Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #11753979 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11751290 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#5179 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#65468 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11745912 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11745910 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11745884 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10602315 | — | 3 | 1 | no | maximal, Hall |
| 9 | #92016 | — | 2 | 1 | no | — |
| 10 | C2×C3×C5×Q16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #91835 | — | 2 | 1 | no | — |
| 12 | C2×#6705 | C22 | 1 | 1 | yes | characteristic |
| 13 | C5×#904 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#4050 | C22 | 1 | 1 | yes | characteristic |
| 15 | #91297 | — | 2 | 1 | no | — |
| 16 | #91280 | — | 2 | 1 | no | — |
| 17 | #91278 | — | 2 | 1 | no | — |
| 18 | #91258 | — | 2 | 1 | no | — |
| 19 | #91257 | — | 2 | 1 | no | — |
| 20 | #91119 | — | 2 | 1 | no | — |
| 21 | #91101 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C5×#829 | — | 2 | 1 | no | — |
| 23 | C5×#828 | — | 2 | 1 | no | — |
| 24 | C5×#812 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3×#3961 | — | 2 | 1 | no | — |
| 26 | C3×#3960 | — | 2 | 1 | no | — |
| 27 | C3×#3944 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #71522 | — | 5 | 1 | no | maximal, Hall |
| 29 | #66102 | — | 3 | 1 | no | — |
| 30 | C5×#510 | — | 3 | 1 | no | — |
| 31 | #65478 | — | 3 | 1 | no | — |
| 32 | #65468 | D3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #64786 | — | 3 | 1 | no | — |
| 34 | #64738 | — | 3 | 1 | no | — |
| 35 | #64734 | — | 3 | 1 | no | — |
| 36 | C2×C3×C5×Q8 | — | 2 | 1 | no | — |
| 37 | C2×C4×D15 | D4 | 1 | 1 | yes | characteristic |
| 38 | C5×#235 | — | 2 | 1 | no | — |
| 39 | C3×#709 | — | 2 | 1 | no | — |
| 40 | #6790 | — | 4 | 1 | no | — |
| 41 | #6780 | — | 4 | 1 | no | — |
| 42 | #6777 | — | 2 | 1 | no | — |
| 43 | C4×D3×D5 | — | 4 | 1 | no | — |
| 44 | #6771 | — | 4 | 1 | no | — |
| 45 | D15⋊Q8 | — | 2 | 1 | no | — |
| 46 | #6768 | — | 2 | 1 | no | — |
| 47 | #6766 | — | 2 | 1 | no | — |
| 48 | C3×C5×Q16 | — | 2 | 1 | no | — |
| 49 | C3×C5×Q16 | — | 2 | 1 | no | — |
| 50 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 51 | #6714 | — | 4 | 1 | no | — |
| 52 | C4⋊Dic15 | — | 2 | 1 | no | — |
| 53 | #6712 | — | 4 | 1 | no | — |
| 54 | C2×C3⋊#168 | D4 | 1 | 1 | yes | characteristic |
| 55 | #6705 | — | 2 | 1 | no | — |
| 56 | #6705 | — | 2 | 1 | no | — |
| 57 | C5×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 58 | C5×D24 | D4 | 1 | 1 | yes | characteristic |
| 59 | C5×#204 | — | 2 | 1 | no | — |
| 60 | C3×Dic20 | D4 | 1 | 1 | yes | characteristic |
| 61 | C3×D40 | D4 | 1 | 1 | yes | characteristic |
| 62 | C3×#677 | — | 2 | 1 | no | — |
| 63 | #6661 | — | 2 | 1 | no | — |
| 64 | #6656 | — | 2 | 1 | no | — |
| 65 | #6655 | — | 2 | 1 | no | — |
| 66 | #6652 | — | 2 | 1 | no | — |
| 67 | C3×#672 | — | 2 | 1 | no | — |
| 68 | C5×C3⋊C16 | — | 2 | 1 | no | — |
| 69 | #5768 | — | 5 | 1 | no | — |
| 70 | C3×#510 | — | 5 | 1 | no | — |
| 71 | #5189 | — | 5 | 1 | no | — |
| 72 | #5179 | D5 | 1 | 1 | yes | characteristic, complemented |
| 73 | #4566 | — | 5 | 1 | no | — |
| 74 | #4518 | — | 5 | 1 | no | — |
| 75 | #4514 | — | 5 | 1 | no | — |
| 76 | D5×#41 | — | 6 | 1 | no | — |
| 77 | C5×#135 | — | 3 | 1 | no | — |
| 78 | C2×C5×Q16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 79 | #4096 | — | 6 | 1 | no | — |
| 80 | #4092 | — | 6 | 1 | no | — |
| 81 | #4064 | — | 6 | 1 | no | — |
| 82 | #4061 | — | 6 | 1 | no | — |
| 83 | #4060 | — | 6 | 1 | no | — |
| 84 | #4057 | — | 6 | 1 | no | — |
| 85 | #4050 | C2×D3 | 1 | 1 | yes | characteristic |
| 86 | C2×#676 | — | 3 | 1 | no | — |
| 87 | C5×Q32 | — | 6 | 1 | no | — |
| 88 | C5×SD32 | — | 6 | 1 | no | — |
| 89 | C5×M32 | — | 3 | 1 | no | — |
| 90 | #3967 | — | 6 | 1 | no | — |
| 91 | #3961 | — | 2 | 1 | no | — |
| 92 | #3960 | — | 2 | 1 | no | — |
| 93 | #3949 | — | 3 | 1 | no | — |
| 94 | #3944 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 95 | #2191 | — | 15 | 1 | no | Sylow |
| 96 | C22×D15 | D8 | 1 | 1 | yes | characteristic |
| 97 | C2×D3×D5 | — | 4 | 1 | no | — |
| 98 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 99 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 100 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 101 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×Dic15 | — | 4 | 1 | no | — |
| 103 | C2×Dic15 | D8 | 1 | 1 | yes | characteristic |
| 104 | C4×D15 | — | 2 | 1 | no | — |
| 105 | C4×D15 | — | 2 | 1 | no | — |
| 106 | C5×#67 | — | 4 | 1 | no | — |
| 107 | C5×D12 | — | 2 | 1 | no | — |
| 108 | C4×C5×D3 | — | 4 | 1 | no | — |
| 109 | C5×Dic6 | — | 2 | 1 | no | — |
| 110 | C3×C22⋊D5 | — | 4 | 1 | no | — |
| 111 | C3×D20 | — | 2 | 1 | no | — |
| 112 | C3×C4×D5 | — | 4 | 1 | no | — |
| 113 | C3×Dic10 | — | 2 | 1 | no | — |
| 114 | #1204 | — | 4 | 1 | no | — |
| 115 | #1203 | — | 4 | 1 | no | — |
| 116 | #1202 | — | 4 | 1 | no | — |
| 117 | #1201 | — | 4 | 1 | no | — |
| 118 | #1200 | — | 4 | 1 | no | — |
| 119 | D3×Dic5 | — | 4 | 1 | no | — |
| 120 | D5×Dic3 | — | 4 | 1 | no | — |
| 121 | C3×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C3×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C3⋊#168 | — | 2 | 1 | no | — |
| 124 | D3×#41 | — | 10 | 1 | no | — |
| 125 | C3×#135 | — | 5 | 1 | no | — |
| 126 | C2×C3×Q16 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 127 | #950 | — | 10 | 1 | no | — |
| 128 | #946 | — | 10 | 1 | no | — |
| 129 | #918 | — | 10 | 1 | no | — |
| 130 | #915 | — | 10 | 1 | no | — |
| 131 | #914 | — | 10 | 1 | no | — |
| 132 | #911 | — | 10 | 1 | no | — |
| 133 | #904 | C2×D5 | 1 | 1 | yes | characteristic |
| 134 | C2×ΓL(1,𝔽25) | — | 5 | 1 | no | — |
| 135 | C3×Q32 | — | 10 | 1 | no | — |
| 136 | C3×SD32 | — | 10 | 1 | no | — |
| 137 | C3×M32 | — | 5 | 1 | no | — |
| 138 | #835 | — | 10 | 1 | no | — |
| 139 | #829 | — | 2 | 1 | no | — |
| 140 | #828 | — | 2 | 1 | no | — |
| 141 | #817 | — | 5 | 1 | no | — |
| 142 | #812 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 143 | C5×#41 | — | 6 | 1 | no | — |
| 144 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 145 | #713 | — | 6 | 1 | no | — |
| 146 | Q8×D5 | — | 6 | 1 | no | — |
| 147 | #711 | — | 6 | 1 | no | — |
| 148 | #711 | — | 12 | 1 | no | — |
| 149 | D4×D5 | — | 6 | 1 | no | — |
| 150 | D4×D5 | — | 12 | 1 | no | — |
| 151 | #709 | — | 2 | 1 | no | — |
| 152 | #709 | — | 12 | 1 | no | — |
| 153 | C2×C4×D5 | — | 3 | 1 | no | — |
| 154 | C2×C4×D5 | — | 12 | 1 | no | — |
| 155 | C5×Q16 | — | 2 | 1 | no | — |
| 156 | C5×Q16 | — | 2 | 1 | no | — |
| 157 | C5×Q16 | — | 3 | 1 | no | — |
| 158 | C5×SD16 | — | 6 | 1 | no | — |
| 159 | C5×D8 | — | 3 | 1 | no | — |
| 160 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 161 | #689 | — | 6 | 1 | no | — |
| 162 | #688 | — | 6 | 1 | no | — |
| 163 | #687 | — | 6 | 1 | no | — |
| 164 | #686 | — | 6 | 1 | no | — |
| 165 | #685 | — | 12 | 1 | no | — |
| 166 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 167 | #683 | — | 12 | 1 | no | — |
| 168 | C2×#168 | — | 3 | 1 | no | — |
| 169 | Dic20 | #67 | 1 | 1 | yes | characteristic |
| 170 | D40 | #67 | 1 | 1 | yes | characteristic |
| 171 | #677 | — | 2 | 1 | no | — |
| 172 | #676 | — | 6 | 1 | no | — |
| 173 | #676 | — | 6 | 1 | no | — |
| 174 | C5×C16 | — | 6 | 1 | no | — |
| 175 | #672 | — | 2 | 1 | no | — |
| 176 | #575 | — | 15 | 1 | no | — |
| 177 | #510 | — | 3 | 1 | no | — |
| 178 | #510 | — | 5 | 1 | no | — |
| 179 | #470 | — | 15 | 1 | no | — |
| 180 | #360 | — | 15 | 1 | no | — |
| 181 | #360 | — | 15 | 1 | no | — |
| 182 | #349 | — | 15 | 1 | no | — |
| 183 | C22×C3×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 184 | C2×D15 | — | 2 | 1 | no | — |
| 185 | C2×D15 | — | 4 | 1 | no | — |
| 186 | C2×C5×D3 | — | 4 | 1 | no | — |
| 187 | C2×C3×D5 | — | 4 | 1 | no | — |
| 188 | D3×D5 | — | 8 | 2 | no | — |
| 189 | C3×C4×C5 | — | 8 | 1 | no | — |
| 190 | C3×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 191 | C3×C4×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 192 | Dic15 | — | 2 | 1 | no | — |
| 193 | Dic15 | — | 8 | 1 | no | — |
| 194 | C3×Dic5 | — | 4 | 1 | no | — |
| 195 | C5×Dic3 | — | 4 | 1 | no | — |
| 196 | C3×#41 | — | 10 | 1 | no | — |
| 197 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 198 | #239 | — | 10 | 1 | no | — |
| 199 | D3×Q8 | — | 10 | 1 | no | — |
| 200 | #237 | — | 10 | 1 | no | — |
| 201 | #237 | — | 20 | 1 | no | — |
| 202 | D3×D4 | — | 10 | 1 | no | — |
| 203 | D3×D4 | — | 20 | 1 | no | — |
| 204 | #235 | — | 2 | 1 | no | — |
| 205 | #235 | — | 20 | 1 | no | — |
| 206 | C2×C4×D3 | — | 5 | 1 | no | — |
| 207 | C2×C4×D3 | — | 20 | 1 | no | — |
| 208 | C3×Q16 | — | 2 | 1 | no | — |
| 209 | C3×Q16 | — | 2 | 1 | no | — |
| 210 | C3×Q16 | — | 5 | 1 | no | — |
| 211 | C3×SD16 | — | 10 | 1 | no | — |
| 212 | C3×D8 | — | 5 | 1 | no | — |
| 213 | C2×C3×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 214 | #216 | — | 10 | 1 | no | — |
| 215 | #215 | — | 10 | 1 | no | — |
| 216 | #214 | — | 10 | 1 | no | — |
| 217 | #213 | — | 10 | 1 | no | — |
| 218 | (C2×D3)⋊C4 | — | 20 | 1 | no | — |
| 219 | C4⋊Dic3 | — | 10 | 1 | no | — |
| 220 | Dic3⋊C4 | — | 20 | 1 | no | — |
| 221 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 222 | Dic12 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 223 | D24 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 224 | #204 | — | 2 | 1 | no | — |
| 225 | ΓL(1,𝔽25) | — | 10 | 1 | no | — |
| 226 | ΓL(1,𝔽25) | — | 10 | 1 | no | — |
| 227 | C3×C16 | — | 10 | 1 | no | — |
| 228 | C3⋊C16 | — | 2 | 1 | no | — |
| 229 | C22×D5 | — | 3 | 1 | no | — |
| 230 | C22×D5 | — | 12 | 1 | no | — |
| 231 | C5×Q8 | — | 4 | 1 | no | — |
| 232 | C5×Q8 | — | 4 | 1 | no | — |
| 233 | C5×Q8 | — | 6 | 1 | no | — |
| 234 | C5×D4 | — | 6 | 1 | no | — |
| 235 | C5×D4 | — | 12 | 1 | no | — |
| 236 | C2×C4×C5 | — | 4 | 1 | no | — |
| 237 | C2×C4×C5 | — | 12 | 1 | no | — |
| 238 | C2×C4×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 239 | C22⋊D5 | — | 4 | 1 | no | — |
| 240 | C22⋊D5 | — | 12 | 1 | no | — |
| 241 | C22⋊D5 | — | 12 | 1 | no | — |
| 242 | C2×Dic5 | — | 3 | 1 | no | — |
| 243 | C2×Dic5 | — | 12 | 1 | no | — |
| 244 | C2×Dic5 | — | 12 | 1 | no | — |
| 245 | D20 | — | 2 | 1 | no | — |
| 246 | D20 | — | 12 | 1 | no | — |
| 247 | C4×D5 | — | 4 | 1 | no | — |
| 248 | C4×D5 | — | 6 | 1 | no | — |
| 249 | C4×D5 | — | 6 | 1 | no | — |
| 250 | C4×D5 | — | 12 | 1 | no | — |
| 251 | C4×D5 | — | 12 | 1 | no | — |
| 252 | Dic10 | — | 2 | 1 | no | — |
| 253 | Dic10 | — | 12 | 1 | no | — |
| 254 | C5×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 255 | C5×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 256 | #168 | — | 6 | 1 | no | — |
| 257 | C2×#41 | — | 30 | 1 | no | — |
| 258 | #137 | — | 30 | 1 | no | — |
| 259 | #137 | — | 30 | 1 | no | — |
| 260 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 261 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 262 | #135 | — | 3 | 1 | no | — |
| 263 | #135 | — | 5 | 1 | no | — |
| 264 | #135 | — | 30 | 1 | no | — |
| 265 | C2×Q16 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 266 | C2×M16 | — | 15 | 1 | no | — |
| 267 | C22⋊Q8 | — | 30 | 1 | no | — |
| 268 | Q32 | — | 6 | 1 | no | — |
| 269 | Q32 | — | 10 | 1 | no | — |
| 270 | SD32 | — | 6 | 1 | no | — |
| 271 | SD32 | — | 10 | 1 | no | — |
| 272 | M32 | — | 3 | 1 | no | — |
| 273 | M32 | — | 5 | 1 | no | — |
| 274 | #106 | — | 15 | 1 | no | — |
| 275 | #103 | — | 30 | 1 | no | — |
| 276 | C2×C3×C5 | — | 2 | 1 | no | — |
| 277 | C2×C3×C5 | #447 | 1 | 1 | yes | characteristic |
| 278 | D15 | — | 4 | 1 | no | — |
| 279 | C3×D5 | — | 8 | 1 | no | — |
| 280 | C5×D3 | — | 8 | 1 | no | — |
| 281 | C22×D3 | — | 5 | 1 | no | — |
| 282 | C22×D3 | — | 20 | 1 | no | — |
| 283 | C3×Q8 | — | 4 | 1 | no | — |
| 284 | C3×Q8 | — | 4 | 1 | no | — |
| 285 | C3×Q8 | — | 10 | 1 | no | — |
| 286 | C3×D4 | — | 10 | 1 | no | — |
| 287 | C3×D4 | — | 20 | 1 | no | — |
| 288 | C2×C3×C4 | — | 4 | 1 | no | — |
| 289 | C2×C3×C4 | — | 20 | 1 | no | — |
| 290 | C2×C3×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 291 | #67 | — | 4 | 1 | no | — |
| 292 | #67 | — | 20 | 1 | no | — |
| 293 | #67 | — | 20 | 1 | no | — |
| 294 | C2×Dic3 | — | 5 | 1 | no | — |
| 295 | C2×Dic3 | — | 20 | 1 | no | — |
| 296 | C2×Dic3 | — | 20 | 1 | no | — |
| 297 | D12 | — | 2 | 1 | no | — |
| 298 | D12 | — | 20 | 1 | no | — |
| 299 | C4×D3 | — | 4 | 1 | no | — |
| 300 | C4×D3 | — | 10 | 1 | no | — |
| 301 | C4×D3 | — | 10 | 1 | no | — |
| 302 | C4×D3 | — | 20 | 1 | no | — |
| 303 | C4×D3 | — | 20 | 1 | no | — |
| 304 | Dic6 | — | 2 | 1 | no | — |
| 305 | Dic6 | — | 20 | 1 | no | — |
| 306 | C3×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 307 | C3×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 308 | C3⋊C8 | — | 10 | 1 | no | — |
| 309 | C22×C5 | — | 12 | 1 | no | — |
| 310 | C22×C5 | D3×D8 | 1 | 1 | yes | characteristic |
| 311 | C2×D5 | — | 4 | 1 | no | — |
| 312 | C2×D5 | — | 6 | 1 | no | — |
| 313 | C2×D5 | — | 12 | 1 | no | — |
| 314 | C2×D5 | — | 24 | 2 | no | — |
| 315 | C4×C5 | — | 8 | 1 | no | — |
| 316 | C4×C5 | — | 12 | 1 | no | — |
| 317 | C4×C5 | #911 | 1 | 1 | yes | characteristic |
| 318 | C4×C5 | #937 | 1 | 1 | yes | characteristic |
| 319 | Dic5 | — | 4 | 1 | no | — |
| 320 | Dic5 | — | 6 | 1 | no | — |
| 321 | Dic5 | — | 24 | 1 | no | — |
| 322 | #41 | — | 6 | 1 | no | — |
| 323 | #41 | — | 10 | 1 | no | — |
| 324 | #41 | — | 30 | 1 | no | — |
| 325 | #41 | — | 30 | 1 | no | — |
| 326 | #41 | — | 60 | 1 | no | — |
| 327 | #41 | — | 60 | 1 | no | — |
| 328 | C2×Q8 | — | 2 | 1 | no | — |
| 329 | C2×Q8 | — | 30 | 1 | no | — |
| 330 | C2×D4 | — | 30 | 1 | no | — |
| 331 | C2×D4 | — | 60 | 1 | no | — |
| 332 | C22×C4 | — | 15 | 1 | no | — |
| 333 | C22×C4 | — | 60 | 1 | no | — |
| 334 | Q16 | — | 2 | 1 | no | — |
| 335 | Q16 | — | 2 | 1 | no | — |
| 336 | Q16 | — | 3 | 1 | no | — |
| 337 | Q16 | — | 5 | 1 | no | — |
| 338 | Q16 | — | 30 | 1 | no | — |
| 339 | SD16 | — | 6 | 1 | no | — |
| 340 | SD16 | — | 10 | 1 | no | — |
| 341 | SD16 | — | 30 | 1 | no | — |
| 342 | SD16 | — | 30 | 1 | no | — |
| 343 | D8 | — | 3 | 1 | no | — |
| 344 | D8 | — | 5 | 1 | no | — |
| 345 | D8 | — | 30 | 1 | no | — |
| 346 | M16 | — | 30 | 1 | no | — |
| 347 | M16 | — | 30 | 1 | no | — |
| 348 | C2×C8 | — | 15 | 1 | no | — |
| 349 | C2×C8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 350 | C4⋊C4 | — | 30 | 1 | no | — |
| 351 | C4⋊C4 | — | 60 | 1 | no | — |
| 352 | C22⋊C4 | — | 60 | 1 | no | — |
| 353 | C16 | — | 6 | 1 | no | — |
| 354 | C16 | — | 10 | 1 | no | — |
| 355 | C3×C5 | #2191 | 1 | 1 | yes | characteristic, complemented, Hall |
| 356 | C22×C3 | — | 20 | 1 | no | — |
| 357 | C22×C3 | D5×D8 | 1 | 1 | yes | characteristic |
| 358 | C2×D3 | — | 4 | 1 | no | — |
| 359 | C2×D3 | — | 10 | 1 | no | — |
| 360 | C2×D3 | — | 20 | 1 | no | — |
| 361 | C2×D3 | — | 40 | 2 | no | — |
| 362 | C3×C4 | — | 8 | 1 | no | — |
| 363 | C3×C4 | — | 20 | 1 | no | — |
| 364 | C3×C4 | #4057 | 1 | 1 | yes | characteristic |
| 365 | C3×C4 | #4083 | 1 | 1 | yes | characteristic |
| 366 | Dic3 | — | 4 | 1 | no | — |
| 367 | Dic3 | — | 10 | 1 | no | — |
| 368 | Dic3 | — | 40 | 1 | no | — |
| 369 | C2×C5 | — | 2 | 1 | no | — |
| 370 | C2×C5 | — | 24 | 1 | no | — |
| 371 | C2×C5 | #5156 | 1 | 1 | yes | characteristic |
| 372 | D5 | — | 8 | 1 | no | — |
| 373 | D5 | — | 12 | 1 | no | — |
| 374 | C23 | — | 15 | 1 | no | — |
| 375 | C23 | — | 60 | 1 | no | — |
| 376 | Q8 | — | 4 | 1 | no | — |
| 377 | Q8 | — | 4 | 1 | no | — |
| 378 | Q8 | — | 6 | 1 | no | — |
| 379 | Q8 | — | 10 | 1 | no | — |
| 380 | Q8 | — | 60 | 1 | no | — |
| 381 | D4 | — | 6 | 1 | no | — |
| 382 | D4 | — | 10 | 1 | no | — |
| 383 | D4 | — | 12 | 1 | no | — |
| 384 | D4 | — | 20 | 1 | no | — |
| 385 | D4 | — | 60 | 1 | no | — |
| 386 | D4 | — | 60 | 1 | no | — |
| 387 | D4 | — | 60 | 1 | no | — |
| 388 | C2×C4 | — | 4 | 1 | no | — |
| 389 | C2×C4 | — | 12 | 1 | no | — |
| 390 | C2×C4 | — | 15 | 1 | no | — |
| 391 | C2×C4 | — | 20 | 1 | no | — |
| 392 | C2×C4 | — | 30 | 1 | no | — |
| 393 | C2×C4 | — | 30 | 1 | no | — |
| 394 | C2×C4 | — | 60 | 1 | no | — |
| 395 | C2×C4 | — | 60 | 1 | no | — |
| 396 | C2×C4 | — | 60 | 1 | no | — |
| 397 | C2×C4 | — | 60 | 1 | no | — |
| 398 | C2×C4 | #6790 | 1 | 1 | yes | characteristic |
| 399 | C8 | — | 30 | 1 | no | — |
| 400 | C8 | D5×#67 | 1 | 1 | yes | characteristic |
| 401 | C8 | D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 402 | C2×C3 | — | 2 | 1 | no | — |
| 403 | C2×C3 | — | 40 | 1 | no | — |
| 404 | C2×C3 | #65445 | 1 | 1 | yes | characteristic |
| 405 | D3 | — | 8 | 1 | no | — |
| 406 | D3 | — | 20 | 1 | no | — |
| 407 | C5 | #71522 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 408 | C22 | — | 12 | 1 | no | — |
| 409 | C22 | — | 20 | 1 | no | — |
| 410 | C22 | — | 30 | 1 | no | — |
| 411 | C22 | — | 60 | 1 | no | — |
| 412 | C22 | — | 120 | 2 | no | — |
| 413 | C22 | #91481 | 1 | 1 | yes | characteristic |
| 414 | C4 | — | 8 | 1 | no | — |
| 415 | C4 | — | 12 | 1 | no | — |
| 416 | C4 | — | 20 | 1 | no | — |
| 417 | C4 | — | 30 | 1 | no | — |
| 418 | C4 | — | 120 | 1 | no | — |
| 419 | C4 | #91482 | 1 | 1 | yes | characteristic |
| 420 | C4 | #91577 | 1 | 1 | yes | characteristic |
| 421 | C3 | #10602315 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 422 | C2 | — | 2 | 1 | no | — |
| 423 | C2 | — | 24 | 1 | no | — |
| 424 | C2 | — | 40 | 1 | no | — |
| 425 | C2 | — | 60 | 1 | no | — |
| 426 | C2 | #11749153 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11751290 | C2 | semidirect |
| 3. C5×#5179 | C2 | semidirect |
| 4. C3×#65468 | C2 | semidirect |
| 5. #11745912 | C2 | semidirect |
| 6. #11745910 | C2 | semidirect |
| 7. #11745884 | C2 | semidirect |
| 10. C2×C3×C5×Q16 | C22 | semidirect |
| 21. #91101 | C22 | semidirect |
| 24. C5×#812 | C22 | semidirect |
| 27. C3×#3944 | C22 | semidirect |
| 32. #65468 | D3 | semidirect |
| 72. #5179 | D5 | semidirect |
| 78. C2×C5×Q16 | C2×D3 | semidirect |
| 94. #3944 | C2×D3 | semidirect |
| 126. C2×C3×Q16 | C2×D5 | semidirect |
| 142. #812 | C2×D5 | semidirect |
| 265. C2×Q16 | D3×D5 | semidirect |
| 355. C3×C5 | #2191 | semidirect |
| 407. C5 | #71522 | semidirect |
| 421. C3 | #10602315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753979 | 2 |
| #11751290 | 2 |
| C5×#5179 | 2 |
| C3×#65468 | 2 |
| #11745912 | 2 |
| #11745910 | 2 |
| #11745884 | 2 |
| #10602315 | 3 |
| #71522 | 5 |