Finite Group DatabasebetaFinite Group DatabasebetaOrder 3360.
524 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 48 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 | D5×A4×D7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D35⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | S4×D35 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D5×C7⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×D5×S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | D7×C5⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C5×D7×S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D4×D5×D7 | — | 3 | 1 | no | maximal, Hall |
| 9 | A4×D35 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C7×D5×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×A4×D7 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C5⋊(C7⋊S4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C7×C5⋊S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C5×C7⋊S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C5×C7×S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | D3×D5×D7 | — | 4 | 1 | no | maximal |
| 17 | C2×D7×S4 | — | 5 | 1 | no | maximal, Hall |
| 18 | C22×D5×D7 | — | 3 | 1 | no | — |
| 19 | C22×D5×D7 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | D4×D35 | — | 3 | 1 | no | — |
| 21 | C7×D4×D5 | — | 3 | 1 | no | — |
| 22 | C5×D4×D7 | — | 3 | 1 | no | — |
| 23 | #10587963 | — | 3 | 1 | no | — |
| 24 | #10587963 | — | 3 | 1 | no | — |
| 25 | D5×C22⋊D7 | — | 3 | 1 | no | — |
| 26 | D5×C22⋊D7 | — | 3 | 1 | no | — |
| 27 | D7×C22⋊D5 | — | 3 | 1 | no | — |
| 28 | D7×C22⋊D5 | — | 3 | 1 | no | — |
| 29 | #10587950 | — | 3 | 1 | no | — |
| 30 | D5×D28 | — | 3 | 1 | no | — |
| 31 | D7×D20 | — | 3 | 1 | no | — |
| 32 | C4×D5×D7 | — | 3 | 1 | no | — |
| 33 | C2×D5×S4 | — | 7 | 1 | no | maximal, Hall |
| 34 | C5×C7×A4 | C23 | 1 | 1 | yes | characteristic, complemented |
| 35 | D15⋊D7 | — | 4 | 1 | no | — |
| 36 | D3×D35 | — | 4 | 1 | no | — |
| 37 | D5×D21 | — | 4 | 1 | no | — |
| 38 | D3×C7×D5 | — | 4 | 1 | no | — |
| 39 | D7×D15 | — | 4 | 1 | no | — |
| 40 | C5×D3×D7 | — | 4 | 1 | no | — |
| 41 | C3×D5×D7 | — | 4 | 1 | no | — |
| 42 | C2×A4×D7 | — | 5 | 1 | no | — |
| 43 | C2×C7⋊S4 | — | 5 | 1 | no | — |
| 44 | C2×C7×S4 | — | 5 | 1 | no | — |
| 45 | D7×S4 | — | 5 | 1 | no | — |
| 46 | D7×S4 | — | 5 | 1 | no | — |
| 47 | D7×S4 | — | 5 | 1 | no | — |
| 48 | D7×S4 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 49 | C22×D35 | — | 3 | 1 | no | — |
| 50 | C22×D35 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | C22×C7×D5 | — | 3 | 1 | no | — |
| 52 | C22×C7×D5 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 53 | C22×C5×D7 | — | 3 | 1 | no | — |
| 54 | C22×C5×D7 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 55 | C2×D5×D7 | — | 3 | 1 | no | — |
| 56 | C2×D5×D7 | — | 3 | 1 | no | — |
| 57 | C2×D5×D7 | — | 3 | 1 | no | — |
| 58 | C2×D5×D7 | — | 3 | 1 | no | — |
| 59 | C2×D5×D7 | — | 3 | 1 | no | — |
| 60 | C2×D5×D7 | — | 3 | 1 | no | — |
| 61 | C2×D5×D7 | — | 3 | 1 | no | — |
| 62 | C2×D5×D7 | — | 6 | 1 | no | — |
| 63 | C2×D5×D7 | — | 6 | 1 | no | — |
| 64 | C2×D5×D7 | — | 6 | 1 | no | — |
| 65 | C2×D5×D7 | — | 6 | 1 | no | — |
| 66 | C5×C7×D4 | — | 3 | 1 | no | — |
| 67 | C22⋊D35 | — | 3 | 1 | no | — |
| 68 | C22⋊D35 | — | 3 | 1 | no | — |
| 69 | D140 | — | 3 | 1 | no | — |
| 70 | C4×D35 | — | 3 | 1 | no | — |
| 71 | C7×C22⋊D5 | — | 3 | 1 | no | — |
| 72 | C7×C22⋊D5 | — | 3 | 1 | no | — |
| 73 | C7×D20 | — | 3 | 1 | no | — |
| 74 | C4×C7×D5 | — | 3 | 1 | no | — |
| 75 | C5×C22⋊D7 | — | 3 | 1 | no | — |
| 76 | C5×C22⋊D7 | — | 3 | 1 | no | — |
| 77 | C5×D28 | — | 3 | 1 | no | — |
| 78 | C4×C5×D7 | — | 3 | 1 | no | — |
| 79 | #63307 | — | 3 | 1 | no | — |
| 80 | #63307 | — | 3 | 1 | no | — |
| 81 | #63306 | — | 3 | 1 | no | — |
| 82 | #63306 | — | 3 | 1 | no | — |
| 83 | #63305 | — | 3 | 1 | no | — |
| 84 | #63305 | — | 3 | 1 | no | — |
| 85 | #63304 | — | 3 | 1 | no | — |
| 86 | D5×Dic7 | — | 3 | 1 | no | — |
| 87 | D7×Dic5 | — | 3 | 1 | no | — |
| 88 | C2×D5×A4 | — | 7 | 1 | no | — |
| 89 | C2×C5⋊S4 | — | 7 | 1 | no | — |
| 90 | C2×C5×S4 | — | 7 | 1 | no | — |
| 91 | D5×S4 | — | 7 | 1 | no | — |
| 92 | D5×S4 | — | 7 | 1 | no | — |
| 93 | D5×S4 | — | 7 | 1 | no | — |
| 94 | D5×S4 | D7 | 1 | 1 | yes | characteristic, direct product factor |
| 95 | C2×D4×D7 | — | 15 | 1 | no | Hall |
| 96 | D105 | — | 4 | 1 | no | — |
| 97 | C7×D15 | — | 4 | 1 | no | — |
| 98 | C5×D21 | — | 4 | 1 | no | — |
| 99 | C5×D3×C7 | — | 4 | 1 | no | — |
| 100 | C3×D35 | — | 4 | 1 | no | — |
| 101 | C3×C7×D5 | — | 4 | 1 | no | — |
| 102 | C3×C5×D7 | — | 4 | 1 | no | — |
| 103 | C2×C7×A4 | — | 5 | 1 | no | — |
| 104 | C2×D3×D7 | — | 20 | 1 | no | — |
| 105 | A4×D7 | — | 5 | 1 | no | — |
| 106 | A4×D7 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 107 | C7⋊S4 | — | 5 | 1 | no | — |
| 108 | C7⋊S4 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 109 | C7×S4 | — | 5 | 1 | no | — |
| 110 | C7×S4 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 111 | C2×D4×D5 | — | 21 | 1 | no | Hall |
| 112 | C22×C5×C7 | — | 3 | 1 | no | — |
| 113 | C22×C5×C7 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 114 | C2×D35 | — | 3 | 1 | no | — |
| 115 | C2×D35 | — | 3 | 1 | no | — |
| 116 | C2×D35 | — | 3 | 1 | no | — |
| 117 | C2×D35 | — | 6 | 1 | no | — |
| 118 | C2×D35 | — | 6 | 1 | no | — |
| 119 | C2×C7×D5 | — | 3 | 1 | no | — |
| 120 | C2×C7×D5 | — | 3 | 1 | no | — |
| 121 | C2×C7×D5 | — | 3 | 1 | no | — |
| 122 | C2×C7×D5 | — | 6 | 1 | no | — |
| 123 | C2×C7×D5 | — | 6 | 1 | no | — |
| 124 | C2×C5×D7 | — | 3 | 1 | no | — |
| 125 | C2×C5×D7 | — | 3 | 1 | no | — |
| 126 | C2×C5×D7 | — | 3 | 1 | no | — |
| 127 | C2×C5×D7 | — | 6 | 1 | no | — |
| 128 | C2×C5×D7 | — | 6 | 1 | no | — |
| 129 | D5×D7 | — | 3 | 1 | no | — |
| 130 | D5×D7 | — | 3 | 1 | no | — |
| 131 | D5×D7 | — | 3 | 1 | no | — |
| 132 | D5×D7 | — | 6 | 1 | no | — |
| 133 | D5×D7 | — | 6 | 1 | no | — |
| 134 | D5×D7 | — | 6 | 1 | no | — |
| 135 | D5×D7 | — | 6 | 1 | no | — |
| 136 | D5×D7 | — | 6 | 1 | no | — |
| 137 | D5×D7 | — | 6 | 1 | no | — |
| 138 | D5×D7 | — | 6 | 1 | no | — |
| 139 | D5×D7 | S4 | 1 | 1 | yes | characteristic, direct product factor |
| 140 | C4×C5×C7 | — | 3 | 1 | no | — |
| 141 | Dic35 | — | 3 | 1 | no | — |
| 142 | C5×Dic7 | — | 3 | 1 | no | — |
| 143 | C7×Dic5 | — | 3 | 1 | no | — |
| 144 | C2×C5×A4 | — | 7 | 1 | no | — |
| 145 | C2×D3×D5 | — | 28 | 1 | no | — |
| 146 | D5×A4 | — | 7 | 1 | no | — |
| 147 | D5×A4 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 148 | C5⋊S4 | — | 7 | 1 | no | — |
| 149 | C5⋊S4 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 150 | C5×S4 | — | 7 | 1 | no | — |
| 151 | C5×S4 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 152 | C23×D7 | — | 5 | 1 | no | — |
| 153 | C23×D7 | — | 15 | 1 | no | — |
| 154 | C2×C7×D4 | — | 15 | 1 | no | — |
| 155 | C2×C22⋊D7 | — | 15 | 1 | no | — |
| 156 | C2×C22⋊D7 | — | 15 | 1 | no | — |
| 157 | D4×D7 | — | 3 | 1 | no | — |
| 158 | D4×D7 | — | 15 | 1 | no | — |
| 159 | D4×D7 | — | 15 | 1 | no | — |
| 160 | D4×D7 | — | 15 | 1 | no | — |
| 161 | D4×D7 | — | 15 | 1 | no | — |
| 162 | D4×D7 | — | 15 | 1 | no | — |
| 163 | D4×D7 | — | 15 | 1 | no | — |
| 164 | D4×D7 | — | 15 | 1 | no | — |
| 165 | C2×D28 | — | 15 | 1 | no | — |
| 166 | C2×C4×D7 | — | 15 | 1 | no | — |
| 167 | C3×C5×C7 | — | 4 | 1 | no | Hall |
| 168 | C22×S4 | — | 35 | 1 | no | Hall |
| 169 | C2×D21 | — | 20 | 1 | no | — |
| 170 | C2×D3×C7 | — | 20 | 1 | no | — |
| 171 | C2×C3×D7 | — | 20 | 1 | no | — |
| 172 | C7×A4 | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 173 | D3×D7 | — | 4 | 1 | no | — |
| 174 | D3×D7 | — | 20 | 1 | no | — |
| 175 | D3×D7 | — | 20 | 1 | no | — |
| 176 | D3×D7 | — | 20 | 1 | no | — |
| 177 | C23×D5 | — | 7 | 1 | no | — |
| 178 | C23×D5 | — | 21 | 1 | no | — |
| 179 | C2×C5×D4 | — | 21 | 1 | no | — |
| 180 | C2×C22⋊D5 | — | 21 | 1 | no | — |
| 181 | C2×C22⋊D5 | — | 21 | 1 | no | — |
| 182 | D4×D5 | — | 3 | 1 | no | — |
| 183 | D4×D5 | — | 21 | 1 | no | — |
| 184 | D4×D5 | — | 21 | 1 | no | — |
| 185 | D4×D5 | — | 21 | 1 | no | — |
| 186 | D4×D5 | — | 21 | 1 | no | — |
| 187 | D4×D5 | — | 21 | 1 | no | — |
| 188 | D4×D5 | — | 21 | 1 | no | — |
| 189 | D4×D5 | — | 21 | 1 | no | — |
| 190 | C2×D20 | — | 21 | 1 | no | — |
| 191 | C2×C4×D5 | — | 21 | 1 | no | — |
| 192 | C2×C5×C7 | — | 3 | 1 | no | — |
| 193 | C2×C5×C7 | — | 6 | 1 | no | — |
| 194 | D35 | — | 3 | 1 | no | — |
| 195 | D35 | — | 6 | 1 | no | — |
| 196 | D35 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 197 | C5×D7 | — | 3 | 1 | no | — |
| 198 | C5×D7 | — | 6 | 1 | no | — |
| 199 | C5×D7 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 200 | C7×D5 | — | 3 | 1 | no | — |
| 201 | C7×D5 | — | 6 | 1 | no | — |
| 202 | C7×D5 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 203 | C2×D15 | — | 28 | 1 | no | — |
| 204 | C2×C5×D3 | — | 28 | 1 | no | — |
| 205 | C2×C3×D5 | — | 28 | 1 | no | — |
| 206 | C5×A4 | C22×D7 | 1 | 1 | yes | characteristic, complemented |
| 207 | D3×D5 | — | 4 | 1 | no | — |
| 208 | D3×D5 | — | 28 | 1 | no | — |
| 209 | D3×D5 | — | 28 | 1 | no | — |
| 210 | D3×D5 | — | 28 | 1 | no | — |
| 211 | C23×C7 | — | 5 | 1 | no | — |
| 212 | C23×C7 | — | 15 | 1 | no | — |
| 213 | C22×D7 | — | 3 | 1 | no | — |
| 214 | C22×D7 | — | 5 | 1 | no | — |
| 215 | C22×D7 | — | 15 | 1 | no | — |
| 216 | C22×D7 | — | 15 | 1 | no | — |
| 217 | C22×D7 | — | 15 | 1 | no | — |
| 218 | C22×D7 | — | 15 | 1 | no | — |
| 219 | C22×D7 | — | 15 | 1 | no | — |
| 220 | C22×D7 | — | 15 | 1 | no | — |
| 221 | C22×D7 | — | 15 | 1 | no | — |
| 222 | C22×D7 | — | 15 | 1 | no | — |
| 223 | C22×D7 | — | 30 | 1 | no | — |
| 224 | C22×D7 | — | 30 | 1 | no | — |
| 225 | C22×D7 | — | 30 | 1 | no | — |
| 226 | C22×D7 | — | 30 | 1 | no | — |
| 227 | C22×D7 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 228 | C7×D4 | — | 3 | 1 | no | — |
| 229 | C7×D4 | — | 15 | 1 | no | — |
| 230 | C7×D4 | — | 15 | 1 | no | — |
| 231 | C7×D4 | — | 15 | 1 | no | — |
| 232 | C2×C4×C7 | — | 15 | 1 | no | — |
| 233 | C22⋊D7 | — | 3 | 1 | no | — |
| 234 | C22⋊D7 | — | 3 | 1 | no | — |
| 235 | C22⋊D7 | — | 15 | 1 | no | — |
| 236 | C22⋊D7 | — | 15 | 1 | no | — |
| 237 | C22⋊D7 | — | 15 | 1 | no | — |
| 238 | C22⋊D7 | — | 15 | 1 | no | — |
| 239 | C22⋊D7 | — | 15 | 1 | no | — |
| 240 | C22⋊D7 | — | 15 | 1 | no | — |
| 241 | C2×Dic7 | — | 15 | 1 | no | — |
| 242 | D28 | — | 3 | 1 | no | — |
| 243 | D28 | — | 15 | 1 | no | — |
| 244 | D28 | — | 15 | 1 | no | — |
| 245 | D28 | — | 15 | 1 | no | — |
| 246 | C4×D7 | — | 3 | 1 | no | — |
| 247 | C4×D7 | — | 15 | 1 | no | — |
| 248 | C4×D7 | — | 15 | 1 | no | — |
| 249 | C4×D7 | — | 15 | 1 | no | — |
| 250 | C22×A4 | — | 35 | 1 | no | — |
| 251 | C2×S4 | — | 5 | 1 | no | — |
| 252 | C2×S4 | — | 7 | 1 | no | — |
| 253 | C2×S4 | — | 35 | 1 | no | — |
| 254 | C2×S4 | — | 35 | 1 | no | — |
| 255 | C2×S4 | — | 35 | 1 | no | — |
| 256 | C2×S4 | — | 35 | 1 | no | — |
| 257 | C2×C3×C7 | — | 20 | 1 | no | — |
| 258 | D21 | — | 4 | 1 | no | — |
| 259 | D21 | — | 20 | 1 | no | — |
| 260 | C3×D7 | — | 4 | 1 | no | — |
| 261 | C3×D7 | — | 20 | 1 | no | — |
| 262 | D3×C7 | — | 4 | 1 | no | — |
| 263 | D3×C7 | — | 20 | 1 | no | — |
| 264 | C23×C5 | — | 7 | 1 | no | — |
| 265 | C23×C5 | — | 21 | 1 | no | — |
| 266 | C22×D5 | — | 3 | 1 | no | — |
| 267 | C22×D5 | — | 7 | 1 | no | — |
| 268 | C22×D5 | — | 21 | 1 | no | — |
| 269 | C22×D5 | — | 21 | 1 | no | — |
| 270 | C22×D5 | — | 21 | 1 | no | — |
| 271 | C22×D5 | — | 21 | 1 | no | — |
| 272 | C22×D5 | — | 21 | 1 | no | — |
| 273 | C22×D5 | — | 21 | 1 | no | — |
| 274 | C22×D5 | — | 21 | 1 | no | — |
| 275 | C22×D5 | — | 21 | 1 | no | — |
| 276 | C22×D5 | — | 42 | 1 | no | — |
| 277 | C22×D5 | — | 42 | 1 | no | — |
| 278 | C22×D5 | — | 42 | 1 | no | — |
| 279 | C22×D5 | — | 42 | 1 | no | — |
| 280 | C22×D5 | D3×D7 | 1 | 1 | yes | characteristic, complemented |
| 281 | C5×D4 | — | 3 | 1 | no | — |
| 282 | C5×D4 | — | 21 | 1 | no | — |
| 283 | C5×D4 | — | 21 | 1 | no | — |
| 284 | C5×D4 | — | 21 | 1 | no | — |
| 285 | C2×C4×C5 | — | 21 | 1 | no | — |
| 286 | C22⋊D5 | — | 3 | 1 | no | — |
| 287 | C22⋊D5 | — | 3 | 1 | no | — |
| 288 | C22⋊D5 | — | 21 | 1 | no | — |
| 289 | C22⋊D5 | — | 21 | 1 | no | — |
| 290 | C22⋊D5 | — | 21 | 1 | no | — |
| 291 | C22⋊D5 | — | 21 | 1 | no | — |
| 292 | C22⋊D5 | — | 21 | 1 | no | — |
| 293 | C22⋊D5 | — | 21 | 1 | no | — |
| 294 | C2×Dic5 | — | 21 | 1 | no | — |
| 295 | D20 | — | 3 | 1 | no | — |
| 296 | D20 | — | 21 | 1 | no | — |
| 297 | D20 | — | 21 | 1 | no | — |
| 298 | D20 | — | 21 | 1 | no | — |
| 299 | C4×D5 | — | 3 | 1 | no | — |
| 300 | C4×D5 | — | 21 | 1 | no | — |
| 301 | C4×D5 | — | 21 | 1 | no | — |
| 302 | C4×D5 | — | 21 | 1 | no | — |
| 303 | C5×C7 | C22×S4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 304 | C22×D4 | — | 105 | 1 | no | Sylow |
| 305 | C2×C3×C5 | — | 28 | 1 | no | — |
| 306 | D15 | — | 4 | 1 | no | — |
| 307 | D15 | — | 28 | 1 | no | — |
| 308 | C3×D5 | — | 4 | 1 | no | — |
| 309 | C3×D5 | — | 28 | 1 | no | — |
| 310 | C5×D3 | — | 4 | 1 | no | — |
| 311 | C5×D3 | — | 28 | 1 | no | — |
| 312 | C22×C7 | — | 3 | 1 | no | — |
| 313 | C22×C7 | — | 15 | 1 | no | — |
| 314 | C22×C7 | — | 15 | 1 | no | — |
| 315 | C22×C7 | — | 15 | 1 | no | — |
| 316 | C22×C7 | — | 30 | 1 | no | — |
| 317 | C22×C7 | — | 30 | 1 | no | — |
| 318 | C22×C7 | C2×D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 319 | C2×D7 | — | 3 | 1 | no | — |
| 320 | C2×D7 | — | 3 | 1 | no | — |
| 321 | C2×D7 | — | 3 | 1 | no | — |
| 322 | C2×D7 | — | 5 | 1 | no | — |
| 323 | C2×D7 | — | 6 | 1 | no | — |
| 324 | C2×D7 | — | 6 | 1 | no | — |
| 325 | C2×D7 | — | 15 | 1 | no | — |
| 326 | C2×D7 | — | 15 | 1 | no | — |
| 327 | C2×D7 | — | 15 | 1 | no | — |
| 328 | C2×D7 | — | 15 | 1 | no | — |
| 329 | C2×D7 | — | 15 | 1 | no | — |
| 330 | C2×D7 | — | 15 | 1 | no | — |
| 331 | C2×D7 | — | 30 | 1 | no | — |
| 332 | C2×D7 | — | 30 | 1 | no | — |
| 333 | C2×D7 | — | 30 | 1 | no | — |
| 334 | C2×D7 | — | 30 | 1 | no | — |
| 335 | C2×D7 | — | 30 | 1 | no | — |
| 336 | C2×D7 | — | 30 | 1 | no | — |
| 337 | C2×D7 | — | 30 | 1 | no | — |
| 338 | C2×D7 | — | 30 | 1 | no | — |
| 339 | C2×D7 | — | 30 | 1 | no | — |
| 340 | C4×C7 | — | 3 | 1 | no | — |
| 341 | C4×C7 | — | 15 | 1 | no | — |
| 342 | Dic7 | — | 3 | 1 | no | — |
| 343 | Dic7 | — | 15 | 1 | no | — |
| 344 | C22×D3 | — | 140 | 1 | no | — |
| 345 | C2×A4 | — | 5 | 1 | no | — |
| 346 | C2×A4 | — | 7 | 1 | no | — |
| 347 | C2×A4 | — | 35 | 1 | no | — |
| 348 | S4 | — | 5 | 1 | no | — |
| 349 | S4 | — | 7 | 1 | no | — |
| 350 | S4 | — | 35 | 1 | no | — |
| 351 | S4 | D5×D7 | 1 | 1 | yes | characteristic, direct product factor |
| 352 | C3×C7 | — | 4 | 1 | no | Hall |
| 353 | C22×C5 | — | 3 | 1 | no | — |
| 354 | C22×C5 | — | 21 | 1 | no | — |
| 355 | C22×C5 | — | 21 | 1 | no | — |
| 356 | C22×C5 | — | 21 | 1 | no | — |
| 357 | C22×C5 | — | 42 | 1 | no | — |
| 358 | C22×C5 | — | 42 | 1 | no | — |
| 359 | C22×C5 | C2×D3×D7 | 1 | 1 | yes | characteristic, complemented |
| 360 | C2×D5 | — | 3 | 1 | no | — |
| 361 | C2×D5 | — | 3 | 1 | no | — |
| 362 | C2×D5 | — | 3 | 1 | no | — |
| 363 | C2×D5 | — | 6 | 1 | no | — |
| 364 | C2×D5 | — | 6 | 1 | no | — |
| 365 | C2×D5 | — | 7 | 1 | no | — |
| 366 | C2×D5 | — | 21 | 1 | no | — |
| 367 | C2×D5 | — | 21 | 1 | no | — |
| 368 | C2×D5 | — | 21 | 1 | no | — |
| 369 | C2×D5 | — | 21 | 1 | no | — |
| 370 | C2×D5 | — | 21 | 1 | no | — |
| 371 | C2×D5 | — | 21 | 1 | no | — |
| 372 | C2×D5 | — | 42 | 1 | no | — |
| 373 | C2×D5 | — | 42 | 1 | no | — |
| 374 | C2×D5 | — | 42 | 1 | no | — |
| 375 | C2×D5 | — | 42 | 1 | no | — |
| 376 | C2×D5 | — | 42 | 1 | no | — |
| 377 | C2×D5 | — | 42 | 1 | no | — |
| 378 | C2×D5 | — | 42 | 1 | no | — |
| 379 | C2×D5 | — | 42 | 1 | no | — |
| 380 | C2×D5 | — | 42 | 1 | no | — |
| 381 | C4×C5 | — | 3 | 1 | no | — |
| 382 | C4×C5 | — | 21 | 1 | no | — |
| 383 | Dic5 | — | 3 | 1 | no | — |
| 384 | Dic5 | — | 21 | 1 | no | — |
| 385 | C24 | — | 35 | 1 | no | — |
| 386 | C24 | — | 105 | 1 | no | — |
| 387 | C2×D4 | — | 15 | 1 | no | — |
| 388 | C2×D4 | — | 21 | 1 | no | — |
| 389 | C2×D4 | — | 105 | 1 | no | — |
| 390 | C2×D4 | — | 105 | 1 | no | — |
| 391 | C2×D4 | — | 105 | 1 | no | — |
| 392 | C2×D4 | — | 105 | 1 | no | — |
| 393 | C2×D4 | — | 105 | 1 | no | — |
| 394 | C2×D4 | — | 105 | 1 | no | — |
| 395 | C2×D4 | — | 105 | 1 | no | — |
| 396 | C2×D4 | — | 105 | 1 | no | — |
| 397 | C2×D4 | — | 105 | 1 | no | — |
| 398 | C2×D4 | — | 105 | 1 | no | — |
| 399 | C22×C4 | — | 105 | 1 | no | — |
| 400 | C3×C5 | — | 4 | 1 | no | Hall |
| 401 | C2×C7 | — | 3 | 1 | no | — |
| 402 | C2×C7 | — | 5 | 1 | no | — |
| 403 | C2×C7 | — | 6 | 1 | no | — |
| 404 | C2×C7 | — | 15 | 1 | no | — |
| 405 | C2×C7 | — | 30 | 1 | no | — |
| 406 | D7 | — | 3 | 1 | no | — |
| 407 | D7 | — | 5 | 1 | no | — |
| 408 | D7 | — | 6 | 1 | no | — |
| 409 | D7 | — | 15 | 1 | no | — |
| 410 | D7 | — | 30 | 1 | no | — |
| 411 | D7 | D5×S4 | 1 | 1 | yes | characteristic, direct product factor |
| 412 | C22×C3 | — | 140 | 1 | no | — |
| 413 | C2×D3 | — | 20 | 1 | no | — |
| 414 | C2×D3 | — | 28 | 1 | no | — |
| 415 | C2×D3 | — | 140 | 1 | no | — |
| 416 | C2×D3 | — | 140 | 1 | no | — |
| 417 | C2×D3 | — | 140 | 1 | no | — |
| 418 | C2×D3 | — | 140 | 1 | no | — |
| 419 | A4 | C2×D5×D7 | 1 | 1 | yes | characteristic, complemented |
| 420 | C2×C5 | — | 3 | 1 | no | — |
| 421 | C2×C5 | — | 6 | 1 | no | — |
| 422 | C2×C5 | — | 7 | 1 | no | — |
| 423 | C2×C5 | — | 21 | 1 | no | — |
| 424 | C2×C5 | — | 42 | 1 | no | — |
| 425 | D5 | — | 3 | 1 | no | — |
| 426 | D5 | — | 6 | 1 | no | — |
| 427 | D5 | — | 7 | 1 | no | — |
| 428 | D5 | — | 21 | 1 | no | — |
| 429 | D5 | — | 42 | 1 | no | — |
| 430 | D5 | D7×S4 | 1 | 1 | yes | characteristic, direct product factor |
| 431 | C23 | — | 5 | 1 | no | — |
| 432 | C23 | — | 7 | 1 | no | — |
| 433 | C23 | — | 15 | 1 | no | — |
| 434 | C23 | — | 21 | 1 | no | — |
| 435 | C23 | — | 35 | 1 | no | — |
| 436 | C23 | — | 105 | 1 | no | — |
| 437 | C23 | — | 105 | 1 | no | — |
| 438 | C23 | — | 105 | 1 | no | — |
| 439 | C23 | — | 105 | 1 | no | — |
| 440 | C23 | — | 105 | 1 | no | — |
| 441 | C23 | — | 105 | 1 | no | — |
| 442 | C23 | — | 105 | 1 | no | — |
| 443 | C23 | — | 105 | 1 | no | — |
| 444 | C23 | — | 210 | 1 | no | — |
| 445 | C23 | — | 210 | 1 | no | — |
| 446 | C23 | — | 210 | 1 | no | — |
| 447 | C23 | — | 210 | 1 | no | — |
| 448 | D4 | — | 3 | 1 | no | — |
| 449 | D4 | — | 15 | 1 | no | — |
| 450 | D4 | — | 15 | 1 | no | — |
| 451 | D4 | — | 15 | 1 | no | — |
| 452 | D4 | — | 21 | 1 | no | — |
| 453 | D4 | — | 21 | 1 | no | — |
| 454 | D4 | — | 21 | 1 | no | — |
| 455 | D4 | — | 105 | 1 | no | — |
| 456 | D4 | — | 105 | 1 | no | — |
| 457 | D4 | — | 105 | 1 | no | — |
| 458 | D4 | — | 105 | 1 | no | — |
| 459 | D4 | — | 105 | 1 | no | — |
| 460 | D4 | — | 105 | 1 | no | — |
| 461 | D4 | — | 105 | 1 | no | — |
| 462 | D4 | — | 105 | 1 | no | — |
| 463 | D4 | — | 105 | 1 | no | — |
| 464 | C2×C4 | — | 15 | 1 | no | — |
| 465 | C2×C4 | — | 21 | 1 | no | — |
| 466 | C2×C4 | — | 105 | 1 | no | — |
| 467 | C2×C4 | — | 105 | 1 | no | — |
| 468 | C2×C4 | — | 105 | 1 | no | — |
| 469 | C2×C4 | — | 105 | 1 | no | — |
| 470 | C7 | C2×D5×S4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 471 | C2×C3 | — | 20 | 1 | no | — |
| 472 | C2×C3 | — | 28 | 1 | no | — |
| 473 | C2×C3 | — | 140 | 1 | no | — |
| 474 | D3 | — | 4 | 1 | no | — |
| 475 | D3 | — | 20 | 1 | no | — |
| 476 | D3 | — | 28 | 1 | no | — |
| 477 | D3 | — | 140 | 1 | no | — |
| 478 | C5 | C2×D7×S4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 479 | C22 | — | 3 | 1 | no | — |
| 480 | C22 | — | 15 | 1 | no | — |
| 481 | C22 | — | 15 | 1 | no | — |
| 482 | C22 | — | 15 | 1 | no | — |
| 483 | C22 | — | 21 | 1 | no | — |
| 484 | C22 | — | 21 | 1 | no | — |
| 485 | C22 | — | 21 | 1 | no | — |
| 486 | C22 | — | 30 | 1 | no | — |
| 487 | C22 | — | 30 | 1 | no | — |
| 488 | C22 | — | 35 | 1 | no | — |
| 489 | C22 | — | 42 | 1 | no | — |
| 490 | C22 | — | 42 | 1 | no | — |
| 491 | C22 | — | 105 | 1 | no | — |
| 492 | C22 | — | 105 | 1 | no | — |
| 493 | C22 | — | 105 | 1 | no | — |
| 494 | C22 | — | 105 | 1 | no | — |
| 495 | C22 | — | 105 | 1 | no | — |
| 496 | C22 | — | 105 | 1 | no | — |
| 497 | C22 | — | 210 | 1 | no | — |
| 498 | C22 | — | 210 | 1 | no | — |
| 499 | C22 | — | 210 | 1 | no | — |
| 500 | C22 | — | 210 | 1 | no | — |
| 501 | C22 | — | 210 | 1 | no | — |
| 502 | C22 | — | 210 | 1 | no | — |
| 503 | C22 | — | 210 | 1 | no | — |
| 504 | C22 | — | 210 | 1 | no | — |
| 505 | C22 | — | 210 | 1 | no | — |
| 506 | C22 | D3×D5×D7 | 1 | 1 | yes | characteristic, complemented |
| 507 | C4 | — | 3 | 1 | no | — |
| 508 | C4 | — | 15 | 1 | no | — |
| 509 | C4 | — | 21 | 1 | no | — |
| 510 | C4 | — | 105 | 1 | no | — |
| 511 | C3 | — | 4 | 1 | no | Sylow |
| 512 | C2 | — | 3 | 1 | no | — |
| 513 | C2 | — | 5 | 1 | no | — |
| 514 | C2 | — | 6 | 1 | no | — |
| 515 | C2 | — | 7 | 1 | no | — |
| 516 | C2 | — | 15 | 1 | no | — |
| 517 | C2 | — | 21 | 1 | no | — |
| 518 | C2 | — | 30 | 1 | no | — |
| 519 | C2 | — | 35 | 1 | no | — |
| 520 | C2 | — | 42 | 1 | no | — |
| 521 | C2 | — | 105 | 1 | no | — |
| 522 | C2 | — | 210 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C7×A4 | C23 |
| Fitting, socle | C22×C5×C7 | C22×D3 |
| LCS | G ▷ C5×C7×A4 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D5×A4×D7 | C2 | semidirect |
| 2. D35⋊S4 | C2 | semidirect |
| 3. S4×D35 | C2 | semidirect |
| 4. D5×C7⋊S4 | C2 | semidirect |
| 5. C7×D5×S4 | C2 | semidirect |
| 6. D7×C5⋊S4 | C2 | semidirect |
| 7. C5×D7×S4 | C2 | semidirect |
| 9. A4×D35 | C22 | semidirect |
| 10. C7×D5×A4 | C22 | semidirect |
| 11. C5×A4×D7 | C22 | semidirect |
| 12. C5⋊(C7⋊S4) | C22 | semidirect |
| 13. C7×C5⋊S4 | C22 | semidirect |
| 14. C5×C7⋊S4 | C22 | semidirect |
| 15. C5×C7×S4 | C22 | semidirect |
| 19. C22×D5×D7 | D3 | semidirect |
| 34. C5×C7×A4 | C23 | semidirect |
| 48. D7×S4 | D5 | direct (N × H) |
| 50. C22×D35 | C2×D3 | semidirect |
| 52. C22×C7×D5 | C2×D3 | semidirect |
| 54. C22×C5×D7 | C2×D3 | semidirect |
| 94. D5×S4 | D7 | direct (N × H) |
| 106. A4×D7 | C2×D5 | semidirect |
| 108. C7⋊S4 | C2×D5 | semidirect |
| 110. C7×S4 | C2×D5 | semidirect |
| 113. C22×C5×C7 | C22×D3 | semidirect |
| 139. D5×D7 | S4 | direct (N × H) |
| 147. D5×A4 | C2×D7 | semidirect |
| 149. C5⋊S4 | C2×D7 | semidirect |
| 151. C5×S4 | C2×D7 | semidirect |
| 172. C7×A4 | C22×D5 | semidirect |
| 196. D35 | C2×S4 | semidirect |
| 199. C5×D7 | C2×S4 | semidirect |
| 202. C7×D5 | C2×S4 | semidirect |
| 206. C5×A4 | C22×D7 | semidirect |
| 227. C22×D7 | D3×D5 | semidirect |
| 280. C22×D5 | D3×D7 | semidirect |
| 303. C5×C7 | C22×S4 | semidirect |
| 318. C22×C7 | C2×D3×D5 | semidirect |
| 351. S4 | D5×D7 | direct (N × H) |
| 359. C22×C5 | C2×D3×D7 | semidirect |
| 411. D7 | D5×S4 | direct (N × H) |
| 419. A4 | C2×D5×D7 | semidirect |
| 430. D5 | D7×S4 | direct (N × H) |
| 470. C7 | C2×D5×S4 | semidirect |
| 478. C5 | C2×D7×S4 | semidirect |
| 506. C22 | D3×D5×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×A4×D7 | 2 |
| D35⋊S4 | 2 |
| S4×D35 | 2 |
| D5×C7⋊S4 | 2 |
| C7×D5×S4 | 2 |
| D7×C5⋊S4 | 2 |
| C5×D7×S4 | 2 |
| D4×D5×D7 | 3 |
| D3×D5×D7 | 4 |
| C2×D7×S4 | 5 |
| C2×D5×S4 | 7 |