Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
766 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 61 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×D5×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | SL(2,𝔽3)×C22⋊D5 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#5421 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11751614 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11751610 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10611794 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×C5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×#6790 | — | 4 | 1 | no | maximal |
| 11 | C2×D5×SL(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 | C2×C5×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | D5×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 17 | Dic5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C5×#859 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | D4×GL(2,𝔽3) | — | 5 | 1 | no | maximal, Hall |
| 20 | Q8×C22⋊D5 | D3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C22×#688 | — | 3 | 1 | no | — |
| 22 | C2×D5×SD16 | — | 3 | 1 | no | — |
| 23 | #65943 | — | 3 | 1 | no | — |
| 24 | C5×#448 | — | 3 | 1 | no | — |
| 25 | #65464 | — | 3 | 1 | no | — |
| 26 | #65458 | — | 3 | 1 | no | — |
| 27 | #65452 | — | 3 | 1 | no | — |
| 28 | #65330 | — | 3 | 1 | no | — |
| 29 | #65107 | — | 3 | 1 | no | — |
| 30 | #65096 | — | 3 | 1 | no | — |
| 31 | #65095 | — | 3 | 1 | no | — |
| 32 | #65077 | — | 3 | 1 | no | — |
| 33 | #65020 | — | 3 | 1 | no | — |
| 34 | #65014 | — | 3 | 1 | no | — |
| 35 | C23×D15 | — | 4 | 1 | no | — |
| 36 | C22×D3×D5 | — | 4 | 1 | no | — |
| 37 | C2×C5×#67 | — | 4 | 1 | no | — |
| 38 | C2×C3×C22⋊D5 | — | 4 | 1 | no | — |
| 39 | C2×C5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 40 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 41 | #6790 | — | 4 | 8 | no | — |
| 42 | C2×#1203 | — | 4 | 1 | no | — |
| 43 | C2×#1202 | — | 4 | 1 | no | — |
| 44 | C2×#1200 | — | 4 | 1 | no | — |
| 45 | D5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 46 | C5⋊GL(2,𝔽3) | — | 2 | 1 | no | — |
| 47 | C5⋊GL(2,𝔽3) | D4 | 1 | 2 | yes | complemented |
| 48 | C5×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 49 | C22×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 50 | C22×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 51 | D4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 52 | #5421 | — | 5 | 1 | no | — |
| 53 | #5421 | D5 | 1 | 1 | yes | characteristic, complemented |
| 54 | C4⋊GL(2,𝔽3) | — | 5 | 1 | no | — |
| 55 | C4×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 56 | C22×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 57 | C2×Q8×D5 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 58 | C2×D4×D5 | — | 3 | 1 | no | — |
| 59 | C2×D4×D5 | — | 6 | 1 | no | — |
| 60 | C22×D20 | — | 3 | 1 | no | — |
| 61 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 62 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 63 | C5×#121 | — | 3 | 1 | no | — |
| 64 | #4092 | — | 3 | 1 | no | — |
| 65 | Q8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 66 | #4090 | — | 3 | 1 | no | — |
| 67 | C2×#688 | — | 3 | 1 | no | — |
| 68 | C2×#688 | — | 3 | 1 | no | — |
| 69 | C2×#688 | — | 3 | 1 | no | — |
| 70 | C2×#688 | — | 3 | 1 | no | — |
| 71 | C2×#688 | — | 6 | 2 | no | — |
| 72 | C2×#688 | — | 6 | 2 | no | — |
| 73 | #4086 | — | 3 | 1 | no | — |
| 74 | #4083 | — | 6 | 1 | no | — |
| 75 | C2×#687 | — | 3 | 1 | no | — |
| 76 | C4×C22⋊D5 | — | 3 | 1 | no | — |
| 77 | #4070 | — | 3 | 1 | no | — |
| 78 | C22×#168 | — | 3 | 1 | no | — |
| 79 | D5×SD16 | — | 6 | 2 | no | — |
| 80 | D5×SD16 | — | 6 | 2 | no | — |
| 81 | C2×#677 | — | 3 | 1 | no | — |
| 82 | C2×#677 | — | 3 | 1 | no | — |
| 83 | C2×C8×D5 | — | 3 | 1 | no | — |
| 84 | #4041 | — | 3 | 1 | no | — |
| 85 | #4039 | — | 3 | 1 | no | — |
| 86 | #4030 | — | 6 | 1 | no | — |
| 87 | #4028 | — | 6 | 1 | no | — |
| 88 | C5×#103 | — | 3 | 1 | no | — |
| 89 | C5×#103 | — | 3 | 1 | no | — |
| 90 | C5×C22⋊C8 | — | 3 | 1 | no | — |
| 91 | #3964 | — | 3 | 1 | no | — |
| 92 | #3953 | — | 3 | 1 | no | — |
| 93 | #3953 | — | 3 | 1 | no | — |
| 94 | #3952 | — | 3 | 1 | no | — |
| 95 | #3946 | — | 3 | 1 | no | — |
| 96 | C8×Dic5 | — | 3 | 1 | no | — |
| 97 | #3942 | — | 3 | 1 | no | — |
| 98 | #3940 | — | 3 | 1 | no | — |
| 99 | D4×SD16 | — | 15 | 1 | no | Sylow |
| 100 | C23×C3×C5 | — | 4 | 1 | no | — |
| 101 | C22×D15 | — | 4 | 1 | no | — |
| 102 | C22×D15 | — | 4 | 1 | no | — |
| 103 | C22×D15 | — | 4 | 4 | no | — |
| 104 | C22×D15 | — | 8 | 2 | no | — |
| 105 | C22×D15 | — | 8 | 2 | no | — |
| 106 | C22×C5×D3 | — | 4 | 1 | no | — |
| 107 | C22×C3×D5 | — | 4 | 1 | no | — |
| 108 | C2×D3×D5 | — | 4 | 4 | no | — |
| 109 | C2×D3×D5 | — | 8 | 2 | no | — |
| 110 | C2×D3×D5 | — | 8 | 2 | no | — |
| 111 | C5×#67 | — | 4 | 4 | no | — |
| 112 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 113 | C3×C22⋊D5 | — | 4 | 4 | no | — |
| 114 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 115 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 116 | #1203 | — | 4 | 4 | no | — |
| 117 | #1202 | — | 4 | 4 | no | — |
| 118 | #1200 | — | 4 | 4 | no | — |
| 119 | C2×D3×D4 | — | 20 | 1 | no | — |
| 120 | C22×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 121 | C22×SL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 122 | C2×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 123 | C2×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 124 | C2×GL(2,𝔽3) | — | 10 | 2 | no | — |
| 125 | C2×GL(2,𝔽3) | — | 10 | 2 | no | — |
| 126 | C2×GL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 127 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 128 | #859 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 129 | C23×D5 | — | 6 | 1 | no | — |
| 130 | C23×D5 | — | 6 | 1 | no | — |
| 131 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 132 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 133 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 134 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 135 | C2×C5×D4 | — | 3 | 1 | no | — |
| 136 | C2×C5×D4 | — | 6 | 1 | no | — |
| 137 | C22×C4×C5 | — | 3 | 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 | S4 | 1 | 1 | yes | characteristic |
| 142 | Q8×D5 | — | 2 | 1 | no | — |
| 143 | Q8×D5 | — | 6 | 1 | no | — |
| 144 | D4×D5 | — | 6 | 2 | no | — |
| 145 | D4×D5 | — | 12 | 1 | no | — |
| 146 | D4×D5 | — | 12 | 4 | no | — |
| 147 | C2×D20 | — | 3 | 1 | no | — |
| 148 | C2×D20 | — | 3 | 1 | no | — |
| 149 | C2×D20 | — | 6 | 2 | no | — |
| 150 | C2×D20 | — | 6 | 1 | no | — |
| 151 | C2×D20 | — | 6 | 1 | no | — |
| 152 | C2×D20 | — | 12 | 1 | no | — |
| 153 | C2×C4×D5 | — | 3 | 1 | no | — |
| 154 | C2×C4×D5 | — | 6 | 1 | no | — |
| 155 | C2×Dic10 | — | 3 | 1 | no | — |
| 156 | C5×SD16 | — | 6 | 1 | no | — |
| 157 | C5×SD16 | — | 6 | 1 | no | — |
| 158 | C5×SD16 | — | 12 | 1 | no | — |
| 159 | C2×C5×C8 | — | 3 | 1 | no | — |
| 160 | C2×C5×C8 | — | 3 | 1 | no | — |
| 161 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 162 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 163 | C22⋊Dic5 | — | 3 | 1 | no | — |
| 164 | #688 | — | 3 | 2 | no | — |
| 165 | #688 | — | 3 | 2 | no | — |
| 166 | #688 | — | 6 | 2 | no | — |
| 167 | #688 | — | 6 | 2 | no | — |
| 168 | #688 | — | 6 | 1 | no | — |
| 169 | #688 | — | 6 | 1 | no | — |
| 170 | #687 | — | 6 | 2 | no | — |
| 171 | #685 | — | 3 | 1 | no | — |
| 172 | #685 | — | 6 | 1 | no | — |
| 173 | #685 | — | 6 | 1 | no | — |
| 174 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 175 | #683 | — | 3 | 1 | no | — |
| 176 | #683 | — | 6 | 1 | no | — |
| 177 | C4×Dic5 | — | 3 | 1 | no | — |
| 178 | C2×#168 | — | 3 | 1 | no | — |
| 179 | C2×#168 | — | 3 | 1 | no | — |
| 180 | C2×#168 | — | 6 | 2 | no | — |
| 181 | #677 | — | 6 | 2 | no | — |
| 182 | #677 | — | 12 | 1 | no | — |
| 183 | C8×D5 | — | 6 | 2 | no | — |
| 184 | C22×SD16 | — | 15 | 1 | no | — |
| 185 | C22×SD16 | — | 15 | 1 | no | — |
| 186 | D4×Q8 | — | 5 | 1 | no | — |
| 187 | D42 | — | 15 | 1 | no | — |
| 188 | #492 | — | 15 | 1 | no | — |
| 189 | #465 | — | 15 | 1 | no | — |
| 190 | #465 | — | 15 | 1 | no | — |
| 191 | #461 | — | 15 | 1 | no | — |
| 192 | #460 | — | 15 | 1 | no | — |
| 193 | #450 | — | 15 | 1 | no | — |
| 194 | #450 | — | 15 | 1 | no | — |
| 195 | #448 | — | 3 | 1 | no | — |
| 196 | #448 | — | 15 | 1 | no | — |
| 197 | C4×SD16 | — | 15 | 1 | no | — |
| 198 | C8×D4 | — | 15 | 1 | no | — |
| 199 | C22×C3×C5 | — | 4 | 2 | no | — |
| 200 | C22×C3×C5 | — | 4 | 1 | no | — |
| 201 | C22×C3×C5 | — | 8 | 1 | no | — |
| 202 | C22×C3×C5 | — | 8 | 1 | no | — |
| 203 | C2×D15 | — | 4 | 2 | no | — |
| 204 | C2×D15 | — | 4 | 2 | no | — |
| 205 | C2×D15 | — | 4 | 2 | no | — |
| 206 | C2×D15 | — | 4 | 2 | no | — |
| 207 | C2×D15 | — | 8 | 1 | no | — |
| 208 | C2×D15 | — | 8 | 1 | no | — |
| 209 | C2×D15 | — | 8 | 8 | no | — |
| 210 | C2×C5×D3 | — | 4 | 2 | no | — |
| 211 | C2×C5×D3 | — | 8 | 1 | no | — |
| 212 | C2×C5×D3 | — | 8 | 1 | no | — |
| 213 | C2×C3×D5 | — | 4 | 2 | no | — |
| 214 | C2×C3×D5 | — | 8 | 1 | no | — |
| 215 | C2×C3×D5 | — | 8 | 1 | no | — |
| 216 | D3×D5 | — | 8 | 8 | no | — |
| 217 | C3×Dic5 | — | 4 | 2 | no | — |
| 218 | C5×Dic3 | — | 4 | 2 | no | — |
| 219 | C23×D3 | — | 20 | 1 | no | — |
| 220 | C23×D3 | — | 20 | 1 | no | — |
| 221 | C2×C3×D4 | — | 20 | 1 | no | — |
| 222 | C2×#67 | — | 4 | 1 | no | — |
| 223 | C2×#67 | — | 20 | 1 | no | — |
| 224 | D3×D4 | — | 20 | 8 | no | — |
| 225 | C2×D12 | — | 20 | 1 | no | — |
| 226 | C2×C4×D3 | — | 20 | 1 | no | — |
| 227 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 228 | C2×SL(2,𝔽3) | — | 10 | 1 | no | — |
| 229 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 230 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 231 | GL(2,𝔽3) | — | 5 | 2 | no | — |
| 232 | GL(2,𝔽3) | — | 10 | 1 | no | — |
| 233 | C23×C5 | — | 6 | 1 | no | — |
| 234 | C23×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 235 | C22×D5 | — | 6 | 1 | no | — |
| 236 | C22×D5 | — | 6 | 1 | no | — |
| 237 | C22×D5 | — | 12 | 2 | no | — |
| 238 | C22×D5 | — | 12 | 2 | no | — |
| 239 | C22×D5 | — | 12 | 2 | no | — |
| 240 | C22×D5 | — | 12 | 2 | no | — |
| 241 | C22×D5 | — | 24 | 1 | no | — |
| 242 | C22×D5 | — | 24 | 1 | no | — |
| 243 | C22×D5 | C2×S4 | 1 | 1 | yes | characteristic |
| 244 | C5×Q8 | — | 3 | 1 | no | — |
| 245 | C5×Q8 | — | 6 | 1 | no | — |
| 246 | C5×Q8 | — | 6 | 1 | no | — |
| 247 | C5×Q8 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 248 | C5×D4 | — | 6 | 1 | no | — |
| 249 | C5×D4 | — | 6 | 1 | no | — |
| 250 | C5×D4 | — | 12 | 2 | no | — |
| 251 | C2×C4×C5 | — | 3 | 1 | no | — |
| 252 | C2×C4×C5 | — | 3 | 1 | no | — |
| 253 | C2×C4×C5 | — | 6 | 1 | no | — |
| 254 | C2×C4×C5 | — | 6 | 1 | no | — |
| 255 | C2×C4×C5 | — | 6 | 1 | no | — |
| 256 | C22⋊D5 | — | 12 | 2 | no | — |
| 257 | C22⋊D5 | — | 12 | 2 | no | — |
| 258 | C22⋊D5 | — | 24 | 1 | no | — |
| 259 | C22⋊D5 | GL(2,𝔽3) | 1 | 4 | yes | complemented |
| 260 | C2×Dic5 | — | 3 | 1 | no | — |
| 261 | C2×Dic5 | — | 3 | 1 | no | — |
| 262 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 263 | D20 | — | 3 | 2 | no | — |
| 264 | D20 | — | 6 | 1 | no | — |
| 265 | D20 | — | 6 | 1 | no | — |
| 266 | D20 | — | 6 | 1 | no | — |
| 267 | D20 | — | 12 | 2 | no | — |
| 268 | D20 | — | 12 | 2 | no | — |
| 269 | C4×D5 | — | 6 | 1 | no | — |
| 270 | C4×D5 | — | 6 | 1 | no | — |
| 271 | C4×D5 | — | 12 | 2 | no | — |
| 272 | Dic10 | — | 6 | 1 | no | — |
| 273 | Dic10 | — | 6 | 1 | no | — |
| 274 | C5×C8 | — | 6 | 1 | no | — |
| 275 | C5×C8 | — | 6 | 1 | no | — |
| 276 | #168 | — | 3 | 2 | no | — |
| 277 | #168 | — | 6 | 1 | no | — |
| 278 | C22×Q8 | — | 5 | 1 | no | — |
| 279 | C22×Q8 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 280 | C22×D4 | — | 15 | 1 | no | — |
| 281 | C22×D4 | — | 15 | 1 | no | — |
| 282 | C22×D4 | — | 30 | 1 | no | — |
| 283 | C2×SD16 | — | 3 | 1 | no | — |
| 284 | C2×SD16 | — | 3 | 1 | no | — |
| 285 | C2×SD16 | — | 15 | 1 | no | — |
| 286 | C2×SD16 | — | 15 | 1 | no | — |
| 287 | C2×SD16 | — | 15 | 1 | no | — |
| 288 | C2×SD16 | — | 15 | 1 | no | — |
| 289 | C2×SD16 | — | 15 | 1 | no | — |
| 290 | C2×SD16 | — | 15 | 1 | no | — |
| 291 | C2×SD16 | — | 15 | 1 | no | — |
| 292 | C2×SD16 | — | 30 | 2 | no | — |
| 293 | C2×SD16 | — | 30 | 2 | no | — |
| 294 | C2×SD16 | — | 30 | 2 | no | — |
| 295 | C2×SD16 | — | 30 | 2 | no | — |
| 296 | C22×C8 | — | 15 | 1 | no | — |
| 297 | C22×C8 | — | 15 | 1 | no | — |
| 298 | C4⋊Q8 | — | 15 | 1 | no | — |
| 299 | #127 | — | 15 | 1 | no | — |
| 300 | C22⋊Q8 | — | 15 | 1 | no | — |
| 301 | C22⋊Q8 | — | 15 | 1 | no | — |
| 302 | #121 | — | 3 | 1 | no | — |
| 303 | #121 | — | 15 | 1 | no | — |
| 304 | #121 | — | 30 | 1 | no | — |
| 305 | #120 | — | 30 | 1 | no | — |
| 306 | #120 | — | 30 | 1 | no | — |
| 307 | C4×Q8 | — | 5 | 1 | no | — |
| 308 | C4×D4 | — | 15 | 1 | no | — |
| 309 | C4×D4 | — | 15 | 1 | no | — |
| 310 | #106 | — | 15 | 1 | no | — |
| 311 | C4⋊C8 | — | 15 | 1 | no | — |
| 312 | #103 | — | 3 | 1 | no | — |
| 313 | #103 | — | 3 | 1 | no | — |
| 314 | #103 | — | 15 | 1 | no | — |
| 315 | #102 | — | 15 | 1 | no | — |
| 316 | #102 | — | 15 | 1 | no | — |
| 317 | #102 | — | 15 | 1 | no | — |
| 318 | C22⋊C8 | — | 3 | 1 | no | — |
| 319 | C22⋊C8 | — | 15 | 1 | no | — |
| 320 | C4×C8 | — | 15 | 1 | no | — |
| 321 | C2×C3×C5 | — | 4 | 1 | no | — |
| 322 | C2×C3×C5 | — | 4 | 1 | no | — |
| 323 | C2×C3×C5 | — | 4 | 1 | no | — |
| 324 | C2×C3×C5 | — | 8 | 2 | no | — |
| 325 | D15 | — | 4 | 4 | no | — |
| 326 | D15 | — | 8 | 2 | no | — |
| 327 | C3×D5 | — | 8 | 2 | no | — |
| 328 | C5×D3 | — | 8 | 2 | no | — |
| 329 | C23×C3 | — | 4 | 1 | no | — |
| 330 | C23×C3 | — | 20 | 1 | no | — |
| 331 | C22×D3 | — | 4 | 1 | no | — |
| 332 | C22×D3 | — | 20 | 1 | no | — |
| 333 | C22×D3 | — | 20 | 1 | no | — |
| 334 | C22×D3 | — | 20 | 4 | no | — |
| 335 | C22×D3 | — | 20 | 4 | no | — |
| 336 | C22×D3 | — | 40 | 2 | no | — |
| 337 | C22×D3 | — | 40 | 2 | no | — |
| 338 | C22×D3 | — | 40 | 2 | no | — |
| 339 | C22×D3 | — | 40 | 2 | no | — |
| 340 | C3×D4 | — | 20 | 4 | no | — |
| 341 | C2×C3×C4 | — | 20 | 1 | no | — |
| 342 | #67 | — | 4 | 4 | no | — |
| 343 | #67 | — | 20 | 4 | no | — |
| 344 | C2×Dic3 | — | 4 | 1 | no | — |
| 345 | D12 | — | 20 | 4 | no | — |
| 346 | C4×D3 | — | 20 | 4 | no | — |
| 347 | SL(2,𝔽3) | D4×D5 | 1 | 1 | yes | characteristic, complemented |
| 348 | C22×C5 | — | 2 | 1 | no | — |
| 349 | C22×C5 | — | 2 | 1 | no | — |
| 350 | C22×C5 | — | 12 | 1 | no | — |
| 351 | C22×C5 | — | 12 | 1 | no | — |
| 352 | C22×C5 | — | 12 | 1 | no | — |
| 353 | C22×C5 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 354 | C22×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 355 | C2×D5 | — | 2 | 1 | no | — |
| 356 | C2×D5 | — | 2 | 1 | no | — |
| 357 | C2×D5 | — | 6 | 2 | no | — |
| 358 | C2×D5 | — | 12 | 1 | no | — |
| 359 | C2×D5 | — | 12 | 1 | no | — |
| 360 | C2×D5 | — | 12 | 1 | no | — |
| 361 | C2×D5 | — | 12 | 1 | no | — |
| 362 | C2×D5 | — | 12 | 1 | no | — |
| 363 | C2×D5 | — | 24 | 4 | no | — |
| 364 | C2×D5 | — | 24 | 4 | no | — |
| 365 | C2×D5 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 366 | C4×C5 | — | 3 | 1 | no | — |
| 367 | C4×C5 | — | 3 | 1 | no | — |
| 368 | C4×C5 | — | 6 | 1 | no | — |
| 369 | C4×C5 | — | 12 | 1 | no | — |
| 370 | Dic5 | — | 6 | 1 | no | — |
| 371 | Dic5 | — | 6 | 1 | no | — |
| 372 | Dic5 | C2×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 373 | C24 | — | 30 | 1 | no | — |
| 374 | C24 | — | 30 | 1 | no | — |
| 375 | C2×Q8 | — | 2 | 1 | no | — |
| 376 | C2×Q8 | — | 3 | 1 | no | — |
| 377 | C2×Q8 | — | 6 | 1 | no | — |
| 378 | C2×Q8 | — | 10 | 1 | no | — |
| 379 | C2×Q8 | — | 15 | 1 | no | — |
| 380 | C2×Q8 | — | 30 | 1 | no | — |
| 381 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 382 | C2×D4 | — | 3 | 1 | no | — |
| 383 | C2×D4 | — | 5 | 1 | no | — |
| 384 | C2×D4 | — | 6 | 1 | no | — |
| 385 | C2×D4 | — | 15 | 1 | no | — |
| 386 | C2×D4 | — | 15 | 1 | no | — |
| 387 | C2×D4 | — | 30 | 1 | no | — |
| 388 | C2×D4 | — | 30 | 1 | no | — |
| 389 | C2×D4 | — | 30 | 2 | no | — |
| 390 | C2×D4 | — | 30 | 1 | no | — |
| 391 | C2×D4 | — | 30 | 1 | no | — |
| 392 | C2×D4 | — | 30 | 1 | no | — |
| 393 | C2×D4 | — | 30 | 2 | no | — |
| 394 | C2×D4 | — | 60 | 1 | no | — |
| 395 | C2×D4 | — | 60 | 1 | no | — |
| 396 | C2×D4 | — | 60 | 4 | no | — |
| 397 | C22×C4 | — | 3 | 1 | no | — |
| 398 | C22×C4 | — | 15 | 1 | no | — |
| 399 | C22×C4 | — | 30 | 1 | no | — |
| 400 | SD16 | — | 6 | 1 | no | — |
| 401 | SD16 | — | 6 | 1 | no | — |
| 402 | SD16 | — | 12 | 1 | no | — |
| 403 | SD16 | — | 15 | 2 | no | — |
| 404 | SD16 | — | 15 | 2 | no | — |
| 405 | SD16 | — | 30 | 2 | no | — |
| 406 | SD16 | — | 30 | 2 | no | — |
| 407 | SD16 | — | 30 | 2 | no | — |
| 408 | SD16 | — | 30 | 2 | no | — |
| 409 | SD16 | — | 30 | 1 | no | — |
| 410 | SD16 | — | 30 | 1 | no | — |
| 411 | SD16 | — | 60 | 1 | no | — |
| 412 | C2×C8 | — | 3 | 1 | no | — |
| 413 | C2×C8 | — | 3 | 1 | no | — |
| 414 | C2×C8 | — | 15 | 1 | no | — |
| 415 | C2×C8 | — | 15 | 1 | no | — |
| 416 | C2×C8 | — | 30 | 2 | no | — |
| 417 | C2×C8 | — | 30 | 2 | no | — |
| 418 | C4⋊C4 | — | 3 | 1 | no | — |
| 419 | C4⋊C4 | — | 15 | 1 | no | — |
| 420 | C4⋊C4 | — | 15 | 1 | no | — |
| 421 | C4⋊C4 | — | 30 | 1 | no | — |
| 422 | C22⋊C4 | — | 6 | 1 | no | — |
| 423 | C22⋊C4 | — | 15 | 1 | no | — |
| 424 | C22⋊C4 | — | 15 | 1 | no | — |
| 425 | C22⋊C4 | — | 30 | 1 | no | — |
| 426 | C22⋊C4 | — | 30 | 1 | no | — |
| 427 | C42 | — | 15 | 1 | no | — |
| 428 | C3×C5 | — | 4 | 1 | no | Hall |
| 429 | C22×C3 | — | 4 | 1 | no | — |
| 430 | C22×C3 | — | 4 | 2 | no | — |
| 431 | C22×C3 | — | 8 | 1 | no | — |
| 432 | C22×C3 | — | 8 | 1 | no | — |
| 433 | C22×C3 | — | 20 | 2 | no | — |
| 434 | C22×C3 | — | 40 | 1 | no | — |
| 435 | C22×C3 | — | 40 | 1 | no | — |
| 436 | C2×D3 | — | 4 | 2 | no | — |
| 437 | C2×D3 | — | 8 | 1 | no | — |
| 438 | C2×D3 | — | 8 | 1 | no | — |
| 439 | C2×D3 | — | 20 | 2 | no | — |
| 440 | C2×D3 | — | 20 | 2 | no | — |
| 441 | C2×D3 | — | 20 | 2 | no | — |
| 442 | C2×D3 | — | 20 | 2 | no | — |
| 443 | C2×D3 | — | 40 | 1 | no | — |
| 444 | C2×D3 | — | 40 | 1 | no | — |
| 445 | C2×D3 | — | 40 | 8 | no | — |
| 446 | C2×D3 | — | 40 | 8 | no | — |
| 447 | C3×C4 | — | 20 | 2 | no | — |
| 448 | Dic3 | — | 4 | 2 | no | — |
| 449 | C2×C5 | — | 2 | 2 | no | — |
| 450 | C2×C5 | — | 24 | 1 | no | — |
| 451 | C2×C5 | D4×S4 | 1 | 1 | yes | characteristic |
| 452 | C2×C5 | C22×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 453 | C2×C5 | #5926 | 1 | 1 | yes | characteristic |
| 454 | D5 | — | 2 | 2 | no | — |
| 455 | D5 | — | 12 | 2 | no | — |
| 456 | D5 | — | 24 | 1 | no | — |
| 457 | C23 | — | 5 | 1 | no | — |
| 458 | C23 | — | 6 | 1 | no | — |
| 459 | C23 | — | 30 | 1 | no | — |
| 460 | C23 | — | 30 | 1 | no | — |
| 461 | C23 | — | 60 | 2 | no | — |
| 462 | C23 | — | 60 | 2 | no | — |
| 463 | C23 | — | 60 | 2 | no | — |
| 464 | C23 | — | 60 | 2 | no | — |
| 465 | C23 | — | 120 | 1 | no | — |
| 466 | C23 | — | 120 | 1 | no | — |
| 467 | C23 | D5×S4 | 1 | 1 | yes | characteristic |
| 468 | Q8 | — | 3 | 1 | no | — |
| 469 | Q8 | — | 6 | 1 | no | — |
| 470 | Q8 | — | 6 | 1 | no | — |
| 471 | Q8 | — | 30 | 1 | no | — |
| 472 | Q8 | — | 30 | 1 | no | — |
| 473 | Q8 | #6790 | 1 | 1 | yes | characteristic, complemented |
| 474 | D4 | — | 5 | 4 | no | — |
| 475 | D4 | — | 6 | 1 | no | — |
| 476 | D4 | — | 6 | 1 | no | — |
| 477 | D4 | — | 12 | 2 | no | — |
| 478 | D4 | — | 15 | 2 | no | — |
| 479 | D4 | — | 30 | 1 | no | — |
| 480 | D4 | — | 30 | 1 | no | — |
| 481 | D4 | — | 30 | 1 | no | — |
| 482 | D4 | — | 60 | 2 | no | — |
| 483 | D4 | — | 60 | 2 | no | — |
| 484 | D4 | — | 60 | 2 | no | — |
| 485 | D4 | — | 60 | 2 | no | — |
| 486 | D4 | — | 120 | 1 | no | — |
| 487 | C2×C4 | — | 3 | 1 | no | — |
| 488 | C2×C4 | — | 3 | 1 | no | — |
| 489 | C2×C4 | — | 5 | 1 | no | — |
| 490 | C2×C4 | — | 6 | 1 | no | — |
| 491 | C2×C4 | — | 6 | 1 | no | — |
| 492 | C2×C4 | — | 6 | 1 | no | — |
| 493 | C2×C4 | — | 15 | 1 | no | — |
| 494 | C2×C4 | — | 15 | 1 | no | — |
| 495 | C2×C4 | — | 30 | 1 | no | — |
| 496 | C2×C4 | — | 30 | 1 | no | — |
| 497 | C2×C4 | — | 60 | 2 | no | — |
| 498 | C8 | — | 6 | 1 | no | — |
| 499 | C8 | — | 6 | 1 | no | — |
| 500 | C8 | — | 15 | 2 | no | — |
| 501 | C8 | — | 30 | 1 | no | — |
| 502 | C2×C3 | — | 4 | 1 | no | — |
| 503 | C2×C3 | — | 4 | 1 | no | — |
| 504 | C2×C3 | — | 4 | 1 | no | — |
| 505 | C2×C3 | — | 8 | 2 | no | — |
| 506 | C2×C3 | — | 40 | 2 | no | — |
| 507 | D3 | — | 8 | 2 | no | — |
| 508 | D3 | — | 20 | 4 | no | — |
| 509 | D3 | — | 40 | 2 | no | — |
| 510 | C5 | D4×GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 511 | C22 | — | 2 | 1 | no | — |
| 512 | C22 | — | 2 | 1 | no | — |
| 513 | C22 | — | 5 | 2 | no | — |
| 514 | C22 | — | 10 | 1 | no | — |
| 515 | C22 | — | 10 | 1 | no | — |
| 516 | C22 | — | 12 | 1 | no | — |
| 517 | C22 | — | 12 | 1 | no | — |
| 518 | C22 | — | 12 | 1 | no | — |
| 519 | C22 | — | 30 | 2 | no | — |
| 520 | C22 | — | 60 | 1 | no | — |
| 521 | C22 | — | 60 | 1 | no | — |
| 522 | C22 | — | 60 | 1 | no | — |
| 523 | C22 | — | 60 | 1 | no | — |
| 524 | C22 | — | 60 | 1 | no | — |
| 525 | C22 | — | 120 | 4 | no | — |
| 526 | C22 | — | 120 | 4 | no | — |
| 527 | C22 | D5×GL(2,𝔽3) | 1 | 2 | yes | complemented |
| 528 | C22 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 529 | C4 | — | 3 | 1 | no | — |
| 530 | C4 | — | 3 | 1 | no | — |
| 531 | C4 | — | 5 | 2 | no | — |
| 532 | C4 | — | 6 | 1 | no | — |
| 533 | C4 | — | 12 | 1 | no | — |
| 534 | C4 | — | 30 | 1 | no | — |
| 535 | C4 | — | 30 | 1 | no | — |
| 536 | C3 | — | 4 | 1 | no | Sylow |
| 537 | C2 | — | 2 | 2 | no | — |
| 538 | C2 | — | 10 | 2 | no | — |
| 539 | C2 | — | 24 | 1 | no | — |
| 540 | C2 | — | 60 | 2 | no | — |
| 541 | C2 | — | 120 | 1 | no | — |
| 542 | C2 | C2×D5×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 543 | C2 | #11756772 | 1 | 1 | yes | characteristic |
| 544 | C2 | #11756799 | 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×D5×GL(2,𝔽3) | C2 | semidirect |
| 3. SL(2,𝔽3)×C22⋊D5 | C2 | semidirect |
| 4. C5×#5421 | C2 | semidirect |
| 5. #11751614 | C2 | semidirect |
| 6. #11751611 | C2 | semidirect |
| 7. #11751610 | C2 | semidirect |
| 9. C22×C5×SL(2,𝔽3) | C22 | semidirect |
| 11. C2×D5×SL(2,𝔽3) | C22 | semidirect |
| 14. C2×C5⋊GL(2,𝔽3) | C22 | semidirect |
| 15. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 17. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 18. C5×#859 | C22 | semidirect |
| 20. Q8×C22⋊D5 | D3 | semidirect |
| 47. C5⋊GL(2,𝔽3) | D4 | semidirect |
| 53. #5421 | D5 | semidirect |
| 56. C22×C5×Q8 | C2×D3 | semidirect |
| 57. C2×Q8×D5 | C2×D3 | semidirect |
| 65. Q8×Dic5 | C2×D3 | semidirect |
| 115. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 121. C22×SL(2,𝔽3) | C2×D5 | semidirect |
| 126. C2×GL(2,𝔽3) | C2×D5 | semidirect |
| 128. #859 | C2×D5 | semidirect |
| 247. C5×Q8 | D3×D4 | semidirect |
| 259. C22⋊D5 | GL(2,𝔽3) | semidirect |
| 279. C22×Q8 | D3×D5 | semidirect |
| 347. SL(2,𝔽3) | D4×D5 | semidirect |
| 353. C22×C5 | C2×GL(2,𝔽3) | semidirect |
| 365. C2×D5 | C2×GL(2,𝔽3) | semidirect |
| 372. Dic5 | C2×GL(2,𝔽3) | semidirect |
| 473. Q8 | #6790 | semidirect |
| 510. C5 | D4×GL(2,𝔽3) | semidirect |
| 527. C22 | D5×GL(2,𝔽3) | 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×D5×GL(2,𝔽3) | 2 |
| SL(2,𝔽3)×C22⋊D5 | 2 |
| C5×#5421 | 2 |
| #11751614 | 2 |
| #11751611 | 2 |
| #11751610 | 2 |
| #10611794 | 3 |
| C2×#6790 | 4 |
| D4×GL(2,𝔽3) | 5 |