Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
614 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 614 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 | C2×#91956 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#91894 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #66168⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#5427 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11751611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751610 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11751602 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10611856 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×C5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×C5⋊(#41⋊C3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #91956 | — | 2 | 2 | no | — |
| 12 | C2×C5⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C5⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×C5×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #91894 | — | 2 | 2 | no | — |
| 16 | #91420 | — | 4 | 1 | no | maximal |
| 17 | Dic5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C5×#859 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #85410 | — | 5 | 1 | no | maximal, Hall |
| 20 | #66168 | D3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#4095 | — | 3 | 1 | no | — |
| 22 | C2×#4060 | — | 3 | 1 | no | — |
| 23 | #65943 | — | 3 | 1 | no | — |
| 24 | C5×#449 | — | 3 | 1 | no | — |
| 25 | #65452 | — | 3 | 1 | no | — |
| 26 | #65445 | — | 3 | 1 | no | — |
| 27 | #65440 | — | 3 | 1 | no | — |
| 28 | #65328 | — | 3 | 1 | no | — |
| 29 | #65100 | — | 3 | 1 | no | — |
| 30 | #65077 | — | 3 | 1 | no | — |
| 31 | #65075 | — | 3 | 1 | no | — |
| 32 | #65071 | — | 3 | 1 | no | — |
| 33 | #65021 | — | 3 | 1 | no | — |
| 34 | #65018 | — | 3 | 1 | no | — |
| 35 | C2×D60 | — | 4 | 1 | no | — |
| 36 | C5×#41⋊C3 | — | 2 | 1 | no | — |
| 37 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×#1203 | — | 4 | 1 | no | — |
| 39 | C2×#1203 | — | 4 | 1 | no | — |
| 40 | C2×#1200 | — | 4 | 1 | no | — |
| 41 | C5⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 42 | C5⋊GL(2,𝔽3) | — | 2 | 1 | no | — |
| 43 | C5⋊GL(2,𝔽3) | D4 | 1 | 2 | yes | complemented |
| 44 | C5×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 45 | C5×(C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 46 | C3×#683 | — | 4 | 1 | no | — |
| 47 | #6667 | — | 4 | 1 | no | — |
| 48 | C2×#986 | — | 5 | 1 | no | — |
| 49 | C2×#986 | — | 5 | 1 | no | — |
| 50 | C4⋊(#41⋊C3) | — | 5 | 1 | no | — |
| 51 | #5427 | — | 5 | 1 | no | — |
| 52 | #5427 | D5 | 1 | 1 | yes | characteristic, complemented |
| 53 | C4⋊GL(2,𝔽3) | — | 5 | 1 | no | — |
| 54 | C4×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 55 | C2×C5×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | C2×#713 | C2×D3 | 1 | 1 | yes | characteristic |
| 57 | C2×D4×D5 | — | 3 | 1 | no | — |
| 58 | C2×D4×D5 | — | 6 | 1 | no | — |
| 59 | C22×D20 | — | 3 | 1 | no | — |
| 60 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 61 | C2×C5×D8 | — | 3 | 1 | no | — |
| 62 | C5×#121 | — | 3 | 1 | no | — |
| 63 | #4095 | — | 6 | 2 | no | — |
| 64 | #4095 | — | 6 | 2 | no | — |
| 65 | Q8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 66 | C2×#688 | — | 3 | 1 | no | — |
| 67 | C2×#688 | — | 3 | 1 | no | — |
| 68 | #4086 | — | 3 | 1 | no | — |
| 69 | #4086 | — | 3 | 1 | no | — |
| 70 | #4084 | — | 3 | 1 | no | — |
| 71 | #4083 | — | 6 | 1 | no | — |
| 72 | C2×#686 | — | 3 | 1 | no | — |
| 73 | C2×#686 | — | 3 | 1 | no | — |
| 74 | C2×#686 | — | 3 | 1 | no | — |
| 75 | #4076 | — | 3 | 1 | no | — |
| 76 | C4×C22⋊D5 | — | 3 | 1 | no | — |
| 77 | C2×#681 | — | 3 | 1 | no | — |
| 78 | #4060 | — | 6 | 2 | no | — |
| 79 | #4060 | — | 6 | 2 | no | — |
| 80 | C2×D40 | — | 3 | 1 | no | — |
| 81 | C2×D40 | — | 3 | 1 | no | — |
| 82 | C2×#676 | — | 3 | 1 | no | — |
| 83 | #4041 | — | 3 | 1 | no | — |
| 84 | #4039 | — | 3 | 1 | no | — |
| 85 | #4030 | — | 6 | 1 | no | — |
| 86 | #4028 | — | 6 | 1 | no | — |
| 87 | C5×#103 | — | 3 | 1 | no | — |
| 88 | C5×#102 | — | 3 | 1 | no | — |
| 89 | C5×C22⋊C8 | — | 3 | 1 | no | — |
| 90 | #3964 | — | 3 | 1 | no | — |
| 91 | #3953 | — | 3 | 1 | no | — |
| 92 | #3953 | — | 3 | 1 | no | — |
| 93 | #3952 | — | 3 | 1 | no | — |
| 94 | #3946 | — | 3 | 1 | no | — |
| 95 | C8×Dic5 | — | 3 | 1 | no | — |
| 96 | #3941 | — | 3 | 1 | no | — |
| 97 | #3940 | — | 3 | 1 | no | — |
| 98 | #3274 | — | 15 | 1 | no | Sylow |
| 99 | C22×D15 | — | 4 | 1 | no | — |
| 100 | C22×D15 | — | 4 | 1 | no | — |
| 101 | C22×C5×D3 | — | 4 | 1 | no | — |
| 102 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 103 | D60 | — | 8 | 2 | no | — |
| 104 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 105 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 106 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 107 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 108 | #1203 | — | 8 | 2 | no | — |
| 109 | #1203 | — | 8 | 2 | no | — |
| 110 | #1200 | — | 8 | 2 | no | — |
| 111 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 112 | C2×#41⋊C3 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 113 | #986 | — | 10 | 2 | no | — |
| 114 | #986 | — | 10 | 2 | no | — |
| 115 | C2×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 116 | C2×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 117 | C2×GL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 118 | #895 | — | 20 | 1 | no | — |
| 119 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 120 | #859 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 121 | C23×D5 | — | 6 | 1 | no | — |
| 122 | C23×D5 | — | 6 | 1 | no | — |
| 123 | C5×#41 | — | 2 | 1 | no | — |
| 124 | C5×#41 | — | 6 | 1 | no | — |
| 125 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 126 | C2×C5×D4 | — | 3 | 1 | no | — |
| 127 | C2×C5×D4 | — | 3 | 1 | no | — |
| 128 | C2×C5×D4 | — | 6 | 1 | no | — |
| 129 | C22×C4×C5 | — | 3 | 1 | no | — |
| 130 | C2×C22⋊D5 | — | 3 | 1 | no | — |
| 131 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 132 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 133 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 134 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 135 | #713 | — | 2 | 1 | no | — |
| 136 | #713 | — | 6 | 1 | no | — |
| 137 | D4×D5 | — | 6 | 2 | no | — |
| 138 | D4×D5 | — | 12 | 1 | no | — |
| 139 | D4×D5 | — | 12 | 4 | no | — |
| 140 | C2×D20 | — | 3 | 1 | no | — |
| 141 | C2×D20 | — | 3 | 1 | no | — |
| 142 | C2×D20 | — | 3 | 1 | no | — |
| 143 | C2×D20 | — | 6 | 2 | no | — |
| 144 | C2×D20 | — | 6 | 1 | no | — |
| 145 | C2×D20 | — | 6 | 1 | no | — |
| 146 | C2×D20 | — | 12 | 1 | no | — |
| 147 | C2×C4×D5 | — | 3 | 1 | no | — |
| 148 | C2×C4×D5 | — | 6 | 1 | no | — |
| 149 | C5×SD16 | — | 6 | 1 | no | — |
| 150 | C5×SD16 | — | 6 | 1 | no | — |
| 151 | C5×D8 | — | 12 | 1 | no | — |
| 152 | C2×C5×C8 | — | 3 | 1 | no | — |
| 153 | C2×C5×C8 | — | 3 | 1 | no | — |
| 154 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 155 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 156 | C22⋊Dic5 | — | 3 | 1 | no | — |
| 157 | #688 | — | 3 | 2 | no | — |
| 158 | #688 | — | 3 | 2 | no | — |
| 159 | #688 | — | 6 | 1 | no | — |
| 160 | #688 | — | 6 | 1 | no | — |
| 161 | #686 | — | 6 | 2 | no | — |
| 162 | #686 | — | 6 | 2 | no | — |
| 163 | #686 | — | 6 | 2 | no | — |
| 164 | #685 | — | 3 | 1 | no | — |
| 165 | #685 | — | 6 | 1 | no | — |
| 166 | #685 | — | 6 | 1 | no | — |
| 167 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 168 | #683 | S4 | 1 | 1 | yes | characteristic |
| 169 | C4×Dic5 | — | 3 | 1 | no | — |
| 170 | #681 | — | 6 | 2 | no | — |
| 171 | C2×#168 | — | 3 | 1 | no | — |
| 172 | C2×#168 | — | 3 | 1 | no | — |
| 173 | D40 | — | 6 | 2 | no | — |
| 174 | D40 | — | 12 | 1 | no | — |
| 175 | #676 | — | 6 | 2 | no | — |
| 176 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 177 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 178 | #550 | — | 5 | 1 | no | — |
| 179 | D42 | — | 15 | 1 | no | — |
| 180 | #493 | — | 15 | 1 | no | — |
| 181 | #469 | — | 15 | 1 | no | — |
| 182 | #469 | — | 15 | 1 | no | — |
| 183 | #460 | — | 15 | 1 | no | — |
| 184 | #459 | — | 15 | 1 | no | — |
| 185 | #449 | — | 3 | 1 | no | — |
| 186 | #449 | — | 15 | 1 | no | — |
| 187 | #447 | — | 15 | 1 | no | — |
| 188 | #447 | — | 15 | 1 | no | — |
| 189 | C4×SD16 | — | 15 | 1 | no | — |
| 190 | #436 | — | 15 | 1 | no | — |
| 191 | C22×C3×C5 | — | 4 | 1 | no | — |
| 192 | C2×D15 | — | 4 | 2 | no | — |
| 193 | C2×D15 | — | 8 | 1 | no | — |
| 194 | C2×D15 | — | 8 | 1 | no | — |
| 195 | C2×D15 | — | 8 | 1 | no | — |
| 196 | C2×D15 | — | 8 | 1 | no | — |
| 197 | C2×D15 | — | 8 | 1 | no | — |
| 198 | C2×C5×D3 | — | 8 | 1 | no | — |
| 199 | C2×C5×D3 | — | 8 | 1 | no | — |
| 200 | C2×C5×D3 | — | 8 | 1 | no | — |
| 201 | C3×C4×C5 | — | 8 | 1 | no | — |
| 202 | C3×Dic5 | — | 4 | 2 | no | — |
| 203 | C3×Dic5 | — | 8 | 1 | no | — |
| 204 | C5×Dic3 | — | 8 | 1 | no | — |
| 205 | C2×D12 | — | 20 | 1 | no | — |
| 206 | C2×D12 | — | 20 | 1 | no | — |
| 207 | C2×D12 | — | 20 | 1 | no | — |
| 208 | C2×C4×D3 | — | 20 | 1 | no | — |
| 209 | #41⋊C3 | — | 2 | 1 | no | — |
| 210 | #41⋊C3 | — | 10 | 1 | no | — |
| 211 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 212 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 213 | GL(2,𝔽3) | — | 5 | 2 | no | — |
| 214 | GL(2,𝔽3) | — | 10 | 1 | no | — |
| 215 | C3×C4⋊C4 | — | 20 | 1 | no | — |
| 216 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 217 | (C2×D3)⋊C4 | — | 20 | 1 | no | — |
| 218 | C23×C5 | — | 3 | 1 | no | — |
| 219 | C23×C5 | — | 6 | 1 | no | — |
| 220 | C22×D5 | — | 3 | 1 | no | — |
| 221 | C22×D5 | — | 6 | 1 | no | — |
| 222 | C22×D5 | — | 6 | 1 | no | — |
| 223 | C22×D5 | — | 12 | 2 | no | — |
| 224 | C22×D5 | — | 12 | 2 | no | — |
| 225 | C22×D5 | — | 12 | 2 | no | — |
| 226 | C22×D5 | — | 12 | 2 | no | — |
| 227 | C22×D5 | — | 24 | 1 | no | — |
| 228 | C22×D5 | — | 24 | 1 | no | — |
| 229 | C5×Q8 | — | 3 | 1 | no | — |
| 230 | C5×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 231 | C5×D4 | — | 6 | 1 | no | — |
| 232 | C5×D4 | — | 6 | 1 | no | — |
| 233 | C5×D4 | — | 6 | 1 | no | — |
| 234 | C5×D4 | — | 6 | 1 | no | — |
| 235 | C5×D4 | — | 12 | 2 | no | — |
| 236 | C2×C4×C5 | — | 3 | 1 | no | — |
| 237 | C2×C4×C5 | — | 6 | 1 | no | — |
| 238 | C2×C4×C5 | — | 6 | 1 | no | — |
| 239 | C2×C4×C5 | — | 6 | 1 | no | — |
| 240 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 241 | C22⋊D5 | — | 6 | 2 | no | — |
| 242 | C22⋊D5 | — | 12 | 2 | no | — |
| 243 | C22⋊D5 | — | 12 | 2 | no | — |
| 244 | C22⋊D5 | — | 24 | 1 | no | — |
| 245 | C22⋊D5 | — | 24 | 1 | no | — |
| 246 | C2×Dic5 | — | 3 | 1 | no | — |
| 247 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 248 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 249 | D20 | — | 3 | 2 | no | — |
| 250 | D20 | — | 6 | 1 | no | — |
| 251 | D20 | — | 6 | 1 | no | — |
| 252 | D20 | — | 6 | 1 | no | — |
| 253 | D20 | — | 6 | 1 | no | — |
| 254 | D20 | — | 6 | 1 | no | — |
| 255 | D20 | — | 12 | 2 | no | — |
| 256 | D20 | — | 12 | 2 | no | — |
| 257 | C4×D5 | — | 6 | 1 | no | — |
| 258 | C4×D5 | — | 6 | 1 | no | — |
| 259 | C4×D5 | — | 12 | 2 | no | — |
| 260 | C5×C8 | — | 6 | 1 | no | — |
| 261 | C5×C8 | — | 6 | 1 | no | — |
| 262 | #168 | — | 3 | 2 | no | — |
| 263 | #168 | — | 6 | 1 | no | — |
| 264 | C2×#41 | — | 5 | 1 | no | — |
| 265 | C2×#41 | D3×D5 | 1 | 1 | yes | characteristic |
| 266 | C22×D4 | — | 15 | 1 | no | — |
| 267 | C22×D4 | — | 15 | 1 | no | — |
| 268 | C22×D4 | — | 30 | 1 | no | — |
| 269 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 270 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 271 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 272 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 273 | C2×SD16 | — | 3 | 1 | no | — |
| 274 | C2×SD16 | — | 15 | 1 | no | — |
| 275 | C2×SD16 | — | 15 | 1 | no | — |
| 276 | C2×D8 | — | 3 | 1 | no | — |
| 277 | C2×D8 | — | 15 | 1 | no | — |
| 278 | C2×D8 | — | 15 | 1 | no | — |
| 279 | C2×D8 | — | 15 | 1 | no | — |
| 280 | C2×D8 | — | 15 | 1 | no | — |
| 281 | C2×D8 | — | 15 | 1 | no | — |
| 282 | C2×M16 | — | 15 | 1 | no | — |
| 283 | C2×M16 | — | 15 | 1 | no | — |
| 284 | #127 | — | 15 | 1 | no | — |
| 285 | #127 | — | 15 | 1 | no | — |
| 286 | #121 | — | 3 | 1 | no | — |
| 287 | #121 | — | 15 | 1 | no | — |
| 288 | #121 | — | 15 | 1 | no | — |
| 289 | #121 | — | 15 | 1 | no | — |
| 290 | #121 | — | 30 | 1 | no | — |
| 291 | #120 | — | 30 | 1 | no | — |
| 292 | #120 | — | 30 | 1 | no | — |
| 293 | C4×Q8 | — | 5 | 1 | no | — |
| 294 | C4×D4 | — | 15 | 1 | no | — |
| 295 | C4×D4 | — | 15 | 1 | no | — |
| 296 | #106 | — | 15 | 1 | no | — |
| 297 | C4⋊C8 | — | 15 | 1 | no | — |
| 298 | #103 | — | 3 | 1 | no | — |
| 299 | #102 | — | 3 | 1 | no | — |
| 300 | #102 | — | 15 | 1 | no | — |
| 301 | #102 | — | 15 | 1 | no | — |
| 302 | #102 | — | 15 | 1 | no | — |
| 303 | #102 | — | 15 | 1 | no | — |
| 304 | C22⋊C8 | — | 3 | 1 | no | — |
| 305 | C22⋊C8 | — | 15 | 1 | no | — |
| 306 | C4×C8 | — | 15 | 1 | no | — |
| 307 | C2×C3×C5 | — | 4 | 1 | no | — |
| 308 | C2×C3×C5 | — | 4 | 1 | no | — |
| 309 | C2×C3×C5 | — | 4 | 1 | no | — |
| 310 | D15 | — | 8 | 2 | no | — |
| 311 | D15 | — | 16 | 1 | no | — |
| 312 | C5×D3 | — | 16 | 1 | no | — |
| 313 | C22×D3 | — | 4 | 1 | no | — |
| 314 | C22×D3 | — | 20 | 1 | no | — |
| 315 | C22×D3 | — | 20 | 1 | no | — |
| 316 | C2×C3×C4 | — | 4 | 1 | no | — |
| 317 | C2×C3×C4 | — | 20 | 1 | no | — |
| 318 | C2×C3×C4 | — | 20 | 1 | no | — |
| 319 | C2×Dic3 | — | 4 | 1 | no | — |
| 320 | D12 | — | 40 | 2 | no | — |
| 321 | D12 | — | 40 | 2 | no | — |
| 322 | D12 | — | 40 | 2 | no | — |
| 323 | C4×D3 | — | 40 | 2 | no | — |
| 324 | SL(2,𝔽3) | D4×D5 | 1 | 1 | yes | characteristic, complemented |
| 325 | C22×C5 | — | 6 | 1 | no | — |
| 326 | C22×C5 | — | 6 | 1 | no | — |
| 327 | C22×C5 | — | 6 | 1 | no | — |
| 328 | C22×C5 | — | 12 | 1 | no | — |
| 329 | C22×C5 | — | 12 | 1 | no | — |
| 330 | C22×C5 | — | 12 | 1 | no | — |
| 331 | C22×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 332 | C2×D5 | — | 6 | 2 | no | — |
| 333 | C2×D5 | — | 6 | 1 | no | — |
| 334 | C2×D5 | — | 6 | 1 | no | — |
| 335 | C2×D5 | — | 6 | 1 | no | — |
| 336 | C2×D5 | — | 12 | 1 | no | — |
| 337 | C2×D5 | — | 12 | 1 | no | — |
| 338 | C2×D5 | — | 12 | 1 | no | — |
| 339 | C2×D5 | — | 12 | 1 | no | — |
| 340 | C2×D5 | — | 12 | 1 | no | — |
| 341 | C2×D5 | — | 24 | 4 | no | — |
| 342 | C2×D5 | — | 24 | 4 | no | — |
| 343 | C4×C5 | — | 2 | 1 | no | — |
| 344 | C4×C5 | — | 3 | 1 | no | — |
| 345 | C4×C5 | — | 3 | 1 | no | — |
| 346 | C4×C5 | — | 12 | 1 | no | — |
| 347 | Dic5 | — | 2 | 1 | no | — |
| 348 | Dic5 | — | 6 | 1 | no | — |
| 349 | Dic5 | #986 | 1 | 2 | yes | complemented |
| 350 | C24 | — | 30 | 1 | no | — |
| 351 | C24 | — | 30 | 1 | no | — |
| 352 | #41 | — | 2 | 1 | no | — |
| 353 | #41 | — | 6 | 1 | no | — |
| 354 | #41 | — | 10 | 1 | no | — |
| 355 | #41 | — | 30 | 1 | no | — |
| 356 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 357 | C2×D4 | — | 3 | 1 | no | — |
| 358 | C2×D4 | — | 3 | 1 | no | — |
| 359 | C2×D4 | — | 6 | 1 | no | — |
| 360 | C2×D4 | — | 15 | 1 | no | — |
| 361 | C2×D4 | — | 15 | 1 | no | — |
| 362 | C2×D4 | — | 15 | 1 | no | — |
| 363 | C2×D4 | — | 15 | 1 | no | — |
| 364 | C2×D4 | — | 30 | 1 | no | — |
| 365 | C2×D4 | — | 30 | 1 | no | — |
| 366 | C2×D4 | — | 30 | 2 | no | — |
| 367 | C2×D4 | — | 30 | 1 | no | — |
| 368 | C2×D4 | — | 30 | 1 | no | — |
| 369 | C2×D4 | — | 30 | 1 | no | — |
| 370 | C2×D4 | — | 30 | 2 | no | — |
| 371 | C2×D4 | — | 30 | 1 | no | — |
| 372 | C2×D4 | — | 60 | 1 | no | — |
| 373 | C2×D4 | — | 60 | 1 | no | — |
| 374 | C2×D4 | — | 60 | 4 | no | — |
| 375 | C22×C4 | — | 3 | 1 | no | — |
| 376 | C22×C4 | — | 15 | 1 | no | — |
| 377 | C22×C4 | — | 30 | 1 | no | — |
| 378 | SD16 | — | 6 | 1 | no | — |
| 379 | SD16 | — | 6 | 1 | no | — |
| 380 | SD16 | — | 15 | 2 | no | — |
| 381 | SD16 | — | 15 | 2 | no | — |
| 382 | SD16 | — | 30 | 1 | no | — |
| 383 | SD16 | — | 30 | 1 | no | — |
| 384 | D8 | — | 12 | 1 | no | — |
| 385 | D8 | — | 30 | 2 | no | — |
| 386 | D8 | — | 30 | 2 | no | — |
| 387 | D8 | — | 30 | 2 | no | — |
| 388 | D8 | — | 30 | 2 | no | — |
| 389 | D8 | — | 60 | 1 | no | — |
| 390 | M16 | — | 30 | 2 | no | — |
| 391 | M16 | — | 30 | 2 | no | — |
| 392 | C2×C8 | — | 3 | 1 | no | — |
| 393 | C2×C8 | — | 3 | 1 | no | — |
| 394 | C2×C8 | — | 15 | 1 | no | — |
| 395 | C2×C8 | — | 15 | 1 | no | — |
| 396 | C4⋊C4 | — | 3 | 1 | no | — |
| 397 | C4⋊C4 | — | 5 | 1 | no | — |
| 398 | C4⋊C4 | — | 15 | 1 | no | — |
| 399 | C22⋊C4 | — | 6 | 1 | no | — |
| 400 | C22⋊C4 | — | 15 | 1 | no | — |
| 401 | C22⋊C4 | — | 15 | 1 | no | — |
| 402 | C22⋊C4 | — | 30 | 1 | no | — |
| 403 | C22⋊C4 | — | 30 | 1 | no | — |
| 404 | C42 | — | 15 | 1 | no | — |
| 405 | C3×C5 | — | 4 | 1 | no | Hall |
| 406 | C22×C3 | — | 4 | 1 | no | — |
| 407 | C2×D3 | — | 8 | 1 | no | — |
| 408 | C2×D3 | — | 8 | 1 | no | — |
| 409 | C2×D3 | — | 8 | 1 | no | — |
| 410 | C2×D3 | — | 20 | 2 | no | — |
| 411 | C2×D3 | — | 40 | 1 | no | — |
| 412 | C2×D3 | — | 40 | 1 | no | — |
| 413 | C2×D3 | — | 40 | 1 | no | — |
| 414 | C2×D3 | — | 40 | 1 | no | — |
| 415 | C2×D3 | — | 40 | 1 | no | — |
| 416 | C3×C4 | — | 8 | 1 | no | — |
| 417 | C3×C4 | — | 20 | 2 | no | — |
| 418 | C3×C4 | — | 40 | 1 | no | — |
| 419 | Dic3 | — | 8 | 1 | no | — |
| 420 | C2×C5 | — | 12 | 1 | no | — |
| 421 | C2×C5 | — | 24 | 1 | no | — |
| 422 | C2×C5 | D4×S4 | 1 | 1 | yes | characteristic |
| 423 | C2×C5 | C2×#986 | 1 | 1 | yes | characteristic |
| 424 | C2×C5 | #5925 | 1 | 1 | yes | characteristic |
| 425 | D5 | — | 12 | 1 | no | — |
| 426 | D5 | — | 12 | 2 | no | — |
| 427 | D5 | — | 24 | 1 | no | — |
| 428 | C23 | — | 3 | 1 | no | — |
| 429 | C23 | — | 6 | 1 | no | — |
| 430 | C23 | — | 15 | 1 | no | — |
| 431 | C23 | — | 30 | 1 | no | — |
| 432 | C23 | — | 30 | 1 | no | — |
| 433 | C23 | — | 60 | 2 | no | — |
| 434 | C23 | — | 60 | 2 | no | — |
| 435 | C23 | — | 60 | 2 | no | — |
| 436 | C23 | — | 60 | 2 | no | — |
| 437 | C23 | — | 120 | 1 | no | — |
| 438 | C23 | — | 120 | 1 | no | — |
| 439 | Q8 | — | 3 | 1 | no | — |
| 440 | Q8 | #6790 | 1 | 1 | yes | characteristic |
| 441 | D4 | — | 6 | 1 | no | — |
| 442 | D4 | — | 6 | 1 | no | — |
| 443 | D4 | — | 6 | 1 | no | — |
| 444 | D4 | — | 6 | 1 | no | — |
| 445 | D4 | — | 12 | 2 | no | — |
| 446 | D4 | — | 15 | 2 | no | — |
| 447 | D4 | — | 30 | 1 | no | — |
| 448 | D4 | — | 30 | 1 | no | — |
| 449 | D4 | — | 30 | 1 | no | — |
| 450 | D4 | — | 30 | 1 | no | — |
| 451 | D4 | — | 30 | 1 | no | — |
| 452 | D4 | — | 30 | 2 | no | — |
| 453 | D4 | — | 60 | 2 | no | — |
| 454 | D4 | — | 60 | 2 | no | — |
| 455 | D4 | — | 60 | 2 | no | — |
| 456 | D4 | — | 60 | 2 | no | — |
| 457 | D4 | — | 120 | 1 | no | — |
| 458 | D4 | — | 120 | 1 | no | — |
| 459 | C2×C4 | — | 3 | 1 | no | — |
| 460 | C2×C4 | — | 5 | 1 | no | — |
| 461 | C2×C4 | — | 5 | 1 | no | — |
| 462 | C2×C4 | — | 6 | 1 | no | — |
| 463 | C2×C4 | — | 6 | 1 | no | — |
| 464 | C2×C4 | — | 6 | 1 | no | — |
| 465 | C2×C4 | — | 15 | 1 | no | — |
| 466 | C2×C4 | — | 30 | 1 | no | — |
| 467 | C2×C4 | — | 30 | 1 | no | — |
| 468 | C2×C4 | — | 60 | 2 | no | — |
| 469 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 470 | C8 | — | 6 | 1 | no | — |
| 471 | C8 | — | 6 | 1 | no | — |
| 472 | C8 | — | 15 | 2 | no | — |
| 473 | C8 | — | 30 | 1 | no | — |
| 474 | C2×C3 | — | 4 | 1 | no | — |
| 475 | C2×C3 | — | 4 | 1 | no | — |
| 476 | C2×C3 | — | 4 | 1 | no | — |
| 477 | D3 | — | 16 | 1 | no | — |
| 478 | D3 | — | 40 | 2 | no | — |
| 479 | D3 | — | 80 | 1 | no | — |
| 480 | C5 | #85410 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 481 | C22 | — | 6 | 1 | no | — |
| 482 | C22 | — | 6 | 1 | no | — |
| 483 | C22 | — | 6 | 1 | no | — |
| 484 | C22 | — | 12 | 1 | no | — |
| 485 | C22 | — | 12 | 1 | no | — |
| 486 | C22 | — | 12 | 1 | no | — |
| 487 | C22 | — | 30 | 1 | no | — |
| 488 | C22 | — | 30 | 1 | no | — |
| 489 | C22 | — | 30 | 1 | no | — |
| 490 | C22 | — | 30 | 2 | no | — |
| 491 | C22 | — | 60 | 1 | no | — |
| 492 | C22 | — | 60 | 1 | no | — |
| 493 | C22 | — | 60 | 1 | no | — |
| 494 | C22 | — | 60 | 1 | no | — |
| 495 | C22 | — | 60 | 1 | no | — |
| 496 | C22 | — | 120 | 4 | no | — |
| 497 | C22 | — | 120 | 4 | no | — |
| 498 | C22 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 499 | C4 | — | 2 | 1 | no | — |
| 500 | C4 | — | 3 | 1 | no | — |
| 501 | C4 | — | 3 | 1 | no | — |
| 502 | C4 | — | 5 | 2 | no | — |
| 503 | C4 | — | 10 | 1 | no | — |
| 504 | C4 | — | 12 | 1 | no | — |
| 505 | C4 | — | 30 | 1 | no | — |
| 506 | C3 | — | 4 | 1 | no | Sylow |
| 507 | C2 | — | 12 | 1 | no | — |
| 508 | C2 | — | 24 | 1 | no | — |
| 509 | C2 | — | 60 | 1 | no | — |
| 510 | C2 | — | 60 | 2 | no | — |
| 511 | C2 | — | 120 | 1 | no | — |
| 512 | C2 | #11756775 | 1 | 1 | yes | characteristic |
| 513 | C2 | D5×#986 | 1 | 1 | yes | characteristic |
| 514 | C2 | #11756799 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#91956 | C2 | semidirect |
| 2. C2×#91894 | C2 | semidirect |
| 3. #66168⋊C3 | C2 | semidirect |
| 4. C5×#5427 | C2 | semidirect |
| 5. #11751611 | C2 | semidirect |
| 6. #11751610 | C2 | semidirect |
| 7. #11751602 | C2 | semidirect |
| 9. C2×C5×#41⋊C3 | C22 | semidirect |
| 10. C2×C5⋊(#41⋊C3) | C22 | semidirect |
| 13. C2×C5⋊GL(2,𝔽3) | C22 | semidirect |
| 14. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 17. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 18. C5×#859 | C22 | semidirect |
| 20. #66168 | D3 | semidirect |
| 43. C5⋊GL(2,𝔽3) | D4 | semidirect |
| 52. #5427 | D5 | semidirect |
| 107. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 112. C2×#41⋊C3 | C2×D5 | semidirect |
| 117. C2×GL(2,𝔽3) | C2×D5 | semidirect |
| 120. #859 | C2×D5 | semidirect |
| 324. SL(2,𝔽3) | D4×D5 | semidirect |
| 349. Dic5 | #986 | semidirect |
| 480. C5 | #85410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91956 | 2 |
| C2×#91894 | 2 |
| #66168⋊C3 | 2 |
| C5×#5427 | 2 |
| #11751611 | 2 |
| #11751610 | 2 |
| #11751602 | 2 |
| #10611856 | 3 |
| #91420 | 4 |
| #85410 | 5 |