319 | C22×D4 | — | 5 | 6 | no | — |
| 320 | C22×D4 | — | 5 | 3 | no | — |
| 321 | C22×D4 | — | 15 | 3 | no | — |
| 322 | C22×D4 | — | 15 | 3 | no | — |
| 323 | C22×D4 | — | 15 | 6 | no | — |
| 324 | C22×D4 | — | 15 | 6 | no | — |
| 325 | C22×D4 | — | 15 | 6 | no | — |
| 326 | C22×D4 | — | 15 | 6 | no | — |
| 327 | C22×D4 | — | 15 | 6 | no | — |
| 328 | C22×D4 | — | 15 | 6 | no | — |
| 329 | C22×D4 | — | 15 | 6 | no | — |
| 330 | C22×D4 | — | 15 | 12 | no | — |
| 331 | C22×D4 | — | 15 | 12 | no | — |
| 332 | C22×D4 | C2×C3×D5 | 1 | 3 | yes | complemented |
| 333 | C23×C4 | — | 5 | 6 | no | — |
| 334 | C23×C4 | C2×C3×D5 | 1 | 3 | yes | complemented |
| 335 | C2×C3×C5 | — | 4 | 1 | no | — |
| 336 | C2×C3×C5 | — | 8 | 3 | no | — |
| 337 | C3×D5 | — | 8 | 6 | no | — |
| 338 | C23×C3 | — | 20 | 6 | no | — |
| 339 | C2×A4 | — | 2 | 3 | no | — |
| 340 | C2×A4 | — | 10 | 6 | no | — |
| 341 | C2×A4 | C23×D5 | 1 | 1 | yes | characteristic |
| 342 | C3×Q8 | — | 4 | 1 | no | — |
| 343 | C3×Q8 | — | 20 | 1 | no | — |
| 344 | C3×D4 | — | 4 | 3 | no | — |
| 345 | C3×D4 | — | 20 | 3 | no | — |
| 346 | C3×D4 | — | 20 | 6 | no | — |
| 347 | C3×D4 | — | 20 | 6 | no | — |
| 348 | C2×C3×C4 | — | 4 | 3 | no | — |
| 349 | C2×C3×C4 | — | 20 | 6 | no | — |
| 350 | C22×C5 | — | 3 | 1 | no | — |
| 351 | C22×C5 | — | 3 | 1 | no | — |
| 352 | C22×C5 | — | 3 | 3 | no | — |
| 353 | C22×C5 | — | 6 | 3 | no | — |
| 354 | C22×C5 | — | 6 | 3 | no | — |
| 355 | C22×C5 | — | 6 | 3 | no | — |
| 356 | C22×C5 | — | 6 | 3 | no | — |
| 357 | C22×C5 | C3×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 358 | C22×C5 | C23×A4 | 1 | 3 | yes | — |
| 359 | C2×D5 | — | 3 | 6 | no | — |
| 360 | C2×D5 | — | 4 | 6 | no | — |
| 361 | C2×D5 | — | 6 | 6 | no | — |
| 362 | C2×D5 | — | 6 | 6 | no | — |
| 363 | C2×D5 | — | 6 | 6 | no | — |
| 364 | C2×D5 | — | 6 | 6 | no | — |
| 365 | C2×D5 | — | 12 | 12 | no | — |
| 366 | C2×D5 | — | 12 | 6 | no | — |
| 367 | C2×D5 | — | 12 | 12 | no | — |
| 368 | C2×D5 | C23×A4 | 1 | 6 | yes | — |
| 369 | C4×C5 | — | 3 | 1 | no | — |
| 370 | C4×C5 | — | 3 | 3 | no | — |
| 371 | C4×C5 | C23×A4 | 1 | 1 | yes | characteristic |
| 372 | C4×C5 | C23×A4 | 1 | 3 | yes | — |
| 373 | Dic5 | — | 3 | 2 | no | — |
| 374 | Dic5 | C23×A4 | 1 | 2 | yes | — |
| 375 | C24 | — | 5 | 6 | no | — |
| 376 | C24 | — | 15 | 6 | no | — |
| 377 | C24 | — | 15 | 12 | no | — |
| 378 | C24 | — | 15 | 6 | no | — |
| 379 | C24 | — | 20 | 6 | no | — |
| 380 | C24 | — | 60 | 6 | no | — |
| 381 | C24 | C22×C3×D5 | 1 | 3 | yes | — |
| 382 | #41 | — | 3 | 6 | no | — |
| 383 | #41 | — | 3 | 6 | no | — |
| 384 | #41 | — | 3 | 2 | no | — |
| 385 | #41 | — | 3 | 1 | no | — |
| 386 | #41 | — | 3 | 3 | no | — |
| 387 | #41 | — | 3 | 3 | no | — |
| 388 | #41 | — | 5 | 2 | no | — |
| 389 | #41 | — | 5 | 3 | no | — |
| 390 | #41 | — | 15 | 6 | no | — |
| 391 | #41 | — | 15 | 6 | no | — |
| 392 | #41 | — | 15 | 3 | no | — |
| 393 | #41 | — | 15 | 3 | no | — |
| 394 | #41 | — | 15 | 12 | no | — |
| 395 | #41 | — | 15 | 12 | no | — |
| 396 | #41 | — | 15 | 6 | no | — |
| 397 | #41 | — | 15 | 6 | no | — |
| 398 | #41 | — | 15 | 6 | no | — |
| 399 | #41 | — | 15 | 6 | no | — |
| 400 | #41 | — | 15 | 6 | no | — |
| 401 | #41 | — | 15 | 4 | no | — |
| 402 | #41 | — | 15 | 12 | no | — |
| 403 | #41 | — | 15 | 12 | no | — |
| 404 | #41 | — | 15 | 2 | no | — |
| 405 | #41 | — | 15 | 3 | no | — |
| 406 | #41 | D5×A4 | 1 | 1 | yes | characteristic, complemented |
| 407 | C2×Q8 | — | 3 | 3 | no | — |
| 408 | C2×Q8 | — | 3 | 1 | no | — |
| 409 | C2×Q8 | — | 15 | 1 | no | — |
| 410 | C2×Q8 | — | 15 | 1 | no | — |
| 411 | C2×Q8 | — | 15 | 2 | no | — |
| 412 | C2×D4 | — | 3 | 3 | no | — |
| 413 | C2×D4 | — | 3 | 3 | no | — |
| 414 | C2×D4 | — | 3 | 6 | no | — |
| 415 | C2×D4 | — | 5 | 6 | no | — |
| 416 | C2×D4 | — | 5 | 3 | no | — |
| 417 | C2×D4 | — | 15 | 3 | no | — |
| 418 | C2×D4 | — | 15 | 6 | no | — |
| 419 | C2×D4 | — | 15 | 6 | no | — |
| 420 | C2×D4 | — | 15 | 6 | no | — |
| 421 | C2×D4 | — | 15 | 6 | no | — |
| 422 | C2×D4 | — | 15 | 24 | no | — |
| 423 | C2×D4 | — | 15 | 6 | no | — |
| 424 | C2×D4 | — | 15 | 6 | no | — |
| 425 | C2×D4 | — | 15 | 6 | no | — |
| 426 | C2×D4 | — | 15 | 3 | no | — |
| 427 | C2×D4 | — | 15 | 6 | no | — |
| 428 | C2×D4 | — | 15 | 6 | no | — |
| 429 | C2×D4 | — | 15 | 12 | no | — |
| 430 | C2×D4 | — | 15 | 6 | no | — |
| 431 | C2×D4 | — | 15 | 12 | no | — |
| 432 | C2×D4 | — | 15 | 6 | no | — |
| 433 | C2×D4 | — | 15 | 12 | no | — |
| 434 | C2×D4 | — | 15 | 12 | no | — |
| 435 | C2×D4 | — | 15 | 12 | no | — |
| 436 | C2×D4 | — | 15 | 24 | no | — |
| 437 | C2×D4 | — | 15 | 24 | no | — |
| 438 | C2×D4 | — | 15 | 12 | no | — |
| 439 | C2×D4 | — | 15 | 6 | no | — |
| 440 | C2×D4 | — | 15 | 6 | no | — |
| 441 | C2×D4 | — | 15 | 6 | no | — |
| 442 | C2×D4 | — | 15 | 6 | no | — |
| 443 | C2×D4 | — | 15 | 6 | no | — |
| 444 | C2×D4 | — | 15 | 3 | no | — |
| 445 | C22×C4 | — | 3 | 3 | no | — |
| 446 | C22×C4 | — | 3 | 3 | no | — |
| 447 | C22×C4 | — | 3 | 3 | no | — |
| 448 | C22×C4 | — | 3 | 3 | no | — |
| 449 | C22×C4 | — | 5 | 2 | no | — |
| 450 | C22×C4 | — | 15 | 6 | no | — |
| 451 | C22×C4 | — | 15 | 6 | no | — |
| 452 | C22×C4 | — | 15 | 6 | no | — |
| 453 | C22×C4 | — | 15 | 6 | no | — |
| 454 | C22×C4 | C22×C3×D5 | 1 | 3 | yes | — |
| 455 | C22×C4 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 456 | C3×C5 | — | 4 | 1 | no | Hall |
| 457 | C22×C3 | — | 4 | 3 | no | — |
| 458 | C22×C3 | — | 20 | 6 | no | — |
| 459 | C22×C3 | — | 80 | 6 | no | — |
| 460 | A4 | #4149 | 1 | 1 | yes | characteristic, direct product factor |
| 461 | C3×C4 | — | 4 | 1 | no | — |
| 462 | C3×C4 | — | 4 | 3 | no | — |
| 463 | C3×C4 | — | 20 | 2 | no | — |
| 464 | C2×C5 | — | 2 | 3 | no | — |
| 465 | C2×C5 | — | 3 | 1 | no | — |
| 466 | C2×C5 | — | 3 | 1 | no | — |
| 467 | C2×C5 | — | 6 | 3 | no | — |
| 468 | C2×C5 | C24×A4 | 1 | 1 | yes | characteristic |
| 469 | D5 | — | 2 | 6 | no | — |
| 470 | D5 | — | 6 | 6 | no | — |
| 471 | C23 | — | 2 | 3 | no | — |
| 472 | C23 | — | 3 | 3 | no | — |
| 473 | C23 | — | 3 | 3 | no | — |
| 474 | C23 | — | 5 | 6 | no | — |
| 475 | C23 | — | 6 | 3 | no | — |
| 476 | C23 | — | 10 | 6 | no | — |
| 477 | C23 | — | 15 | 6 | no | — |
| 478 | C23 | — | 15 | 12 | no | — |
| 479 | C23 | — | 15 | 12 | no | — |
| 480 | C23 | — | 15 | 6 | no | — |
| 481 | C23 | — | 15 | 6 | no | — |
| 482 | C23 | — | 30 | 6 | no | — |
| 483 | C23 | — | 60 | 6 | no | — |
| 484 | C23 | — | 60 | 6 | no | — |
| 485 | C23 | — | 60 | 6 | no | — |
| 486 | C23 | — | 60 | 12 | no | — |
| 487 | C23 | — | 60 | 6 | no | — |
| 488 | C23 | — | 60 | 12 | no | — |
| 489 | C23 | C23×C3×D5 | 1 | 1 | yes | characteristic |
| 490 | Q8 | — | 3 | 2 | no | — |
| 491 | Q8 | — | 3 | 3 | no | — |
| 492 | Q8 | — | 5 | 1 | no | — |
| 493 | Q8 | — | 15 | 2 | no | — |
| 494 | Q8 | — | 15 | 2 | no | — |
| 495 | Q8 | — | 15 | 1 | no | — |
| 496 | Q8 | C2×D5×A4 | 1 | 1 | yes | characteristic, complemented |
| 497 | D4 | — | 3 | 6 | no | — |
| 498 | D4 | — | 3 | 6 | no | — |
| 499 | D4 | — | 3 | 3 | no | — |
| 500 | D4 | — | 5 | 6 | no | — |
| 501 | D4 | — | 5 | 3 | no | — |
| 502 | D4 | — | 5 | 6 | no | — |
| 503 | D4 | — | 15 | 6 | no | — |
| 504 | D4 | — | 15 | 12 | no | — |
| 505 | D4 | — | 15 | 6 | no | — |
| 506 | D4 | — | 15 | 12 | no | — |
| 507 | D4 | — | 15 | 6 | no | — |
| 508 | D4 | — | 15 | 6 | no | — |
| 509 | D4 | — | 15 | 12 | no | — |
| 510 | D4 | — | 15 | 6 | no | — |
| 511 | D4 | — | 15 | 3 | no | — |
| 512 | D4 | — | 15 | 6 | no | — |
| 513 | D4 | C2×D5×A4 | 1 | 3 | yes | complemented |
| 514 | C2×C4 | — | 3 | 6 | no | — |
| 515 | C2×C4 | — | 3 | 3 | no | — |
| 516 | C2×C4 | — | 3 | 1 | no | — |
| 517 | C2×C4 | — | 3 | 3 | no | — |
| 518 | C2×C4 | — | 3 | 3 | no | — |
| 519 | C2×C4 | — | 3 | 3 | no | — |
| 520 | C2×C4 | — | 3 | 1 | no | — |
| 521 | C2×C4 | — | 3 | 3 | no | — |
| 522 | C2×C4 | — | 5 | 6 | no | — |
| 523 | C2×C4 | — | 15 | 6 | no | — |
| 524 | C2×C4 | — | 15 | 6 | no | — |
| 525 | C2×C4 | — | 15 | 12 | no | — |
| 526 | C2×C4 | — | 15 | 2 | no | — |
| 527 | C2×C4 | — | 15 | 6 | no | — |
| 528 | C2×C4 | — | 15 | 2 | no | — |
| 529 | C2×C4 | C2×D5×A4 | 1 | 3 | yes | complemented |
| 530 | C2×C3 | — | 4 | 1 | no | — |
| 531 | C2×C3 | — | 8 | 3 | no | — |
| 532 | C2×C3 | — | 40 | 6 | no | — |
| 533 | C5 | A4×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 534 | C22 | — | 3 | 1 | no | — |
| 535 | C22 | — | 3 | 1 | no | — |
| 536 | C22 | — | 3 | 3 | no | — |
| 537 | C22 | — | 5 | 6 | no | — |
| 538 | C22 | — | 6 | 3 | no | — |
| 539 | C22 | — | 6 | 3 | no | — |
| 540 | C22 | — | 6 | 3 | no | — |
| 541 | C22 | — | 6 | 3 | no | — |
| 542 | C22 | — | 15 | 6 | no | — |
| 543 | C22 | — | 20 | 6 | no | — |
| 544 | C22 | — | 30 | 6 | no | — |
| 545 | C22 | — | 30 | 6 | no | — |
| 546 | C22 | — | 30 | 6 | no | — |
| 547 | C22 | — | 30 | 6 | no | — |
| 548 | C22 | — | 60 | 6 | no | — |
| 549 | C22 | — | 60 | 12 | no | — |
| 550 | C22 | — | 60 | 12 | no | — |
| 551 | C22 | C3×#4149 | 1 | 1 | yes | characteristic, complemented |
| 552 | C22 | C22×D5×A4 | 1 | 3 | yes | — |
| 553 | C4 | — | 3 | 1 | no | — |
| 554 | C4 | — | 3 | 3 | no | — |
| 555 | C4 | — | 5 | 2 | no | — |
| 556 | C4 | — | 15 | 2 | no | — |
| 557 | C4 | C22×D5×A4 | 1 | 1 | yes | characteristic |
| 558 | C4 | C22×D5×A4 | 1 | 3 | yes | — |
| 559 | C3 | — | 4 | 1 | no | Sylow |
| 560 | C2 | — | 2 | 3 | no | — |
| 561 | C2 | — | 3 | 1 | no | — |
| 562 | C2 | — | 3 | 1 | no | — |
| 563 | C2 | — | 6 | 3 | no | — |
| 564 | C2 | — | 10 | 6 | no | — |
| 565 | C2 | — | 30 | 6 | no | — |
| 566 | C2 | C23×D5×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D5×A4 |
| commutator, socle, cosocle | C23×C5 | C24×C3 |
| Fitting | C22×C5×#41 | C2×C3 |
| hypercenter | #41 | D5×A4 |
| hypocenter | C22×C5 | C3×H(5,𝔽2) |
| LCS | G ▷ C23×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×A4×#41 | C2 | semidirect |
| 2. A4×#713 | C2 | semidirect |
| 3. D4×D5×A4 | C2 | semidirect |
| 4. A4×#709 | C2 | semidirect |
| 5. C2×A4×D20 | C2 | semidirect |
| 6. C22×#4149 | C3 | semidirect |
| 7. C22×D5×A4 | C22 | semidirect |
| 9. C5×Q8×A4 | C22 | semidirect |
| 10. C5×D4×A4 | C22 | semidirect |
| 11. C2×C4×C5×A4 | C22 | semidirect |
| 12. A4×C22⋊D5 | C22 | semidirect |
| 13. A4×D20 | C22 | semidirect |
| 14. A4×D20 | C22 | semidirect |
| 15. C4×D5×A4 | C22 | semidirect |
| 16. A4×Dic10 | C22 | semidirect |
| 18. C22×C5×#41 | C2×C3 | semidirect |
| 25. C22×#713 | C2×C3 | semidirect |
| 26. C22×D4×D5 | C2×C3 | semidirect |
| 27. C22×#709 | C2×C3 | semidirect |
| 28. C23×D20 | C2×C3 | semidirect |
| 42. A4×#41 | D5 | semidirect |
| 45. C24×D5 | C22×C3 | semidirect |
| 50. C22×C5×Q8 | C22×C3 | semidirect |
| 51. C22×C5×D4 | C22×C3 | semidirect |
| 52. C23×C4×C5 | C22×C3 | semidirect |
| 53. C22×C22⋊D5 | C22×C3 | semidirect |
| 68. #4149 | A4 | direct (N × H) |
| 90. C22×D20 | C22×C3 | semidirect |
| 91. C22×D20 | C22×C3 | semidirect |
| 92. C22×C4×D5 | C22×C3 | semidirect |
| 93. C22×Dic10 | C22×C3 | semidirect |
| 110. Q8×A4 | C2×D5 | semidirect |
| 114. D4×A4 | C2×D5 | semidirect |
| 116. C2×C4×A4 | C2×D5 | semidirect |
| 130. C5×#41 | C2×A4 | semidirect |
| 153. #713 | C2×A4 | semidirect |
| 164. D4×D5 | C2×A4 | semidirect |
| 175. #709 | C2×A4 | semidirect |
| 190. C2×D20 | C2×A4 | semidirect |
| 206. C22×#41 | C3×D5 | semidirect |
| 212. C5×A4 | H(5,𝔽2) | semidirect |
| 245. C22×D5 | C22×A4 | semidirect |
| 248. C5×Q8 | C22×A4 | semidirect |
| 252. C5×D4 | C22×A4 | semidirect |
| 261. C2×C4×C5 | C22×A4 | semidirect |
| 266. C22⋊D5 | C22×A4 | semidirect |
| 275. D20 | C22×A4 | semidirect |
| 276. D20 | C22×A4 | semidirect |
| 281. C4×D5 | C22×A4 | semidirect |
| 285. Dic10 | C22×A4 | semidirect |
| 317. C22×Q8 | C2×C3×D5 | semidirect |
| 332. C22×D4 | C2×C3×D5 | semidirect |
| 334. C23×C4 | C2×C3×D5 | semidirect |
| 357. C22×C5 | C3×H(5,𝔽2) | semidirect |
| 406. #41 | D5×A4 | semidirect |
| 460. A4 | #4149 | direct (N × H) |
| 496. Q8 | C2×D5×A4 | semidirect |
| 513. D4 | C2×D5×A4 | semidirect |
| 529. C2×C4 | C2×D5×A4 | semidirect |
| 533. C5 | A4×H(5,𝔽2) | semidirect |
| 551. C22 | C3×#4149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×#41 | 2 |
| A4×#713 | 2 |
| D4×D5×A4 | 2 |
| A4×#709 | 2 |
| C2×A4×D20 | 2 |
| C22×#4149 | 3 |
| C3×#4149 | 4 |
| A4×H(5,𝔽2) | 5 |