Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
700 conjugacy classes of subgroups.
The subgroup lattice has 496 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11753988 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11753987 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11751010 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#4909 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#65196 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#90948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11747546 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11746833 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11746828 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11746827 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | D5×Dic24 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10613772 | — | 3 | 1 | no | maximal, Hall |
| 13 | #92001 | — | 2 | 1 | no | — |
| 14 | #92000 | — | 2 | 1 | no | — |
| 15 | C2×Dic60 | C22 | 1 | 1 | yes | characteristic |
| 16 | #91793 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C5×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 18 | C5×#904 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#4047 | C22 | 1 | 1 | yes | characteristic |
| 20 | #91322 | — | 2 | 1 | no | — |
| 21 | #91321 | — | 2 | 1 | no | — |
| 22 | #91271 | C22 | 1 | 2 | yes | — |
| 23 | #91270 | C22 | 1 | 2 | yes | — |
| 24 | #91261 | — | 2 | 2 | no | — |
| 25 | #91260 | — | 2 | 2 | no | — |
| 26 | D5×Dic12 | C22 | 1 | 2 | yes | — |
| 27 | D5×Dic12 | C22 | 1 | 2 | yes | — |
| 28 | C3×C5×M32 | C22 | 1 | 1 | yes | characteristic |
| 29 | Dic120 | C22 | 1 | 2 | yes | — |
| 30 | #91084 | C22 | 1 | 2 | yes | — |
| 31 | C5×Dic24 | C22 | 1 | 2 | yes | — |
| 32 | C5×#800 | C22 | 1 | 2 | yes | — |
| 33 | C2×C3×#672 | C22 | 1 | 1 | yes | characteristic |
| 34 | C3×#3930 | C22 | 1 | 2 | yes | — |
| 35 | C3×D5×C16 | C22 | 1 | 2 | yes | — |
| 36 | #90948 | C22 | 1 | 1 | yes | characteristic |
| 37 | #90948 | C22 | 1 | 2 | yes | — |
| 38 | #90948 | C22 | 1 | 2 | yes | — |
| 39 | #90945 | C22 | 1 | 1 | yes | characteristic |
| 40 | #90944 | C22 | 1 | 1 | yes | characteristic |
| 41 | #90939 | C22 | 1 | 1 | yes | characteristic |
| 42 | #82015 | — | 5 | 1 | no | maximal, Hall |
| 43 | #66105 | — | 3 | 1 | no | — |
| 44 | #66100 | — | 3 | 1 | no | — |
| 45 | C5×#510 | — | 3 | 1 | no | — |
| 46 | #65483 | — | 3 | 1 | no | — |
| 47 | C2×#3961 | — | 3 | 1 | no | — |
| 48 | #65207 | — | 3 | 2 | no | — |
| 49 | D5×Q32 | — | 3 | 2 | no | — |
| 50 | #65205 | — | 3 | 2 | no | — |
| 51 | #65204 | — | 3 | 2 | no | — |
| 52 | #65198 | — | 3 | 1 | no | — |
| 53 | #65196 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #6817 | — | 2 | 1 | no | — |
| 55 | C2×Dic30 | — | 2 | 1 | no | — |
| 56 | C5×#235 | — | 2 | 1 | no | — |
| 57 | C2×C5×Dic6 | — | 2 | 1 | no | — |
| 58 | C3×#709 | D4 | 1 | 1 | yes | characteristic |
| 59 | #6780 | — | 4 | 2 | no | — |
| 60 | #6779 | — | 4 | 2 | no | — |
| 61 | #6773 | — | 2 | 2 | no | — |
| 62 | #6772 | — | 2 | 2 | no | — |
| 63 | D15⋊Q8 | — | 4 | 1 | no | — |
| 64 | D3×Dic10 | — | 4 | 1 | no | — |
| 65 | #6766 | — | 4 | 1 | no | — |
| 66 | #6765 | — | 4 | 1 | no | — |
| 67 | D5×Dic6 | — | 2 | 2 | no | — |
| 68 | D5×Dic6 | — | 2 | 2 | no | — |
| 69 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 70 | Dic60 | — | 2 | 1 | no | — |
| 71 | Dic60 | C23 | 1 | 1 | yes | characteristic |
| 72 | Dic60 | C23 | 1 | 2 | yes | — |
| 73 | D120 | C23 | 1 | 1 | yes | characteristic |
| 74 | #6706 | — | 2 | 1 | no | — |
| 75 | C5×Dic12 | — | 2 | 1 | no | — |
| 76 | C5×Dic12 | C23 | 1 | 1 | yes | characteristic |
| 77 | C5×Dic12 | C23 | 1 | 2 | yes | — |
| 78 | C5×D24 | C23 | 1 | 1 | yes | characteristic |
| 79 | C5×#204 | — | 2 | 1 | no | — |
| 80 | C3×#681 | D4 | 1 | 1 | yes | characteristic |
| 81 | C3×#676 | D4 | 1 | 2 | yes | — |
| 82 | C3×C8×D5 | C23 | 1 | 2 | yes | — |
| 83 | #6663 | — | 2 | 2 | no | — |
| 84 | #6663 | — | 2 | 2 | no | — |
| 85 | #6660 | — | 2 | 2 | no | — |
| 86 | #6659 | — | 2 | 2 | no | — |
| 87 | C3×C5×C16 | C23 | 1 | 2 | yes | — |
| 88 | C3×#672 | C23 | 1 | 1 | yes | characteristic |
| 89 | C3×#672 | C23 | 1 | 1 | yes | characteristic |
| 90 | #5753 | — | 5 | 1 | no | — |
| 91 | #5753 | — | 5 | 1 | no | — |
| 92 | C3×#504 | — | 5 | 1 | no | — |
| 93 | #4909 | — | 5 | 1 | no | — |
| 94 | #4909 | — | 5 | 2 | no | — |
| 95 | #4909 | — | 5 | 2 | no | — |
| 96 | #4909 | D5 | 1 | 1 | yes | characteristic, complemented |
| 97 | C2×Dic24 | — | 5 | 1 | no | — |
| 98 | C2×Dic24 | — | 5 | 2 | no | — |
| 99 | #4904 | — | 5 | 1 | no | — |
| 100 | #4904 | — | 5 | 2 | no | — |
| 101 | #4150 | — | 6 | 1 | no | — |
| 102 | #4147 | — | 6 | 1 | no | — |
| 103 | C5×#135 | — | 3 | 1 | no | — |
| 104 | C2×C5×Q16 | — | 3 | 1 | no | — |
| 105 | #4097 | — | 6 | 1 | no | — |
| 106 | #4088 | — | 6 | 1 | no | — |
| 107 | #4065 | — | 3 | 2 | no | — |
| 108 | #4064 | — | 6 | 2 | no | — |
| 109 | D5×Q16 | — | 3 | 2 | no | — |
| 110 | D5×Q16 | — | 3 | 2 | no | — |
| 111 | #4061 | — | 6 | 2 | no | — |
| 112 | #4058 | — | 3 | 2 | no | — |
| 113 | C2×Dic20 | — | 3 | 1 | no | — |
| 114 | #4050 | — | 3 | 1 | no | — |
| 115 | #4047 | C2×D3 | 1 | 1 | yes | characteristic |
| 116 | C5×Q32 | — | 3 | 2 | no | — |
| 117 | C5×SD32 | — | 3 | 2 | no | — |
| 118 | C5×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 119 | #3961 | — | 3 | 2 | no | — |
| 120 | #3961 | — | 3 | 2 | no | — |
| 121 | #3961 | — | 3 | 1 | no | — |
| 122 | #3960 | — | 3 | 1 | no | — |
| 123 | #3959 | — | 3 | 1 | no | — |
| 124 | #3958 | — | 3 | 1 | no | — |
| 125 | C2×#672 | C2×D3 | 1 | 1 | yes | characteristic |
| 126 | Dic40 | — | 3 | 2 | no | — |
| 127 | #3932 | — | 3 | 2 | no | — |
| 128 | #3930 | C2×D3 | 1 | 2 | yes | — |
| 129 | D5×C16 | C2×D3 | 1 | 2 | yes | — |
| 130 | #3417 | — | 15 | 1 | no | Sylow |
| 131 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | #1220 | — | 4 | 1 | no | — |
| 133 | C2×Dic15 | — | 4 | 1 | no | — |
| 134 | D60 | — | 2 | 1 | no | — |
| 135 | C4×D15 | — | 4 | 1 | no | — |
| 136 | Dic30 | — | 2 | 2 | no | — |
| 137 | Dic30 | — | 2 | 1 | no | — |
| 138 | Dic30 | — | 4 | 1 | no | — |
| 139 | C5×#67 | — | 4 | 1 | no | — |
| 140 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 141 | C5×D12 | — | 2 | 1 | no | — |
| 142 | C4×C5×D3 | — | 4 | 1 | no | — |
| 143 | C5×Dic6 | — | 2 | 2 | no | — |
| 144 | C5×Dic6 | — | 2 | 1 | no | — |
| 145 | C5×Dic6 | — | 4 | 1 | no | — |
| 146 | C3×C22⋊D5 | D8 | 1 | 2 | yes | — |
| 147 | C3×D20 | D8 | 1 | 1 | yes | characteristic |
| 148 | C3×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 149 | C3×Dic10 | D8 | 1 | 1 | yes | characteristic |
| 150 | #1204 | — | 4 | 2 | no | — |
| 151 | #1204 | — | 4 | 2 | no | — |
| 152 | #1202 | — | 4 | 2 | no | — |
| 153 | #1201 | — | 4 | 2 | no | — |
| 154 | #1200 | — | 4 | 2 | no | — |
| 155 | D3×Dic5 | — | 4 | 2 | no | — |
| 156 | D5×Dic3 | — | 4 | 2 | no | — |
| 157 | D5×Dic3 | — | 4 | 2 | no | — |
| 158 | C3×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C3×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 160 | C3×#168 | C2×D4 | 1 | 2 | yes | — |
| 161 | #1010 | — | 10 | 1 | no | — |
| 162 | #1010 | — | 10 | 1 | no | — |
| 163 | C3×#131 | — | 5 | 1 | no | — |
| 164 | #909 | — | 10 | 2 | no | — |
| 165 | #909 | — | 10 | 2 | no | — |
| 166 | #909 | — | 10 | 1 | no | — |
| 167 | #909 | — | 10 | 1 | no | — |
| 168 | C2×Dic12 | — | 5 | 1 | no | — |
| 169 | C2×Dic12 | — | 5 | 2 | no | — |
| 170 | C2×Dic12 | — | 5 | 2 | no | — |
| 171 | C2×Dic12 | C2×D5 | 1 | 1 | yes | characteristic |
| 172 | #904 | — | 5 | 1 | no | — |
| 173 | #904 | — | 5 | 2 | no | — |
| 174 | #904 | — | 5 | 2 | no | — |
| 175 | #904 | C2×D5 | 1 | 1 | yes | characteristic |
| 176 | C3×M32 | — | 5 | 2 | no | — |
| 177 | C3×M32 | C2×D5 | 1 | 1 | yes | characteristic |
| 178 | C2×C3×C16 | — | 5 | 1 | no | — |
| 179 | C2×C3×C16 | — | 5 | 2 | no | — |
| 180 | Dic24 | — | 5 | 1 | no | — |
| 181 | Dic24 | — | 5 | 2 | no | — |
| 182 | Dic24 | — | 5 | 2 | no | — |
| 183 | Dic24 | — | 5 | 2 | no | — |
| 184 | Dic24 | C2×D5 | 1 | 2 | yes | — |
| 185 | #800 | — | 5 | 1 | no | — |
| 186 | #800 | — | 5 | 1 | no | — |
| 187 | #800 | — | 5 | 2 | no | — |
| 188 | #800 | C2×D5 | 1 | 2 | yes | — |
| 189 | D48 | — | 5 | 1 | no | — |
| 190 | C5×#41 | — | 6 | 1 | no | — |
| 191 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 192 | #713 | — | 6 | 2 | no | — |
| 193 | #713 | — | 12 | 1 | no | — |
| 194 | Q8×D5 | — | 6 | 2 | no | — |
| 195 | Q8×D5 | — | 6 | 2 | no | — |
| 196 | Q8×D5 | — | 12 | 1 | no | — |
| 197 | #711 | — | 6 | 2 | no | — |
| 198 | #711 | — | 12 | 2 | no | — |
| 199 | #709 | — | 6 | 1 | no | — |
| 200 | #709 | — | 12 | 2 | no | — |
| 201 | #709 | — | 12 | 1 | no | — |
| 202 | #709 | D12 | 1 | 1 | yes | characteristic |
| 203 | C2×Dic10 | — | 6 | 1 | no | — |
| 204 | C2×Dic10 | — | 12 | 1 | no | — |
| 205 | C5×Q16 | — | 3 | 2 | no | — |
| 206 | C5×Q16 | — | 3 | 1 | no | — |
| 207 | C5×Q16 | — | 6 | 1 | no | — |
| 208 | C5×SD16 | — | 6 | 1 | no | — |
| 209 | C5×D8 | — | 3 | 1 | no | — |
| 210 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 211 | #689 | — | 6 | 2 | no | — |
| 212 | #689 | — | 6 | 2 | no | — |
| 213 | #688 | — | 6 | 2 | no | — |
| 214 | #687 | — | 6 | 2 | no | — |
| 215 | #681 | D12 | 1 | 1 | yes | characteristic |
| 216 | Dic20 | — | 3 | 2 | no | — |
| 217 | Dic20 | — | 3 | 1 | no | — |
| 218 | Dic20 | — | 6 | 1 | no | — |
| 219 | D40 | — | 3 | 1 | no | — |
| 220 | #677 | — | 6 | 1 | no | — |
| 221 | #676 | D12 | 1 | 2 | yes | — |
| 222 | C8×D5 | C22×D3 | 1 | 2 | yes | — |
| 223 | C5×C16 | C22×D3 | 1 | 2 | yes | — |
| 224 | #672 | C22×D3 | 1 | 1 | yes | characteristic |
| 225 | #672 | C22×D3 | 1 | 1 | yes | characteristic |
| 226 | #578 | — | 15 | 1 | no | — |
| 227 | #578 | — | 15 | 1 | no | — |
| 228 | #510 | — | 3 | 1 | no | — |
| 229 | #510 | — | 15 | 2 | no | — |
| 230 | #510 | — | 15 | 2 | no | — |
| 231 | #510 | — | 15 | 1 | no | — |
| 232 | #508 | — | 15 | 2 | no | — |
| 233 | #508 | — | 15 | 1 | no | — |
| 234 | C2×Q32 | — | 15 | 2 | no | — |
| 235 | C2×Q32 | — | 15 | 1 | no | — |
| 236 | #504 | — | 5 | 1 | no | — |
| 237 | C22×C3×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 238 | C2×D15 | — | 4 | 1 | no | — |
| 239 | C2×C5×D3 | — | 4 | 1 | no | — |
| 240 | C2×C3×D5 | C2×D8 | 1 | 2 | yes | — |
| 241 | C3×C4×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 242 | C3×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 243 | Dic15 | — | 4 | 1 | no | — |
| 244 | Dic15 | — | 4 | 2 | no | — |
| 245 | C3×Dic5 | C2×D8 | 1 | 2 | yes | — |
| 246 | C5×Dic3 | — | 4 | 1 | no | — |
| 247 | C5×Dic3 | — | 4 | 2 | no | — |
| 248 | C3×#41 | — | 5 | 1 | no | — |
| 249 | D3×Q8 | — | 20 | 1 | no | — |
| 250 | D3×Q8 | — | 20 | 1 | no | — |
| 251 | #237 | — | 20 | 1 | no | — |
| 252 | #237 | — | 20 | 1 | no | — |
| 253 | #237 | — | 20 | 2 | no | — |
| 254 | #237 | — | 20 | 2 | no | — |
| 255 | #235 | — | 2 | 1 | no | — |
| 256 | #235 | — | 10 | 2 | no | — |
| 257 | #235 | — | 10 | 2 | no | — |
| 258 | #235 | — | 10 | 1 | no | — |
| 259 | C2×Dic6 | — | 2 | 1 | no | — |
| 260 | C2×Dic6 | — | 10 | 2 | no | — |
| 261 | C2×Dic6 | — | 10 | 2 | no | — |
| 262 | C2×Dic6 | — | 10 | 1 | no | — |
| 263 | C3×M16 | — | 5 | 1 | no | — |
| 264 | C3×M16 | — | 5 | 2 | no | — |
| 265 | C2×C3×C8 | — | 5 | 2 | no | — |
| 266 | C2×C3×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 267 | Dic12 | — | 2 | 1 | no | — |
| 268 | Dic12 | — | 5 | 1 | no | — |
| 269 | Dic12 | — | 5 | 2 | no | — |
| 270 | Dic12 | — | 10 | 2 | no | — |
| 271 | Dic12 | — | 10 | 2 | no | — |
| 272 | Dic12 | — | 10 | 1 | no | — |
| 273 | Dic12 | C22×D5 | 1 | 1 | yes | characteristic |
| 274 | Dic12 | C22×D5 | 1 | 2 | yes | — |
| 275 | D24 | — | 5 | 1 | no | — |
| 276 | D24 | C22×D5 | 1 | 1 | yes | characteristic |
| 277 | #204 | — | 2 | 1 | no | — |
| 278 | #204 | — | 10 | 2 | no | — |
| 279 | #204 | — | 10 | 2 | no | — |
| 280 | #204 | — | 10 | 1 | no | — |
| 281 | C3×C16 | — | 5 | 1 | no | — |
| 282 | C3×C16 | — | 5 | 1 | no | — |
| 283 | C3×C16 | C22×D5 | 1 | 2 | yes | — |
| 284 | C5×Q8 | — | 6 | 2 | no | — |
| 285 | C5×Q8 | — | 6 | 1 | no | — |
| 286 | C5×Q8 | — | 12 | 1 | no | — |
| 287 | C5×D4 | — | 6 | 1 | no | — |
| 288 | C5×D4 | — | 12 | 1 | no | — |
| 289 | C2×C4×C5 | — | 12 | 1 | no | — |
| 290 | C2×C4×C5 | — | 12 | 1 | no | — |
| 291 | C2×C4×C5 | C2×D12 | 1 | 1 | yes | characteristic |
| 292 | C22⋊D5 | — | 12 | 1 | no | — |
| 293 | C22⋊D5 | — | 12 | 2 | no | — |
| 294 | C22⋊D5 | D24 | 1 | 2 | yes | — |
| 295 | C2×Dic5 | — | 12 | 1 | no | — |
| 296 | C2×Dic5 | — | 12 | 2 | no | — |
| 297 | D20 | — | 6 | 1 | no | — |
| 298 | D20 | — | 12 | 2 | no | — |
| 299 | D20 | D24 | 1 | 1 | yes | characteristic |
| 300 | C4×D5 | — | 12 | 2 | no | — |
| 301 | C4×D5 | — | 12 | 2 | no | — |
| 302 | C4×D5 | — | 12 | 1 | no | — |
| 303 | C4×D5 | — | 12 | 2 | no | — |
| 304 | C4×D5 | C2×D12 | 1 | 2 | yes | — |
| 305 | Dic10 | — | 6 | 1 | no | — |
| 306 | Dic10 | — | 6 | 2 | no | — |
| 307 | Dic10 | — | 12 | 1 | no | — |
| 308 | Dic10 | — | 12 | 2 | no | — |
| 309 | Dic10 | — | 12 | 2 | no | — |
| 310 | Dic10 | D24 | 1 | 1 | yes | characteristic |
| 311 | C5×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 312 | C5×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 313 | #168 | C2×D12 | 1 | 2 | yes | — |
| 314 | 2−1+4 | — | 30 | 1 | no | — |
| 315 | 2−1+4 | — | 30 | 1 | no | — |
| 316 | #137 | — | 30 | 2 | no | — |
| 317 | #137 | — | 30 | 2 | no | — |
| 318 | #137 | — | 30 | 1 | no | — |
| 319 | #137 | — | 30 | 1 | no | — |
| 320 | #135 | — | 3 | 1 | no | — |
| 321 | #135 | — | 15 | 2 | no | — |
| 322 | #135 | — | 15 | 2 | no | — |
| 323 | #135 | — | 15 | 1 | no | — |
| 324 | C2×Q16 | — | 3 | 1 | no | — |
| 325 | C2×Q16 | — | 15 | 2 | no | — |
| 326 | C2×Q16 | — | 15 | 2 | no | — |
| 327 | C2×Q16 | — | 15 | 1 | no | — |
| 328 | #131 | — | 5 | 1 | no | — |
| 329 | Q32 | — | 3 | 2 | no | — |
| 330 | Q32 | — | 15 | 2 | no | — |
| 331 | Q32 | — | 15 | 1 | no | — |
| 332 | Q32 | — | 15 | 2 | no | — |
| 333 | Q32 | — | 15 | 2 | no | — |
| 334 | SD32 | — | 3 | 2 | no | — |
| 335 | SD32 | — | 15 | 1 | no | — |
| 336 | SD32 | — | 15 | 1 | no | — |
| 337 | SD32 | — | 15 | 2 | no | — |
| 338 | D16 | — | 15 | 1 | no | — |
| 339 | M32 | — | 5 | 2 | no | — |
| 340 | M32 | D3×D5 | 1 | 1 | yes | characteristic |
| 341 | C2×C16 | — | 5 | 1 | no | — |
| 342 | C2×C16 | — | 5 | 2 | no | — |
| 343 | C2×C3×C5 | — | 2 | 1 | no | — |
| 344 | C2×C3×C5 | C22×D8 | 1 | 1 | yes | characteristic |
| 345 | D15 | — | 8 | 1 | no | — |
| 346 | C3×D5 | — | 2 | 2 | no | — |
| 347 | C5×D3 | — | 8 | 1 | no | — |
| 348 | C3×Q8 | — | 5 | 1 | no | — |
| 349 | C3×D4 | — | 5 | 2 | no | — |
| 350 | C3×D4 | — | 5 | 1 | no | — |
| 351 | C2×C3×C4 | — | 5 | 2 | no | — |
| 352 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 353 | #67 | — | 4 | 1 | no | — |
| 354 | #67 | — | 20 | 2 | no | — |
| 355 | #67 | — | 20 | 2 | no | — |
| 356 | #67 | — | 20 | 1 | no | — |
| 357 | C2×Dic3 | — | 4 | 1 | no | — |
| 358 | C2×Dic3 | — | 20 | 2 | no | — |
| 359 | C2×Dic3 | — | 20 | 2 | no | — |
| 360 | C2×Dic3 | — | 20 | 1 | no | — |
| 361 | D12 | — | 2 | 1 | no | — |
| 362 | D12 | — | 10 | 1 | no | — |
| 363 | C4×D3 | — | 4 | 1 | no | — |
| 364 | C4×D3 | — | 20 | 2 | no | — |
| 365 | C4×D3 | — | 20 | 2 | no | — |
| 366 | C4×D3 | — | 20 | 1 | no | — |
| 367 | Dic6 | — | 2 | 1 | no | — |
| 368 | Dic6 | — | 2 | 2 | no | — |
| 369 | Dic6 | — | 4 | 1 | no | — |
| 370 | Dic6 | — | 10 | 2 | no | — |
| 371 | Dic6 | — | 10 | 1 | no | — |
| 372 | Dic6 | — | 20 | 2 | no | — |
| 373 | Dic6 | — | 20 | 2 | no | — |
| 374 | Dic6 | — | 20 | 1 | no | — |
| 375 | C3×C8 | — | 5 | 2 | no | — |
| 376 | C3×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 377 | C3×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 378 | C22×C5 | — | 12 | 1 | no | — |
| 379 | C22×C5 | C2×D24 | 1 | 1 | yes | characteristic |
| 380 | C2×D5 | — | 12 | 1 | no | — |
| 381 | C2×D5 | C2×D24 | 1 | 2 | yes | — |
| 382 | C4×C5 | — | 12 | 1 | no | — |
| 383 | C4×C5 | — | 12 | 2 | no | — |
| 384 | C4×C5 | C2×D24 | 1 | 1 | yes | characteristic |
| 385 | C4×C5 | C22×D12 | 1 | 1 | yes | characteristic |
| 386 | Dic5 | — | 12 | 1 | no | — |
| 387 | Dic5 | — | 12 | 2 | no | — |
| 388 | Dic5 | C2×D24 | 1 | 2 | yes | — |
| 389 | #41 | — | 5 | 1 | no | — |
| 390 | #41 | — | 6 | 1 | no | — |
| 391 | #41 | — | 30 | 2 | no | — |
| 392 | #41 | — | 30 | 2 | no | — |
| 393 | #41 | — | 30 | 1 | no | — |
| 394 | #41 | — | 60 | 2 | no | — |
| 395 | #41 | — | 60 | 1 | no | — |
| 396 | #41 | — | 60 | 2 | no | — |
| 397 | #41 | — | 60 | 1 | no | — |
| 398 | C2×Q8 | — | 6 | 1 | no | — |
| 399 | C2×Q8 | — | 30 | 2 | no | — |
| 400 | C2×Q8 | — | 30 | 2 | no | — |
| 401 | C2×Q8 | — | 30 | 1 | no | — |
| 402 | C2×Q8 | — | 60 | 1 | no | — |
| 403 | C2×Q8 | — | 60 | 1 | no | — |
| 404 | Q16 | — | 3 | 2 | no | — |
| 405 | Q16 | — | 3 | 1 | no | — |
| 406 | Q16 | — | 6 | 1 | no | — |
| 407 | Q16 | — | 15 | 1 | no | — |
| 408 | Q16 | — | 15 | 2 | no | — |
| 409 | Q16 | — | 30 | 2 | no | — |
| 410 | Q16 | — | 30 | 2 | no | — |
| 411 | Q16 | — | 30 | 1 | no | — |
| 412 | SD16 | — | 6 | 1 | no | — |
| 413 | SD16 | — | 30 | 2 | no | — |
| 414 | SD16 | — | 30 | 2 | no | — |
| 415 | SD16 | — | 30 | 1 | no | — |
| 416 | D8 | — | 3 | 1 | no | — |
| 417 | D8 | — | 15 | 1 | no | — |
| 418 | M16 | — | 5 | 1 | no | — |
| 419 | M16 | — | 5 | 2 | no | — |
| 420 | C2×C8 | — | 5 | 2 | no | — |
| 421 | C2×C8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 422 | C16 | — | 5 | 1 | no | — |
| 423 | C16 | — | 5 | 1 | no | — |
| 424 | C16 | C2×D3×D5 | 1 | 2 | yes | — |
| 425 | C3×C5 | #3417 | 1 | 1 | yes | characteristic, complemented, Hall |
| 426 | C22×C3 | — | 5 | 2 | no | — |
| 427 | C22×C3 | D5×D8 | 1 | 1 | yes | characteristic |
| 428 | C2×D3 | — | 4 | 1 | no | — |
| 429 | C2×D3 | — | 20 | 1 | no | — |
| 430 | C3×C4 | — | 5 | 2 | no | — |
| 431 | C3×C4 | D5×D8 | 1 | 1 | yes | characteristic |
| 432 | C3×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 433 | Dic3 | — | 4 | 2 | no | — |
| 434 | Dic3 | — | 4 | 1 | no | — |
| 435 | Dic3 | — | 20 | 1 | no | — |
| 436 | Dic3 | — | 20 | 2 | no | — |
| 437 | C2×C5 | — | 2 | 1 | no | — |
| 438 | C2×C5 | — | 24 | 1 | no | — |
| 439 | C2×C5 | C22×D24 | 1 | 1 | yes | characteristic |
| 440 | D5 | — | 2 | 2 | no | — |
| 441 | D5 | — | 24 | 1 | no | — |
| 442 | Q8 | — | 5 | 1 | no | — |
| 443 | Q8 | — | 6 | 1 | no | — |
| 444 | Q8 | — | 6 | 2 | no | — |
| 445 | Q8 | — | 12 | 1 | no | — |
| 446 | Q8 | — | 30 | 2 | no | — |
| 447 | Q8 | — | 30 | 1 | no | — |
| 448 | Q8 | — | 60 | 2 | no | — |
| 449 | Q8 | — | 60 | 2 | no | — |
| 450 | Q8 | — | 60 | 1 | no | — |
| 451 | D4 | — | 5 | 2 | no | — |
| 452 | D4 | — | 5 | 1 | no | — |
| 453 | D4 | — | 6 | 1 | no | — |
| 454 | D4 | — | 12 | 1 | no | — |
| 455 | D4 | — | 30 | 1 | no | — |
| 456 | D4 | — | 60 | 2 | no | — |
| 457 | D4 | — | 60 | 2 | no | — |
| 458 | D4 | — | 60 | 1 | no | — |
| 459 | C2×C4 | — | 5 | 2 | no | — |
| 460 | C2×C4 | — | 12 | 1 | no | — |
| 461 | C2×C4 | — | 12 | 1 | no | — |
| 462 | C2×C4 | — | 60 | 2 | no | — |
| 463 | C2×C4 | — | 60 | 2 | no | — |
| 464 | C2×C4 | — | 60 | 2 | no | — |
| 465 | C2×C4 | — | 60 | 2 | no | — |
| 466 | C2×C4 | — | 60 | 1 | no | — |
| 467 | C2×C4 | — | 60 | 1 | no | — |
| 468 | C2×C4 | D5×D12 | 1 | 1 | yes | characteristic |
| 469 | C8 | — | 5 | 2 | no | — |
| 470 | C8 | D5×D12 | 1 | 1 | yes | characteristic |
| 471 | C8 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 472 | C2×C3 | — | 2 | 1 | no | — |
| 473 | C2×C3 | — | 10 | 2 | no | — |
| 474 | C2×C3 | C2×D5×D8 | 1 | 1 | yes | characteristic |
| 475 | D3 | — | 8 | 1 | no | — |
| 476 | D3 | — | 40 | 1 | no | — |
| 477 | C5 | #82015 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 478 | C22 | — | 5 | 2 | no | — |
| 479 | C22 | — | 12 | 1 | no | — |
| 480 | C22 | — | 60 | 1 | no | — |
| 481 | C22 | D5×D24 | 1 | 1 | yes | characteristic |
| 482 | C4 | — | 5 | 2 | no | — |
| 483 | C4 | — | 12 | 1 | no | — |
| 484 | C4 | — | 12 | 2 | no | — |
| 485 | C4 | — | 60 | 2 | no | — |
| 486 | C4 | — | 60 | 1 | no | — |
| 487 | C4 | D5×D24 | 1 | 1 | yes | characteristic |
| 488 | C4 | C2×D5×D12 | 1 | 1 | yes | characteristic |
| 489 | C3 | #10613772 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 490 | C2 | — | 2 | 1 | no | — |
| 491 | C2 | — | 10 | 2 | no | — |
| 492 | C2 | — | 24 | 1 | no | — |
| 493 | C2 | — | 120 | 1 | no | — |
| 494 | C2 | C2×D5×D24 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11753988 | C2 | semidirect |
| 2. #11753987 | C2 | semidirect |
| 3. #11751010 | C2 | semidirect |
| 4. C5×#4909 | C2 | semidirect |
| 5. C3×#65196 | C2 | semidirect |
| 6. C2×#90948 | C2 | semidirect |
| 7. #11747546 | C2 | semidirect |
| 8. #11746833 | C2 | semidirect |
| 9. #11746828 | C2 | semidirect |
| 10. #11746827 | C2 | semidirect |
| 11. D5×Dic24 | C2 | semidirect |
| 53. #65196 | D3 | semidirect |
| 96. #4909 | D5 | semidirect |
| 425. C3×C5 | #3417 | semidirect |
| 477. C5 | #82015 | semidirect |
| 489. C3 | #10613772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753988 | 2 |
| #11753987 | 2 |
| #11751010 | 2 |
| C5×#4909 | 2 |
| C3×#65196 | 2 |
| C2×#90948 | 2 |
| #11747546 | 2 |
| #11746833 | 2 |
| #11746828 | 2 |
| #11746827 | 2 |
| D5×Dic24 | 2 |
| #10613772 | 3 |
| #82015 | 5 |