Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 75 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×#5912 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | A4×#681 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×A4⋊#168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11751571 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | S4×#168 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10614649 | — | 3 | 1 | no | maximal, Hall |
| 7 | C2×C4×C5×A4 | C22 | 1 | 1 | yes | characteristic |
| 8 | C5×GL(2,ℤ/4) | C4 | 1 | 2 | yes | — |
| 9 | C5×C4⋊S4 | C4 | 1 | 1 | yes | characteristic |
| 10 | C4×C5×S4 | C22 | 1 | 2 | yes | — |
| 11 | C5×A4⋊Q8 | C4 | 1 | 1 | yes | characteristic |
| 12 | #91288 | — | 4 | 1 | no | maximal |
| 13 | A4×#168 | C22 | 1 | 2 | yes | — |
| 14 | A4⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 15 | A4⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 16 | #85442 | — | 5 | 1 | no | maximal, Hall |
| 17 | C5×#525 | — | 3 | 1 | no | — |
| 18 | C2×#4094 | — | 3 | 1 | no | — |
| 19 | C22×#681 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | #65523 | — | 3 | 1 | no | — |
| 21 | C2×C22⋊#168 | — | 3 | 1 | no | — |
| 22 | #65301 | — | 3 | 2 | no | — |
| 23 | #65300 | — | 3 | 2 | no | — |
| 24 | #65300 | — | 3 | 2 | no | — |
| 25 | D4×#168 | — | 3 | 2 | no | — |
| 26 | #65288 | — | 3 | 1 | no | — |
| 27 | #65286 | — | 3 | 1 | no | — |
| 28 | C22×C5×A4 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C2×C5×S4 | C2×C4 | 1 | 2 | yes | — |
| 30 | C5×#235 | — | 4 | 1 | no | — |
| 31 | C4×C5×A4 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 33 | C5×SL(2,ℤ/4) | C2×C4 | 1 | 2 | yes | — |
| 34 | C2×C3⋊#168 | — | 4 | 1 | no | — |
| 35 | C3×#681 | — | 4 | 1 | no | — |
| 36 | #6650 | — | 4 | 2 | no | — |
| 37 | D3×#168 | — | 4 | 2 | no | — |
| 38 | #5912 | D5 | 1 | 1 | yes | characteristic |
| 39 | A4×M16 | — | 5 | 1 | no | — |
| 40 | C2×A4⋊C8 | — | 5 | 1 | no | — |
| 41 | #5400 | — | 5 | 2 | no | — |
| 42 | C8×S4 | — | 5 | 2 | no | — |
| 43 | C2×C5×#41 | — | 3 | 1 | no | — |
| 44 | C23×C4×C5 | C2×D3 | 1 | 1 | yes | characteristic |
| 45 | C5×#123 | — | 3 | 2 | no | — |
| 46 | C5×C22⋊Q8 | — | 3 | 1 | no | — |
| 47 | C5×C22⋊Q8 | — | 3 | 1 | no | — |
| 48 | C5×#121 | — | 3 | 1 | no | — |
| 49 | C5×#121 | — | 3 | 1 | no | — |
| 50 | C5×#120 | — | 3 | 2 | no | — |
| 51 | C4×C5×D4 | — | 3 | 2 | no | — |
| 52 | C4×C5×D4 | — | 3 | 2 | no | — |
| 53 | C5×#117 | — | 3 | 1 | no | — |
| 54 | #4094 | — | 6 | 1 | no | — |
| 55 | #4094 | — | 6 | 2 | no | — |
| 56 | #4094 | — | 6 | 1 | no | — |
| 57 | C2×#681 | — | 3 | 1 | no | — |
| 58 | C2×#681 | — | 3 | 1 | no | — |
| 59 | C2×#681 | — | 3 | 2 | no | — |
| 60 | C2×#681 | — | 3 | 2 | no | — |
| 61 | C22×#168 | — | 3 | 1 | no | — |
| 62 | C22×#168 | — | 3 | 1 | no | — |
| 63 | C22×#168 | — | 3 | 2 | no | — |
| 64 | C22×#168 | C2×D3 | 1 | 2 | yes | — |
| 65 | C22⋊#168 | — | 3 | 2 | no | — |
| 66 | C22⋊#168 | — | 3 | 1 | no | — |
| 67 | C22⋊#168 | — | 3 | 2 | no | — |
| 68 | C22⋊#168 | — | 3 | 1 | no | — |
| 69 | C22⋊#168 | — | 3 | 1 | no | — |
| 70 | C22⋊#168 | — | 3 | 1 | no | — |
| 71 | C4⋊#168 | — | 3 | 2 | no | — |
| 72 | C4⋊#168 | — | 3 | 2 | no | — |
| 73 | #3935 | — | 3 | 2 | no | — |
| 74 | C4×#168 | — | 3 | 2 | no | — |
| 75 | #2933 | — | 15 | 1 | no | Sylow |
| 76 | C2×C5×A4 | — | 2 | 1 | no | — |
| 77 | C2×C5×A4 | C22×C4 | 1 | 1 | yes | characteristic |
| 78 | C5×S4 | — | 2 | 2 | no | — |
| 79 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 80 | C5×#67 | — | 4 | 2 | no | — |
| 81 | C5×D12 | — | 4 | 1 | no | — |
| 82 | C4×C5×D3 | — | 4 | 2 | no | — |
| 83 | C5×Dic6 | — | 4 | 1 | no | — |
| 84 | C3⋊#168 | — | 4 | 1 | no | — |
| 85 | C3⋊#168 | — | 4 | 1 | no | — |
| 86 | C3×#168 | — | 4 | 2 | no | — |
| 87 | C2×C4×A4 | C2×D5 | 1 | 1 | yes | characteristic |
| 88 | GL(2,ℤ/4) | Dic5 | 1 | 2 | yes | — |
| 89 | C4⋊S4 | Dic5 | 1 | 1 | yes | characteristic |
| 90 | C4×S4 | C2×D5 | 1 | 2 | yes | — |
| 91 | A4⋊Q8 | Dic5 | 1 | 1 | yes | characteristic |
| 92 | #907 | — | 20 | 1 | no | — |
| 93 | C8×A4 | — | 5 | 2 | no | — |
| 94 | A4⋊C8 | — | 5 | 1 | no | — |
| 95 | A4⋊C8 | — | 5 | 1 | no | — |
| 96 | C24×C5 | C4×D3 | 1 | 1 | yes | characteristic |
| 97 | C5×#41 | — | 6 | 1 | no | — |
| 98 | C5×#41 | — | 6 | 1 | no | — |
| 99 | C5×#41 | — | 6 | 1 | no | — |
| 100 | C5×#41 | — | 6 | 1 | no | — |
| 101 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 102 | C2×C5×D4 | — | 3 | 2 | no | — |
| 103 | C2×C5×D4 | — | 3 | 1 | no | — |
| 104 | C2×C5×D4 | — | 3 | 2 | no | — |
| 105 | C2×C5×D4 | — | 3 | 2 | no | — |
| 106 | C22×C4×C5 | — | 3 | 1 | no | — |
| 107 | C22×C4×C5 | — | 3 | 1 | no | — |
| 108 | C22×C4×C5 | — | 3 | 1 | no | — |
| 109 | C22×C4×C5 | — | 3 | 1 | no | — |
| 110 | C22×C4×C5 | — | 3 | 2 | no | — |
| 111 | C22×C4×C5 | C4×D3 | 1 | 1 | yes | characteristic |
| 112 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 113 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 114 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 115 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 116 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 117 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 118 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 119 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 120 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 121 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 122 | C42×C5 | — | 3 | 2 | no | — |
| 123 | #681 | — | 3 | 1 | no | — |
| 124 | #681 | — | 3 | 2 | no | — |
| 125 | #681 | — | 6 | 1 | no | — |
| 126 | #681 | — | 6 | 2 | no | — |
| 127 | #681 | — | 6 | 2 | no | — |
| 128 | #681 | S4 | 1 | 1 | yes | characteristic, complemented |
| 129 | C2×#168 | — | 3 | 2 | no | — |
| 130 | C2×#168 | — | 3 | 2 | no | — |
| 131 | C2×#168 | — | 3 | 1 | no | — |
| 132 | C2×#168 | — | 3 | 1 | no | — |
| 133 | C2×#168 | — | 3 | 1 | no | — |
| 134 | C2×#168 | — | 3 | 1 | no | — |
| 135 | C2×#168 | — | 6 | 2 | no | — |
| 136 | C2×#168 | — | 6 | 1 | no | — |
| 137 | C2×#168 | — | 6 | 1 | no | — |
| 138 | C2×#168 | — | 6 | 1 | no | — |
| 139 | C2×#168 | — | 6 | 1 | no | — |
| 140 | C2×#168 | — | 6 | 2 | no | — |
| 141 | C2×#131 | — | 15 | 1 | no | — |
| 142 | C22×M16 | — | 5 | 1 | no | — |
| 143 | #525 | — | 3 | 1 | no | — |
| 144 | #436 | — | 15 | 2 | no | — |
| 145 | #435 | — | 15 | 2 | no | — |
| 146 | #435 | — | 15 | 2 | no | — |
| 147 | C8×D4 | — | 15 | 2 | no | — |
| 148 | #424 | — | 15 | 1 | no | — |
| 149 | #408 | — | 15 | 1 | no | — |
| 150 | C2×C22⋊C8 | — | 15 | 1 | no | — |
| 151 | #405 | — | 15 | 1 | no | — |
| 152 | C22×C3×C5 | — | 4 | 1 | no | — |
| 153 | C2×C5×D3 | — | 4 | 2 | no | — |
| 154 | C5×A4 | #131 | 1 | 1 | yes | characteristic, complemented |
| 155 | C3×C4×C5 | — | 4 | 1 | no | — |
| 156 | C3×C4×C5 | — | 4 | 1 | no | — |
| 157 | C5×Dic3 | — | 4 | 2 | no | — |
| 158 | C22×A4 | C2×Dic5 | 1 | 1 | yes | characteristic |
| 159 | C2×S4 | C2×Dic5 | 1 | 2 | yes | — |
| 160 | #235 | — | 4 | 1 | no | — |
| 161 | C4×A4 | C2×Dic5 | 1 | 1 | yes | characteristic |
| 162 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 163 | SL(2,ℤ/4) | C2×Dic5 | 1 | 2 | yes | — |
| 164 | C3×M16 | — | 20 | 1 | no | — |
| 165 | C2×C3⋊C8 | — | 20 | 1 | no | — |
| 166 | ΓL(1,𝔽25) | — | 20 | 2 | no | — |
| 167 | D3×C8 | — | 20 | 2 | no | — |
| 168 | C23×C5 | — | 2 | 1 | no | — |
| 169 | C23×C5 | — | 3 | 1 | no | — |
| 170 | C23×C5 | — | 3 | 1 | no | — |
| 171 | C23×C5 | — | 3 | 2 | no | — |
| 172 | C23×C5 | — | 6 | 1 | no | — |
| 173 | C23×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 174 | C5×Q8 | — | 6 | 1 | no | — |
| 175 | C5×Q8 | — | 6 | 1 | no | — |
| 176 | C5×D4 | — | 6 | 1 | no | — |
| 177 | C5×D4 | — | 6 | 2 | no | — |
| 178 | C5×D4 | — | 6 | 2 | no | — |
| 179 | C5×D4 | — | 6 | 2 | no | — |
| 180 | C5×D4 | — | 6 | 2 | no | — |
| 181 | C5×D4 | — | 6 | 1 | no | — |
| 182 | C5×D4 | — | 12 | 2 | no | — |
| 183 | C2×C4×C5 | — | 3 | 1 | no | — |
| 184 | C2×C4×C5 | — | 3 | 1 | no | — |
| 185 | C2×C4×C5 | — | 3 | 1 | no | — |
| 186 | C2×C4×C5 | — | 3 | 1 | no | — |
| 187 | C2×C4×C5 | — | 3 | 1 | no | — |
| 188 | C2×C4×C5 | — | 3 | 1 | no | — |
| 189 | C2×C4×C5 | — | 3 | 1 | no | — |
| 190 | C2×C4×C5 | — | 3 | 2 | no | — |
| 191 | C2×C4×C5 | — | 3 | 2 | no | — |
| 192 | C2×C4×C5 | — | 3 | 2 | no | — |
| 193 | C2×C4×C5 | — | 6 | 1 | no | — |
| 194 | C2×C4×C5 | — | 6 | 2 | no | — |
| 195 | C2×C4×C5 | — | 6 | 2 | no | — |
| 196 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 197 | #168 | — | 3 | 2 | no | — |
| 198 | #168 | — | 6 | 1 | no | — |
| 199 | #168 | — | 6 | 1 | no | — |
| 200 | #168 | — | 6 | 1 | no | — |
| 201 | #168 | — | 6 | 1 | no | — |
| 202 | #168 | C2×S4 | 1 | 2 | yes | — |
| 203 | C2×#41 | — | 3 | 1 | no | — |
| 204 | C23×C4 | D3×D5 | 1 | 1 | yes | characteristic |
| 205 | #131 | — | 30 | 1 | no | — |
| 206 | #131 | — | 30 | 2 | no | — |
| 207 | #131 | — | 30 | 1 | no | — |
| 208 | C2×M16 | — | 15 | 1 | no | — |
| 209 | C2×M16 | — | 15 | 1 | no | — |
| 210 | C2×M16 | — | 15 | 2 | no | — |
| 211 | C2×M16 | — | 15 | 2 | no | — |
| 212 | C22×C8 | — | 5 | 2 | no | — |
| 213 | C22×C8 | — | 15 | 1 | no | — |
| 214 | C22×C8 | — | 15 | 2 | no | — |
| 215 | C22×C8 | — | 15 | 1 | no | — |
| 216 | #123 | — | 3 | 2 | no | — |
| 217 | C22⋊Q8 | — | 3 | 1 | no | — |
| 218 | C22⋊Q8 | — | 3 | 1 | no | — |
| 219 | #121 | — | 3 | 1 | no | — |
| 220 | #121 | — | 3 | 1 | no | — |
| 221 | #120 | — | 3 | 2 | no | — |
| 222 | C4×D4 | — | 3 | 2 | no | — |
| 223 | C4×D4 | — | 3 | 2 | no | — |
| 224 | #117 | — | 3 | 1 | no | — |
| 225 | C4⋊C8 | — | 15 | 2 | no | — |
| 226 | C4⋊C8 | — | 15 | 2 | no | — |
| 227 | C22⋊C8 | — | 15 | 1 | no | — |
| 228 | C22⋊C8 | — | 15 | 1 | no | — |
| 229 | C22⋊C8 | — | 15 | 2 | no | — |
| 230 | C22⋊C8 | — | 15 | 2 | no | — |
| 231 | C22⋊C8 | — | 15 | 1 | no | — |
| 232 | C22⋊C8 | — | 15 | 1 | no | — |
| 233 | #97 | — | 15 | 2 | no | — |
| 234 | C4×C8 | — | 15 | 2 | no | — |
| 235 | C2×C3×C5 | — | 4 | 1 | no | — |
| 236 | C2×C3×C5 | — | 8 | 1 | no | — |
| 237 | C5×D3 | — | 8 | 2 | no | — |
| 238 | C2×A4 | — | 2 | 1 | no | — |
| 239 | C2×A4 | C22×Dic5 | 1 | 1 | yes | characteristic |
| 240 | S4 | — | 2 | 2 | no | — |
| 241 | C2×C3×C4 | — | 4 | 1 | no | — |
| 242 | #67 | — | 4 | 2 | no | — |
| 243 | D12 | — | 4 | 1 | no | — |
| 244 | C4×D3 | — | 4 | 2 | no | — |
| 245 | Dic6 | — | 4 | 1 | no | — |
| 246 | C3×C8 | — | 20 | 2 | no | — |
| 247 | C3⋊C8 | — | 20 | 1 | no | — |
| 248 | C3⋊C8 | — | 20 | 1 | no | — |
| 249 | C22×C5 | — | 3 | 1 | no | — |
| 250 | C22×C5 | — | 3 | 1 | no | — |
| 251 | C22×C5 | — | 3 | 1 | no | — |
| 252 | C22×C5 | — | 6 | 1 | no | — |
| 253 | C22×C5 | — | 6 | 1 | no | — |
| 254 | C22×C5 | — | 6 | 1 | no | — |
| 255 | C22×C5 | — | 6 | 1 | no | — |
| 256 | C22×C5 | — | 6 | 2 | no | — |
| 257 | C22×C5 | — | 6 | 2 | no | — |
| 258 | C22×C5 | — | 6 | 2 | no | — |
| 259 | C22×C5 | #907 | 1 | 1 | yes | characteristic, complemented |
| 260 | C22×C5 | C4×S4 | 1 | 1 | yes | characteristic |
| 261 | C4×C5 | — | 3 | 1 | no | — |
| 262 | C4×C5 | — | 3 | 1 | no | — |
| 263 | C4×C5 | — | 6 | 2 | no | — |
| 264 | C4×C5 | — | 6 | 2 | no | — |
| 265 | C4×C5 | — | 6 | 2 | no | — |
| 266 | C4×C5 | C4×S4 | 1 | 1 | yes | characteristic |
| 267 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 268 | C24 | D3×Dic5 | 1 | 1 | yes | characteristic |
| 269 | #41 | — | 6 | 1 | no | — |
| 270 | #41 | — | 6 | 1 | no | — |
| 271 | #41 | — | 6 | 1 | no | — |
| 272 | #41 | — | 6 | 1 | no | — |
| 273 | C2×Q8 | — | 3 | 1 | no | — |
| 274 | C2×D4 | — | 3 | 2 | no | — |
| 275 | C2×D4 | — | 3 | 1 | no | — |
| 276 | C2×D4 | — | 3 | 2 | no | — |
| 277 | C2×D4 | — | 3 | 2 | no | — |
| 278 | C22×C4 | — | 3 | 1 | no | — |
| 279 | C22×C4 | — | 3 | 1 | no | — |
| 280 | C22×C4 | — | 3 | 1 | no | — |
| 281 | C22×C4 | — | 3 | 1 | no | — |
| 282 | C22×C4 | — | 3 | 2 | no | — |
| 283 | C22×C4 | D3×Dic5 | 1 | 1 | yes | characteristic |
| 284 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 285 | M16 | — | 5 | 1 | no | — |
| 286 | M16 | — | 15 | 2 | no | — |
| 287 | M16 | — | 15 | 1 | no | — |
| 288 | M16 | — | 30 | 2 | no | — |
| 289 | M16 | — | 30 | 1 | no | — |
| 290 | M16 | — | 30 | 2 | no | — |
| 291 | C2×C8 | — | 15 | 2 | no | — |
| 292 | C2×C8 | — | 15 | 2 | no | — |
| 293 | C2×C8 | — | 15 | 1 | no | — |
| 294 | C2×C8 | — | 15 | 1 | no | — |
| 295 | C2×C8 | — | 15 | 1 | no | — |
| 296 | C2×C8 | — | 15 | 1 | no | — |
| 297 | C2×C8 | — | 30 | 2 | no | — |
| 298 | C2×C8 | — | 30 | 2 | no | — |
| 299 | C2×C8 | — | 30 | 1 | no | — |
| 300 | C2×C8 | — | 30 | 1 | no | — |
| 301 | C2×C8 | — | 30 | 1 | no | — |
| 302 | C2×C8 | — | 30 | 1 | no | — |
| 303 | C4⋊C4 | — | 3 | 1 | no | — |
| 304 | C4⋊C4 | — | 3 | 1 | no | — |
| 305 | C4⋊C4 | — | 3 | 2 | no | — |
| 306 | C4⋊C4 | — | 3 | 2 | no | — |
| 307 | C22⋊C4 | — | 3 | 2 | no | — |
| 308 | C22⋊C4 | — | 3 | 2 | no | — |
| 309 | C22⋊C4 | — | 3 | 2 | no | — |
| 310 | C22⋊C4 | — | 3 | 2 | no | — |
| 311 | C22⋊C4 | — | 3 | 2 | no | — |
| 312 | C42 | — | 3 | 2 | no | — |
| 313 | C3×C5 | — | 4 | 1 | no | Hall |
| 314 | C22×C3 | — | 4 | 1 | no | — |
| 315 | C2×D3 | — | 4 | 2 | no | — |
| 316 | A4 | #4094 | 1 | 1 | yes | characteristic, complemented |
| 317 | C3×C4 | — | 4 | 1 | no | — |
| 318 | C3×C4 | — | 4 | 1 | no | — |
| 319 | Dic3 | — | 4 | 2 | no | — |
| 320 | C2×C5 | — | 2 | 1 | no | — |
| 321 | C2×C5 | — | 3 | 1 | no | — |
| 322 | C2×C5 | — | 3 | 1 | no | — |
| 323 | C2×C5 | — | 6 | 1 | no | — |
| 324 | C2×C5 | — | 12 | 2 | no | — |
| 325 | C2×C5 | C2×C4×S4 | 1 | 1 | yes | characteristic |
| 326 | C23 | — | 2 | 1 | no | — |
| 327 | C23 | — | 3 | 1 | no | — |
| 328 | C23 | — | 3 | 1 | no | — |
| 329 | C23 | — | 3 | 2 | no | — |
| 330 | C23 | — | 6 | 1 | no | — |
| 331 | C23 | C2×D3×Dic5 | 1 | 1 | yes | characteristic |
| 332 | Q8 | — | 6 | 1 | no | — |
| 333 | Q8 | — | 6 | 1 | no | — |
| 334 | D4 | — | 6 | 1 | no | — |
| 335 | D4 | — | 6 | 2 | no | — |
| 336 | D4 | — | 6 | 2 | no | — |
| 337 | D4 | — | 6 | 2 | no | — |
| 338 | D4 | — | 6 | 2 | no | — |
| 339 | D4 | — | 6 | 1 | no | — |
| 340 | D4 | — | 12 | 2 | no | — |
| 341 | C2×C4 | — | 3 | 1 | no | — |
| 342 | C2×C4 | — | 3 | 1 | no | — |
| 343 | C2×C4 | — | 3 | 1 | no | — |
| 344 | C2×C4 | — | 3 | 1 | no | — |
| 345 | C2×C4 | — | 3 | 1 | no | — |
| 346 | C2×C4 | — | 3 | 1 | no | — |
| 347 | C2×C4 | — | 3 | 1 | no | — |
| 348 | C2×C4 | — | 3 | 2 | no | — |
| 349 | C2×C4 | — | 3 | 2 | no | — |
| 350 | C2×C4 | — | 3 | 2 | no | — |
| 351 | C2×C4 | — | 6 | 1 | no | — |
| 352 | C2×C4 | — | 6 | 2 | no | — |
| 353 | C2×C4 | — | 6 | 2 | no | — |
| 354 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 355 | C8 | — | 5 | 2 | no | — |
| 356 | C8 | — | 15 | 2 | no | — |
| 357 | C8 | — | 30 | 1 | no | — |
| 358 | C8 | — | 30 | 1 | no | — |
| 359 | C8 | — | 30 | 1 | no | — |
| 360 | C8 | — | 30 | 1 | no | — |
| 361 | C2×C3 | — | 4 | 1 | no | — |
| 362 | C2×C3 | — | 8 | 1 | no | — |
| 363 | D3 | — | 8 | 2 | no | — |
| 364 | C5 | #85442 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 365 | C22 | — | 3 | 1 | no | — |
| 366 | C22 | — | 3 | 1 | no | — |
| 367 | C22 | — | 3 | 1 | no | — |
| 368 | C22 | — | 6 | 1 | no | — |
| 369 | C22 | — | 6 | 1 | no | — |
| 370 | C22 | — | 6 | 1 | no | — |
| 371 | C22 | — | 6 | 1 | no | — |
| 372 | C22 | — | 6 | 2 | no | — |
| 373 | C22 | — | 6 | 2 | no | — |
| 374 | C22 | — | 6 | 2 | no | — |
| 375 | C22 | #91288 | 1 | 1 | yes | characteristic, complemented |
| 376 | C22 | Dic5×S4 | 1 | 1 | yes | characteristic |
| 377 | C4 | — | 3 | 1 | no | — |
| 378 | C4 | — | 3 | 1 | no | — |
| 379 | C4 | — | 6 | 2 | no | — |
| 380 | C4 | — | 6 | 2 | no | — |
| 381 | C4 | — | 6 | 2 | no | — |
| 382 | C4 | Dic5×S4 | 1 | 1 | yes | characteristic |
| 383 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 384 | C3 | — | 4 | 1 | no | Sylow |
| 385 | C2 | — | 2 | 1 | no | — |
| 386 | C2 | — | 3 | 1 | no | — |
| 387 | C2 | — | 3 | 1 | no | — |
| 388 | C2 | — | 6 | 1 | no | — |
| 389 | C2 | — | 12 | 2 | no | — |
| 390 | C2 | C2×Dic5×S4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. A4×#681 | C2 | semidirect |
| 3. C2×A4⋊#168 | C2 | semidirect |
| 4. #11751571 | C2 | semidirect |
| 5. S4×#168 | C2 | semidirect |
| 19. C22×#681 | D3 | semidirect |
| 128. #681 | S4 | semidirect |
| 154. C5×A4 | #131 | semidirect |
| 259. C22×C5 | #907 | semidirect |
| 316. A4 | #4094 | semidirect |
| 364. C5 | #85442 | semidirect |
| 375. C22 | #91288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5912 | 2 |
| A4×#681 | 2 |
| C2×A4⋊#168 | 2 |
| #11751571 | 2 |
| S4×#168 | 2 |
| #10614649 | 3 |
| #91288 | 4 |
| #85442 | 5 |