Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
594 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #66283⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#5923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#91185 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11751631 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11751629 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11751625 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10615735 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×C5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 10 | #4150⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 11 | D5×#41⋊C3 | — | 2 | 1 | no | — |
| 12 | C5⋊#994 | C22 | 1 | 1 | yes | characteristic |
| 13 | #4147⋊C3 | — | 2 | 1 | no | — |
| 14 | C5×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C5×#985 | — | 2 | 1 | no | — |
| 16 | C5×#984 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C5×#983 | — | 2 | 1 | no | — |
| 18 | #91297 | — | 4 | 1 | no | maximal |
| 19 | #91185 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #91185 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #85544 | — | 5 | 1 | no | maximal, Hall |
| 22 | #66283 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | C5×#575 | — | 3 | 1 | no | — |
| 24 | #66166 | — | 3 | 1 | no | — |
| 25 | #66156 | — | 3 | 1 | no | — |
| 26 | C2×#3969 | — | 3 | 1 | no | — |
| 27 | #65494 | — | 3 | 1 | no | — |
| 28 | #65494 | — | 3 | 1 | no | — |
| 29 | #65491 | — | 3 | 1 | no | — |
| 30 | #65491 | — | 3 | 1 | no | — |
| 31 | #65490 | — | 3 | 1 | no | — |
| 32 | #65490 | — | 3 | 1 | no | — |
| 33 | #65487 | — | 3 | 1 | no | — |
| 34 | #65487 | — | 3 | 1 | no | — |
| 35 | C2×#3957 | — | 3 | 1 | no | — |
| 36 | #65421 | — | 3 | 1 | no | — |
| 37 | C5×#235 | — | 4 | 1 | no | — |
| 38 | C3×#709 | — | 4 | 1 | no | — |
| 39 | C5×#41⋊C3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 40 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 41 | C2×C5×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic, complemented |
| 42 | D5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 43 | C5⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 44 | C5×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 45 | C5×#226 | — | 2 | 1 | no | — |
| 46 | C2×C3⋊#168 | — | 4 | 1 | no | — |
| 47 | #6661 | — | 4 | 1 | no | — |
| 48 | #6656 | — | 4 | 1 | no | — |
| 49 | #6655 | — | 4 | 1 | no | — |
| 50 | #6652 | — | 4 | 1 | no | — |
| 51 | #5945 | — | 5 | 1 | no | — |
| 52 | #5923 | D5 | 1 | 1 | yes | characteristic, complemented |
| 53 | #5431 | — | 5 | 1 | no | — |
| 54 | #5430 | — | 5 | 1 | no | — |
| 55 | #5429 | — | 5 | 1 | no | — |
| 56 | #5428 | — | 5 | 1 | no | — |
| 57 | C2×GU(2,𝔽3) | — | 5 | 1 | no | — |
| 58 | C2×C5×#41 | — | 3 | 1 | no | — |
| 59 | C2×C5×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 60 | #4150 | — | 3 | 1 | no | — |
| 61 | #4150 | C2×D3 | 1 | 1 | yes | characteristic |
| 62 | #4149 | — | 3 | 1 | no | — |
| 63 | #4149 | C2×D3 | 1 | 1 | yes | characteristic |
| 64 | D5×#41 | — | 2 | 1 | no | — |
| 65 | D5×#41 | — | 6 | 1 | no | — |
| 66 | #4147 | — | 2 | 1 | no | — |
| 67 | #4144 | — | 6 | 1 | no | — |
| 68 | C2×#709 | — | 3 | 1 | no | — |
| 69 | C2×#709 | — | 3 | 1 | no | — |
| 70 | C5×#137 | — | 3 | 1 | no | — |
| 71 | C5×#137 | — | 3 | 1 | no | — |
| 72 | C5×#137 | — | 6 | 1 | no | — |
| 73 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 74 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 75 | C5×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 76 | C5×#135 | — | 6 | 1 | no | — |
| 77 | C5×#135 | — | 6 | 1 | no | — |
| 78 | C2×C5×M16 | — | 3 | 1 | no | — |
| 79 | #4097 | — | 6 | 1 | no | — |
| 80 | #4096 | — | 6 | 1 | no | — |
| 81 | #4096 | — | 6 | 1 | no | — |
| 82 | #4095 | — | 6 | 1 | no | — |
| 83 | #4093 | — | 3 | 1 | no | — |
| 84 | #4090 | — | 3 | 1 | no | — |
| 85 | #4088 | — | 3 | 1 | no | — |
| 86 | #4088 | — | 3 | 1 | no | — |
| 87 | #4086 | — | 3 | 1 | no | — |
| 88 | #4085 | — | 6 | 2 | no | — |
| 89 | #4082 | — | 3 | 1 | no | — |
| 90 | #4078 | — | 3 | 1 | no | — |
| 91 | #4078 | — | 3 | 1 | no | — |
| 92 | C4×C22⋊D5 | — | 6 | 2 | no | — |
| 93 | C2×C4×Dic5 | — | 3 | 1 | no | — |
| 94 | C2×#681 | — | 3 | 1 | no | — |
| 95 | #3969 | — | 3 | 1 | no | — |
| 96 | #3969 | — | 3 | 1 | no | — |
| 97 | #3969 | — | 3 | 1 | no | — |
| 98 | #3969 | — | 3 | 1 | no | — |
| 99 | #3957 | — | 3 | 1 | no | — |
| 100 | #3957 | — | 3 | 1 | no | — |
| 101 | #3957 | — | 3 | 1 | no | — |
| 102 | #3957 | — | 3 | 1 | no | — |
| 103 | #3956 | — | 3 | 1 | no | — |
| 104 | #3956 | — | 3 | 1 | no | — |
| 105 | #3955 | — | 3 | 1 | no | — |
| 106 | #3955 | — | 3 | 1 | no | — |
| 107 | #3018 | — | 15 | 1 | no | Sylow |
| 108 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 109 | C5×#67 | — | 8 | 1 | no | — |
| 110 | C5×D12 | — | 4 | 1 | no | — |
| 111 | C4×C5×D3 | — | 8 | 1 | no | — |
| 112 | C5×Dic6 | — | 4 | 1 | no | — |
| 113 | C3×C22⋊D5 | — | 8 | 1 | no | — |
| 114 | C3×D20 | — | 4 | 1 | no | — |
| 115 | C3×C4×D5 | — | 8 | 1 | no | — |
| 116 | C3×Dic10 | — | 4 | 1 | no | — |
| 117 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C3⋊#168 | — | 4 | 1 | no | — |
| 119 | C3⋊#168 | — | 4 | 1 | no | — |
| 120 | 2−1+4⋊C3 | — | 5 | 1 | no | — |
| 121 | 2−1+4⋊C3 | — | 10 | 1 | no | — |
| 122 | #994 | — | 5 | 1 | no | — |
| 123 | C2×#41⋊C3 | — | 10 | 1 | no | — |
| 124 | C2×#41⋊C3 | C2×D5 | 1 | 1 | yes | characteristic |
| 125 | #986 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 126 | #985 | — | 2 | 1 | no | — |
| 127 | #984 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 128 | #983 | — | 2 | 1 | no | — |
| 129 | #950 | — | 20 | 1 | no | — |
| 130 | GU(2,𝔽3) | — | 5 | 1 | no | — |
| 131 | GU(2,𝔽3) | — | 5 | 1 | no | — |
| 132 | C5×#41 | — | 3 | 1 | no | — |
| 133 | C5×#41 | — | 3 | 1 | no | — |
| 134 | C5×#41 | — | 6 | 1 | no | — |
| 135 | C5×#41 | — | 6 | 1 | no | — |
| 136 | C5×#41 | — | 6 | 1 | no | — |
| 137 | C5×#41 | — | 6 | 1 | no | — |
| 138 | C5×#41 | #67 | 1 | 1 | yes | characteristic |
| 139 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 141 | C2×C5×Q8 | #67 | 1 | 1 | yes | characteristic |
| 142 | C2×C5×D4 | — | 3 | 1 | no | — |
| 143 | C2×C5×D4 | — | 3 | 1 | no | — |
| 144 | C2×C5×D4 | — | 6 | 1 | no | — |
| 145 | C22×C4×C5 | — | 3 | 1 | no | — |
| 146 | C22×C4×C5 | — | 6 | 1 | no | — |
| 147 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 148 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 149 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 150 | C22×Dic5 | — | 6 | 1 | no | — |
| 151 | #713 | — | 2 | 1 | no | — |
| 152 | #713 | — | 6 | 1 | no | — |
| 153 | Q8×D5 | — | 2 | 1 | no | — |
| 154 | Q8×D5 | — | 6 | 1 | no | — |
| 155 | #711 | — | 6 | 1 | no | — |
| 156 | #711 | — | 6 | 2 | no | — |
| 157 | #711 | — | 6 | 1 | no | — |
| 158 | D4×D5 | — | 6 | 1 | no | — |
| 159 | D4×D5 | — | 6 | 2 | no | — |
| 160 | D4×D5 | — | 6 | 1 | no | — |
| 161 | #709 | — | 3 | 1 | no | — |
| 162 | #709 | — | 3 | 1 | no | — |
| 163 | #709 | — | 3 | 1 | no | — |
| 164 | #709 | — | 6 | 1 | no | — |
| 165 | #709 | — | 6 | 1 | no | — |
| 166 | #709 | — | 6 | 1 | no | — |
| 167 | #709 | — | 6 | 1 | no | — |
| 168 | #709 | — | 6 | 1 | no | — |
| 169 | #709 | S4 | 1 | 1 | yes | characteristic |
| 170 | C2×D20 | — | 3 | 1 | no | — |
| 171 | C2×D20 | — | 3 | 1 | no | — |
| 172 | C2×C4×D5 | — | 3 | 2 | no | — |
| 173 | C2×C4×D5 | — | 6 | 1 | no | — |
| 174 | C2×Dic10 | — | 3 | 1 | no | — |
| 175 | C2×Dic10 | — | 3 | 1 | no | — |
| 176 | C5×Q16 | — | 6 | 1 | no | — |
| 177 | C5×Q16 | — | 6 | 1 | no | — |
| 178 | C5×SD16 | — | 6 | 1 | no | — |
| 179 | C5×SD16 | — | 6 | 1 | no | — |
| 180 | C5×SD16 | — | 6 | 1 | no | — |
| 181 | C5×SD16 | — | 6 | 1 | no | — |
| 182 | C5×D8 | — | 6 | 1 | no | — |
| 183 | C5×D8 | — | 6 | 1 | no | — |
| 184 | C5×M16 | — | 3 | 1 | no | — |
| 185 | C5×M16 | — | 3 | 1 | no | — |
| 186 | C5×M16 | — | 6 | 1 | no | — |
| 187 | C2×C5×C8 | — | 6 | 1 | no | — |
| 188 | C22⋊Dic5 | — | 6 | 2 | no | — |
| 189 | #689 | — | 6 | 1 | no | — |
| 190 | #689 | — | 6 | 1 | no | — |
| 191 | #688 | — | 6 | 1 | no | — |
| 192 | #688 | — | 6 | 1 | no | — |
| 193 | #687 | — | 6 | 1 | no | — |
| 194 | #687 | — | 6 | 1 | no | — |
| 195 | #686 | — | 6 | 1 | no | — |
| 196 | #686 | — | 6 | 1 | no | — |
| 197 | #685 | — | 6 | 2 | no | — |
| 198 | #683 | — | 6 | 2 | no | — |
| 199 | C4×Dic5 | — | 3 | 1 | no | — |
| 200 | C4×Dic5 | — | 3 | 1 | no | — |
| 201 | C4×Dic5 | — | 6 | 1 | no | — |
| 202 | #681 | — | 3 | 1 | no | — |
| 203 | #681 | — | 3 | 1 | no | — |
| 204 | #681 | — | 6 | 1 | no | — |
| 205 | C2×#168 | — | 6 | 1 | no | — |
| 206 | #585 | — | 5 | 1 | no | — |
| 207 | #575 | — | 3 | 1 | no | — |
| 208 | #575 | — | 15 | 1 | no | — |
| 209 | #532 | — | 15 | 1 | no | — |
| 210 | #456 | — | 15 | 1 | no | — |
| 211 | #456 | — | 15 | 1 | no | — |
| 212 | #455 | — | 15 | 1 | no | — |
| 213 | #455 | — | 15 | 1 | no | — |
| 214 | #454 | — | 15 | 1 | no | — |
| 215 | #454 | — | 15 | 1 | no | — |
| 216 | #453 | — | 15 | 1 | no | — |
| 217 | #453 | — | 15 | 1 | no | — |
| 218 | C2×#104 | — | 15 | 1 | no | — |
| 219 | C2×#104 | — | 15 | 1 | no | — |
| 220 | #413 | — | 15 | 1 | no | — |
| 221 | C22×C3×C5 | — | 4 | 1 | no | — |
| 222 | C2×C5×D3 | — | 8 | 1 | no | — |
| 223 | C2×C3×D5 | — | 8 | 1 | no | — |
| 224 | C3×C4×C5 | — | 4 | 1 | no | — |
| 225 | C3×C4×C5 | — | 4 | 1 | no | — |
| 226 | C3×Dic5 | — | 8 | 1 | no | — |
| 227 | C5×Dic3 | — | 8 | 1 | no | — |
| 228 | C3×#41 | — | 20 | 1 | no | — |
| 229 | #235 | — | 4 | 1 | no | — |
| 230 | #41⋊C3 | — | 10 | 1 | no | — |
| 231 | #41⋊C3 | C22⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 232 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 233 | C2×SL(2,𝔽3) | — | 10 | 1 | no | — |
| 234 | C2×SL(2,𝔽3) | C22⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 235 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 236 | #226 | — | 2 | 1 | no | — |
| 237 | #216 | — | 20 | 1 | no | — |
| 238 | #215 | — | 20 | 1 | no | — |
| 239 | #214 | — | 20 | 1 | no | — |
| 240 | #213 | — | 20 | 1 | no | — |
| 241 | C2×C3⋊C8 | — | 20 | 1 | no | — |
| 242 | C23×C5 | — | 3 | 1 | no | — |
| 243 | C23×C5 | — | 6 | 1 | no | — |
| 244 | C22×D5 | — | 3 | 2 | no | — |
| 245 | C22×D5 | — | 6 | 1 | no | — |
| 246 | C5×Q8 | — | 3 | 1 | no | — |
| 247 | C5×Q8 | — | 6 | 1 | no | — |
| 248 | C5×Q8 | — | 6 | 1 | no | — |
| 249 | C5×Q8 | C2×#67 | 1 | 1 | yes | characteristic |
| 250 | C5×D4 | — | 3 | 1 | no | — |
| 251 | C5×D4 | — | 3 | 1 | no | — |
| 252 | C5×D4 | — | 6 | 1 | no | — |
| 253 | C5×D4 | — | 6 | 1 | no | — |
| 254 | C5×D4 | — | 6 | 1 | no | — |
| 255 | C5×D4 | — | 12 | 1 | no | — |
| 256 | C5×D4 | — | 12 | 1 | no | — |
| 257 | C2×C4×C5 | — | 3 | 1 | no | — |
| 258 | C2×C4×C5 | — | 3 | 1 | no | — |
| 259 | C2×C4×C5 | — | 3 | 1 | no | — |
| 260 | C2×C4×C5 | — | 3 | 1 | no | — |
| 261 | C2×C4×C5 | — | 3 | 1 | no | — |
| 262 | C2×C4×C5 | — | 6 | 1 | no | — |
| 263 | C2×C4×C5 | — | 12 | 1 | no | — |
| 264 | C2×C4×C5 | — | 12 | 1 | no | — |
| 265 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 266 | C22⋊D5 | — | 2 | 1 | no | — |
| 267 | C22⋊D5 | — | 6 | 1 | no | — |
| 268 | C22⋊D5 | — | 6 | 1 | no | — |
| 269 | C22⋊D5 | — | 6 | 2 | no | — |
| 270 | C22⋊D5 | — | 6 | 1 | no | — |
| 271 | C22⋊D5 | — | 12 | 4 | no | — |
| 272 | C2×Dic5 | — | 3 | 2 | no | — |
| 273 | C2×Dic5 | — | 6 | 1 | no | — |
| 274 | C2×Dic5 | — | 6 | 1 | no | — |
| 275 | C2×Dic5 | — | 6 | 1 | no | — |
| 276 | C2×Dic5 | — | 12 | 2 | no | — |
| 277 | D20 | — | 3 | 1 | no | — |
| 278 | D20 | — | 6 | 1 | no | — |
| 279 | D20 | — | 6 | 1 | no | — |
| 280 | D20 | C2×S4 | 1 | 1 | yes | characteristic |
| 281 | C4×D5 | — | 2 | 1 | no | — |
| 282 | C4×D5 | — | 6 | 1 | no | — |
| 283 | C4×D5 | — | 6 | 1 | no | — |
| 284 | C4×D5 | — | 6 | 2 | no | — |
| 285 | C4×D5 | — | 6 | 1 | no | — |
| 286 | Dic10 | — | 3 | 1 | no | — |
| 287 | Dic10 | — | 6 | 1 | no | — |
| 288 | Dic10 | — | 6 | 1 | no | — |
| 289 | Dic10 | C2×S4 | 1 | 1 | yes | characteristic |
| 290 | C5×C8 | — | 6 | 1 | no | — |
| 291 | C5×C8 | — | 6 | 1 | no | — |
| 292 | #168 | — | 6 | 1 | no | — |
| 293 | #168 | — | 6 | 1 | no | — |
| 294 | 2−1+4 | — | 5 | 1 | no | — |
| 295 | 2−1+4 | — | 10 | 1 | no | — |
| 296 | 2−1+4 | — | 15 | 1 | no | — |
| 297 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 298 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 299 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 300 | C2×#41 | — | 3 | 1 | no | — |
| 301 | C2×#41 | — | 10 | 1 | no | — |
| 302 | C2×#41 | — | 15 | 1 | no | — |
| 303 | C2×#41 | — | 15 | 1 | no | — |
| 304 | C2×#41 | — | 30 | 1 | no | — |
| 305 | C2×#41 | D3×D5 | 1 | 1 | yes | characteristic |
| 306 | #137 | — | 3 | 1 | no | — |
| 307 | #137 | — | 3 | 1 | no | — |
| 308 | #137 | — | 6 | 1 | no | — |
| 309 | #137 | — | 15 | 1 | no | — |
| 310 | #137 | — | 15 | 1 | no | — |
| 311 | #137 | — | 30 | 1 | no | — |
| 312 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 313 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 314 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 315 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 316 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 317 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 318 | #135 | — | 6 | 1 | no | — |
| 319 | #135 | — | 6 | 1 | no | — |
| 320 | #135 | — | 30 | 1 | no | — |
| 321 | #135 | — | 30 | 1 | no | — |
| 322 | C2×M16 | — | 3 | 1 | no | — |
| 323 | C2×M16 | — | 15 | 1 | no | — |
| 324 | C4⋊Q8 | — | 15 | 1 | no | — |
| 325 | #127 | — | 15 | 1 | no | — |
| 326 | #124 | — | 15 | 1 | no | — |
| 327 | #124 | — | 15 | 1 | no | — |
| 328 | #121 | — | 30 | 2 | no | — |
| 329 | C4×D4 | — | 30 | 2 | no | — |
| 330 | C2×C42 | — | 15 | 1 | no | — |
| 331 | #104 | — | 15 | 1 | no | — |
| 332 | #104 | — | 15 | 1 | no | — |
| 333 | #104 | — | 15 | 1 | no | — |
| 334 | #104 | — | 15 | 1 | no | — |
| 335 | #104 | — | 15 | 1 | no | — |
| 336 | #104 | — | 15 | 1 | no | — |
| 337 | #104 | — | 15 | 1 | no | — |
| 338 | #104 | — | 15 | 1 | no | — |
| 339 | #101 | — | 15 | 1 | no | — |
| 340 | #101 | — | 15 | 1 | no | — |
| 341 | #100 | — | 15 | 1 | no | — |
| 342 | #100 | — | 15 | 1 | no | — |
| 343 | C2×C3×C5 | — | 4 | 1 | no | — |
| 344 | C2×C3×C5 | — | 8 | 1 | no | — |
| 345 | C3×D5 | — | 16 | 1 | no | — |
| 346 | C5×D3 | — | 16 | 1 | no | — |
| 347 | C3×Q8 | — | 20 | 1 | no | — |
| 348 | C3×D4 | — | 20 | 1 | no | — |
| 349 | C3×D4 | — | 40 | 1 | no | — |
| 350 | C2×C3×C4 | — | 4 | 1 | no | — |
| 351 | C2×C3×C4 | — | 40 | 1 | no | — |
| 352 | #67 | — | 8 | 1 | no | — |
| 353 | D12 | — | 4 | 1 | no | — |
| 354 | C4×D3 | — | 8 | 1 | no | — |
| 355 | Dic6 | — | 4 | 1 | no | — |
| 356 | SL(2,𝔽3) | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 357 | C3⋊C8 | — | 20 | 1 | no | — |
| 358 | C3⋊C8 | — | 20 | 1 | no | — |
| 359 | C22×C5 | — | 3 | 1 | no | — |
| 360 | C22×C5 | — | 3 | 1 | no | — |
| 361 | C22×C5 | — | 12 | 1 | no | — |
| 362 | C22×C5 | — | 12 | 2 | no | — |
| 363 | C22×C5 | — | 12 | 1 | no | — |
| 364 | C22×C5 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 365 | C2×D5 | — | 2 | 1 | no | — |
| 366 | C2×D5 | — | 6 | 1 | no | — |
| 367 | C2×D5 | — | 12 | 2 | no | — |
| 368 | C2×D5 | — | 24 | 1 | no | — |
| 369 | C4×C5 | — | 3 | 1 | no | — |
| 370 | C4×C5 | — | 3 | 1 | no | — |
| 371 | C4×C5 | — | 12 | 1 | no | — |
| 372 | C4×C5 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 373 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 374 | Dic5 | — | 2 | 1 | no | — |
| 375 | Dic5 | — | 6 | 2 | no | — |
| 376 | Dic5 | — | 6 | 1 | no | — |
| 377 | Dic5 | — | 12 | 1 | no | — |
| 378 | #41 | — | 3 | 1 | no | — |
| 379 | #41 | — | 3 | 1 | no | — |
| 380 | #41 | — | 5 | 1 | no | — |
| 381 | #41 | — | 6 | 1 | no | — |
| 382 | #41 | — | 6 | 1 | no | — |
| 383 | #41 | — | 6 | 1 | no | — |
| 384 | #41 | — | 6 | 1 | no | — |
| 385 | #41 | — | 10 | 1 | no | — |
| 386 | #41 | — | 15 | 1 | no | — |
| 387 | #41 | — | 15 | 1 | no | — |
| 388 | #41 | — | 15 | 1 | no | — |
| 389 | #41 | — | 30 | 1 | no | — |
| 390 | #41 | — | 30 | 1 | no | — |
| 391 | #41 | — | 30 | 1 | no | — |
| 392 | #41 | — | 30 | 1 | no | — |
| 393 | #41 | — | 30 | 1 | no | — |
| 394 | #41 | — | 30 | 1 | no | — |
| 395 | #41 | — | 30 | 2 | no | — |
| 396 | #41 | — | 30 | 1 | no | — |
| 397 | #41 | — | 30 | 1 | no | — |
| 398 | #41 | #1201 | 1 | 1 | yes | characteristic |
| 399 | #41 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 400 | C2×Q8 | — | 3 | 1 | no | — |
| 401 | C2×Q8 | — | 10 | 1 | no | — |
| 402 | C2×Q8 | — | 15 | 1 | no | — |
| 403 | C2×Q8 | — | 15 | 1 | no | — |
| 404 | C2×Q8 | — | 30 | 1 | no | — |
| 405 | C2×Q8 | #1201 | 1 | 1 | yes | characteristic |
| 406 | C2×D4 | — | 3 | 1 | no | — |
| 407 | C2×D4 | — | 3 | 1 | no | — |
| 408 | C2×D4 | — | 6 | 1 | no | — |
| 409 | C2×D4 | — | 15 | 1 | no | — |
| 410 | C2×D4 | — | 15 | 1 | no | — |
| 411 | C2×D4 | — | 15 | 2 | no | — |
| 412 | C2×D4 | — | 30 | 1 | no | — |
| 413 | C2×D4 | — | 30 | 1 | no | — |
| 414 | C2×D4 | — | 30 | 2 | no | — |
| 415 | C2×D4 | — | 30 | 1 | no | — |
| 416 | C2×D4 | — | 30 | 2 | no | — |
| 417 | C22×C4 | — | 3 | 1 | no | — |
| 418 | C22×C4 | — | 6 | 1 | no | — |
| 419 | C22×C4 | — | 15 | 2 | no | — |
| 420 | C22×C4 | — | 30 | 1 | no | — |
| 421 | C22×C4 | — | 30 | 1 | no | — |
| 422 | Q16 | — | 6 | 1 | no | — |
| 423 | Q16 | — | 6 | 1 | no | — |
| 424 | Q16 | — | 30 | 1 | no | — |
| 425 | Q16 | — | 30 | 1 | no | — |
| 426 | SD16 | — | 6 | 1 | no | — |
| 427 | SD16 | — | 6 | 1 | no | — |
| 428 | SD16 | — | 6 | 1 | no | — |
| 429 | SD16 | — | 6 | 1 | no | — |
| 430 | SD16 | — | 30 | 1 | no | — |
| 431 | SD16 | — | 30 | 1 | no | — |
| 432 | SD16 | — | 30 | 1 | no | — |
| 433 | SD16 | — | 30 | 1 | no | — |
| 434 | D8 | — | 6 | 1 | no | — |
| 435 | D8 | — | 6 | 1 | no | — |
| 436 | D8 | — | 30 | 1 | no | — |
| 437 | D8 | — | 30 | 1 | no | — |
| 438 | M16 | — | 3 | 1 | no | — |
| 439 | M16 | — | 3 | 1 | no | — |
| 440 | M16 | — | 6 | 1 | no | — |
| 441 | M16 | — | 15 | 1 | no | — |
| 442 | M16 | — | 15 | 1 | no | — |
| 443 | M16 | — | 30 | 1 | no | — |
| 444 | C2×C8 | — | 6 | 1 | no | — |
| 445 | C2×C8 | — | 30 | 1 | no | — |
| 446 | C4⋊C4 | — | 30 | 2 | no | — |
| 447 | C22⋊C4 | — | 30 | 2 | no | — |
| 448 | C22⋊C4 | — | 30 | 2 | no | — |
| 449 | C42 | — | 15 | 1 | no | — |
| 450 | C42 | — | 15 | 1 | no | — |
| 451 | C42 | — | 30 | 1 | no | — |
| 452 | C3×C5 | — | 4 | 1 | no | Hall |
| 453 | C22×C3 | — | 4 | 1 | no | — |
| 454 | C22×C3 | — | 40 | 1 | no | — |
| 455 | C2×D3 | — | 8 | 1 | no | — |
| 456 | C3×C4 | — | 4 | 1 | no | — |
| 457 | C3×C4 | — | 4 | 1 | no | — |
| 458 | C3×C4 | — | 40 | 1 | no | — |
| 459 | Dic3 | — | 8 | 1 | no | — |
| 460 | C2×C5 | — | 2 | 1 | no | — |
| 461 | C2×C5 | — | 6 | 1 | no | — |
| 462 | C2×C5 | — | 6 | 1 | no | — |
| 463 | C2×C5 | — | 24 | 1 | no | — |
| 464 | C2×C5 | C2×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 465 | D5 | — | 4 | 1 | no | — |
| 466 | D5 | — | 12 | 1 | no | — |
| 467 | C23 | — | 3 | 1 | no | — |
| 468 | C23 | — | 6 | 1 | no | — |
| 469 | C23 | — | 15 | 2 | no | — |
| 470 | C23 | — | 30 | 1 | no | — |
| 471 | Q8 | — | 3 | 1 | no | — |
| 472 | Q8 | — | 5 | 1 | no | — |
| 473 | Q8 | — | 6 | 1 | no | — |
| 474 | Q8 | — | 6 | 1 | no | — |
| 475 | Q8 | — | 15 | 1 | no | — |
| 476 | Q8 | — | 30 | 1 | no | — |
| 477 | Q8 | — | 30 | 1 | no | — |
| 478 | Q8 | C2×#1201 | 1 | 1 | yes | characteristic |
| 479 | D4 | — | 3 | 1 | no | — |
| 480 | D4 | — | 3 | 1 | no | — |
| 481 | D4 | — | 5 | 1 | no | — |
| 482 | D4 | — | 6 | 1 | no | — |
| 483 | D4 | — | 6 | 1 | no | — |
| 484 | D4 | — | 6 | 1 | no | — |
| 485 | D4 | — | 10 | 1 | no | — |
| 486 | D4 | — | 12 | 1 | no | — |
| 487 | D4 | — | 12 | 1 | no | — |
| 488 | D4 | — | 15 | 1 | no | — |
| 489 | D4 | — | 30 | 1 | no | — |
| 490 | D4 | — | 30 | 1 | no | — |
| 491 | D4 | — | 30 | 1 | no | — |
| 492 | D4 | — | 30 | 1 | no | — |
| 493 | D4 | — | 30 | 2 | no | — |
| 494 | D4 | — | 30 | 1 | no | — |
| 495 | D4 | — | 60 | 4 | no | — |
| 496 | C2×C4 | — | 3 | 1 | no | — |
| 497 | C2×C4 | — | 3 | 1 | no | — |
| 498 | C2×C4 | — | 3 | 1 | no | — |
| 499 | C2×C4 | — | 3 | 1 | no | — |
| 500 | C2×C4 | — | 3 | 1 | no | — |
| 501 | C2×C4 | — | 6 | 1 | no | — |
| 502 | C2×C4 | — | 10 | 1 | no | — |
| 503 | C2×C4 | — | 12 | 1 | no | — |
| 504 | C2×C4 | — | 12 | 1 | no | — |
| 505 | C2×C4 | — | 15 | 2 | no | — |
| 506 | C2×C4 | — | 30 | 1 | no | — |
| 507 | C2×C4 | — | 30 | 1 | no | — |
| 508 | C2×C4 | — | 30 | 2 | no | — |
| 509 | C2×C4 | — | 30 | 1 | no | — |
| 510 | C2×C4 | — | 30 | 1 | no | — |
| 511 | C2×C4 | — | 30 | 1 | no | — |
| 512 | C2×C4 | — | 30 | 1 | no | — |
| 513 | C2×C4 | — | 60 | 2 | no | — |
| 514 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 515 | C8 | — | 6 | 1 | no | — |
| 516 | C8 | — | 6 | 1 | no | — |
| 517 | C8 | — | 30 | 1 | no | — |
| 518 | C8 | — | 30 | 1 | no | — |
| 519 | C2×C3 | — | 4 | 1 | no | — |
| 520 | C2×C3 | — | 8 | 1 | no | — |
| 521 | C2×C3 | — | 80 | 1 | no | — |
| 522 | D3 | — | 16 | 1 | no | — |
| 523 | C5 | #85544 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 524 | C22 | — | 3 | 1 | no | — |
| 525 | C22 | — | 3 | 1 | no | — |
| 526 | C22 | — | 10 | 1 | no | — |
| 527 | C22 | — | 12 | 1 | no | — |
| 528 | C22 | — | 12 | 2 | no | — |
| 529 | C22 | — | 12 | 1 | no | — |
| 530 | C22 | — | 30 | 1 | no | — |
| 531 | C22 | — | 60 | 2 | no | — |
| 532 | C22 | — | 120 | 1 | no | — |
| 533 | C22 | #91904 | 1 | 1 | yes | characteristic |
| 534 | C4 | — | 3 | 1 | no | — |
| 535 | C4 | — | 3 | 1 | no | — |
| 536 | C4 | — | 10 | 1 | no | — |
| 537 | C4 | — | 12 | 1 | no | — |
| 538 | C4 | — | 30 | 2 | no | — |
| 539 | C4 | — | 30 | 1 | no | — |
| 540 | C4 | — | 60 | 1 | no | — |
| 541 | C4 | #91904 | 1 | 1 | yes | characteristic |
| 542 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 543 | C3 | — | 4 | 1 | no | Sylow |
| 544 | C2 | — | 2 | 1 | no | — |
| 545 | C2 | — | 6 | 1 | no | — |
| 546 | C2 | — | 6 | 1 | no | — |
| 547 | C2 | — | 20 | 1 | no | — |
| 548 | C2 | — | 24 | 1 | no | — |
| 549 | C2 | — | 60 | 1 | no | — |
| 550 | C2 | C2×#91904 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #66283⋊C3 | C2 | semidirect |
| 2. C5×#5923 | C2 | semidirect |
| 3. C2×#91185 | C2 | semidirect |
| 4. #11751631 | C2 | semidirect |
| 5. #11751629 | C2 | semidirect |
| 6. #11751627 | C2 | semidirect |
| 7. #11751625 | C2 | semidirect |
| 14. C5×#986 | C22 | semidirect |
| 16. C5×#984 | C22 | semidirect |
| 19. #91185 | C22 | semidirect |
| 20. #91185 | C22 | semidirect |
| 22. #66283 | D3 | semidirect |
| 39. C5×#41⋊C3 | D4 | semidirect |
| 41. C2×C5×SL(2,𝔽3) | D4 | semidirect |
| 52. #5923 | D5 | semidirect |
| 125. #986 | C2×D5 | semidirect |
| 127. #984 | C2×D5 | semidirect |
| 231. #41⋊C3 | C22⋊D5 | semidirect |
| 234. C2×SL(2,𝔽3) | C22⋊D5 | semidirect |
| 523. C5 | #85544 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66283⋊C3 | 2 |
| C5×#5923 | 2 |
| C2×#91185 | 2 |
| #11751631 | 2 |
| #11751629 | 2 |
| #11751627 | 2 |
| #11751625 | 2 |
| #10615735 | 3 |
| #91297 | 4 |
| #85544 | 5 |