Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
528 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 51 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×Q8×S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11756750 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | A4×#688 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11752135 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11751581 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751576 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11751571 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10615290 | — | 3 | 1 | no | maximal, Hall |
| 9 | C5×Q8×A4 | C22 | 1 | 1 | yes | characteristic |
| 10 | A4×D20 | C22 | 1 | 1 | yes | characteristic |
| 11 | #91948 | C22 | 1 | 1 | yes | characteristic |
| 12 | C4×C5×S4 | — | 2 | 1 | no | — |
| 13 | C4×C5×S4 | C22 | 1 | 1 | yes | characteristic |
| 14 | C5×A4⋊Q8 | — | 2 | 1 | no | — |
| 15 | C5×A4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 16 | #91904 | — | 2 | 1 | no | — |
| 17 | D5×SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 18 | #91518 | — | 4 | 1 | no | maximal |
| 19 | A4×#168 | C22 | 1 | 1 | yes | characteristic |
| 20 | A4⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 21 | #85461 | — | 5 | 1 | no | maximal, Hall |
| 22 | C5×D4×Q8 | — | 3 | 1 | no | — |
| 23 | C2×#4088 | — | 3 | 1 | no | — |
| 24 | C22×#688 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #65884 | — | 3 | 1 | no | — |
| 26 | #65517 | — | 3 | 1 | no | — |
| 27 | #65516 | — | 3 | 1 | no | — |
| 28 | #65375 | — | 3 | 1 | no | — |
| 29 | #65372 | — | 3 | 1 | no | — |
| 30 | #65340 | — | 3 | 1 | no | — |
| 31 | #65338 | — | 3 | 1 | no | — |
| 32 | #65336 | — | 3 | 1 | no | — |
| 33 | #65335 | — | 3 | 1 | no | — |
| 34 | #65317 | — | 3 | 1 | no | — |
| 35 | #65315 | — | 3 | 1 | no | — |
| 36 | #65300 | — | 3 | 1 | no | — |
| 37 | C2×D5×A4 | — | 2 | 1 | no | — |
| 38 | C2×C5×S4 | D4 | 1 | 1 | yes | characteristic |
| 39 | C5×D3×Q8 | — | 4 | 1 | no | — |
| 40 | C4×C5×A4 | — | 2 | 1 | no | — |
| 41 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 42 | #6765 | — | 4 | 1 | no | — |
| 43 | A4⋊Dic5 | — | 2 | 1 | no | — |
| 44 | C5×SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 45 | C5×SL(2,ℤ/4) | D4 | 1 | 1 | yes | characteristic |
| 46 | #6718 | — | 4 | 1 | no | — |
| 47 | C3×#688 | — | 4 | 1 | no | — |
| 48 | #6663 | — | 4 | 1 | no | — |
| 49 | #6655 | — | 4 | 1 | no | — |
| 50 | #6650 | — | 4 | 1 | no | — |
| 51 | Q8×S4 | D5 | 1 | 1 | yes | characteristic, complemented |
| 52 | #5914 | — | 5 | 1 | no | — |
| 53 | A4×SD16 | — | 5 | 1 | no | — |
| 54 | #5416 | — | 5 | 1 | no | — |
| 55 | #5414 | — | 5 | 1 | no | — |
| 56 | #5400 | — | 5 | 1 | no | — |
| 57 | #5398 | — | 5 | 1 | no | — |
| 58 | C22×C5×Q8 | — | 3 | 1 | no | — |
| 59 | C22×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 60 | C2×#709 | — | 3 | 1 | no | — |
| 61 | C22×D20 | C2×D3 | 1 | 1 | yes | characteristic |
| 62 | C5×C4⋊Q8 | — | 3 | 1 | no | — |
| 63 | C5×C4⋊Q8 | — | 6 | 1 | no | — |
| 64 | C5×C22⋊Q8 | — | 3 | 1 | no | — |
| 65 | C5×C22⋊Q8 | — | 3 | 1 | no | — |
| 66 | C5×C22⋊Q8 | — | 6 | 1 | no | — |
| 67 | C5×C22⋊Q8 | — | 6 | 1 | no | — |
| 68 | C4×C5×Q8 | — | 3 | 1 | no | — |
| 69 | C4×C5×D4 | — | 3 | 1 | no | — |
| 70 | C4×C5×D4 | — | 6 | 1 | no | — |
| 71 | C2×#689 | — | 3 | 1 | no | — |
| 72 | C2×#689 | — | 3 | 1 | no | — |
| 73 | C2×#689 | — | 3 | 1 | no | — |
| 74 | #4088 | — | 6 | 1 | no | — |
| 75 | #4088 | — | 6 | 1 | no | — |
| 76 | #4088 | — | 6 | 1 | no | — |
| 77 | #4088 | — | 6 | 1 | no | — |
| 78 | C2×#688 | — | 3 | 1 | no | — |
| 79 | C2×#688 | — | 3 | 1 | no | — |
| 80 | C2×#688 | — | 3 | 1 | no | — |
| 81 | C2×#688 | — | 3 | 1 | no | — |
| 82 | C2×#688 | — | 3 | 1 | no | — |
| 83 | C2×#688 | — | 3 | 1 | no | — |
| 84 | #4083 | — | 6 | 1 | no | — |
| 85 | #4076 | — | 3 | 1 | no | — |
| 86 | #4070 | — | 3 | 1 | no | — |
| 87 | C2×#681 | — | 3 | 1 | no | — |
| 88 | C22×#168 | C2×D3 | 1 | 1 | yes | characteristic |
| 89 | #4040 | — | 6 | 1 | no | — |
| 90 | #4030 | — | 6 | 1 | no | — |
| 91 | D5×C22⋊C4 | — | 6 | 1 | no | — |
| 92 | #4021 | — | 3 | 1 | no | — |
| 93 | C4×D20 | — | 3 | 1 | no | — |
| 94 | #3967 | — | 3 | 1 | no | — |
| 95 | #3967 | — | 3 | 1 | no | — |
| 96 | #3967 | — | 3 | 1 | no | — |
| 97 | C22⋊#168 | — | 3 | 1 | no | — |
| 98 | C22⋊#168 | — | 3 | 1 | no | — |
| 99 | #3942 | — | 3 | 1 | no | — |
| 100 | #3941 | — | 3 | 1 | no | — |
| 101 | #3941 | — | 3 | 1 | no | — |
| 102 | #3939 | — | 3 | 1 | no | — |
| 103 | C4⋊#168 | — | 3 | 1 | no | — |
| 104 | #3935 | — | 3 | 1 | no | — |
| 105 | #3266 | — | 15 | 1 | no | Sylow |
| 106 | C2×C5×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | D5×A4 | — | 4 | 1 | no | — |
| 108 | C5×S4 | — | 2 | 1 | no | — |
| 109 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 110 | Dic30 | — | 4 | 1 | no | — |
| 111 | C4×C5×D3 | — | 4 | 1 | no | — |
| 112 | C4×C5×D3 | — | 8 | 1 | no | — |
| 113 | C5×Dic6 | — | 4 | 1 | no | — |
| 114 | C5×Dic6 | — | 8 | 1 | no | — |
| 115 | C3×D20 | — | 4 | 1 | no | — |
| 116 | #1201 | — | 8 | 1 | no | — |
| 117 | D5×Dic3 | — | 8 | 1 | no | — |
| 118 | C3⋊#168 | — | 4 | 1 | no | — |
| 119 | C3×#168 | — | 4 | 1 | no | — |
| 120 | Q8×A4 | C2×D5 | 1 | 1 | yes | characteristic |
| 121 | D4×A4 | — | 5 | 1 | no | — |
| 122 | GL(2,ℤ/4) | — | 10 | 1 | no | — |
| 123 | C2×SL(2,ℤ/4) | — | 10 | 1 | no | — |
| 124 | C4×S4 | — | 2 | 1 | no | — |
| 125 | C4×S4 | C2×D5 | 1 | 1 | yes | characteristic |
| 126 | A4⋊Q8 | — | 2 | 1 | no | — |
| 127 | A4⋊Q8 | — | 5 | 1 | no | — |
| 128 | A4⋊Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 129 | #915 | — | 20 | 1 | no | — |
| 130 | C8×A4 | — | 5 | 1 | no | — |
| 131 | A4⋊C8 | — | 5 | 1 | no | — |
| 132 | C23×D5 | — | 2 | 1 | no | — |
| 133 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 134 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 135 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 136 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 137 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 138 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 139 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 140 | C2×C5×Q8 | — | 12 | 1 | no | — |
| 141 | C2×C5×D4 | — | 3 | 1 | no | — |
| 142 | C22×C4×C5 | — | 2 | 1 | no | — |
| 143 | C22×C4×C5 | — | 3 | 1 | no | — |
| 144 | C22×C4×C5 | — | 6 | 1 | no | — |
| 145 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 146 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 147 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 148 | #709 | — | 6 | 1 | no | — |
| 149 | #709 | — | 6 | 1 | no | — |
| 150 | #709 | — | 12 | 1 | no | — |
| 151 | C2×D20 | — | 3 | 1 | no | — |
| 152 | C2×D20 | — | 3 | 1 | no | — |
| 153 | C2×D20 | — | 6 | 1 | no | — |
| 154 | C2×C4×D5 | — | 6 | 1 | no | — |
| 155 | C2×C4×D5 | — | 6 | 1 | no | — |
| 156 | C2×Dic10 | — | 3 | 1 | no | — |
| 157 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 158 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 159 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 160 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 161 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 162 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 163 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 164 | C5×C22⋊C4 | — | 3 | 1 | no | — |
| 165 | C5×C22⋊C4 | — | 3 | 1 | no | — |
| 166 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 167 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 168 | C42×C5 | — | 3 | 1 | no | — |
| 169 | C42×C5 | — | 6 | 1 | no | — |
| 170 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 171 | #689 | — | 6 | 1 | no | — |
| 172 | #689 | — | 6 | 1 | no | — |
| 173 | #689 | — | 6 | 1 | no | — |
| 174 | #689 | — | 6 | 1 | no | — |
| 175 | #689 | — | 12 | 1 | no | — |
| 176 | #688 | — | 3 | 1 | no | — |
| 177 | #688 | — | 3 | 1 | no | — |
| 178 | #688 | — | 3 | 1 | no | — |
| 179 | #688 | — | 6 | 1 | no | — |
| 180 | #688 | — | 6 | 1 | no | — |
| 181 | #688 | — | 6 | 1 | no | — |
| 182 | #688 | — | 12 | 1 | no | — |
| 183 | #688 | S4 | 1 | 1 | yes | characteristic, complemented |
| 184 | #685 | — | 6 | 1 | no | — |
| 185 | #685 | — | 6 | 1 | no | — |
| 186 | #685 | — | 6 | 1 | no | — |
| 187 | #685 | — | 6 | 1 | no | — |
| 188 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 189 | #683 | — | 6 | 1 | no | — |
| 190 | #681 | — | 6 | 1 | no | — |
| 191 | #681 | — | 6 | 1 | no | — |
| 192 | C2×#168 | — | 3 | 1 | no | — |
| 193 | C2×#168 | — | 3 | 1 | no | — |
| 194 | C2×#168 | — | 3 | 1 | no | — |
| 195 | C2×#168 | — | 3 | 1 | no | — |
| 196 | C2×#137 | — | 15 | 1 | no | — |
| 197 | C22×SD16 | — | 5 | 1 | no | — |
| 198 | D4×Q8 | — | 3 | 1 | no | — |
| 199 | #546 | — | 15 | 1 | no | — |
| 200 | #497 | — | 15 | 1 | no | — |
| 201 | #468 | — | 15 | 1 | no | — |
| 202 | #467 | — | 15 | 1 | no | — |
| 203 | #464 | — | 15 | 1 | no | — |
| 204 | #461 | — | 15 | 1 | no | — |
| 205 | #452 | — | 15 | 1 | no | — |
| 206 | #451 | — | 15 | 1 | no | — |
| 207 | #450 | — | 15 | 1 | no | — |
| 208 | #448 | — | 15 | 1 | no | — |
| 209 | #440 | — | 15 | 1 | no | — |
| 210 | #435 | — | 15 | 1 | no | — |
| 211 | C2×C5×D3 | — | 4 | 1 | no | — |
| 212 | C2×C3×D5 | — | 8 | 1 | no | — |
| 213 | C5×A4 | #137 | 1 | 1 | yes | characteristic, complemented |
| 214 | C3×C4×C5 | — | 4 | 1 | no | — |
| 215 | C3×C4×C5 | — | 8 | 1 | no | — |
| 216 | Dic15 | — | 8 | 1 | no | — |
| 217 | C5×Dic3 | — | 4 | 1 | no | — |
| 218 | C5×Dic3 | — | 8 | 1 | no | — |
| 219 | C22×A4 | — | 10 | 1 | no | — |
| 220 | C2×S4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 221 | D3×Q8 | — | 4 | 1 | no | — |
| 222 | #237 | — | 20 | 1 | no | — |
| 223 | C4×A4 | — | 2 | 1 | no | — |
| 224 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 225 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 226 | SL(2,ℤ/4) | — | 10 | 1 | no | — |
| 227 | SL(2,ℤ/4) | C22⋊D5 | 1 | 1 | yes | characteristic |
| 228 | C3×SD16 | — | 20 | 1 | no | — |
| 229 | #216 | — | 20 | 1 | no | — |
| 230 | #214 | — | 20 | 1 | no | — |
| 231 | Dic12 | — | 20 | 1 | no | — |
| 232 | ΓL(1,𝔽25) | — | 20 | 1 | no | — |
| 233 | C23×C5 | — | 3 | 1 | no | — |
| 234 | C23×C5 | D3×D4 | 1 | 1 | yes | characteristic |
| 235 | C22×D5 | — | 4 | 1 | no | — |
| 236 | C22×D5 | — | 6 | 1 | no | — |
| 237 | C22×D5 | — | 6 | 1 | no | — |
| 238 | C22×D5 | — | 12 | 1 | no | — |
| 239 | C5×Q8 | — | 3 | 1 | no | — |
| 240 | C5×Q8 | — | 6 | 1 | no | — |
| 241 | C5×Q8 | — | 6 | 1 | no | — |
| 242 | C5×Q8 | — | 6 | 1 | no | — |
| 243 | C5×Q8 | — | 6 | 1 | no | — |
| 244 | C5×Q8 | — | 12 | 1 | no | — |
| 245 | C5×Q8 | — | 12 | 1 | no | — |
| 246 | C5×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 247 | C5×D4 | — | 6 | 1 | no | — |
| 248 | C5×D4 | — | 6 | 1 | no | — |
| 249 | C2×C4×C5 | — | 3 | 1 | no | — |
| 250 | C2×C4×C5 | — | 3 | 1 | no | — |
| 251 | C2×C4×C5 | — | 3 | 1 | no | — |
| 252 | C2×C4×C5 | — | 3 | 1 | no | — |
| 253 | C2×C4×C5 | — | 3 | 1 | no | — |
| 254 | C2×C4×C5 | — | 6 | 1 | no | — |
| 255 | C2×C4×C5 | — | 6 | 1 | no | — |
| 256 | C2×C4×C5 | — | 6 | 1 | no | — |
| 257 | C2×C4×C5 | — | 6 | 1 | no | — |
| 258 | C2×C4×C5 | — | 6 | 1 | no | — |
| 259 | C2×C4×C5 | — | 6 | 1 | no | — |
| 260 | C2×C4×C5 | — | 12 | 1 | no | — |
| 261 | C2×C4×C5 | — | 12 | 1 | no | — |
| 262 | C22⋊D5 | — | 12 | 1 | no | — |
| 263 | C22⋊D5 | — | 12 | 1 | no | — |
| 264 | C22⋊D5 | — | 24 | 1 | no | — |
| 265 | C2×Dic5 | — | 6 | 1 | no | — |
| 266 | C2×Dic5 | — | 6 | 1 | no | — |
| 267 | D20 | — | 3 | 1 | no | — |
| 268 | D20 | — | 6 | 1 | no | — |
| 269 | D20 | — | 6 | 1 | no | — |
| 270 | D20 | C2×S4 | 1 | 1 | yes | characteristic |
| 271 | C4×D5 | — | 12 | 1 | no | — |
| 272 | C4×D5 | — | 12 | 1 | no | — |
| 273 | C4×D5 | — | 24 | 1 | no | — |
| 274 | Dic10 | — | 6 | 1 | no | — |
| 275 | Dic10 | — | 6 | 1 | no | — |
| 276 | #168 | — | 3 | 1 | no | — |
| 277 | #168 | — | 6 | 1 | no | — |
| 278 | #168 | — | 6 | 1 | no | — |
| 279 | #168 | C2×S4 | 1 | 1 | yes | characteristic |
| 280 | C2×#41 | — | 15 | 1 | no | — |
| 281 | C22×Q8 | — | 3 | 1 | no | — |
| 282 | C22×Q8 | D3×D5 | 1 | 1 | yes | characteristic |
| 283 | C22×D4 | — | 5 | 1 | no | — |
| 284 | #137 | — | 30 | 1 | no | — |
| 285 | #137 | — | 30 | 1 | no | — |
| 286 | #137 | — | 30 | 1 | no | — |
| 287 | #137 | — | 30 | 1 | no | — |
| 288 | C2×Q16 | — | 15 | 1 | no | — |
| 289 | C2×Q16 | — | 15 | 1 | no | — |
| 290 | C2×Q16 | — | 15 | 1 | no | — |
| 291 | C2×SD16 | — | 15 | 1 | no | — |
| 292 | C2×SD16 | — | 15 | 1 | no | — |
| 293 | C2×SD16 | — | 15 | 1 | no | — |
| 294 | C2×SD16 | — | 15 | 1 | no | — |
| 295 | C2×SD16 | — | 15 | 1 | no | — |
| 296 | C2×SD16 | — | 15 | 1 | no | — |
| 297 | C2×M16 | — | 15 | 1 | no | — |
| 298 | C22×C8 | — | 5 | 1 | no | — |
| 299 | C4⋊Q8 | — | 3 | 1 | no | — |
| 300 | C4⋊Q8 | — | 6 | 1 | no | — |
| 301 | #124 | — | 15 | 1 | no | — |
| 302 | #123 | — | 30 | 1 | no | — |
| 303 | C22⋊Q8 | — | 3 | 1 | no | — |
| 304 | C22⋊Q8 | — | 3 | 1 | no | — |
| 305 | C22⋊Q8 | — | 6 | 1 | no | — |
| 306 | C22⋊Q8 | — | 6 | 1 | no | — |
| 307 | C22⋊Q8 | — | 15 | 1 | no | — |
| 308 | #121 | — | 15 | 1 | no | — |
| 309 | #121 | — | 30 | 1 | no | — |
| 310 | #120 | — | 30 | 1 | no | — |
| 311 | C4×Q8 | — | 3 | 1 | no | — |
| 312 | C4×D4 | — | 3 | 1 | no | — |
| 313 | C4×D4 | — | 6 | 1 | no | — |
| 314 | C4×D4 | — | 15 | 1 | no | — |
| 315 | C2×C22⋊C4 | — | 30 | 1 | no | — |
| 316 | #107 | — | 15 | 1 | no | — |
| 317 | C4⋊C8 | — | 15 | 1 | no | — |
| 318 | #103 | — | 15 | 1 | no | — |
| 319 | #103 | — | 15 | 1 | no | — |
| 320 | #103 | — | 15 | 1 | no | — |
| 321 | #103 | — | 15 | 1 | no | — |
| 322 | #102 | — | 15 | 1 | no | — |
| 323 | #102 | — | 15 | 1 | no | — |
| 324 | C22⋊C8 | — | 15 | 1 | no | — |
| 325 | C22⋊C8 | — | 15 | 1 | no | — |
| 326 | #97 | — | 15 | 1 | no | — |
| 327 | C2×C3×C5 | — | 4 | 1 | no | — |
| 328 | C3×D5 | — | 16 | 1 | no | — |
| 329 | C5×D3 | — | 8 | 1 | no | — |
| 330 | C2×A4 | — | 20 | 1 | no | — |
| 331 | C2×A4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 332 | S4 | — | 2 | 1 | no | — |
| 333 | C3×Q8 | — | 4 | 1 | no | — |
| 334 | C3×D4 | — | 20 | 1 | no | — |
| 335 | #67 | — | 40 | 1 | no | — |
| 336 | C2×Dic3 | — | 40 | 1 | no | — |
| 337 | C4×D3 | — | 4 | 1 | no | — |
| 338 | C4×D3 | — | 8 | 1 | no | — |
| 339 | Dic6 | — | 4 | 1 | no | — |
| 340 | Dic6 | — | 8 | 1 | no | — |
| 341 | Dic6 | — | 20 | 1 | no | — |
| 342 | C3×C8 | — | 20 | 1 | no | — |
| 343 | C3⋊C8 | — | 20 | 1 | no | — |
| 344 | C22×C5 | — | 3 | 1 | no | — |
| 345 | C22×C5 | — | 3 | 1 | no | — |
| 346 | C22×C5 | — | 6 | 1 | no | — |
| 347 | C22×C5 | — | 6 | 1 | no | — |
| 348 | C22×C5 | — | 6 | 1 | no | — |
| 349 | C22×C5 | #915 | 1 | 1 | yes | characteristic, complemented |
| 350 | C2×D5 | — | 2 | 1 | no | — |
| 351 | C2×D5 | — | 6 | 1 | no | — |
| 352 | C2×D5 | — | 12 | 1 | no | — |
| 353 | C2×D5 | — | 12 | 1 | no | — |
| 354 | C2×D5 | — | 12 | 1 | no | — |
| 355 | C2×D5 | — | 12 | 1 | no | — |
| 356 | C4×C5 | — | 2 | 1 | no | — |
| 357 | C4×C5 | — | 3 | 1 | no | — |
| 358 | C4×C5 | — | 6 | 1 | no | — |
| 359 | C4×C5 | — | 6 | 1 | no | — |
| 360 | C4×C5 | — | 6 | 1 | no | — |
| 361 | C4×C5 | — | 6 | 1 | no | — |
| 362 | C4×C5 | — | 12 | 1 | no | — |
| 363 | C4×C5 | — | 12 | 1 | no | — |
| 364 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 365 | Dic5 | — | 12 | 1 | no | — |
| 366 | Dic5 | — | 12 | 1 | no | — |
| 367 | C24 | — | 10 | 1 | no | — |
| 368 | #41 | — | 30 | 1 | no | — |
| 369 | #41 | — | 30 | 1 | no | — |
| 370 | #41 | — | 60 | 1 | no | — |
| 371 | C2×Q8 | — | 3 | 1 | no | — |
| 372 | C2×Q8 | — | 3 | 1 | no | — |
| 373 | C2×Q8 | — | 3 | 1 | no | — |
| 374 | C2×Q8 | — | 6 | 1 | no | — |
| 375 | C2×Q8 | — | 6 | 1 | no | — |
| 376 | C2×Q8 | — | 6 | 1 | no | — |
| 377 | C2×Q8 | — | 6 | 1 | no | — |
| 378 | C2×Q8 | — | 12 | 1 | no | — |
| 379 | C2×Q8 | — | 15 | 1 | no | — |
| 380 | C2×D4 | — | 3 | 1 | no | — |
| 381 | C2×D4 | — | 15 | 1 | no | — |
| 382 | C2×D4 | — | 15 | 1 | no | — |
| 383 | C2×D4 | — | 30 | 1 | no | — |
| 384 | C2×D4 | — | 30 | 1 | no | — |
| 385 | C2×D4 | — | 30 | 1 | no | — |
| 386 | C22×C4 | — | 2 | 1 | no | — |
| 387 | C22×C4 | — | 3 | 1 | no | — |
| 388 | C22×C4 | — | 6 | 1 | no | — |
| 389 | C22×C4 | — | 30 | 1 | no | — |
| 390 | C22×C4 | — | 30 | 1 | no | — |
| 391 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 392 | Q16 | — | 30 | 1 | no | — |
| 393 | Q16 | — | 30 | 1 | no | — |
| 394 | Q16 | — | 30 | 1 | no | — |
| 395 | Q16 | — | 30 | 1 | no | — |
| 396 | Q16 | — | 60 | 1 | no | — |
| 397 | SD16 | — | 5 | 1 | no | — |
| 398 | SD16 | — | 15 | 1 | no | — |
| 399 | SD16 | — | 15 | 1 | no | — |
| 400 | SD16 | — | 15 | 1 | no | — |
| 401 | SD16 | — | 30 | 1 | no | — |
| 402 | SD16 | — | 30 | 1 | no | — |
| 403 | SD16 | — | 30 | 1 | no | — |
| 404 | SD16 | — | 60 | 1 | no | — |
| 405 | M16 | — | 30 | 1 | no | — |
| 406 | M16 | — | 30 | 1 | no | — |
| 407 | C2×C8 | — | 15 | 1 | no | — |
| 408 | C2×C8 | — | 15 | 1 | no | — |
| 409 | C2×C8 | — | 15 | 1 | no | — |
| 410 | C2×C8 | — | 15 | 1 | no | — |
| 411 | C4⋊C4 | — | 3 | 1 | no | — |
| 412 | C4⋊C4 | — | 3 | 1 | no | — |
| 413 | C4⋊C4 | — | 6 | 1 | no | — |
| 414 | C4⋊C4 | — | 6 | 1 | no | — |
| 415 | C4⋊C4 | — | 6 | 1 | no | — |
| 416 | C4⋊C4 | — | 6 | 1 | no | — |
| 417 | C4⋊C4 | — | 6 | 1 | no | — |
| 418 | C4⋊C4 | — | 15 | 1 | no | — |
| 419 | C4⋊C4 | — | 30 | 1 | no | — |
| 420 | C22⋊C4 | — | 3 | 1 | no | — |
| 421 | C22⋊C4 | — | 3 | 1 | no | — |
| 422 | C22⋊C4 | — | 6 | 1 | no | — |
| 423 | C22⋊C4 | — | 6 | 1 | no | — |
| 424 | C22⋊C4 | — | 30 | 1 | no | — |
| 425 | C22⋊C4 | — | 30 | 1 | no | — |
| 426 | C22⋊C4 | — | 30 | 1 | no | — |
| 427 | C22⋊C4 | — | 30 | 1 | no | — |
| 428 | C22⋊C4 | — | 30 | 1 | no | — |
| 429 | C42 | — | 3 | 1 | no | — |
| 430 | C42 | — | 6 | 1 | no | — |
| 431 | C3×C5 | — | 4 | 1 | no | Hall |
| 432 | C22×C3 | — | 40 | 1 | no | — |
| 433 | C2×D3 | — | 4 | 1 | no | — |
| 434 | A4 | #4088 | 1 | 1 | yes | characteristic, complemented |
| 435 | C3×C4 | — | 4 | 1 | no | — |
| 436 | C3×C4 | — | 8 | 1 | no | — |
| 437 | Dic3 | — | 4 | 1 | no | — |
| 438 | Dic3 | — | 8 | 1 | no | — |
| 439 | Dic3 | — | 40 | 1 | no | — |
| 440 | C2×C5 | — | 3 | 1 | no | — |
| 441 | C2×C5 | — | 3 | 1 | no | — |
| 442 | C2×C5 | — | 12 | 1 | no | — |
| 443 | C2×C5 | D4×S4 | 1 | 1 | yes | characteristic |
| 444 | D5 | — | 4 | 1 | no | — |
| 445 | D5 | — | 12 | 1 | no | — |
| 446 | C23 | — | 3 | 1 | no | — |
| 447 | C23 | — | 20 | 1 | no | — |
| 448 | C23 | — | 30 | 1 | no | — |
| 449 | C23 | — | 30 | 1 | no | — |
| 450 | C23 | — | 60 | 1 | no | — |
| 451 | C23 | D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 452 | Q8 | — | 3 | 1 | no | — |
| 453 | Q8 | — | 6 | 1 | no | — |
| 454 | Q8 | — | 6 | 1 | no | — |
| 455 | Q8 | — | 6 | 1 | no | — |
| 456 | Q8 | — | 6 | 1 | no | — |
| 457 | Q8 | — | 12 | 1 | no | — |
| 458 | Q8 | — | 12 | 1 | no | — |
| 459 | Q8 | — | 30 | 1 | no | — |
| 460 | Q8 | — | 30 | 1 | no | — |
| 461 | Q8 | D5×S4 | 1 | 1 | yes | characteristic |
| 462 | D4 | — | 5 | 1 | no | — |
| 463 | D4 | — | 6 | 1 | no | — |
| 464 | D4 | — | 6 | 1 | no | — |
| 465 | D4 | — | 15 | 1 | no | — |
| 466 | D4 | — | 30 | 1 | no | — |
| 467 | D4 | — | 30 | 1 | no | — |
| 468 | D4 | — | 60 | 1 | no | — |
| 469 | D4 | — | 60 | 1 | no | — |
| 470 | D4 | — | 120 | 1 | no | — |
| 471 | C2×C4 | — | 3 | 1 | no | — |
| 472 | C2×C4 | — | 3 | 1 | no | — |
| 473 | C2×C4 | — | 3 | 1 | no | — |
| 474 | C2×C4 | — | 3 | 1 | no | — |
| 475 | C2×C4 | — | 3 | 1 | no | — |
| 476 | C2×C4 | — | 6 | 1 | no | — |
| 477 | C2×C4 | — | 6 | 1 | no | — |
| 478 | C2×C4 | — | 6 | 1 | no | — |
| 479 | C2×C4 | — | 6 | 1 | no | — |
| 480 | C2×C4 | — | 6 | 1 | no | — |
| 481 | C2×C4 | — | 6 | 1 | no | — |
| 482 | C2×C4 | — | 12 | 1 | no | — |
| 483 | C2×C4 | — | 12 | 1 | no | — |
| 484 | C2×C4 | — | 30 | 1 | no | — |
| 485 | C2×C4 | — | 30 | 1 | no | — |
| 486 | C2×C4 | — | 60 | 1 | no | — |
| 487 | C2×C4 | — | 60 | 1 | no | — |
| 488 | C2×C4 | — | 120 | 1 | no | — |
| 489 | C8 | — | 5 | 1 | no | — |
| 490 | C8 | — | 15 | 1 | no | — |
| 491 | C8 | — | 30 | 1 | no | — |
| 492 | C8 | — | 30 | 1 | no | — |
| 493 | C2×C3 | — | 4 | 1 | no | — |
| 494 | C2×C3 | — | 80 | 1 | no | — |
| 495 | D3 | — | 8 | 1 | no | — |
| 496 | C5 | #85461 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 497 | C22 | — | 3 | 1 | no | — |
| 498 | C22 | — | 3 | 1 | no | — |
| 499 | C22 | — | 6 | 1 | no | — |
| 500 | C22 | — | 6 | 1 | no | — |
| 501 | C22 | — | 6 | 1 | no | — |
| 502 | C22 | — | 10 | 1 | no | — |
| 503 | C22 | — | 30 | 1 | no | — |
| 504 | C22 | — | 60 | 1 | no | — |
| 505 | C22 | — | 60 | 1 | no | — |
| 506 | C22 | — | 60 | 1 | no | — |
| 507 | C22 | — | 60 | 1 | no | — |
| 508 | C22 | #91518 | 1 | 1 | yes | characteristic, complemented |
| 509 | C4 | — | 2 | 1 | no | — |
| 510 | C4 | — | 3 | 1 | no | — |
| 511 | C4 | — | 6 | 1 | no | — |
| 512 | C4 | — | 6 | 1 | no | — |
| 513 | C4 | — | 6 | 1 | no | — |
| 514 | C4 | — | 6 | 1 | no | — |
| 515 | C4 | — | 12 | 1 | no | — |
| 516 | C4 | — | 12 | 1 | no | — |
| 517 | C4 | — | 60 | 1 | no | — |
| 518 | C4 | — | 60 | 1 | no | — |
| 519 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 520 | C3 | — | 4 | 1 | no | Sylow |
| 521 | C2 | — | 3 | 1 | no | — |
| 522 | C2 | — | 3 | 1 | no | — |
| 523 | C2 | — | 12 | 1 | no | — |
| 524 | C2 | — | 20 | 1 | no | — |
| 525 | C2 | — | 60 | 1 | no | — |
| 526 | C2 | S4×C22⋊D5 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×Q8×S4 | C2 | semidirect |
| 3. A4×#688 | C2 | semidirect |
| 4. #11752135 | C2 | semidirect |
| 5. #11751581 | C2 | semidirect |
| 6. #11751576 | C2 | semidirect |
| 7. #11751571 | C2 | semidirect |
| 24. C22×#688 | D3 | semidirect |
| 51. Q8×S4 | D5 | semidirect |
| 183. #688 | S4 | semidirect |
| 213. C5×A4 | #137 | semidirect |
| 349. C22×C5 | #915 | semidirect |
| 434. A4 | #4088 | semidirect |
| 496. C5 | #85461 | semidirect |
| 508. C22 | #91518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×S4 | 2 |
| #11756750 | 2 |
| A4×#688 | 2 |
| #11752135 | 2 |
| #11751581 | 2 |
| #11751576 | 2 |
| #11751571 | 2 |
| #10615290 | 3 |
| #91518 | 4 |
| #85461 | 5 |