Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2432 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 2432 conjugacy classes of subgroups — too many to draw. Only its 251 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×C5×2−1+4⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #66287⋊C3 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | D5×2−1+4⋊C3 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #66283⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#4147⋊C3 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10619439 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 7 | C3×#4144 | — | 4 | 1 | no | maximal |
| 8 | C5×2−1+4⋊C3 | C22 | 1 | 4 | yes | complemented |
| 9 | C2×C5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C22×C5×SL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 11 | #4150⋊C3 | C22 | 1 | 2 | yes | complemented |
| 12 | D5×#41⋊C3 | C22 | 1 | 4 | yes | complemented |
| 13 | C5⋊#994 | C22 | 1 | 2 | yes | complemented |
| 14 | #4147⋊C3 | C22 | 1 | 4 | yes | complemented |
| 15 | #4147⋊C3 | C22 | 1 | 8 | yes | complemented |
| 16 | C2×D5×SL(2,𝔽3) | C22 | 1 | 4 | yes | complemented |
| 17 | C2×C5⋊(#41⋊C3) | C22 | 1 | 4 | yes | complemented |
| 18 | #87537 | — | 5 | 1 | no | maximal, Hall |
| 19 | C2×C5×2−1+4 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | #66287 | — | 3 | 4 | no | — |
| 21 | #66287 | C2×C3 | 1 | 4 | yes | complemented |
| 22 | D5×2−1+4 | — | 3 | 4 | no | — |
| 23 | D5×2−1+4 | C2×C3 | 1 | 4 | yes | complemented |
| 24 | #66283 | — | 3 | 1 | no | — |
| 25 | #66283 | — | 3 | 4 | no | — |
| 26 | #66283 | — | 3 | 1 | no | — |
| 27 | #66283 | C2×C3 | 1 | 2 | yes | complemented |
| 28 | C2×#4147 | — | 3 | 2 | no | — |
| 29 | C2×#4147 | C2×C3 | 1 | 4 | yes | complemented |
| 30 | C2×C3×C5×D4 | — | 4 | 1 | no | — |
| 31 | C2×C3×C22⋊D5 | — | 4 | 4 | no | — |
| 32 | C3×#711 | — | 4 | 4 | no | — |
| 33 | C3×D4×D5 | — | 4 | 4 | no | — |
| 34 | C3×#709 | — | 4 | 2 | no | — |
| 35 | C5×#41⋊C3 | C23 | 1 | 2 | yes | — |
| 36 | C2×C5×SL(2,𝔽3) | C23 | 1 | 4 | yes | — |
| 37 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 38 | D5×SL(2,𝔽3) | C23 | 1 | 4 | yes | — |
| 39 | C5⋊(#41⋊C3) | C23 | 1 | 4 | yes | — |
| 40 | #5945 | — | 5 | 4 | no | — |
| 41 | #5945 | — | 5 | 2 | no | — |
| 42 | C2×2−1+4⋊C3 | — | 5 | 4 | no | — |
| 43 | C2×2−1+4⋊C3 | — | 5 | 4 | no | — |
| 44 | C2×2−1+4⋊C3 | D5 | 1 | 1 | yes | characteristic, complemented |
| 45 | C5×2−1+4 | — | 3 | 4 | no | — |
| 46 | C5×2−1+4 | C22×C3 | 1 | 4 | yes | complemented |
| 47 | C2×C5×#41 | — | 3 | 1 | no | — |
| 48 | C2×C5×#41 | — | 3 | 2 | no | — |
| 49 | C2×C5×#41 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 50 | C22×C5×Q8 | — | 3 | 1 | no | — |
| 51 | C22×C5×Q8 | C22×C3 | 1 | 2 | yes | complemented |
| 52 | #4150 | — | 3 | 8 | no | — |
| 53 | #4150 | — | 3 | 4 | no | — |
| 54 | #4150 | — | 3 | 8 | no | — |
| 55 | #4150 | — | 3 | 4 | no | — |
| 56 | #4150 | — | 3 | 2 | no | — |
| 57 | #4150 | C22×C3 | 1 | 2 | yes | complemented |
| 58 | #4149 | — | 3 | 8 | no | — |
| 59 | #4149 | — | 3 | 4 | no | — |
| 60 | #4149 | — | 3 | 4 | no | — |
| 61 | #4149 | — | 3 | 8 | no | — |
| 62 | #4149 | — | 3 | 2 | no | — |
| 63 | #4149 | C22×C3 | 1 | 2 | yes | complemented |
| 64 | D5×#41 | — | 3 | 8 | no | — |
| 65 | D5×#41 | — | 3 | 16 | no | — |
| 66 | D5×#41 | — | 3 | 4 | no | — |
| 67 | D5×#41 | — | 3 | 8 | no | — |
| 68 | D5×#41 | — | 3 | 4 | no | — |
| 69 | D5×#41 | — | 3 | 8 | no | — |
| 70 | D5×#41 | — | 3 | 4 | no | — |
| 71 | D5×#41 | C22×C3 | 1 | 4 | yes | complemented |
| 72 | #4147 | — | 3 | 2 | no | — |
| 73 | #4147 | — | 3 | 8 | no | — |
| 74 | #4147 | — | 3 | 4 | no | — |
| 75 | #4147 | — | 3 | 4 | no | — |
| 76 | #4147 | — | 3 | 2 | no | — |
| 77 | #4147 | — | 3 | 8 | no | — |
| 78 | #4147 | — | 3 | 8 | no | — |
| 79 | #4147 | C22×C3 | 1 | 4 | yes | complemented |
| 80 | #4147 | C22×C3 | 1 | 8 | yes | complemented |
| 81 | C2×#713 | — | 3 | 4 | no | — |
| 82 | C2×#713 | — | 3 | 4 | no | — |
| 83 | C2×#713 | — | 3 | 4 | no | — |
| 84 | C2×#713 | C22×C3 | 1 | 4 | yes | complemented |
| 85 | C2×Q8×D5 | — | 3 | 4 | no | — |
| 86 | C2×Q8×D5 | — | 3 | 4 | no | — |
| 87 | C2×Q8×D5 | — | 3 | 4 | no | — |
| 88 | C2×Q8×D5 | C22×C3 | 1 | 4 | yes | complemented |
| 89 | #4144 | — | 3 | 4 | no | — |
| 90 | #4144 | — | 3 | 1 | no | — |
| 91 | #4144 | — | 3 | 4 | no | — |
| 92 | #4144 | — | 3 | 4 | no | — |
| 93 | #4144 | A4 | 1 | 1 | yes | characteristic |
| 94 | C2×#709 | — | 3 | 8 | no | — |
| 95 | C2×#709 | — | 3 | 4 | no | — |
| 96 | C2×#709 | — | 3 | 4 | no | — |
| 97 | C2×#709 | — | 3 | 2 | no | — |
| 98 | C2×#709 | — | 3 | 2 | no | — |
| 99 | 2−1+6 | — | 5 | 1 | no | Sylow |
| 100 | C23×C3×C5 | — | 4 | 2 | no | — |
| 101 | C22×C3×D5 | — | 4 | 4 | no | — |
| 102 | C3×C5×D4 | — | 4 | 4 | no | — |
| 103 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 104 | C3×C22⋊D5 | — | 4 | 4 | no | — |
| 105 | C3×C22⋊D5 | — | 4 | 8 | no | — |
| 106 | C2×C3×Dic5 | — | 4 | 4 | no | — |
| 107 | C3×D20 | — | 4 | 2 | no | — |
| 108 | C3×C4×D5 | — | 4 | 4 | no | — |
| 109 | C3×Dic10 | — | 4 | 2 | no | — |
| 110 | C5×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 111 | C3×H(5,𝔽2) | — | 20 | 1 | no | — |
| 112 | 2−1+4⋊C3 | — | 5 | 2 | no | — |
| 113 | 2−1+4⋊C3 | — | 5 | 8 | no | — |
| 114 | 2−1+4⋊C3 | — | 5 | 4 | no | — |
| 115 | 2−1+4⋊C3 | C2×D5 | 1 | 4 | yes | complemented |
| 116 | #994 | — | 5 | 2 | no | — |
| 117 | C2×#41⋊C3 | — | 5 | 4 | no | — |
| 118 | C2×#41⋊C3 | — | 5 | 4 | no | — |
| 119 | C2×#41⋊C3 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 120 | C22×SL(2,𝔽3) | — | 5 | 4 | no | — |
| 121 | C22×SL(2,𝔽3) | C2×D5 | 1 | 2 | yes | complemented |
| 122 | C5×#41 | — | 3 | 8 | no | — |
| 123 | C5×#41 | — | 3 | 4 | no | — |
| 124 | C5×#41 | — | 3 | 4 | no | — |
| 125 | C5×#41 | — | 3 | 8 | no | — |
| 126 | C5×#41 | — | 3 | 2 | no | — |
| 127 | C5×#41 | C23×C3 | 1 | 2 | yes | — |
| 128 | C2×C5×Q8 | — | 3 | 4 | no | — |
| 129 | C2×C5×Q8 | — | 3 | 4 | no | — |
| 130 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 131 | C2×C5×Q8 | — | 3 | 4 | no | — |
| 132 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 133 | C2×C5×Q8 | C23×C3 | 1 | 4 | yes | — |
| 134 | C2×C5×Q8 | C23×C3 | 1 | 1 | yes | characteristic |
| 135 | C2×C5×D4 | — | 3 | 1 | no | — |
| 136 | C2×C5×D4 | — | 3 | 2 | no | — |
| 137 | C2×C5×D4 | C2×A4 | 1 | 1 | yes | characteristic |
| 138 | C22×C4×C5 | — | 3 | 2 | no | — |
| 139 | C22×C4×C5 | — | 3 | 2 | no | — |
| 140 | C22×C4×C5 | — | 3 | 1 | no | — |
| 141 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 142 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 143 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 144 | C2×C22⋊D5 | C2×A4 | 1 | 4 | yes | — |
| 145 | #713 | — | 3 | 16 | no | — |
| 146 | #713 | — | 3 | 8 | no | — |
| 147 | #713 | — | 3 | 4 | no | — |
| 148 | #713 | — | 3 | 8 | no | — |
| 149 | #713 | — | 3 | 4 | no | — |
| 150 | #713 | — | 3 | 4 | no | — |
| 151 | #713 | — | 3 | 8 | no | — |
| 152 | #713 | C23×C3 | 1 | 4 | yes | — |
| 153 | Q8×D5 | — | 3 | 8 | no | — |
| 154 | Q8×D5 | — | 3 | 16 | no | — |
| 155 | Q8×D5 | — | 3 | 4 | no | — |
| 156 | Q8×D5 | — | 3 | 8 | no | — |
| 157 | Q8×D5 | — | 3 | 4 | no | — |
| 158 | Q8×D5 | — | 3 | 8 | no | — |
| 159 | Q8×D5 | — | 3 | 4 | no | — |
| 160 | Q8×D5 | C23×C3 | 1 | 4 | yes | — |
| 161 | #711 | — | 3 | 16 | no | — |
| 162 | #711 | — | 3 | 8 | no | — |
| 163 | #711 | — | 3 | 4 | no | — |
| 164 | #711 | — | 3 | 8 | no | — |
| 165 | #711 | — | 3 | 4 | no | — |
| 166 | #711 | — | 3 | 8 | no | — |
| 167 | #711 | — | 3 | 4 | no | — |
| 168 | #711 | C2×A4 | 1 | 4 | yes | — |
| 169 | D4×D5 | — | 3 | 4 | no | — |
| 170 | D4×D5 | — | 3 | 16 | no | — |
| 171 | D4×D5 | — | 3 | 8 | no | — |
| 172 | D4×D5 | — | 3 | 8 | no | — |
| 173 | D4×D5 | — | 3 | 4 | no | — |
| 174 | D4×D5 | — | 3 | 8 | no | — |
| 175 | D4×D5 | — | 3 | 4 | no | — |
| 176 | D4×D5 | C2×A4 | 1 | 4 | yes | — |
| 177 | #709 | — | 3 | 8 | no | — |
| 178 | #709 | — | 3 | 8 | no | — |
| 179 | #709 | — | 3 | 16 | no | — |
| 180 | #709 | — | 3 | 4 | no | — |
| 181 | #709 | — | 3 | 16 | no | — |
| 182 | #709 | — | 3 | 2 | no | — |
| 183 | #709 | — | 3 | 8 | no | — |
| 184 | #709 | — | 3 | 4 | no | — |
| 185 | #709 | — | 3 | 8 | no | — |
| 186 | #709 | — | 3 | 8 | no | — |
| 187 | #709 | — | 3 | 4 | no | — |
| 188 | #709 | — | 3 | 8 | no | — |
| 189 | #709 | — | 3 | 2 | no | — |
| 190 | #709 | — | 3 | 4 | no | — |
| 191 | #709 | — | 3 | 4 | no | — |
| 192 | #709 | — | 3 | 2 | no | — |
| 193 | #709 | C2×A4 | 1 | 2 | yes | — |
| 194 | C2×D20 | — | 3 | 4 | no | — |
| 195 | C2×D20 | — | 3 | 8 | no | — |
| 196 | C2×D20 | — | 3 | 4 | no | — |
| 197 | C2×D20 | — | 3 | 2 | no | — |
| 198 | C2×D20 | — | 3 | 2 | no | — |
| 199 | C2×C4×D5 | — | 3 | 8 | no | — |
| 200 | C2×C4×D5 | — | 3 | 8 | no | — |
| 201 | C2×C4×D5 | — | 3 | 4 | no | — |
| 202 | C2×C4×D5 | — | 3 | 8 | no | — |
| 203 | C2×C4×D5 | — | 3 | 4 | no | — |
| 204 | C2×C4×D5 | — | 3 | 4 | no | — |
| 205 | C2×C4×D5 | — | 3 | 4 | no | — |
| 206 | C2×Dic10 | — | 3 | 8 | no | — |
| 207 | C2×Dic10 | — | 3 | 4 | no | — |
| 208 | C2×Dic10 | — | 3 | 4 | no | — |
| 209 | C2×Dic10 | — | 3 | 2 | no | — |
| 210 | C2×Dic10 | — | 3 | 2 | no | — |
| 211 | #585 | — | 5 | 4 | no | — |
| 212 | #585 | — | 5 | 2 | no | — |
| 213 | #585 | — | 15 | 1 | no | — |
| 214 | #585 | — | 15 | 1 | no | — |
| 215 | #585 | — | 15 | 4 | no | — |
| 216 | #585 | — | 15 | 4 | no | — |
| 217 | C2×2−1+4 | — | 5 | 4 | no | — |
| 218 | C2×2−1+4 | — | 5 | 4 | no | — |
| 219 | C2×2−1+4 | — | 15 | 2 | no | — |
| 220 | C2×2−1+4 | — | 15 | 4 | no | — |
| 221 | C2×2−1+4 | C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 222 | C22×C3×C5 | — | 4 | 4 | no | — |
| 223 | C22×C3×C5 | — | 4 | 1 | no | — |
| 224 | C22×C3×C5 | — | 16 | 2 | no | — |
| 225 | C2×C3×D5 | — | 4 | 4 | no | — |
| 226 | C2×C3×D5 | — | 16 | 4 | no | — |
| 227 | C3×C4×C5 | — | 4 | 2 | no | — |
| 228 | C3×Dic5 | — | 4 | 4 | no | — |
| 229 | C3×#41 | — | 20 | 2 | no | — |
| 230 | C3×#41 | — | 20 | 4 | no | — |
| 231 | C2×C3×D4 | — | 4 | 1 | no | — |
| 232 | C2×C3×D4 | — | 20 | 4 | no | — |
| 233 | C2×C3×D4 | — | 20 | 4 | no | — |
| 234 | #41⋊C3 | — | 5 | 4 | no | — |
| 235 | #41⋊C3 | C22×D5 | 1 | 2 | yes | — |
| 236 | C2×SL(2,𝔽3) | — | 5 | 4 | no | — |
| 237 | C2×SL(2,𝔽3) | C22×D5 | 1 | 4 | yes | — |
| 238 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 239 | C23×C5 | — | 3 | 1 | no | — |
| 240 | C23×C5 | C22×A4 | 1 | 2 | yes | — |
| 241 | C22×D5 | — | 3 | 4 | no | — |
| 242 | C22×D5 | — | 3 | 4 | no | — |
| 243 | C22×D5 | — | 3 | 4 | no | — |
| 244 | C22×D5 | C22×A4 | 1 | 4 | yes | — |
| 245 | C5×Q8 | — | 3 | 4 | no | — |
| 246 | C5×Q8 | — | 3 | 1 | no | — |
| 247 | C5×Q8 | — | 3 | 4 | no | — |
| 248 | C5×Q8 | — | 3 | 4 | no | — |
| 249 | C5×Q8 | C24×C3 | 1 | 1 | yes | characteristic |
| 250 | C5×D4 | — | 3 | 2 | no | — |
| 251 | C5×D4 | — | 3 | 2 | no | — |
| 252 | C5×D4 | — | 3 | 8 | no | — |
| 253 | C5×D4 | C22×A4 | 1 | 4 | yes | — |
| 254 | C2×C4×C5 | — | 3 | 8 | no | — |
| 255 | C2×C4×C5 | — | 3 | 4 | no | — |
| 256 | C2×C4×C5 | — | 3 | 4 | no | — |
| 257 | C2×C4×C5 | — | 3 | 2 | no | — |
| 258 | C2×C4×C5 | — | 3 | 1 | no | — |
| 259 | C2×C4×C5 | — | 3 | 2 | no | — |
| 260 | C2×C4×C5 | — | 3 | 2 | no | — |
| 261 | C2×C4×C5 | C22×A4 | 1 | 1 | yes | characteristic |
| 262 | C22⋊D5 | — | 3 | 8 | no | — |
| 263 | C22⋊D5 | — | 3 | 4 | no | — |
| 264 | C22⋊D5 | — | 3 | 8 | no | — |
| 265 | C22⋊D5 | — | 3 | 4 | no | — |
| 266 | C22⋊D5 | — | 3 | 4 | no | — |
| 267 | C22⋊D5 | C22×A4 | 1 | 4 | yes | — |
| 268 | C22⋊D5 | C22×A4 | 1 | 8 | yes | — |
| 269 | C2×Dic5 | — | 3 | 4 | no | — |
| 270 | C2×Dic5 | — | 3 | 4 | no | — |
| 271 | C2×Dic5 | — | 3 | 4 | no | — |
| 272 | C2×Dic5 | C22×A4 | 1 | 4 | yes | — |
| 273 | D20 | — | 3 | 4 | no | — |
| 274 | D20 | — | 3 | 8 | no | — |
| 275 | D20 | — | 3 | 8 | no | — |
| 276 | D20 | — | 3 | 4 | no | — |
| 277 | D20 | — | 3 | 2 | no | — |
| 278 | D20 | C22×A4 | 1 | 2 | yes | — |
| 279 | C4×D5 | — | 3 | 16 | no | — |
| 280 | C4×D5 | — | 3 | 8 | no | — |
| 281 | C4×D5 | — | 3 | 4 | no | — |
| 282 | C4×D5 | — | 3 | 8 | no | — |
| 283 | C4×D5 | — | 3 | 4 | no | — |
| 284 | C4×D5 | — | 3 | 8 | no | — |
| 285 | C4×D5 | — | 3 | 4 | no | — |
| 286 | C4×D5 | C22×A4 | 1 | 4 | yes | — |
| 287 | Dic10 | — | 3 | 8 | no | — |
| 288 | Dic10 | — | 3 | 2 | no | — |
| 289 | Dic10 | — | 3 | 8 | no | — |
| 290 | Dic10 | — | 3 | 4 | no | — |
| 291 | Dic10 | — | 3 | 4 | no | — |
| 292 | Dic10 | C22×A4 | 1 | 2 | yes | — |
| 293 | 2−1+4 | — | 3 | 4 | no | — |
| 294 | 2−1+4 | — | 5 | 2 | no | — |
| 295 | 2−1+4 | — | 5 | 8 | no | — |
| 296 | 2−1+4 | — | 5 | 4 | no | — |
| 297 | 2−1+4 | — | 15 | 2 | no | — |
| 298 | 2−1+4 | — | 15 | 4 | no | — |
| 299 | 2−1+4 | — | 15 | 8 | no | — |
| 300 | 2−1+4 | — | 15 | 8 | no | — |
| 301 | 2−1+4 | — | 15 | 8 | no | — |
| 302 | 2−1+4 | — | 15 | 2 | no | — |
| 303 | 2−1+4 | — | 15 | 4 | no | — |
| 304 | 2−1+4 | — | 15 | 4 | no | — |
| 305 | 2−1+4 | — | 15 | 4 | no | — |
| 306 | 2−1+4 | — | 15 | 8 | no | — |
| 307 | 2−1+4 | — | 15 | 8 | no | — |
| 308 | 2−1+4 | — | 15 | 2 | no | — |
| 309 | 2−1+4 | C2×C3×D5 | 1 | 4 | yes | complemented |
| 310 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 311 | H(5,𝔽2) | — | 5 | 2 | no | — |
| 312 | H(5,𝔽2) | — | 15 | 4 | no | — |
| 313 | H(5,𝔽2) | — | 15 | 4 | no | — |
| 314 | H(5,𝔽2) | — | 15 | 4 | no | — |
| 315 | H(5,𝔽2) | — | 15 | 4 | no | — |
| 316 | H(5,𝔽2) | — | 15 | 8 | no | — |
| 317 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 318 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 319 | H(5,𝔽2) | — | 15 | 4 | no | — |
| 320 | H(5,𝔽2) | — | 15 | 8 | no | — |
| 321 | C2×#41 | — | 3 | 1 | no | — |
| 322 | C2×#41 | — | 3 | 2 | no | — |
| 323 | C2×#41 | — | 5 | 4 | no | — |
| 324 | C2×#41 | — | 5 | 4 | no | — |
| 325 | C2×#41 | — | 15 | 4 | no | — |
| 326 | C2×#41 | — | 15 | 2 | no | — |
| 327 | C2×#41 | — | 15 | 2 | no | — |
| 328 | C2×#41 | — | 15 | 8 | no | — |
| 329 | C2×#41 | — | 15 | 4 | no | — |
| 330 | C2×#41 | — | 15 | 4 | no | — |
| 331 | C2×#41 | — | 15 | 4 | no | — |
| 332 | C2×#41 | — | 15 | 4 | no | — |
| 333 | C2×#41 | — | 15 | 4 | no | — |
| 334 | C2×#41 | — | 15 | 8 | no | — |
| 335 | C2×#41 | — | 15 | 4 | no | — |
| 336 | C2×#41 | — | 15 | 16 | no | — |
| 337 | C2×#41 | — | 15 | 8 | no | — |
| 338 | C2×#41 | — | 15 | 4 | no | — |
| 339 | C2×#41 | — | 15 | 8 | no | — |
| 340 | C2×#41 | C2×C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 341 | C22×Q8 | — | 3 | 1 | no | — |
| 342 | C22×Q8 | — | 5 | 4 | no | — |
| 343 | C22×Q8 | — | 15 | 4 | no | — |
| 344 | C22×Q8 | — | 15 | 4 | no | — |
| 345 | C22×Q8 | — | 15 | 4 | no | — |
| 346 | C22×Q8 | C2×C3×D5 | 1 | 2 | yes | complemented |
| 347 | C2×C3×C5 | — | 4 | 1 | no | — |
| 348 | C2×C3×C5 | — | 8 | 4 | no | — |
| 349 | C2×C3×C5 | — | 8 | 1 | no | — |
| 350 | C3×D5 | — | 8 | 4 | no | — |
| 351 | C23×C3 | — | 4 | 2 | no | — |
| 352 | C23×C3 | — | 20 | 4 | no | — |
| 353 | C3×Q8 | — | 20 | 2 | no | — |
| 354 | C3×D4 | — | 4 | 4 | no | — |
| 355 | C3×D4 | — | 20 | 2 | no | — |
| 356 | C3×D4 | — | 20 | 4 | no | — |
| 357 | C3×D4 | — | 20 | 8 | no | — |
| 358 | C2×C3×C4 | — | 4 | 1 | no | — |
| 359 | C2×C3×C4 | — | 20 | 4 | no | — |
| 360 | C2×C3×C4 | — | 20 | 4 | no | — |
| 361 | SL(2,𝔽3) | C23×D5 | 1 | 1 | yes | characteristic |
| 362 | C22×C5 | — | 3 | 2 | no | — |
| 363 | C22×C5 | — | 4 | 2 | no | — |
| 364 | C22×C5 | — | 12 | 1 | no | — |
| 365 | C22×C5 | C23×A4 | 1 | 4 | yes | — |
| 366 | C22×C5 | C23×A4 | 1 | 1 | yes | characteristic |
| 367 | C2×D5 | — | 3 | 4 | no | — |
| 368 | C2×D5 | — | 4 | 4 | no | — |
| 369 | C2×D5 | — | 12 | 4 | no | — |
| 370 | C2×D5 | — | 12 | 4 | no | — |
| 371 | C2×D5 | — | 12 | 4 | no | — |
| 372 | C2×D5 | C23×A4 | 1 | 4 | yes | — |
| 373 | C4×C5 | — | 3 | 4 | no | — |
| 374 | C4×C5 | — | 3 | 1 | no | — |
| 375 | C4×C5 | — | 3 | 1 | no | — |
| 376 | C4×C5 | C23×A4 | 1 | 2 | yes | — |
| 377 | Dic5 | — | 3 | 4 | no | — |
| 378 | Dic5 | C23×A4 | 1 | 4 | yes | — |
| 379 | #41 | — | 3 | 8 | no | — |
| 380 | #41 | — | 3 | 4 | no | — |
| 381 | #41 | — | 3 | 4 | no | — |
| 382 | #41 | — | 3 | 8 | no | — |
| 383 | #41 | — | 3 | 2 | no | — |
| 384 | #41 | — | 5 | 4 | no | — |
| 385 | #41 | — | 5 | 2 | no | — |
| 386 | #41 | — | 5 | 4 | no | — |
| 387 | #41 | — | 15 | 4 | no | — |
| 388 | #41 | — | 15 | 4 | no | — |
| 389 | #41 | — | 15 | 8 | no | — |
| 390 | #41 | — | 15 | 2 | no | — |
| 391 | #41 | — | 15 | 8 | no | — |
| 392 | #41 | — | 15 | 8 | no | — |
| 393 | #41 | — | 15 | 2 | no | — |
| 394 | #41 | — | 15 | 16 | no | — |
| 395 | #41 | — | 15 | 16 | no | — |
| 396 | #41 | — | 15 | 8 | no | — |
| 397 | #41 | — | 15 | 8 | no | — |
| 398 | #41 | — | 15 | 4 | no | — |
| 399 | #41 | — | 15 | 4 | no | — |
| 400 | #41 | — | 15 | 8 | no | — |
| 401 | #41 | — | 15 | 4 | no | — |
| 402 | #41 | — | 15 | 8 | no | — |
| 403 | #41 | — | 15 | 4 | no | — |
| 404 | #41 | — | 15 | 8 | no | — |
| 405 | #41 | — | 15 | 8 | no | — |
| 406 | #41 | — | 15 | 16 | no | — |
| 407 | #41 | — | 15 | 4 | no | — |
| 408 | #41 | — | 15 | 4 | no | — |
| 409 | #41 | — | 15 | 16 | no | — |
| 410 | #41 | — | 15 | 8 | no | — |
| 411 | #41 | — | 15 | 4 | no | — |
| 412 | #41 | — | 15 | 8 | no | — |
| 413 | #41 | — | 15 | 4 | no | — |
| 414 | #41 | — | 15 | 2 | no | — |
| 415 | #41 | — | 15 | 4 | no | — |
| 416 | #41 | — | 15 | 8 | no | — |
| 417 | #41 | C22×C3×D5 | 1 | 2 | yes | — |
| 418 | C2×Q8 | — | 3 | 4 | no | — |
| 419 | C2×Q8 | — | 3 | 4 | no | — |
| 420 | C2×Q8 | — | 3 | 1 | no | — |
| 421 | C2×Q8 | — | 3 | 2 | no | — |
| 422 | C2×Q8 | — | 3 | 4 | no | — |
| 423 | C2×Q8 | — | 5 | 4 | no | — |
| 424 | C2×Q8 | — | 15 | 4 | no | — |
| 425 | C2×Q8 | — | 15 | 2 | no | — |
| 426 | C2×Q8 | — | 15 | 2 | no | — |
| 427 | C2×Q8 | — | 15 | 8 | no | — |
| 428 | C2×Q8 | — | 15 | 4 | no | — |
| 429 | C2×Q8 | — | 15 | 4 | no | — |
| 430 | C2×Q8 | — | 15 | 4 | no | — |
| 431 | C2×Q8 | — | 15 | 4 | no | — |
| 432 | C2×Q8 | — | 15 | 8 | no | — |
| 433 | C2×Q8 | — | 15 | 16 | no | — |
| 434 | C2×Q8 | — | 15 | 8 | no | — |
| 435 | C2×Q8 | — | 15 | 8 | no | — |
| 436 | C2×Q8 | C22×C3×D5 | 1 | 4 | yes | — |
| 437 | C2×Q8 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 438 | C2×D4 | — | 3 | 1 | no | — |
| 439 | C2×D4 | — | 3 | 2 | no | — |
| 440 | C2×D4 | — | 5 | 4 | no | — |
| 441 | C2×D4 | — | 5 | 4 | no | — |
| 442 | C2×D4 | — | 15 | 2 | no | — |
| 443 | C2×D4 | — | 15 | 4 | no | — |
| 444 | C2×D4 | — | 15 | 4 | no | — |
| 445 | C2×D4 | — | 15 | 8 | no | — |
| 446 | C2×D4 | — | 15 | 2 | no | — |
| 447 | C2×D4 | — | 15 | 8 | no | — |
| 448 | C2×D4 | — | 15 | 8 | no | — |
| 449 | C2×D4 | — | 15 | 4 | no | — |
| 450 | C2×D4 | — | 15 | 8 | no | — |
| 451 | C2×D4 | — | 15 | 16 | no | — |
| 452 | C2×D4 | — | 15 | 4 | no | — |
| 453 | C2×D4 | — | 15 | 4 | no | — |
| 454 | C2×D4 | — | 15 | 4 | no | — |
| 455 | C2×D4 | — | 15 | 4 | no | — |
| 456 | C2×D4 | — | 15 | 4 | no | — |
| 457 | C2×D4 | D5×A4 | 1 | 1 | yes | characteristic |
| 458 | C22×C4 | — | 3 | 2 | no | — |
| 459 | C22×C4 | — | 3 | 2 | no | — |
| 460 | C22×C4 | — | 3 | 1 | no | — |
| 461 | C22×C4 | — | 15 | 4 | no | — |
| 462 | C22×C4 | — | 15 | 4 | no | — |
| 463 | C22×C4 | — | 15 | 4 | no | — |
| 464 | C22×C4 | — | 15 | 8 | no | — |
| 465 | C22×C4 | — | 15 | 8 | no | — |
| 466 | C22×C4 | — | 15 | 8 | no | — |
| 467 | C22×C4 | — | 15 | 4 | no | — |
| 468 | C3×C5 | — | 4 | 1 | no | Hall |
| 469 | C22×C3 | — | 4 | 1 | no | — |
| 470 | C22×C3 | — | 4 | 4 | no | — |
| 471 | C22×C3 | — | 16 | 2 | no | — |
| 472 | C22×C3 | — | 20 | 4 | no | — |
| 473 | C22×C3 | — | 80 | 4 | no | — |
| 474 | C3×C4 | — | 4 | 2 | no | — |
| 475 | C3×C4 | — | 20 | 4 | no | — |
| 476 | C2×C5 | — | 2 | 4 | no | — |
| 477 | C2×C5 | — | 2 | 1 | no | — |
| 478 | C2×C5 | — | 6 | 2 | no | — |
| 479 | C2×C5 | C24×A4 | 1 | 1 | yes | characteristic |
| 480 | D5 | — | 2 | 4 | no | — |
| 481 | D5 | — | 6 | 4 | no | — |
| 482 | C23 | — | 3 | 1 | no | — |
| 483 | C23 | — | 5 | 4 | no | — |
| 484 | C23 | — | 15 | 4 | no | — |
| 485 | C23 | — | 15 | 4 | no | — |
| 486 | C23 | — | 15 | 4 | no | — |
| 487 | C23 | C2×D5×A4 | 1 | 2 | yes | — |
| 488 | Q8 | — | 3 | 4 | no | — |
| 489 | Q8 | — | 3 | 1 | no | — |
| 490 | Q8 | — | 3 | 4 | no | — |
| 491 | Q8 | — | 3 | 4 | no | — |
| 492 | Q8 | — | 5 | 2 | no | — |
| 493 | Q8 | — | 15 | 4 | no | — |
| 494 | Q8 | — | 15 | 8 | no | — |
| 495 | Q8 | — | 15 | 4 | no | — |
| 496 | Q8 | — | 15 | 8 | no | — |
| 497 | Q8 | — | 15 | 2 | no | — |
| 498 | Q8 | C23×C3×D5 | 1 | 1 | yes | characteristic |
| 499 | D4 | — | 3 | 2 | no | — |
| 500 | D4 | — | 3 | 2 | no | — |
| 501 | D4 | — | 3 | 8 | no | — |
| 502 | D4 | — | 5 | 4 | no | — |
| 503 | D4 | — | 5 | 8 | no | — |
| 504 | D4 | — | 5 | 2 | no | — |
| 505 | D4 | — | 15 | 4 | no | — |
| 506 | D4 | — | 15 | 8 | no | — |
| 507 | D4 | — | 15 | 4 | no | — |
| 508 | D4 | — | 15 | 8 | no | — |
| 509 | D4 | — | 15 | 4 | no | — |
| 510 | D4 | — | 15 | 4 | no | — |
| 511 | D4 | — | 15 | 8 | no | — |
| 512 | D4 | — | 15 | 4 | no | — |
| 513 | D4 | — | 15 | 8 | no | — |
| 514 | D4 | — | 15 | 2 | no | — |
| 515 | D4 | C2×D5×A4 | 1 | 4 | yes | — |
| 516 | C2×C4 | — | 3 | 8 | no | — |
| 517 | C2×C4 | — | 3 | 1 | no | — |
| 518 | C2×C4 | — | 3 | 2 | no | — |
| 519 | C2×C4 | — | 3 | 4 | no | — |
| 520 | C2×C4 | — | 3 | 4 | no | — |
| 521 | C2×C4 | — | 3 | 2 | no | — |
| 522 | C2×C4 | — | 3 | 2 | no | — |
| 523 | C2×C4 | — | 5 | 4 | no | — |
| 524 | C2×C4 | — | 5 | 4 | no | — |
| 525 | C2×C4 | — | 15 | 4 | no | — |
| 526 | C2×C4 | — | 15 | 8 | no | — |
| 527 | C2×C4 | — | 15 | 4 | no | — |
| 528 | C2×C4 | — | 15 | 8 | no | — |
| 529 | C2×C4 | — | 15 | 16 | no | — |
| 530 | C2×C4 | — | 15 | 8 | no | — |
| 531 | C2×C4 | — | 15 | 4 | no | — |
| 532 | C2×C4 | — | 15 | 4 | no | — |
| 533 | C2×C4 | — | 15 | 4 | no | — |
| 534 | C2×C4 | — | 15 | 4 | no | — |
| 535 | C2×C4 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 536 | C2×C3 | — | 4 | 1 | no | — |
| 537 | C2×C3 | — | 8 | 1 | no | — |
| 538 | C2×C3 | — | 8 | 4 | no | — |
| 539 | C2×C3 | — | 40 | 4 | no | — |
| 540 | C5 | #87537 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 541 | C22 | — | 3 | 2 | no | — |
| 542 | C22 | — | 4 | 2 | no | — |
| 543 | C22 | — | 5 | 4 | no | — |
| 544 | C22 | — | 12 | 1 | no | — |
| 545 | C22 | — | 15 | 4 | no | — |
| 546 | C22 | — | 20 | 4 | no | — |
| 547 | C22 | — | 60 | 4 | no | — |
| 548 | C22 | — | 60 | 4 | no | — |
| 549 | C22 | — | 60 | 4 | no | — |
| 550 | C22 | C22×D5×A4 | 1 | 1 | yes | characteristic |
| 551 | C22 | C22×D5×A4 | 1 | 4 | yes | — |
| 552 | C4 | — | 3 | 1 | no | — |
| 553 | C4 | — | 3 | 4 | no | — |
| 554 | C4 | — | 3 | 1 | no | — |
| 555 | C4 | — | 5 | 4 | no | — |
| 556 | C4 | — | 15 | 4 | no | — |
| 557 | C4 | C22×D5×A4 | 1 | 2 | yes | — |
| 558 | C3 | — | 4 | 1 | no | Sylow |
| 559 | C2 | — | 2 | 1 | no | — |
| 560 | C2 | — | 2 | 4 | no | — |
| 561 | C2 | — | 6 | 2 | no | — |
| 562 | C2 | — | 10 | 4 | no | — |
| 563 | C2 | — | 30 | 4 | no | — |
| 564 | C2 | C23×D5×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D5×A4 |
| commutator, cosocle, hypocenter | C5×Q8 | C24×C3 |
| Fitting | C2×C5×2−1+4 | C2×C3 |
| socle | C2×C5 | C24×A4 |
| hypercenter | C2×D4 | D5×A4 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×2−1+4⋊C3 | C2 | semidirect |
| 2. #66287⋊C3 | C2 | semidirect |
| 3. D5×2−1+4⋊C3 | C2 | semidirect |
| 4. #66283⋊C3 | C2 | semidirect |
| 5. C2×#4147⋊C3 | C2 | semidirect |
| 6. #10619439 | C3 | semidirect |
| 8. C5×2−1+4⋊C3 | C22 | semidirect |
| 9. C2×C5×#41⋊C3 | C22 | semidirect |
| 10. C22×C5×SL(2,𝔽3) | C22 | semidirect |
| 11. #4150⋊C3 | C22 | semidirect |
| 12. D5×#41⋊C3 | C22 | semidirect |
| 13. C5⋊#994 | C22 | semidirect |
| 14. #4147⋊C3 | C22 | semidirect |
| 15. #4147⋊C3 | C22 | semidirect |
| 16. C2×D5×SL(2,𝔽3) | C22 | semidirect |
| 17. C2×C5⋊(#41⋊C3) | C22 | semidirect |
| 19. C2×C5×2−1+4 | C2×C3 | semidirect |
| 21. #66287 | C2×C3 | semidirect |
| 23. D5×2−1+4 | C2×C3 | semidirect |
| 27. #66283 | C2×C3 | semidirect |
| 29. C2×#4147 | C2×C3 | semidirect |
| 44. C2×2−1+4⋊C3 | D5 | semidirect |
| 46. C5×2−1+4 | C22×C3 | semidirect |
| 49. C2×C5×#41 | C22×C3 | semidirect |
| 51. C22×C5×Q8 | C22×C3 | semidirect |
| 57. #4150 | C22×C3 | semidirect |
| 63. #4149 | C22×C3 | semidirect |
| 71. D5×#41 | C22×C3 | semidirect |
| 79. #4147 | C22×C3 | semidirect |
| 80. #4147 | C22×C3 | semidirect |
| 84. C2×#713 | C22×C3 | semidirect |
| 88. C2×Q8×D5 | C22×C3 | semidirect |
| 115. 2−1+4⋊C3 | C2×D5 | semidirect |
| 119. C2×#41⋊C3 | C2×D5 | semidirect |
| 121. C22×SL(2,𝔽3) | C2×D5 | semidirect |
| 221. C2×2−1+4 | C3×D5 | semidirect |
| 309. 2−1+4 | C2×C3×D5 | semidirect |
| 340. C2×#41 | C2×C3×D5 | semidirect |
| 346. C22×Q8 | C2×C3×D5 | semidirect |
| 540. C5 | #87537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×2−1+4⋊C3 | 2 |
| #66287⋊C3 | 2 |
| D5×2−1+4⋊C3 | 2 |
| #66283⋊C3 | 2 |
| C2×#4147⋊C3 | 2 |
| #10619439 | 3 |
| C3×#4144 | 4 |
| #87537 | 5 |