Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
896 conjugacy classes of subgroups.
The subgroup lattice has 520 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11756595 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11756538 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×C5×#455 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11751305 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11751163 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751161 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11750927 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11750924 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11750849 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10612026 | — | 3 | 1 | no | maximal, Hall |
| 11 | C3×C5×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 12 | #92101 | C22 | 1 | 2 | yes | — |
| 13 | #92098 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C3×C5×#137 | C22 | 1 | 2 | yes | — |
| 15 | C3×C5×#124 | C22 | 1 | 1 | yes | characteristic |
| 16 | #91840 | — | 2 | 2 | no | — |
| 17 | #91840 | C22 | 1 | 2 | yes | — |
| 18 | #91839 | — | 2 | 2 | no | — |
| 19 | #91839 | C22 | 1 | 2 | yes | — |
| 20 | #91837 | C22 | 1 | 2 | yes | — |
| 21 | C2×#6718 | C22 | 1 | 2 | yes | complemented |
| 22 | C2×#6716 | — | 2 | 2 | no | — |
| 23 | C2×#6716 | C22 | 1 | 2 | yes | — |
| 24 | #91821 | — | 2 | 2 | no | — |
| 25 | #91821 | C22 | 1 | 2 | yes | — |
| 26 | #91807 | — | 2 | 2 | no | — |
| 27 | Q16×D15 | — | 2 | 2 | no | — |
| 28 | #91805 | — | 2 | 2 | no | — |
| 29 | #91804 | — | 2 | 2 | no | — |
| 30 | #91798 | C22 | 1 | 2 | yes | complemented |
| 31 | #91796 | C22 | 1 | 2 | yes | complemented |
| 32 | #91758 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | C3×C5×#104 | C22 | 1 | 2 | yes | — |
| 34 | C3×C5×#100 | C22 | 1 | 1 | yes | characteristic |
| 35 | #91120 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #91108 | C22 | 1 | 2 | yes | complemented |
| 37 | #91106 | C22 | 1 | 2 | yes | complemented |
| 38 | #91089 | C22 | 1 | 2 | yes | complemented |
| 39 | #91087 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #80295 | — | 5 | 1 | no | maximal, Hall |
| 41 | #66170 | — | 3 | 2 | no | — |
| 42 | #66113 | — | 3 | 2 | no | — |
| 43 | C5×#455 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | #65493 | — | 3 | 2 | no | — |
| 45 | #65351 | — | 3 | 1 | no | — |
| 46 | #65349 | — | 3 | 1 | no | — |
| 47 | #65115 | — | 3 | 2 | no | — |
| 48 | #65112 | — | 3 | 2 | no | — |
| 49 | #65037 | — | 3 | 2 | no | — |
| 50 | C3×C5×#41 | — | 2 | 2 | no | — |
| 51 | C3×C5×#41 | C23 | 1 | 2 | yes | — |
| 52 | C2×C3×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×C3×C5×D4 | — | 2 | 2 | no | — |
| 54 | C2×C3×C5×D4 | — | 4 | 1 | no | — |
| 55 | C2×C3×C5×D4 | C23 | 1 | 1 | yes | characteristic |
| 56 | #6821 | — | 2 | 2 | no | — |
| 57 | Q8×D15 | — | 2 | 2 | no | — |
| 58 | Q8×D15 | — | 2 | 2 | no | — |
| 59 | #6819 | — | 2 | 2 | no | — |
| 60 | #6819 | — | 4 | 2 | no | — |
| 61 | #6817 | — | 2 | 2 | no | — |
| 62 | #6817 | — | 4 | 1 | no | — |
| 63 | #6817 | C23 | 1 | 2 | yes | — |
| 64 | C2×Dic30 | — | 2 | 2 | no | — |
| 65 | C2×Dic30 | C23 | 1 | 2 | yes | — |
| 66 | C3×C5×Q16 | — | 2 | 2 | no | — |
| 67 | C3×C5×SD16 | — | 2 | 2 | no | — |
| 68 | C3×C5×M16 | C23 | 1 | 2 | yes | — |
| 69 | C3×C5×C22⋊C4 | — | 4 | 1 | no | — |
| 70 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 71 | #6718 | — | 2 | 2 | no | — |
| 72 | #6718 | — | 2 | 2 | no | — |
| 73 | #6718 | — | 2 | 2 | no | — |
| 74 | #6718 | D4 | 1 | 2 | yes | — |
| 75 | #6717 | D4 | 1 | 2 | yes | — |
| 76 | #6716 | — | 2 | 2 | no | — |
| 77 | #6716 | — | 2 | 2 | no | — |
| 78 | #6716 | — | 2 | 2 | no | — |
| 79 | #6716 | — | 2 | 2 | no | — |
| 80 | #6716 | D4 | 1 | 2 | yes | — |
| 81 | #6715 | — | 2 | 2 | no | — |
| 82 | #6715 | D4 | 1 | 2 | yes | — |
| 83 | C4⋊Dic15 | — | 4 | 1 | no | — |
| 84 | #6710 | — | 2 | 2 | no | — |
| 85 | #6710 | C23 | 1 | 2 | yes | — |
| 86 | C2×C3⋊#168 | — | 2 | 2 | no | — |
| 87 | C2×C3⋊#168 | C23 | 1 | 2 | yes | — |
| 88 | Dic60 | — | 2 | 2 | no | — |
| 89 | #6706 | — | 2 | 2 | no | — |
| 90 | #6705 | — | 2 | 2 | no | — |
| 91 | C8×D15 | — | 2 | 2 | no | — |
| 92 | #5836 | — | 5 | 2 | no | — |
| 93 | #5779 | — | 5 | 2 | no | — |
| 94 | C3×#455 | D5 | 1 | 1 | yes | characteristic, complemented |
| 95 | #5204 | — | 5 | 2 | no | — |
| 96 | #5062 | — | 5 | 1 | no | — |
| 97 | #5060 | — | 5 | 1 | no | — |
| 98 | #4826 | — | 5 | 2 | no | — |
| 99 | #4823 | — | 5 | 2 | no | — |
| 100 | #4748 | — | 5 | 2 | no | — |
| 101 | C5×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 102 | #4150 | — | 3 | 2 | no | — |
| 103 | #4147 | — | 3 | 1 | no | — |
| 104 | C5×#137 | C2×D3 | 1 | 2 | yes | — |
| 105 | C5×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 106 | #4097 | — | 3 | 2 | no | — |
| 107 | #4097 | — | 6 | 2 | no | — |
| 108 | #4096 | — | 3 | 2 | no | — |
| 109 | #4096 | — | 6 | 2 | no | — |
| 110 | #4094 | — | 3 | 2 | no | — |
| 111 | C2×#689 | — | 3 | 2 | no | — |
| 112 | C2×#687 | — | 3 | 2 | no | — |
| 113 | C2×#687 | — | 6 | 2 | no | — |
| 114 | #4078 | — | 3 | 2 | no | — |
| 115 | #4078 | — | 6 | 2 | no | — |
| 116 | #4064 | — | 6 | 2 | no | — |
| 117 | D5×Q16 | — | 6 | 2 | no | — |
| 118 | #4062 | — | 6 | 2 | no | — |
| 119 | #4061 | — | 6 | 2 | no | — |
| 120 | #4055 | — | 3 | 2 | no | — |
| 121 | #4053 | — | 3 | 2 | no | — |
| 122 | #4015 | — | 3 | 1 | no | — |
| 123 | C5×#104 | C2×D3 | 1 | 2 | yes | — |
| 124 | C5×#100 | C2×D3 | 1 | 1 | yes | characteristic |
| 125 | #3968 | — | 3 | 1 | no | — |
| 126 | #3956 | — | 3 | 2 | no | — |
| 127 | #3954 | — | 3 | 2 | no | — |
| 128 | #3937 | — | 3 | 2 | no | — |
| 129 | #3935 | — | 3 | 1 | no | — |
| 130 | #3289 | — | 15 | 1 | no | Sylow |
| 131 | C23×C3×C5 | — | 2 | 1 | no | — |
| 132 | C23×C3×C5 | — | 4 | 1 | no | — |
| 133 | C3×C5×Q8 | — | 2 | 2 | no | — |
| 134 | C3×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 135 | C3×C5×D4 | — | 2 | 2 | no | — |
| 136 | C3×C5×D4 | — | 2 | 2 | no | — |
| 137 | C3×C5×D4 | — | 4 | 2 | no | — |
| 138 | C3×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 139 | C2×C3×C4×C5 | — | 2 | 2 | no | — |
| 140 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 141 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 142 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 143 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 144 | #1220 | — | 2 | 2 | no | — |
| 145 | #1220 | — | 4 | 2 | no | — |
| 146 | C2×Dic15 | — | 2 | 2 | no | — |
| 147 | C2×Dic15 | — | 4 | 2 | no | — |
| 148 | D60 | — | 4 | 1 | no | — |
| 149 | D60 | C2×D4 | 1 | 2 | yes | — |
| 150 | C4×D15 | — | 2 | 2 | no | — |
| 151 | C4×D15 | — | 4 | 2 | no | — |
| 152 | C4×D15 | — | 4 | 2 | no | — |
| 153 | Dic30 | — | 2 | 2 | no | — |
| 154 | Dic30 | — | 2 | 2 | no | — |
| 155 | Dic30 | — | 4 | 1 | no | — |
| 156 | Dic30 | — | 4 | 2 | no | — |
| 157 | Dic30 | C2×D4 | 1 | 2 | yes | — |
| 158 | C3×C5×C8 | — | 2 | 2 | no | — |
| 159 | C3⋊#168 | — | 2 | 2 | no | — |
| 160 | C3⋊#168 | C2×D4 | 1 | 2 | yes | — |
| 161 | C3⋊#168 | C2×D4 | 1 | 2 | yes | — |
| 162 | C3×H(5,𝔽2) | C2×D5 | 1 | 1 | yes | characteristic |
| 163 | #1010 | — | 5 | 2 | no | — |
| 164 | #1007 | — | 5 | 1 | no | — |
| 165 | C3×#137 | C2×D5 | 1 | 2 | yes | — |
| 166 | C3×#124 | C2×D5 | 1 | 1 | yes | characteristic |
| 167 | #951 | — | 5 | 2 | no | — |
| 168 | #951 | — | 10 | 2 | no | — |
| 169 | #950 | — | 5 | 2 | no | — |
| 170 | #950 | — | 10 | 2 | no | — |
| 171 | #948 | — | 5 | 2 | no | — |
| 172 | C2×#216 | — | 5 | 2 | no | — |
| 173 | C2×#214 | — | 5 | 2 | no | — |
| 174 | C2×#214 | — | 10 | 2 | no | — |
| 175 | #932 | — | 5 | 2 | no | — |
| 176 | #932 | — | 10 | 2 | no | — |
| 177 | #918 | — | 10 | 2 | no | — |
| 178 | D3×Q16 | — | 10 | 2 | no | — |
| 179 | #916 | — | 10 | 2 | no | — |
| 180 | #915 | — | 10 | 2 | no | — |
| 181 | #909 | — | 5 | 2 | no | — |
| 182 | #907 | — | 5 | 2 | no | — |
| 183 | #869 | — | 5 | 1 | no | — |
| 184 | C3×#104 | C2×D5 | 1 | 2 | yes | — |
| 185 | C3×#100 | C2×D5 | 1 | 1 | yes | characteristic |
| 186 | #836 | — | 5 | 1 | no | — |
| 187 | #824 | — | 5 | 2 | no | — |
| 188 | #822 | — | 5 | 2 | no | — |
| 189 | #805 | — | 5 | 2 | no | — |
| 190 | #803 | — | 5 | 1 | no | — |
| 191 | C5×#41 | — | 2 | 2 | no | — |
| 192 | C5×#41 | C22×D3 | 1 | 2 | yes | — |
| 193 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 194 | C2×C5×D4 | — | 2 | 2 | no | — |
| 195 | C2×C5×D4 | — | 4 | 1 | no | — |
| 196 | C2×C5×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 197 | #713 | — | 6 | 2 | no | — |
| 198 | Q8×D5 | — | 6 | 2 | no | — |
| 199 | Q8×D5 | — | 6 | 2 | no | — |
| 200 | #711 | — | 6 | 2 | no | — |
| 201 | #711 | — | 12 | 2 | no | — |
| 202 | #709 | — | 3 | 2 | no | — |
| 203 | #709 | — | 6 | 2 | no | — |
| 204 | #709 | — | 12 | 1 | no | — |
| 205 | C2×Dic10 | — | 3 | 2 | no | — |
| 206 | C2×Dic10 | — | 6 | 2 | no | — |
| 207 | C5×Q16 | — | 2 | 2 | no | — |
| 208 | C5×SD16 | — | 2 | 2 | no | — |
| 209 | C5×M16 | C22×D3 | 1 | 2 | yes | — |
| 210 | C5×C22⋊C4 | — | 4 | 1 | no | — |
| 211 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 212 | #689 | — | 3 | 2 | no | — |
| 213 | #689 | — | 6 | 2 | no | — |
| 214 | #689 | — | 6 | 2 | no | — |
| 215 | #689 | — | 6 | 2 | no | — |
| 216 | #688 | — | 3 | 2 | no | — |
| 217 | #687 | — | 3 | 2 | no | — |
| 218 | #687 | — | 6 | 2 | no | — |
| 219 | #687 | — | 6 | 2 | no | — |
| 220 | #687 | — | 6 | 2 | no | — |
| 221 | #687 | — | 6 | 2 | no | — |
| 222 | #686 | — | 3 | 2 | no | — |
| 223 | #686 | — | 6 | 2 | no | — |
| 224 | C4⋊Dic5 | — | 12 | 1 | no | — |
| 225 | #681 | — | 3 | 2 | no | — |
| 226 | #681 | — | 6 | 2 | no | — |
| 227 | C2×#168 | — | 3 | 2 | no | — |
| 228 | C2×#168 | — | 6 | 2 | no | — |
| 229 | Dic20 | — | 6 | 2 | no | — |
| 230 | #677 | — | 6 | 2 | no | — |
| 231 | #676 | — | 6 | 2 | no | — |
| 232 | C8×D5 | — | 6 | 2 | no | — |
| 233 | #578 | — | 15 | 2 | no | — |
| 234 | #577 | — | 15 | 2 | no | — |
| 235 | #497 | — | 15 | 1 | no | — |
| 236 | #473 | — | 15 | 2 | no | — |
| 237 | #471 | — | 15 | 2 | no | — |
| 238 | #456 | — | 15 | 2 | no | — |
| 239 | #455 | D15 | 1 | 1 | yes | characteristic, complemented |
| 240 | #454 | — | 15 | 1 | no | — |
| 241 | #444 | — | 15 | 2 | no | — |
| 242 | C22×C3×C5 | — | 2 | 2 | no | — |
| 243 | C22×C3×C5 | — | 4 | 1 | no | — |
| 244 | C22×C3×C5 | — | 8 | 1 | no | — |
| 245 | C22×C3×C5 | — | 16 | 1 | no | — |
| 246 | C22×C3×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 247 | C2×D15 | — | 2 | 2 | no | — |
| 248 | C3×C4×C5 | — | 2 | 2 | no | — |
| 249 | C3×C4×C5 | — | 4 | 1 | no | — |
| 250 | C3×C4×C5 | — | 4 | 1 | no | — |
| 251 | C3×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 252 | Dic15 | — | 2 | 2 | no | — |
| 253 | Dic15 | — | 4 | 2 | no | — |
| 254 | C3×#41 | — | 2 | 2 | no | — |
| 255 | C3×#41 | C22×D5 | 1 | 2 | yes | — |
| 256 | C2×C3×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 257 | C2×C3×D4 | — | 2 | 2 | no | — |
| 258 | C2×C3×D4 | — | 4 | 1 | no | — |
| 259 | C2×C3×D4 | C22×D5 | 1 | 1 | yes | characteristic |
| 260 | #239 | — | 10 | 2 | no | — |
| 261 | D3×Q8 | — | 10 | 2 | no | — |
| 262 | D3×Q8 | — | 10 | 2 | no | — |
| 263 | #237 | — | 10 | 2 | no | — |
| 264 | #237 | — | 20 | 2 | no | — |
| 265 | #235 | — | 5 | 2 | no | — |
| 266 | #235 | — | 10 | 2 | no | — |
| 267 | #235 | — | 20 | 1 | no | — |
| 268 | C2×Dic6 | — | 5 | 2 | no | — |
| 269 | C2×Dic6 | — | 10 | 2 | no | — |
| 270 | C3×Q16 | — | 2 | 2 | no | — |
| 271 | C3×SD16 | — | 2 | 2 | no | — |
| 272 | C3×M16 | C22×D5 | 1 | 2 | yes | — |
| 273 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 274 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 275 | #216 | — | 5 | 2 | no | — |
| 276 | #216 | — | 10 | 2 | no | — |
| 277 | #216 | — | 10 | 2 | no | — |
| 278 | #216 | — | 10 | 2 | no | — |
| 279 | #215 | — | 5 | 2 | no | — |
| 280 | #214 | — | 5 | 2 | no | — |
| 281 | #214 | — | 10 | 2 | no | — |
| 282 | #214 | — | 10 | 2 | no | — |
| 283 | #214 | — | 10 | 2 | no | — |
| 284 | #214 | — | 10 | 2 | no | — |
| 285 | #213 | — | 5 | 2 | no | — |
| 286 | #213 | — | 10 | 2 | no | — |
| 287 | C4⋊Dic3 | — | 20 | 1 | no | — |
| 288 | #208 | — | 5 | 2 | no | — |
| 289 | #208 | — | 10 | 2 | no | — |
| 290 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 291 | C2×C3⋊C8 | — | 10 | 2 | no | — |
| 292 | Dic12 | — | 10 | 2 | no | — |
| 293 | #204 | — | 10 | 2 | no | — |
| 294 | ΓL(1,𝔽25) | — | 10 | 2 | no | — |
| 295 | D3×C8 | — | 10 | 2 | no | — |
| 296 | C23×C5 | — | 2 | 1 | no | — |
| 297 | C23×C5 | — | 4 | 1 | no | — |
| 298 | C5×Q8 | — | 2 | 2 | no | — |
| 299 | C5×Q8 | D3×D4 | 1 | 2 | yes | — |
| 300 | C5×D4 | — | 2 | 2 | no | — |
| 301 | C5×D4 | — | 2 | 2 | no | — |
| 302 | C5×D4 | — | 4 | 2 | no | — |
| 303 | C5×D4 | D3×D4 | 1 | 2 | yes | — |
| 304 | C2×C4×C5 | — | 2 | 2 | no | — |
| 305 | C2×C4×C5 | — | 2 | 1 | no | — |
| 306 | C2×C4×C5 | — | 2 | 1 | no | — |
| 307 | C2×C4×C5 | — | 4 | 1 | no | — |
| 308 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 309 | C22⋊D5 | — | 6 | 2 | no | — |
| 310 | C22⋊D5 | — | 12 | 2 | no | — |
| 311 | C2×Dic5 | — | 6 | 2 | no | — |
| 312 | C2×Dic5 | — | 12 | 2 | no | — |
| 313 | D20 | — | 3 | 2 | no | — |
| 314 | D20 | — | 12 | 1 | no | — |
| 315 | C4×D5 | — | 6 | 2 | no | — |
| 316 | C4×D5 | — | 12 | 2 | no | — |
| 317 | C4×D5 | — | 12 | 2 | no | — |
| 318 | Dic10 | — | 3 | 2 | no | — |
| 319 | Dic10 | — | 6 | 2 | no | — |
| 320 | Dic10 | — | 6 | 2 | no | — |
| 321 | Dic10 | — | 12 | 1 | no | — |
| 322 | Dic10 | — | 12 | 2 | no | — |
| 323 | C5×C8 | — | 2 | 2 | no | — |
| 324 | #168 | — | 3 | 2 | no | — |
| 325 | #168 | — | 3 | 2 | no | — |
| 326 | #168 | — | 6 | 2 | no | — |
| 327 | 2−1+4 | — | 15 | 2 | no | — |
| 328 | 2−1+4 | — | 15 | 1 | no | — |
| 329 | H(5,𝔽2) | C2×D15 | 1 | 1 | yes | characteristic |
| 330 | #137 | — | 15 | 2 | no | — |
| 331 | #137 | — | 15 | 2 | no | — |
| 332 | #137 | — | 30 | 2 | no | — |
| 333 | #137 | — | 30 | 2 | no | — |
| 334 | #137 | — | 30 | 2 | no | — |
| 335 | #137 | C2×D15 | 1 | 2 | yes | — |
| 336 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 337 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 338 | #135 | — | 15 | 2 | no | — |
| 339 | #135 | — | 30 | 2 | no | — |
| 340 | #135 | — | 30 | 2 | no | — |
| 341 | C2×Q16 | — | 15 | 2 | no | — |
| 342 | C2×Q16 | — | 30 | 2 | no | — |
| 343 | C2×SD16 | — | 15 | 2 | no | — |
| 344 | C2×SD16 | — | 30 | 2 | no | — |
| 345 | #131 | — | 15 | 2 | no | — |
| 346 | #131 | — | 15 | 2 | no | — |
| 347 | C4⋊Q8 | — | 15 | 1 | no | — |
| 348 | #124 | C2×D15 | 1 | 1 | yes | characteristic |
| 349 | #108 | — | 15 | 2 | no | — |
| 350 | #104 | — | 15 | 2 | no | — |
| 351 | #104 | C2×D15 | 1 | 2 | yes | — |
| 352 | #101 | — | 15 | 1 | no | — |
| 353 | #101 | — | 15 | 2 | no | — |
| 354 | #100 | C2×D15 | 1 | 1 | yes | characteristic |
| 355 | #97 | — | 15 | 1 | no | — |
| 356 | C2×C3×C5 | — | 2 | 1 | no | — |
| 357 | C2×C3×C5 | — | 4 | 2 | no | — |
| 358 | C2×C3×C5 | — | 8 | 1 | no | — |
| 359 | C2×C3×C5 | D42 | 1 | 1 | yes | characteristic |
| 360 | D15 | — | 4 | 2 | no | — |
| 361 | C23×C3 | — | 2 | 1 | no | — |
| 362 | C23×C3 | — | 4 | 1 | no | — |
| 363 | C3×Q8 | — | 2 | 2 | no | — |
| 364 | C3×Q8 | D4×D5 | 1 | 2 | yes | — |
| 365 | C3×D4 | — | 2 | 2 | no | — |
| 366 | C3×D4 | — | 2 | 2 | no | — |
| 367 | C3×D4 | — | 4 | 2 | no | — |
| 368 | C3×D4 | D4×D5 | 1 | 2 | yes | — |
| 369 | C2×C3×C4 | — | 2 | 2 | no | — |
| 370 | C2×C3×C4 | — | 2 | 1 | no | — |
| 371 | C2×C3×C4 | — | 2 | 1 | no | — |
| 372 | C2×C3×C4 | — | 4 | 1 | no | — |
| 373 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 374 | #67 | — | 10 | 2 | no | — |
| 375 | #67 | — | 20 | 2 | no | — |
| 376 | C2×Dic3 | — | 10 | 2 | no | — |
| 377 | C2×Dic3 | — | 20 | 2 | no | — |
| 378 | D12 | — | 5 | 2 | no | — |
| 379 | D12 | — | 20 | 1 | no | — |
| 380 | C4×D3 | — | 10 | 2 | no | — |
| 381 | C4×D3 | — | 20 | 2 | no | — |
| 382 | C4×D3 | — | 20 | 2 | no | — |
| 383 | Dic6 | — | 5 | 2 | no | — |
| 384 | Dic6 | — | 10 | 2 | no | — |
| 385 | Dic6 | — | 10 | 2 | no | — |
| 386 | Dic6 | — | 20 | 1 | no | — |
| 387 | Dic6 | — | 20 | 2 | no | — |
| 388 | C3×C8 | — | 2 | 2 | no | — |
| 389 | C3⋊C8 | — | 5 | 2 | no | — |
| 390 | C3⋊C8 | — | 5 | 2 | no | — |
| 391 | C3⋊C8 | — | 10 | 2 | no | — |
| 392 | C22×C5 | — | 2 | 2 | no | — |
| 393 | C22×C5 | — | 4 | 1 | no | — |
| 394 | C22×C5 | — | 8 | 1 | no | — |
| 395 | C22×C5 | — | 16 | 1 | no | — |
| 396 | C22×C5 | #1004 | 1 | 1 | yes | characteristic |
| 397 | C2×D5 | — | 6 | 2 | no | — |
| 398 | C4×C5 | — | 2 | 2 | no | — |
| 399 | C4×C5 | — | 4 | 1 | no | — |
| 400 | C4×C5 | — | 4 | 1 | no | — |
| 401 | C4×C5 | C2×D3×D4 | 1 | 2 | yes | — |
| 402 | Dic5 | — | 6 | 2 | no | — |
| 403 | Dic5 | — | 12 | 2 | no | — |
| 404 | #41 | — | 2 | 2 | no | — |
| 405 | #41 | — | 15 | 2 | no | — |
| 406 | #41 | — | 30 | 2 | no | — |
| 407 | #41 | — | 30 | 2 | no | — |
| 408 | #41 | — | 30 | 2 | no | — |
| 409 | #41 | — | 60 | 1 | no | — |
| 410 | #41 | — | 60 | 2 | no | — |
| 411 | #41 | C22×D15 | 1 | 2 | yes | — |
| 412 | C2×Q8 | — | 15 | 2 | no | — |
| 413 | C2×Q8 | — | 30 | 2 | no | — |
| 414 | C2×Q8 | — | 30 | 2 | no | — |
| 415 | C2×Q8 | — | 30 | 2 | no | — |
| 416 | C2×Q8 | C22×D15 | 1 | 1 | yes | characteristic |
| 417 | C2×D4 | — | 2 | 2 | no | — |
| 418 | C2×D4 | — | 4 | 1 | no | — |
| 419 | C2×D4 | C22×D15 | 1 | 1 | yes | characteristic |
| 420 | Q16 | — | 2 | 2 | no | — |
| 421 | Q16 | — | 15 | 2 | no | — |
| 422 | Q16 | — | 30 | 2 | no | — |
| 423 | Q16 | — | 30 | 2 | no | — |
| 424 | Q16 | — | 30 | 2 | no | — |
| 425 | Q16 | — | 30 | 2 | no | — |
| 426 | SD16 | — | 2 | 2 | no | — |
| 427 | SD16 | — | 15 | 2 | no | — |
| 428 | SD16 | — | 15 | 2 | no | — |
| 429 | SD16 | — | 30 | 2 | no | — |
| 430 | SD16 | — | 30 | 2 | no | — |
| 431 | SD16 | — | 30 | 2 | no | — |
| 432 | SD16 | — | 30 | 2 | no | — |
| 433 | SD16 | — | 30 | 2 | no | — |
| 434 | D8 | — | 15 | 2 | no | — |
| 435 | D8 | — | 30 | 2 | no | — |
| 436 | M16 | — | 15 | 2 | no | — |
| 437 | M16 | — | 30 | 2 | no | — |
| 438 | M16 | — | 30 | 2 | no | — |
| 439 | M16 | C22×D15 | 1 | 2 | yes | — |
| 440 | C2×C8 | — | 15 | 2 | no | — |
| 441 | C2×C8 | — | 30 | 2 | no | — |
| 442 | C2×C8 | — | 30 | 2 | no | — |
| 443 | C4⋊C4 | — | 60 | 1 | no | — |
| 444 | C22⋊C4 | — | 4 | 1 | no | — |
| 445 | C42 | C22×D15 | 1 | 1 | yes | characteristic |
| 446 | C3×C5 | #3289 | 1 | 1 | yes | characteristic, complemented, Hall |
| 447 | C22×C3 | — | 2 | 2 | no | — |
| 448 | C22×C3 | — | 4 | 1 | no | — |
| 449 | C22×C3 | — | 8 | 1 | no | — |
| 450 | C22×C3 | — | 16 | 1 | no | — |
| 451 | C22×C3 | #4144 | 1 | 1 | yes | characteristic |
| 452 | C2×D3 | — | 10 | 2 | no | — |
| 453 | C3×C4 | — | 2 | 2 | no | — |
| 454 | C3×C4 | — | 4 | 1 | no | — |
| 455 | C3×C4 | — | 4 | 1 | no | — |
| 456 | C3×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 457 | Dic3 | — | 10 | 2 | no | — |
| 458 | Dic3 | — | 20 | 2 | no | — |
| 459 | C2×C5 | — | 2 | 1 | no | — |
| 460 | C2×C5 | — | 4 | 2 | no | — |
| 461 | C2×C5 | — | 8 | 1 | no | — |
| 462 | C2×C5 | #5590 | 1 | 1 | yes | characteristic |
| 463 | D5 | — | 12 | 2 | no | — |
| 464 | C23 | — | 2 | 1 | no | — |
| 465 | C23 | — | 4 | 1 | no | — |
| 466 | Q8 | — | 2 | 2 | no | — |
| 467 | Q8 | — | 15 | 2 | no | — |
| 468 | Q8 | — | 30 | 2 | no | — |
| 469 | Q8 | — | 30 | 2 | no | — |
| 470 | Q8 | — | 60 | 2 | no | — |
| 471 | Q8 | — | 60 | 1 | no | — |
| 472 | Q8 | D4×D15 | 1 | 2 | yes | — |
| 473 | D4 | — | 2 | 2 | no | — |
| 474 | D4 | — | 2 | 2 | no | — |
| 475 | D4 | — | 4 | 2 | no | — |
| 476 | D4 | — | 15 | 2 | no | — |
| 477 | D4 | — | 30 | 2 | no | — |
| 478 | D4 | — | 60 | 1 | no | — |
| 479 | D4 | — | 60 | 2 | no | — |
| 480 | D4 | D4×D15 | 1 | 2 | yes | — |
| 481 | C2×C4 | — | 2 | 2 | no | — |
| 482 | C2×C4 | — | 2 | 1 | no | — |
| 483 | C2×C4 | — | 2 | 1 | no | — |
| 484 | C2×C4 | — | 4 | 1 | no | — |
| 485 | C2×C4 | — | 30 | 2 | no | — |
| 486 | C2×C4 | — | 30 | 2 | no | — |
| 487 | C2×C4 | — | 60 | 2 | no | — |
| 488 | C2×C4 | — | 60 | 2 | no | — |
| 489 | C2×C4 | — | 60 | 2 | no | — |
| 490 | C2×C4 | C23×D15 | 1 | 1 | yes | characteristic |
| 491 | C8 | — | 2 | 2 | no | — |
| 492 | C8 | — | 15 | 2 | no | — |
| 493 | C8 | — | 15 | 2 | no | — |
| 494 | C8 | — | 30 | 2 | no | — |
| 495 | C2×C3 | — | 2 | 1 | no | — |
| 496 | C2×C3 | — | 4 | 2 | no | — |
| 497 | C2×C3 | — | 8 | 1 | no | — |
| 498 | C2×C3 | #65924 | 1 | 1 | yes | characteristic |
| 499 | D3 | — | 20 | 2 | no | — |
| 500 | C5 | #80295 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 501 | C22 | — | 2 | 2 | no | — |
| 502 | C22 | — | 4 | 1 | no | — |
| 503 | C22 | — | 8 | 1 | no | — |
| 504 | C22 | — | 16 | 1 | no | — |
| 505 | C22 | — | 30 | 2 | no | — |
| 506 | C22 | #92095 | 1 | 1 | yes | characteristic |
| 507 | C4 | — | 2 | 2 | no | — |
| 508 | C4 | — | 4 | 1 | no | — |
| 509 | C4 | — | 4 | 1 | no | — |
| 510 | C4 | — | 30 | 2 | no | — |
| 511 | C4 | — | 60 | 2 | no | — |
| 512 | C4 | C2×D4×D15 | 1 | 2 | yes | — |
| 513 | C3 | #10612026 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 514 | C2 | — | 2 | 1 | no | — |
| 515 | C2 | — | 4 | 2 | no | — |
| 516 | C2 | — | 8 | 1 | no | — |
| 517 | C2 | — | 60 | 2 | no | — |
| 518 | C2 | #11756349 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11756595 | C2 | semidirect |
| 2. #11756538 | C2 | semidirect |
| 3. C3×C5×#455 | C2 | semidirect |
| 4. #11751305 | C2 | semidirect |
| 5. #11751163 | C2 | semidirect |
| 6. #11751161 | C2 | semidirect |
| 7. #11750927 | C2 | semidirect |
| 8. #11750924 | C2 | semidirect |
| 9. #11750849 | C2 | semidirect |
| 13. #92098 | C22 | semidirect |
| 21. C2×#6718 | C22 | semidirect |
| 30. #91798 | C22 | semidirect |
| 31. #91796 | C22 | semidirect |
| 32. #91758 | C22 | semidirect |
| 35. #91120 | C22 | semidirect |
| 36. #91108 | C22 | semidirect |
| 37. #91106 | C22 | semidirect |
| 38. #91089 | C22 | semidirect |
| 39. #91087 | C22 | semidirect |
| 43. C5×#455 | D3 | semidirect |
| 94. C3×#455 | D5 | semidirect |
| 239. #455 | D15 | semidirect |
| 446. C3×C5 | #3289 | semidirect |
| 500. C5 | #80295 | semidirect |
| 513. C3 | #10612026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756595 | 2 |
| #11756538 | 2 |
| C3×C5×#455 | 2 |
| #11751305 | 2 |
| #11751163 | 2 |
| #11751161 | 2 |
| #11750927 | 2 |
| #11750924 | 2 |
| #11750849 | 2 |
| #10612026 | 3 |
| #80295 | 5 |