Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
650 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 650 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 | C22×C5×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#91894 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #66151⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11752140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11751611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751600 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11751599 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10615595 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×C5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×C5⋊(#41⋊C3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×C5⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×C5×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 13 | C2×C5×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C5×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #91894 | — | 2 | 2 | no | — |
| 16 | #91570 | — | 4 | 1 | no | maximal |
| 17 | Dic5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #91184 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #85382 | — | 5 | 1 | no | maximal, Hall |
| 20 | C22×C5×SD16 | — | 3 | 1 | no | — |
| 21 | #66151 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | D4×C22⋊D5 | — | 3 | 1 | no | — |
| 23 | C2×#4060 | — | 3 | 1 | no | — |
| 24 | #65516 | — | 3 | 1 | no | — |
| 25 | #65506 | — | 3 | 1 | no | — |
| 26 | #65465 | — | 3 | 1 | no | — |
| 27 | #65463 | — | 3 | 1 | no | — |
| 28 | #65461 | — | 3 | 1 | no | — |
| 29 | #65458 | — | 3 | 1 | no | — |
| 30 | #65454 | — | 3 | 1 | no | — |
| 31 | #65453 | — | 3 | 1 | no | — |
| 32 | #65452 | — | 3 | 1 | no | — |
| 33 | #65404 | — | 3 | 1 | no | — |
| 34 | #65400 | — | 3 | 1 | no | — |
| 35 | C23×C5×D3 | — | 4 | 1 | no | — |
| 36 | C2×#1220 | — | 4 | 1 | no | — |
| 37 | C2×C5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 38 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×#1203 | — | 4 | 1 | no | — |
| 40 | C2×#1203 | — | 4 | 1 | no | — |
| 41 | C5⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 42 | C5⋊GL(2,𝔽3) | — | 2 | 1 | no | — |
| 43 | C5×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 44 | C5×GL(2,𝔽3) | D4 | 1 | 2 | yes | complemented |
| 45 | C3×C22⋊Dic5 | — | 4 | 1 | no | — |
| 46 | (C2×D3)⋊Dic5 | — | 4 | 1 | no | — |
| 47 | (C2×D3)⋊Dic5 | — | 4 | 1 | no | — |
| 48 | C2×#986 | — | 5 | 1 | no | — |
| 49 | C22×GL(2,𝔽3) | D5 | 1 | 1 | yes | characteristic, complemented |
| 50 | #548⋊C3 | — | 5 | 1 | no | — |
| 51 | #5427 | — | 5 | 1 | no | — |
| 52 | #5421 | — | 5 | 1 | no | — |
| 53 | #5394 | — | 5 | 1 | no | — |
| 54 | C4⋊GL(2,𝔽3) | — | 5 | 1 | no | — |
| 55 | C22×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | C22×C5×D4 | — | 3 | 1 | no | — |
| 57 | C22×C22⋊D5 | — | 6 | 1 | no | — |
| 58 | C2×#713 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 59 | C2×D4×D5 | — | 3 | 1 | no | — |
| 60 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 61 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 62 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 63 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 64 | C2×C5×SD16 | — | 6 | 2 | no | — |
| 65 | C2×C5×SD16 | — | 6 | 2 | no | — |
| 66 | C22×C5×C8 | — | 3 | 1 | no | — |
| 67 | #4099 | — | 6 | 1 | no | — |
| 68 | #4093 | — | 3 | 1 | no | — |
| 69 | #4092 | — | 3 | 1 | no | — |
| 70 | Q8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 71 | C2×#688 | — | 3 | 1 | no | — |
| 72 | C2×#688 | — | 3 | 1 | no | — |
| 73 | #4086 | — | 3 | 1 | no | — |
| 74 | #4085 | — | 6 | 1 | no | — |
| 75 | #4084 | — | 3 | 1 | no | — |
| 76 | #4083 | — | 6 | 1 | no | — |
| 77 | D4×Dic5 | — | 3 | 1 | no | — |
| 78 | C2×#686 | — | 3 | 1 | no | — |
| 79 | C2×#686 | — | 3 | 1 | no | — |
| 80 | #4076 | — | 3 | 1 | no | — |
| 81 | #4076 | — | 3 | 1 | no | — |
| 82 | C4×C22⋊D5 | — | 3 | 1 | no | — |
| 83 | #4060 | — | 6 | 2 | no | — |
| 84 | #4060 | — | 6 | 2 | no | — |
| 85 | C2×D40 | — | 3 | 1 | no | — |
| 86 | C2×#676 | — | 3 | 1 | no | — |
| 87 | #3967 | — | 3 | 1 | no | — |
| 88 | #3967 | — | 3 | 1 | no | — |
| 89 | #3964 | — | 3 | 1 | no | — |
| 90 | #3964 | — | 3 | 1 | no | — |
| 91 | C22⋊#168 | — | 3 | 1 | no | — |
| 92 | #3953 | — | 3 | 1 | no | — |
| 93 | #3953 | — | 3 | 1 | no | — |
| 94 | #3952 | — | 3 | 1 | no | — |
| 95 | #3950 | — | 3 | 1 | no | — |
| 96 | #3947 | — | 3 | 1 | no | — |
| 97 | #3946 | — | 3 | 1 | no | — |
| 98 | #3265 | — | 15 | 1 | no | Sylow |
| 99 | C23×C3×C5 | — | 4 | 1 | no | — |
| 100 | C22×D15 | — | 4 | 1 | no | — |
| 101 | C22×C5×D3 | — | 4 | 1 | no | — |
| 102 | C22×C5×D3 | — | 4 | 1 | no | — |
| 103 | C22×C5×D3 | — | 8 | 2 | no | — |
| 104 | C22×C5×D3 | — | 8 | 2 | no | — |
| 105 | C22×C5×D3 | — | 8 | 2 | no | — |
| 106 | #1220 | — | 8 | 2 | no | — |
| 107 | C2×Dic15 | — | 4 | 1 | no | — |
| 108 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 109 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 110 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 111 | #1203 | — | 8 | 2 | no | — |
| 112 | #1203 | — | 8 | 2 | no | — |
| 113 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 114 | C22×SL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 115 | #986 | — | 10 | 2 | no | — |
| 116 | C2×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 117 | C2×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 118 | C2×GL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic |
| 119 | C2×GL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 120 | #882 | — | 20 | 1 | no | — |
| 121 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 122 | #859 | — | 5 | 1 | no | — |
| 123 | C24×C5 | — | 6 | 1 | no | — |
| 124 | C23×D5 | — | 6 | 1 | no | — |
| 125 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 126 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 127 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 128 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 129 | C2×C5×D4 | — | 3 | 1 | no | — |
| 130 | C2×C5×D4 | — | 3 | 1 | no | — |
| 131 | C2×C5×D4 | — | 6 | 1 | no | — |
| 132 | C2×C5×D4 | — | 6 | 2 | no | — |
| 133 | C2×C5×D4 | — | 12 | 1 | no | — |
| 134 | C22×C4×C5 | — | 3 | 1 | no | — |
| 135 | C2×C22⋊D5 | — | 3 | 1 | no | — |
| 136 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 137 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 138 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 139 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 140 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 141 | C2×C22⋊D5 | — | 12 | 4 | no | — |
| 142 | C22×Dic5 | — | 6 | 1 | no | — |
| 143 | #713 | — | 2 | 1 | no | — |
| 144 | #713 | — | 6 | 1 | no | — |
| 145 | D4×D5 | — | 6 | 2 | no | — |
| 146 | D4×D5 | — | 12 | 1 | no | — |
| 147 | C2×D20 | — | 3 | 1 | no | — |
| 148 | C2×D20 | — | 3 | 1 | no | — |
| 149 | C2×C4×D5 | — | 3 | 1 | no | — |
| 150 | C5×SD16 | — | 3 | 2 | no | — |
| 151 | C5×SD16 | — | 3 | 2 | no | — |
| 152 | C5×SD16 | — | 6 | 2 | no | — |
| 153 | C5×SD16 | — | 6 | 2 | no | — |
| 154 | C5×SD16 | — | 6 | 1 | no | — |
| 155 | C5×SD16 | — | 6 | 1 | no | — |
| 156 | C2×C5×C8 | — | 3 | 1 | no | — |
| 157 | C2×C5×C8 | — | 3 | 1 | no | — |
| 158 | C2×C5×C8 | — | 6 | 2 | no | — |
| 159 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 160 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 161 | C22⋊Dic5 | S4 | 1 | 1 | yes | characteristic |
| 162 | #688 | — | 6 | 1 | no | — |
| 163 | #688 | — | 6 | 1 | no | — |
| 164 | #688 | — | 12 | 1 | no | — |
| 165 | #686 | — | 6 | 2 | no | — |
| 166 | #686 | — | 12 | 1 | no | — |
| 167 | #685 | — | 3 | 1 | no | — |
| 168 | #685 | — | 6 | 1 | no | — |
| 169 | #685 | — | 6 | 1 | no | — |
| 170 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 171 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 172 | #683 | — | 3 | 1 | no | — |
| 173 | C4×Dic5 | — | 3 | 1 | no | — |
| 174 | C2×#168 | — | 3 | 1 | no | — |
| 175 | C2×#168 | — | 3 | 1 | no | — |
| 176 | D40 | — | 6 | 2 | no | — |
| 177 | #676 | — | 6 | 2 | no | — |
| 178 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 179 | C22×SD16 | — | 3 | 1 | no | — |
| 180 | #548 | — | 5 | 1 | no | — |
| 181 | D42 | — | 15 | 1 | no | — |
| 182 | #496 | — | 15 | 1 | no | — |
| 183 | #468 | — | 15 | 1 | no | — |
| 184 | #466 | — | 15 | 1 | no | — |
| 185 | #463 | — | 15 | 1 | no | — |
| 186 | #460 | — | 15 | 1 | no | — |
| 187 | #450 | — | 15 | 1 | no | — |
| 188 | #449 | — | 15 | 1 | no | — |
| 189 | #448 | — | 15 | 1 | no | — |
| 190 | #447 | — | 15 | 1 | no | — |
| 191 | #440 | — | 15 | 1 | no | — |
| 192 | #435 | — | 15 | 1 | no | — |
| 193 | C22×C3×C5 | — | 4 | 2 | no | — |
| 194 | C22×C3×C5 | — | 4 | 1 | no | — |
| 195 | C22×C3×C5 | — | 8 | 1 | no | — |
| 196 | C22×C3×C5 | — | 8 | 1 | no | — |
| 197 | C2×D15 | — | 8 | 1 | no | — |
| 198 | C2×D15 | — | 8 | 1 | no | — |
| 199 | C2×D15 | — | 8 | 1 | no | — |
| 200 | C2×C5×D3 | — | 4 | 2 | no | — |
| 201 | C2×C5×D3 | — | 4 | 2 | no | — |
| 202 | C2×C5×D3 | — | 8 | 1 | no | — |
| 203 | C2×C5×D3 | — | 8 | 1 | no | — |
| 204 | C2×C5×D3 | — | 8 | 1 | no | — |
| 205 | C2×C5×D3 | — | 8 | 1 | no | — |
| 206 | C2×C5×D3 | — | 8 | 8 | no | — |
| 207 | Dic15 | — | 8 | 1 | no | — |
| 208 | C3×Dic5 | — | 8 | 1 | no | — |
| 209 | C3×Dic5 | — | 8 | 1 | no | — |
| 210 | C23×D3 | — | 4 | 1 | no | — |
| 211 | C2×#67 | — | 20 | 1 | no | — |
| 212 | C2×D12 | — | 20 | 1 | no | — |
| 213 | C2×D12 | — | 20 | 1 | no | — |
| 214 | #41⋊C3 | — | 10 | 1 | no | — |
| 215 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 216 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 217 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 218 | GL(2,𝔽3) | — | 10 | 1 | no | — |
| 219 | GL(2,𝔽3) | C22⋊D5 | 1 | 2 | yes | complemented |
| 220 | C3×C22⋊C4 | — | 20 | 1 | no | — |
| 221 | (C2×D3)⋊C4 | — | 20 | 1 | no | — |
| 222 | (C2×D3)⋊C4 | — | 20 | 1 | no | — |
| 223 | C23×C5 | — | 6 | 1 | no | — |
| 224 | C23×C5 | — | 6 | 1 | no | — |
| 225 | C23×C5 | — | 12 | 2 | no | — |
| 226 | C23×C5 | — | 12 | 2 | no | — |
| 227 | C23×C5 | — | 24 | 1 | no | — |
| 228 | C23×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 229 | C22×D5 | — | 3 | 1 | no | — |
| 230 | C22×D5 | — | 6 | 1 | no | — |
| 231 | C22×D5 | — | 12 | 2 | no | — |
| 232 | C22×D5 | — | 12 | 2 | no | — |
| 233 | C22×D5 | — | 24 | 1 | no | — |
| 234 | C5×Q8 | — | 3 | 1 | no | — |
| 235 | C5×Q8 | — | 6 | 1 | no | — |
| 236 | C5×Q8 | — | 6 | 1 | no | — |
| 237 | C5×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 238 | C5×D4 | — | 3 | 2 | no | — |
| 239 | C5×D4 | — | 6 | 1 | no | — |
| 240 | C5×D4 | — | 6 | 1 | no | — |
| 241 | C5×D4 | — | 6 | 1 | no | — |
| 242 | C5×D4 | — | 12 | 2 | no | — |
| 243 | C2×C4×C5 | — | 3 | 1 | no | — |
| 244 | C2×C4×C5 | — | 3 | 1 | no | — |
| 245 | C2×C4×C5 | — | 6 | 1 | no | — |
| 246 | C2×C4×C5 | — | 6 | 1 | no | — |
| 247 | C22⋊D5 | — | 6 | 2 | no | — |
| 248 | C22⋊D5 | — | 12 | 2 | no | — |
| 249 | C22⋊D5 | — | 12 | 2 | no | — |
| 250 | C22⋊D5 | — | 12 | 2 | no | — |
| 251 | C22⋊D5 | — | 12 | 2 | no | — |
| 252 | C22⋊D5 | — | 24 | 1 | no | — |
| 253 | C2×Dic5 | — | 3 | 1 | no | — |
| 254 | C2×Dic5 | — | 6 | 1 | no | — |
| 255 | C2×Dic5 | — | 12 | 2 | no | — |
| 256 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 257 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 258 | D20 | — | 6 | 1 | no | — |
| 259 | D20 | — | 6 | 1 | no | — |
| 260 | D20 | — | 6 | 1 | no | — |
| 261 | D20 | — | 6 | 1 | no | — |
| 262 | C4×D5 | — | 6 | 1 | no | — |
| 263 | C4×D5 | — | 6 | 1 | no | — |
| 264 | C5×C8 | — | 3 | 2 | no | — |
| 265 | C5×C8 | — | 6 | 1 | no | — |
| 266 | #168 | — | 6 | 1 | no | — |
| 267 | #168 | — | 6 | 1 | no | — |
| 268 | C2×#41 | — | 5 | 1 | no | — |
| 269 | C22×Q8 | D3×D5 | 1 | 1 | yes | characteristic |
| 270 | C22×D4 | — | 3 | 1 | no | — |
| 271 | C22×D4 | — | 15 | 1 | no | — |
| 272 | C22×D4 | — | 30 | 1 | no | — |
| 273 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 274 | AGL(1,ℤ/8) | — | 30 | 2 | no | — |
| 275 | C2×SD16 | — | 3 | 1 | no | — |
| 276 | C2×SD16 | — | 3 | 1 | no | — |
| 277 | C2×SD16 | — | 3 | 1 | no | — |
| 278 | C2×SD16 | — | 3 | 1 | no | — |
| 279 | C2×SD16 | — | 6 | 2 | no | — |
| 280 | C2×SD16 | — | 6 | 2 | no | — |
| 281 | C2×SD16 | — | 15 | 1 | no | — |
| 282 | C2×SD16 | — | 15 | 1 | no | — |
| 283 | C2×D8 | — | 15 | 1 | no | — |
| 284 | C2×D8 | — | 15 | 1 | no | — |
| 285 | C2×D8 | — | 15 | 1 | no | — |
| 286 | C2×M16 | — | 15 | 1 | no | — |
| 287 | C22×C8 | — | 3 | 1 | no | — |
| 288 | #127 | — | 15 | 1 | no | — |
| 289 | #124 | — | 15 | 1 | no | — |
| 290 | C22⋊Q8 | — | 15 | 1 | no | — |
| 291 | #121 | — | 15 | 1 | no | — |
| 292 | #121 | — | 15 | 1 | no | — |
| 293 | #121 | — | 15 | 1 | no | — |
| 294 | #121 | — | 30 | 1 | no | — |
| 295 | #120 | — | 30 | 1 | no | — |
| 296 | #120 | — | 30 | 1 | no | — |
| 297 | C4×Q8 | — | 5 | 1 | no | — |
| 298 | C4×D4 | — | 15 | 1 | no | — |
| 299 | C4×D4 | — | 15 | 1 | no | — |
| 300 | #107 | — | 15 | 1 | no | — |
| 301 | C4⋊C8 | — | 15 | 1 | no | — |
| 302 | #103 | — | 15 | 1 | no | — |
| 303 | #103 | — | 15 | 1 | no | — |
| 304 | #102 | — | 15 | 1 | no | — |
| 305 | #102 | — | 15 | 1 | no | — |
| 306 | #102 | — | 15 | 1 | no | — |
| 307 | #102 | — | 15 | 1 | no | — |
| 308 | C22⋊C8 | — | 15 | 1 | no | — |
| 309 | C22⋊C8 | — | 15 | 1 | no | — |
| 310 | #97 | — | 15 | 1 | no | — |
| 311 | C2×C3×C5 | — | 4 | 1 | no | — |
| 312 | C2×C3×C5 | — | 4 | 1 | no | — |
| 313 | C2×C3×C5 | — | 4 | 1 | no | — |
| 314 | C2×C3×C5 | — | 8 | 2 | no | — |
| 315 | D15 | — | 16 | 1 | no | — |
| 316 | C5×D3 | — | 8 | 2 | no | — |
| 317 | C5×D3 | — | 8 | 2 | no | — |
| 318 | C23×C3 | — | 4 | 1 | no | — |
| 319 | C22×D3 | — | 4 | 1 | no | — |
| 320 | C22×D3 | — | 4 | 1 | no | — |
| 321 | C22×D3 | — | 8 | 2 | no | — |
| 322 | C22×D3 | — | 8 | 2 | no | — |
| 323 | C22×D3 | — | 8 | 2 | no | — |
| 324 | C22×D3 | — | 20 | 1 | no | — |
| 325 | C2×C3×C4 | — | 20 | 1 | no | — |
| 326 | C2×C3×C4 | — | 20 | 1 | no | — |
| 327 | #67 | — | 40 | 2 | no | — |
| 328 | C2×Dic3 | — | 20 | 1 | no | — |
| 329 | D12 | — | 40 | 2 | no | — |
| 330 | D12 | — | 40 | 2 | no | — |
| 331 | SL(2,𝔽3) | C2×C22⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 332 | C22×C5 | — | 2 | 1 | no | — |
| 333 | C22×C5 | — | 2 | 1 | no | — |
| 334 | C22×C5 | — | 6 | 2 | no | — |
| 335 | C22×C5 | — | 12 | 1 | no | — |
| 336 | C22×C5 | — | 12 | 1 | no | — |
| 337 | C22×C5 | — | 12 | 1 | no | — |
| 338 | C22×C5 | — | 12 | 1 | no | — |
| 339 | C22×C5 | — | 12 | 1 | no | — |
| 340 | C22×C5 | — | 24 | 4 | no | — |
| 341 | C22×C5 | #986 | 1 | 2 | yes | complemented |
| 342 | C22×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 343 | C2×D5 | — | 6 | 1 | no | — |
| 344 | C2×D5 | — | 6 | 1 | no | — |
| 345 | C2×D5 | — | 6 | 1 | no | — |
| 346 | C2×D5 | — | 12 | 1 | no | — |
| 347 | C2×D5 | — | 12 | 1 | no | — |
| 348 | C2×D5 | — | 12 | 1 | no | — |
| 349 | C2×D5 | — | 24 | 4 | no | — |
| 350 | C4×C5 | — | 3 | 1 | no | — |
| 351 | C4×C5 | — | 3 | 1 | no | — |
| 352 | C4×C5 | — | 6 | 1 | no | — |
| 353 | Dic5 | — | 2 | 1 | no | — |
| 354 | Dic5 | — | 2 | 1 | no | — |
| 355 | Dic5 | — | 6 | 1 | no | — |
| 356 | Dic5 | — | 12 | 1 | no | — |
| 357 | C24 | — | 6 | 1 | no | — |
| 358 | C24 | — | 30 | 1 | no | — |
| 359 | #41 | — | 10 | 1 | no | — |
| 360 | #41 | — | 30 | 1 | no | — |
| 361 | C2×Q8 | — | 2 | 1 | no | — |
| 362 | C2×Q8 | — | 3 | 1 | no | — |
| 363 | C2×Q8 | — | 6 | 1 | no | — |
| 364 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 365 | C2×D4 | — | 3 | 1 | no | — |
| 366 | C2×D4 | — | 3 | 1 | no | — |
| 367 | C2×D4 | — | 6 | 1 | no | — |
| 368 | C2×D4 | — | 6 | 2 | no | — |
| 369 | C2×D4 | — | 12 | 1 | no | — |
| 370 | C2×D4 | — | 15 | 1 | no | — |
| 371 | C2×D4 | — | 15 | 1 | no | — |
| 372 | C2×D4 | — | 15 | 1 | no | — |
| 373 | C2×D4 | — | 30 | 1 | no | — |
| 374 | C2×D4 | — | 30 | 1 | no | — |
| 375 | C2×D4 | — | 30 | 1 | no | — |
| 376 | C2×D4 | — | 30 | 2 | no | — |
| 377 | C2×D4 | — | 30 | 1 | no | — |
| 378 | C2×D4 | — | 30 | 1 | no | — |
| 379 | C2×D4 | — | 60 | 1 | no | — |
| 380 | C2×D4 | — | 60 | 4 | no | — |
| 381 | C22×C4 | — | 3 | 1 | no | — |
| 382 | C22×C4 | — | 15 | 1 | no | — |
| 383 | C22×C4 | — | 30 | 1 | no | — |
| 384 | SD16 | — | 3 | 2 | no | — |
| 385 | SD16 | — | 3 | 2 | no | — |
| 386 | SD16 | — | 6 | 2 | no | — |
| 387 | SD16 | — | 6 | 2 | no | — |
| 388 | SD16 | — | 6 | 1 | no | — |
| 389 | SD16 | — | 6 | 1 | no | — |
| 390 | SD16 | — | 30 | 1 | no | — |
| 391 | SD16 | — | 30 | 1 | no | — |
| 392 | SD16 | — | 60 | 1 | no | — |
| 393 | D8 | — | 30 | 2 | no | — |
| 394 | D8 | — | 30 | 2 | no | — |
| 395 | D8 | — | 60 | 1 | no | — |
| 396 | M16 | — | 30 | 2 | no | — |
| 397 | C2×C8 | — | 3 | 1 | no | — |
| 398 | C2×C8 | — | 3 | 1 | no | — |
| 399 | C2×C8 | — | 6 | 2 | no | — |
| 400 | C2×C8 | — | 15 | 1 | no | — |
| 401 | C2×C8 | — | 15 | 1 | no | — |
| 402 | C4⋊C4 | — | 15 | 1 | no | — |
| 403 | C4⋊C4 | — | 15 | 1 | no | — |
| 404 | C4⋊C4 | — | 15 | 1 | no | — |
| 405 | C22⋊C4 | — | 5 | 1 | no | — |
| 406 | C22⋊C4 | — | 15 | 1 | no | — |
| 407 | C22⋊C4 | — | 30 | 1 | no | — |
| 408 | C22⋊C4 | — | 30 | 1 | no | — |
| 409 | C22⋊C4 | — | 30 | 1 | no | — |
| 410 | C22⋊C4 | — | 30 | 1 | no | — |
| 411 | C42 | — | 15 | 1 | no | — |
| 412 | C3×C5 | — | 4 | 1 | no | Hall |
| 413 | C22×C3 | — | 4 | 1 | no | — |
| 414 | C22×C3 | — | 4 | 2 | no | — |
| 415 | C22×C3 | — | 8 | 1 | no | — |
| 416 | C22×C3 | — | 8 | 1 | no | — |
| 417 | C2×D3 | — | 4 | 2 | no | — |
| 418 | C2×D3 | — | 4 | 2 | no | — |
| 419 | C2×D3 | — | 8 | 1 | no | — |
| 420 | C2×D3 | — | 8 | 1 | no | — |
| 421 | C2×D3 | — | 8 | 1 | no | — |
| 422 | C2×D3 | — | 8 | 1 | no | — |
| 423 | C2×D3 | — | 8 | 8 | no | — |
| 424 | C2×D3 | — | 40 | 1 | no | — |
| 425 | C2×D3 | — | 40 | 1 | no | — |
| 426 | C2×D3 | — | 40 | 1 | no | — |
| 427 | C3×C4 | — | 40 | 1 | no | — |
| 428 | C3×C4 | — | 40 | 1 | no | — |
| 429 | Dic3 | — | 40 | 1 | no | — |
| 430 | C2×C5 | — | 2 | 2 | no | — |
| 431 | C2×C5 | — | 12 | 2 | no | — |
| 432 | C2×C5 | — | 24 | 1 | no | — |
| 433 | C2×C5 | D4×S4 | 1 | 1 | yes | characteristic |
| 434 | C2×C5 | C2×#986 | 1 | 1 | yes | characteristic |
| 435 | C2×C5 | #5926 | 1 | 1 | yes | characteristic |
| 436 | D5 | — | 12 | 1 | no | — |
| 437 | D5 | — | 24 | 1 | no | — |
| 438 | C23 | — | 6 | 1 | no | — |
| 439 | C23 | — | 6 | 1 | no | — |
| 440 | C23 | — | 12 | 2 | no | — |
| 441 | C23 | — | 12 | 2 | no | — |
| 442 | C23 | — | 15 | 1 | no | — |
| 443 | C23 | — | 24 | 1 | no | — |
| 444 | C23 | — | 30 | 1 | no | — |
| 445 | C23 | — | 60 | 2 | no | — |
| 446 | C23 | — | 60 | 2 | no | — |
| 447 | C23 | — | 120 | 1 | no | — |
| 448 | C23 | D5×S4 | 1 | 1 | yes | characteristic |
| 449 | Q8 | — | 3 | 1 | no | — |
| 450 | Q8 | — | 6 | 1 | no | — |
| 451 | Q8 | — | 6 | 1 | no | — |
| 452 | Q8 | D3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 453 | D4 | — | 3 | 2 | no | — |
| 454 | D4 | — | 6 | 1 | no | — |
| 455 | D4 | — | 6 | 1 | no | — |
| 456 | D4 | — | 6 | 1 | no | — |
| 457 | D4 | — | 12 | 2 | no | — |
| 458 | D4 | — | 30 | 1 | no | — |
| 459 | D4 | — | 30 | 1 | no | — |
| 460 | D4 | — | 30 | 1 | no | — |
| 461 | D4 | — | 30 | 1 | no | — |
| 462 | D4 | — | 30 | 2 | no | — |
| 463 | D4 | — | 60 | 2 | no | — |
| 464 | D4 | — | 60 | 2 | no | — |
| 465 | D4 | — | 60 | 2 | no | — |
| 466 | D4 | — | 60 | 2 | no | — |
| 467 | D4 | — | 120 | 1 | no | — |
| 468 | C2×C4 | — | 3 | 1 | no | — |
| 469 | C2×C4 | — | 3 | 1 | no | — |
| 470 | C2×C4 | — | 5 | 1 | no | — |
| 471 | C2×C4 | — | 5 | 1 | no | — |
| 472 | C2×C4 | — | 6 | 1 | no | — |
| 473 | C2×C4 | — | 6 | 1 | no | — |
| 474 | C2×C4 | — | 15 | 1 | no | — |
| 475 | C2×C4 | — | 30 | 1 | no | — |
| 476 | C2×C4 | — | 30 | 1 | no | — |
| 477 | C2×C4 | — | 30 | 1 | no | — |
| 478 | C2×C4 | — | 60 | 2 | no | — |
| 479 | C8 | — | 3 | 2 | no | — |
| 480 | C8 | — | 6 | 1 | no | — |
| 481 | C8 | — | 30 | 1 | no | — |
| 482 | C8 | — | 30 | 1 | no | — |
| 483 | C2×C3 | — | 4 | 1 | no | — |
| 484 | C2×C3 | — | 4 | 1 | no | — |
| 485 | C2×C3 | — | 4 | 1 | no | — |
| 486 | C2×C3 | — | 8 | 2 | no | — |
| 487 | D3 | — | 8 | 2 | no | — |
| 488 | D3 | — | 8 | 2 | no | — |
| 489 | D3 | — | 80 | 1 | no | — |
| 490 | C5 | #85382 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 491 | C22 | — | 2 | 1 | no | — |
| 492 | C22 | — | 2 | 1 | no | — |
| 493 | C22 | — | 6 | 2 | no | — |
| 494 | C22 | — | 12 | 1 | no | — |
| 495 | C22 | — | 12 | 1 | no | — |
| 496 | C22 | — | 12 | 1 | no | — |
| 497 | C22 | — | 12 | 1 | no | — |
| 498 | C22 | — | 12 | 1 | no | — |
| 499 | C22 | — | 24 | 4 | no | — |
| 500 | C22 | — | 30 | 1 | no | — |
| 501 | C22 | — | 30 | 1 | no | — |
| 502 | C22 | — | 30 | 1 | no | — |
| 503 | C22 | — | 60 | 1 | no | — |
| 504 | C22 | — | 60 | 1 | no | — |
| 505 | C22 | — | 60 | 1 | no | — |
| 506 | C22 | — | 120 | 4 | no | — |
| 507 | C22 | #91894 | 1 | 2 | yes | complemented |
| 508 | C22 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 509 | C4 | — | 3 | 1 | no | — |
| 510 | C4 | — | 3 | 1 | no | — |
| 511 | C4 | — | 6 | 1 | no | — |
| 512 | C4 | — | 10 | 1 | no | — |
| 513 | C4 | — | 10 | 1 | no | — |
| 514 | C4 | — | 30 | 1 | no | — |
| 515 | C4 | — | 60 | 1 | no | — |
| 516 | C3 | — | 4 | 1 | no | Sylow |
| 517 | C2 | — | 2 | 2 | no | — |
| 518 | C2 | — | 12 | 2 | no | — |
| 519 | C2 | — | 24 | 1 | no | — |
| 520 | C2 | — | 60 | 1 | no | — |
| 521 | C2 | — | 120 | 1 | no | — |
| 522 | C2 | C2×#91894 | 1 | 1 | yes | characteristic |
| 523 | C2 | #11756771 | 1 | 1 | yes | characteristic |
| 524 | C2 | S4×C22⋊D5 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×GL(2,𝔽3) | C2 | semidirect |
| 2. C2×#91894 | C2 | semidirect |
| 3. #66151⋊C3 | C2 | semidirect |
| 4. #11752140 | C2 | semidirect |
| 5. #11751611 | C2 | semidirect |
| 6. #11751600 | C2 | semidirect |
| 7. #11751599 | C2 | semidirect |
| 9. C22×C5×SL(2,𝔽3) | C22 | semidirect |
| 10. C2×C5⋊(#41⋊C3) | C22 | semidirect |
| 11. C2×C5⋊GL(2,𝔽3) | C22 | semidirect |
| 14. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 17. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 18. #91184 | C22 | semidirect |
| 21. #66151 | D3 | semidirect |
| 44. C5×GL(2,𝔽3) | D4 | semidirect |
| 49. C22×GL(2,𝔽3) | D5 | semidirect |
| 58. C2×#713 | C2×D3 | semidirect |
| 70. Q8×Dic5 | C2×D3 | semidirect |
| 110. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 114. C22×SL(2,𝔽3) | C2×D5 | semidirect |
| 119. C2×GL(2,𝔽3) | C2×D5 | semidirect |
| 219. GL(2,𝔽3) | C22⋊D5 | semidirect |
| 331. SL(2,𝔽3) | C2×C22⋊D5 | semidirect |
| 341. C22×C5 | #986 | semidirect |
| 490. C5 | #85382 | semidirect |
| 507. C22 | #91894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×GL(2,𝔽3) | 2 |
| C2×#91894 | 2 |
| #66151⋊C3 | 2 |
| #11752140 | 2 |
| #11751611 | 2 |
| #11751600 | 2 |
| #11751599 | 2 |
| #10615595 | 3 |
| #91570 | 4 |
| #85382 | 5 |