Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
626 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 81 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×D5×#41⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11752142 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#5423 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11751624 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | D5×GU(2,𝔽3) | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | D5×#421 | — | 3 | 1 | no | maximal, Hall |
| 7 | C2×C5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 8 | D5×#41⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | D5×#41⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | D5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 11 | D5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×D5×SL(2,𝔽3) | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×C5⋊(#41⋊C3) | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | D5×#208 | — | 4 | 1 | no | maximal |
| 15 | #91185 | C22 | 1 | 2 | yes | complemented |
| 16 | C5×GU(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 17 | C2×#5423 | — | 5 | 1 | no | maximal, Hall |
| 18 | C2×D5×#41 | D3 | 1 | 1 | yes | characteristic |
| 19 | C2×D5×M16 | — | 3 | 1 | no | — |
| 20 | D5×#117 | — | 3 | 1 | no | — |
| 21 | C5×#421 | — | 3 | 1 | no | — |
| 22 | #65525 | — | 3 | 1 | no | — |
| 23 | #65428 | — | 3 | 1 | no | — |
| 24 | #65294 | — | 3 | 1 | no | — |
| 25 | #65110 | — | 3 | 2 | no | — |
| 26 | #65110 | — | 3 | 2 | no | — |
| 27 | D5×#104 | — | 3 | 2 | no | — |
| 28 | D5×#104 | — | 3 | 2 | no | — |
| 29 | C2×C3×C4×D5 | — | 4 | 1 | no | — |
| 30 | C5×#41⋊C3 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 31 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 32 | C2×C5×SL(2,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | D5×SL(2,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | D5×SL(2,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | C5⋊(#41⋊C3) | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C5⋊(#41⋊C3) | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 37 | #6710 | — | 4 | 1 | no | — |
| 38 | C5×#208 | — | 4 | 1 | no | — |
| 39 | #6649 | — | 4 | 2 | no | — |
| 40 | D5×C3⋊C8 | — | 4 | 2 | no | — |
| 41 | C22×#41⋊C3 | — | 5 | 1 | no | — |
| 42 | #5423 | — | 5 | 1 | no | — |
| 43 | #5423 | — | 5 | 2 | no | — |
| 44 | #5423 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 45 | C2×GU(2,𝔽3) | — | 5 | 2 | no | — |
| 46 | C2×C5×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 47 | D5×#41 | — | 3 | 1 | no | — |
| 48 | D5×#41 | — | 3 | 1 | no | — |
| 49 | D5×#41 | — | 3 | 1 | no | — |
| 50 | D5×#41 | — | 3 | 1 | no | — |
| 51 | D5×#41 | Dic3 | 1 | 1 | yes | characteristic |
| 52 | D5×#41 | Dic3 | 1 | 1 | yes | characteristic |
| 53 | D5×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 54 | D5×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 55 | C2×#713 | Dic3 | 1 | 1 | yes | characteristic |
| 56 | C2×Q8×D5 | Dic3 | 1 | 1 | yes | characteristic |
| 57 | C2×#711 | — | 3 | 1 | no | — |
| 58 | C2×D4×D5 | — | 3 | 1 | no | — |
| 59 | C2×#709 | — | 3 | 1 | no | — |
| 60 | C22×C4×D5 | — | 3 | 1 | no | — |
| 61 | C2×C5×M16 | — | 3 | 1 | no | — |
| 62 | C5×#117 | — | 3 | 1 | no | — |
| 63 | #4072 | — | 3 | 1 | no | — |
| 64 | C2×#681 | — | 3 | 1 | no | — |
| 65 | D5×M16 | — | 3 | 2 | no | — |
| 66 | D5×M16 | — | 3 | 2 | no | — |
| 67 | D5×M16 | — | 6 | 1 | no | — |
| 68 | D5×M16 | — | 6 | 1 | no | — |
| 69 | C2×#676 | — | 6 | 1 | no | — |
| 70 | C2×C8×D5 | — | 6 | 1 | no | — |
| 71 | #4038 | — | 6 | 1 | no | — |
| 72 | D5×C4⋊C4 | — | 6 | 1 | no | — |
| 73 | D5×C22⋊C4 | — | 6 | 1 | no | — |
| 74 | #4023 | — | 6 | 1 | no | — |
| 75 | #4018 | — | 3 | 2 | no | — |
| 76 | C42×D5 | — | 3 | 2 | no | — |
| 77 | C5×#104 | — | 3 | 2 | no | — |
| 78 | C5×#104 | — | 3 | 2 | no | — |
| 79 | #3969 | — | 3 | 2 | no | — |
| 80 | #3969 | — | 3 | 2 | no | — |
| 81 | #3957 | — | 3 | 2 | no | — |
| 82 | #3957 | — | 3 | 2 | no | — |
| 83 | #3937 | — | 3 | 2 | no | — |
| 84 | #3937 | — | 3 | 2 | no | — |
| 85 | C2×#421 | — | 15 | 1 | no | Sylow |
| 86 | C22×C3×D5 | — | 4 | 1 | no | — |
| 87 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 88 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 89 | C3×C4×D5 | — | 4 | 1 | no | — |
| 90 | C3×C4×D5 | — | 4 | 1 | no | — |
| 91 | C3×C4×D5 | — | 4 | 1 | no | — |
| 92 | C3×C4×D5 | — | 4 | 1 | no | — |
| 93 | C5×SL(2,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 94 | C3⋊#168 | — | 4 | 2 | no | — |
| 95 | C5×C3⋊C8 | — | 4 | 2 | no | — |
| 96 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 97 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 98 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 99 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 100 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 101 | C2×#41⋊C3 | C2×D5 | 1 | 1 | yes | characteristic |
| 102 | C22×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 103 | C2×#208 | — | 20 | 1 | no | — |
| 104 | GU(2,𝔽3) | — | 5 | 2 | no | — |
| 105 | GU(2,𝔽3) | C2×D5 | 1 | 2 | yes | complemented |
| 106 | C23×D5 | — | 3 | 1 | no | — |
| 107 | C5×#41 | — | 3 | 1 | no | — |
| 108 | C5×#41 | — | 3 | 1 | no | — |
| 109 | C5×#41 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 110 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 111 | C2×C5×Q8 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 112 | C2×C5×D4 | — | 3 | 1 | no | — |
| 113 | C22×C4×C5 | — | 3 | 1 | no | — |
| 114 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 115 | C22×Dic5 | — | 3 | 1 | no | — |
| 116 | #713 | — | 3 | 1 | no | — |
| 117 | #713 | — | 3 | 1 | no | — |
| 118 | #713 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 119 | #713 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 120 | Q8×D5 | — | 3 | 1 | no | — |
| 121 | Q8×D5 | — | 3 | 1 | no | — |
| 122 | Q8×D5 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 123 | Q8×D5 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 124 | #711 | — | 3 | 1 | no | — |
| 125 | #711 | — | 3 | 1 | no | — |
| 126 | #711 | — | 3 | 1 | no | — |
| 127 | #711 | — | 3 | 1 | no | — |
| 128 | #711 | — | 6 | 1 | no | — |
| 129 | #711 | — | 6 | 1 | no | — |
| 130 | D4×D5 | — | 3 | 1 | no | — |
| 131 | D4×D5 | — | 3 | 1 | no | — |
| 132 | D4×D5 | — | 3 | 1 | no | — |
| 133 | D4×D5 | — | 3 | 1 | no | — |
| 134 | D4×D5 | — | 6 | 1 | no | — |
| 135 | D4×D5 | — | 6 | 1 | no | — |
| 136 | #709 | — | 3 | 1 | no | — |
| 137 | #709 | — | 3 | 1 | no | — |
| 138 | #709 | — | 3 | 1 | no | — |
| 139 | #709 | — | 3 | 1 | no | — |
| 140 | #709 | — | 6 | 1 | no | — |
| 141 | #709 | — | 6 | 1 | no | — |
| 142 | C2×D20 | — | 3 | 1 | no | — |
| 143 | C2×C4×D5 | — | 3 | 1 | no | — |
| 144 | C2×C4×D5 | — | 3 | 1 | no | — |
| 145 | C2×C4×D5 | — | 3 | 1 | no | — |
| 146 | C2×C4×D5 | — | 3 | 1 | no | — |
| 147 | C2×C4×D5 | — | 3 | 1 | no | — |
| 148 | C2×C4×D5 | — | 3 | 1 | no | — |
| 149 | C2×C4×D5 | — | 3 | 1 | no | — |
| 150 | C2×C4×D5 | — | 3 | 1 | no | — |
| 151 | C2×C4×D5 | — | 3 | 1 | no | — |
| 152 | C2×C4×D5 | — | 3 | 1 | no | — |
| 153 | C2×C4×D5 | — | 3 | 1 | no | — |
| 154 | C2×C4×D5 | — | 6 | 2 | no | — |
| 155 | C2×C4×D5 | S4 | 1 | 1 | yes | characteristic |
| 156 | C2×Dic10 | — | 3 | 1 | no | — |
| 157 | C5×M16 | — | 3 | 2 | no | — |
| 158 | C5×M16 | — | 6 | 1 | no | — |
| 159 | C2×C5×C8 | — | 6 | 1 | no | — |
| 160 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 161 | C5×C22⋊C4 | — | 6 | 1 | no | — |
| 162 | C42×C5 | — | 3 | 2 | no | — |
| 163 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 164 | #685 | — | 6 | 2 | no | — |
| 165 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 166 | #683 | — | 6 | 2 | no | — |
| 167 | C4×Dic5 | — | 3 | 2 | no | — |
| 168 | C4×Dic5 | — | 6 | 2 | no | — |
| 169 | #681 | — | 3 | 2 | no | — |
| 170 | #681 | — | 6 | 1 | no | — |
| 171 | C2×#168 | — | 6 | 1 | no | — |
| 172 | #676 | — | 6 | 2 | no | — |
| 173 | #676 | — | 6 | 2 | no | — |
| 174 | C8×D5 | — | 6 | 2 | no | — |
| 175 | C8×D5 | — | 6 | 2 | no | — |
| 176 | C22×#41 | — | 5 | 1 | no | — |
| 177 | C22×M16 | — | 15 | 1 | no | — |
| 178 | C2×#117 | — | 15 | 1 | no | — |
| 179 | #421 | — | 3 | 1 | no | — |
| 180 | #421 | — | 15 | 2 | no | — |
| 181 | #421 | — | 15 | 2 | no | — |
| 182 | #421 | — | 15 | 1 | no | — |
| 183 | #421 | — | 15 | 1 | no | — |
| 184 | #421 | — | 15 | 1 | no | — |
| 185 | C2×#104 | — | 15 | 2 | no | — |
| 186 | C2×#104 | — | 15 | 2 | no | — |
| 187 | C22×C3×C5 | — | 4 | 1 | no | — |
| 188 | C2×C3×D5 | — | 4 | 1 | no | — |
| 189 | C2×C3×D5 | — | 4 | 1 | no | — |
| 190 | C2×C3×D5 | — | 8 | 2 | no | — |
| 191 | C3×C4×C5 | — | 4 | 1 | no | — |
| 192 | C3×C4×C5 | — | 4 | 1 | no | — |
| 193 | C3×Dic5 | — | 4 | 1 | no | — |
| 194 | C3×Dic5 | — | 4 | 1 | no | — |
| 195 | C22×C3×C4 | — | 20 | 1 | no | — |
| 196 | #41⋊C3 | — | 5 | 1 | no | — |
| 197 | #41⋊C3 | — | 5 | 1 | no | — |
| 198 | #41⋊C3 | C4×D5 | 1 | 1 | yes | characteristic, complemented |
| 199 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 200 | C2×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 201 | C2×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 202 | C2×SL(2,𝔽3) | C4×D5 | 1 | 1 | yes | characteristic, complemented |
| 203 | #208 | — | 4 | 1 | no | — |
| 204 | #208 | — | 20 | 2 | no | — |
| 205 | #208 | — | 20 | 1 | no | — |
| 206 | C2×C3⋊C8 | — | 20 | 2 | no | — |
| 207 | C23×C5 | — | 3 | 1 | no | — |
| 208 | C22×D5 | — | 3 | 1 | no | — |
| 209 | C22×D5 | — | 3 | 1 | no | — |
| 210 | C22×D5 | — | 3 | 1 | no | — |
| 211 | C22×D5 | — | 3 | 1 | no | — |
| 212 | C22×D5 | — | 3 | 1 | no | — |
| 213 | C22×D5 | — | 12 | 2 | no | — |
| 214 | C22×D5 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 215 | C5×Q8 | — | 3 | 1 | no | — |
| 216 | C5×Q8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 217 | C5×D4 | — | 3 | 1 | no | — |
| 218 | C5×D4 | — | 3 | 1 | no | — |
| 219 | C5×D4 | — | 6 | 1 | no | — |
| 220 | C2×C4×C5 | — | 3 | 1 | no | — |
| 221 | C2×C4×C5 | — | 3 | 1 | no | — |
| 222 | C2×C4×C5 | — | 3 | 1 | no | — |
| 223 | C2×C4×C5 | — | 3 | 1 | no | — |
| 224 | C2×C4×C5 | — | 3 | 1 | no | — |
| 225 | C2×C4×C5 | — | 6 | 2 | no | — |
| 226 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 227 | C22⋊D5 | — | 6 | 1 | no | — |
| 228 | C22⋊D5 | — | 6 | 1 | no | — |
| 229 | C22⋊D5 | — | 6 | 1 | no | — |
| 230 | C22⋊D5 | — | 6 | 1 | no | — |
| 231 | C2×Dic5 | — | 3 | 1 | no | — |
| 232 | C2×Dic5 | — | 3 | 1 | no | — |
| 233 | C2×Dic5 | — | 3 | 1 | no | — |
| 234 | C2×Dic5 | — | 3 | 1 | no | — |
| 235 | C2×Dic5 | — | 3 | 1 | no | — |
| 236 | C2×Dic5 | — | 6 | 2 | no | — |
| 237 | C2×Dic5 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 238 | D20 | — | 3 | 1 | no | — |
| 239 | D20 | — | 3 | 1 | no | — |
| 240 | D20 | — | 6 | 1 | no | — |
| 241 | C4×D5 | — | 3 | 1 | no | — |
| 242 | C4×D5 | — | 3 | 1 | no | — |
| 243 | C4×D5 | — | 3 | 1 | no | — |
| 244 | C4×D5 | — | 3 | 1 | no | — |
| 245 | C4×D5 | — | 3 | 1 | no | — |
| 246 | C4×D5 | — | 3 | 1 | no | — |
| 247 | C4×D5 | — | 3 | 1 | no | — |
| 248 | C4×D5 | — | 3 | 1 | no | — |
| 249 | C4×D5 | — | 3 | 1 | no | — |
| 250 | C4×D5 | — | 3 | 1 | no | — |
| 251 | C4×D5 | — | 3 | 1 | no | — |
| 252 | C4×D5 | — | 3 | 1 | no | — |
| 253 | C4×D5 | — | 12 | 4 | no | — |
| 254 | C4×D5 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 255 | C4×D5 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 256 | C4×D5 | C2×S4 | 1 | 1 | yes | characteristic |
| 257 | C4×D5 | C2×S4 | 1 | 1 | yes | characteristic |
| 258 | Dic10 | — | 3 | 1 | no | — |
| 259 | Dic10 | — | 3 | 1 | no | — |
| 260 | Dic10 | — | 6 | 1 | no | — |
| 261 | C5×C8 | — | 6 | 2 | no | — |
| 262 | #168 | — | 6 | 2 | no | — |
| 263 | C2×#41 | — | 5 | 1 | no | — |
| 264 | C2×#41 | — | 5 | 1 | no | — |
| 265 | C2×#41 | — | 5 | 1 | no | — |
| 266 | C2×#41 | — | 5 | 1 | no | — |
| 267 | C2×#41 | — | 5 | 1 | no | — |
| 268 | C2×#41 | — | 15 | 1 | no | — |
| 269 | C2×#41 | — | 15 | 1 | no | — |
| 270 | C2×#41 | — | 15 | 1 | no | — |
| 271 | C2×#41 | — | 15 | 1 | no | — |
| 272 | C2×#41 | — | 15 | 1 | no | — |
| 273 | C2×#41 | — | 15 | 1 | no | — |
| 274 | C2×#41 | D3×D5 | 1 | 1 | yes | characteristic |
| 275 | C22×Q8 | — | 5 | 1 | no | — |
| 276 | C22×D4 | — | 15 | 1 | no | — |
| 277 | C23×C4 | — | 15 | 1 | no | — |
| 278 | C2×M16 | — | 3 | 1 | no | — |
| 279 | C2×M16 | — | 15 | 2 | no | — |
| 280 | C2×M16 | — | 15 | 2 | no | — |
| 281 | C2×M16 | — | 15 | 1 | no | — |
| 282 | C2×M16 | — | 30 | 1 | no | — |
| 283 | C2×M16 | — | 30 | 1 | no | — |
| 284 | C2×M16 | — | 30 | 1 | no | — |
| 285 | C22×C8 | — | 30 | 1 | no | — |
| 286 | #117 | — | 3 | 1 | no | — |
| 287 | #117 | — | 15 | 2 | no | — |
| 288 | #117 | — | 15 | 1 | no | — |
| 289 | #117 | — | 30 | 1 | no | — |
| 290 | #117 | — | 30 | 1 | no | — |
| 291 | C2×C4⋊C4 | — | 30 | 1 | no | — |
| 292 | C2×C22⋊C4 | — | 30 | 1 | no | — |
| 293 | C2×C42 | — | 15 | 2 | no | — |
| 294 | #104 | — | 3 | 2 | no | — |
| 295 | #104 | — | 3 | 2 | no | — |
| 296 | #104 | — | 15 | 2 | no | — |
| 297 | #104 | — | 15 | 2 | no | — |
| 298 | #104 | — | 15 | 2 | no | — |
| 299 | #104 | — | 15 | 2 | no | — |
| 300 | #104 | — | 15 | 2 | no | — |
| 301 | #104 | — | 15 | 2 | no | — |
| 302 | C2×C3×C5 | — | 4 | 1 | no | — |
| 303 | C2×C3×C5 | — | 8 | 1 | no | — |
| 304 | C3×D5 | — | 4 | 2 | no | — |
| 305 | C3×D5 | — | 8 | 1 | no | — |
| 306 | C23×C3 | — | 20 | 1 | no | — |
| 307 | C2×C3×C4 | — | 4 | 1 | no | — |
| 308 | C2×C3×C4 | — | 20 | 1 | no | — |
| 309 | C2×C3×C4 | — | 20 | 1 | no | — |
| 310 | C2×C3×C4 | — | 20 | 1 | no | — |
| 311 | C2×C3×C4 | — | 20 | 1 | no | — |
| 312 | C2×C3×C4 | — | 20 | 1 | no | — |
| 313 | SL(2,𝔽3) | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 314 | C3⋊C8 | — | 4 | 2 | no | — |
| 315 | C3⋊C8 | — | 20 | 2 | no | — |
| 316 | C22×C5 | — | 3 | 1 | no | — |
| 317 | C22×C5 | — | 3 | 1 | no | — |
| 318 | C22×C5 | — | 12 | 1 | no | — |
| 319 | C22×C5 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 320 | C2×D5 | — | 2 | 2 | no | — |
| 321 | C2×D5 | — | 3 | 1 | no | — |
| 322 | C2×D5 | — | 3 | 1 | no | — |
| 323 | C2×D5 | — | 6 | 2 | no | — |
| 324 | C2×D5 | — | 6 | 2 | no | — |
| 325 | C2×D5 | — | 12 | 1 | no | — |
| 326 | C2×D5 | — | 12 | 1 | no | — |
| 327 | C2×D5 | — | 12 | 1 | no | — |
| 328 | C2×D5 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 329 | C2×D5 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 330 | C4×C5 | — | 3 | 1 | no | — |
| 331 | C4×C5 | — | 3 | 1 | no | — |
| 332 | C4×C5 | — | 12 | 2 | no | — |
| 333 | C4×C5 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 334 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 335 | Dic5 | — | 3 | 1 | no | — |
| 336 | Dic5 | — | 3 | 1 | no | — |
| 337 | Dic5 | — | 12 | 2 | no | — |
| 338 | Dic5 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 339 | Dic5 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 340 | C24 | — | 15 | 1 | no | — |
| 341 | #41 | — | 3 | 1 | no | — |
| 342 | #41 | — | 3 | 1 | no | — |
| 343 | #41 | — | 5 | 1 | no | — |
| 344 | #41 | — | 5 | 1 | no | — |
| 345 | #41 | — | 15 | 1 | no | — |
| 346 | #41 | — | 15 | 1 | no | — |
| 347 | #41 | — | 15 | 1 | no | — |
| 348 | #41 | — | 15 | 1 | no | — |
| 349 | #41 | — | 15 | 1 | no | — |
| 350 | #41 | — | 15 | 1 | no | — |
| 351 | #41 | — | 15 | 1 | no | — |
| 352 | #41 | — | 15 | 1 | no | — |
| 353 | #41 | — | 15 | 1 | no | — |
| 354 | #41 | — | 15 | 1 | no | — |
| 355 | #41 | — | 30 | 1 | no | — |
| 356 | #41 | — | 30 | 1 | no | — |
| 357 | #41 | — | 30 | 1 | no | — |
| 358 | #41 | — | 30 | 1 | no | — |
| 359 | #41 | D5×Dic3 | 1 | 1 | yes | characteristic |
| 360 | #41 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 361 | C2×Q8 | — | 5 | 1 | no | — |
| 362 | C2×Q8 | — | 5 | 1 | no | — |
| 363 | C2×Q8 | — | 15 | 1 | no | — |
| 364 | C2×Q8 | — | 15 | 1 | no | — |
| 365 | C2×Q8 | — | 15 | 1 | no | — |
| 366 | C2×Q8 | D5×Dic3 | 1 | 1 | yes | characteristic |
| 367 | C2×D4 | — | 3 | 1 | no | — |
| 368 | C2×D4 | — | 15 | 1 | no | — |
| 369 | C2×D4 | — | 15 | 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 | C22×C4 | — | 3 | 1 | no | — |
| 377 | C22×C4 | — | 5 | 1 | no | — |
| 378 | C22×C4 | — | 15 | 1 | no | — |
| 379 | C22×C4 | — | 15 | 1 | no | — |
| 380 | C22×C4 | — | 15 | 1 | no | — |
| 381 | C22×C4 | — | 15 | 1 | no | — |
| 382 | C22×C4 | — | 15 | 1 | no | — |
| 383 | C22×C4 | — | 15 | 1 | no | — |
| 384 | C22×C4 | — | 15 | 1 | no | — |
| 385 | C22×C4 | — | 15 | 1 | no | — |
| 386 | C22×C4 | — | 15 | 1 | no | — |
| 387 | C22×C4 | — | 15 | 1 | no | — |
| 388 | C22×C4 | — | 15 | 1 | no | — |
| 389 | C22×C4 | — | 15 | 1 | no | — |
| 390 | C22×C4 | — | 30 | 2 | no | — |
| 391 | M16 | — | 3 | 2 | no | — |
| 392 | M16 | — | 6 | 1 | no | — |
| 393 | M16 | — | 15 | 2 | no | — |
| 394 | M16 | — | 30 | 2 | no | — |
| 395 | M16 | — | 30 | 2 | no | — |
| 396 | M16 | — | 30 | 1 | no | — |
| 397 | C2×C8 | — | 6 | 1 | no | — |
| 398 | C2×C8 | — | 30 | 2 | no | — |
| 399 | C2×C8 | — | 30 | 2 | no | — |
| 400 | C2×C8 | — | 30 | 1 | no | — |
| 401 | C4⋊C4 | — | 6 | 1 | no | — |
| 402 | C4⋊C4 | — | 30 | 1 | no | — |
| 403 | C4⋊C4 | — | 30 | 2 | no | — |
| 404 | C22⋊C4 | — | 6 | 1 | no | — |
| 405 | C22⋊C4 | — | 30 | 2 | no | — |
| 406 | C22⋊C4 | — | 30 | 1 | no | — |
| 407 | C42 | — | 3 | 2 | no | — |
| 408 | C42 | — | 15 | 2 | no | — |
| 409 | C42 | — | 30 | 2 | no | — |
| 410 | C3×C5 | — | 4 | 1 | no | Hall |
| 411 | C22×C3 | — | 4 | 1 | no | — |
| 412 | C22×C3 | — | 20 | 1 | no | — |
| 413 | C22×C3 | — | 20 | 1 | no | — |
| 414 | C22×C3 | — | 40 | 2 | no | — |
| 415 | C3×C4 | — | 4 | 1 | no | — |
| 416 | C3×C4 | — | 4 | 1 | no | — |
| 417 | C3×C4 | — | 20 | 1 | no | — |
| 418 | C3×C4 | — | 20 | 1 | no | — |
| 419 | C2×C5 | — | 2 | 1 | no | — |
| 420 | C2×C5 | — | 6 | 1 | no | — |
| 421 | C2×C5 | — | 6 | 1 | no | — |
| 422 | C2×C5 | C22×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 423 | D5 | — | 2 | 1 | no | — |
| 424 | D5 | — | 6 | 1 | no | — |
| 425 | D5 | — | 6 | 1 | no | — |
| 426 | D5 | #5423 | 1 | 2 | yes | direct product factor |
| 427 | C23 | — | 3 | 1 | no | — |
| 428 | C23 | — | 5 | 1 | no | — |
| 429 | C23 | — | 15 | 1 | no | — |
| 430 | C23 | — | 15 | 1 | no | — |
| 431 | C23 | — | 15 | 1 | no | — |
| 432 | C23 | — | 15 | 1 | no | — |
| 433 | C23 | — | 15 | 1 | no | — |
| 434 | C23 | — | 60 | 2 | no | — |
| 435 | Q8 | — | 3 | 1 | no | — |
| 436 | Q8 | — | 15 | 1 | no | — |
| 437 | Q8 | — | 15 | 1 | no | — |
| 438 | Q8 | — | 30 | 1 | no | — |
| 439 | Q8 | C2×D5×Dic3 | 1 | 1 | yes | characteristic |
| 440 | D4 | — | 3 | 1 | no | — |
| 441 | D4 | — | 3 | 1 | no | — |
| 442 | D4 | — | 6 | 1 | no | — |
| 443 | D4 | — | 15 | 1 | no | — |
| 444 | D4 | — | 15 | 1 | no | — |
| 445 | D4 | — | 30 | 1 | no | — |
| 446 | D4 | — | 30 | 1 | no | — |
| 447 | D4 | — | 30 | 1 | no | — |
| 448 | D4 | — | 30 | 1 | no | — |
| 449 | D4 | — | 30 | 1 | no | — |
| 450 | C2×C4 | — | 3 | 1 | no | — |
| 451 | C2×C4 | — | 3 | 1 | no | — |
| 452 | C2×C4 | — | 3 | 1 | no | — |
| 453 | C2×C4 | — | 3 | 1 | no | — |
| 454 | C2×C4 | — | 3 | 1 | no | — |
| 455 | C2×C4 | — | 5 | 1 | no | — |
| 456 | C2×C4 | — | 5 | 1 | no | — |
| 457 | C2×C4 | — | 5 | 1 | no | — |
| 458 | C2×C4 | — | 5 | 1 | no | — |
| 459 | C2×C4 | — | 5 | 1 | no | — |
| 460 | C2×C4 | — | 6 | 2 | no | — |
| 461 | C2×C4 | — | 15 | 1 | no | — |
| 462 | C2×C4 | — | 15 | 1 | no | — |
| 463 | C2×C4 | — | 15 | 1 | no | — |
| 464 | C2×C4 | — | 15 | 1 | no | — |
| 465 | C2×C4 | — | 15 | 1 | no | — |
| 466 | C2×C4 | — | 15 | 1 | no | — |
| 467 | C2×C4 | — | 15 | 1 | no | — |
| 468 | C2×C4 | — | 15 | 1 | no | — |
| 469 | C2×C4 | — | 15 | 1 | no | — |
| 470 | C2×C4 | — | 15 | 1 | no | — |
| 471 | C2×C4 | — | 15 | 1 | no | — |
| 472 | C2×C4 | — | 15 | 1 | no | — |
| 473 | C2×C4 | — | 15 | 1 | no | — |
| 474 | C2×C4 | — | 15 | 1 | no | — |
| 475 | C2×C4 | — | 15 | 1 | no | — |
| 476 | C2×C4 | — | 15 | 1 | no | — |
| 477 | C2×C4 | — | 15 | 1 | no | — |
| 478 | C2×C4 | — | 30 | 2 | no | — |
| 479 | C2×C4 | — | 60 | 4 | no | — |
| 480 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 481 | C8 | — | 6 | 2 | no | — |
| 482 | C8 | — | 30 | 2 | no | — |
| 483 | C2×C3 | — | 4 | 1 | no | — |
| 484 | C2×C3 | — | 8 | 1 | no | — |
| 485 | C2×C3 | — | 20 | 2 | no | — |
| 486 | C2×C3 | — | 40 | 1 | no | — |
| 487 | C5 | C2×#5423 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 488 | C22 | — | 3 | 1 | no | — |
| 489 | C22 | — | 3 | 1 | no | — |
| 490 | C22 | — | 5 | 1 | no | — |
| 491 | C22 | — | 5 | 1 | no | — |
| 492 | C22 | — | 10 | 2 | no | — |
| 493 | C22 | — | 12 | 1 | no | — |
| 494 | C22 | — | 15 | 1 | no | — |
| 495 | C22 | — | 15 | 1 | no | — |
| 496 | C22 | — | 30 | 2 | no | — |
| 497 | C22 | — | 30 | 2 | no | — |
| 498 | C22 | — | 60 | 1 | no | — |
| 499 | C22 | — | 60 | 1 | no | — |
| 500 | C22 | — | 60 | 1 | no | — |
| 501 | C22 | D5×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 502 | C4 | — | 3 | 1 | no | — |
| 503 | C4 | — | 3 | 1 | no | — |
| 504 | C4 | — | 5 | 1 | no | — |
| 505 | C4 | — | 5 | 1 | no | — |
| 506 | C4 | — | 12 | 2 | no | — |
| 507 | C4 | — | 15 | 1 | no | — |
| 508 | C4 | — | 15 | 1 | no | — |
| 509 | C4 | — | 60 | 2 | no | — |
| 510 | C4 | D5×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 511 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 512 | C3 | — | 4 | 1 | no | Sylow |
| 513 | C2 | — | 2 | 1 | no | — |
| 514 | C2 | — | 5 | 2 | no | — |
| 515 | C2 | — | 6 | 1 | no | — |
| 516 | C2 | — | 6 | 1 | no | — |
| 517 | C2 | — | 10 | 1 | no | — |
| 518 | C2 | — | 30 | 1 | no | — |
| 519 | C2 | — | 30 | 1 | no | — |
| 520 | C2 | C2×D5×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11752142 | C2 | semidirect |
| 3. C5×#5423 | C2 | semidirect |
| 4. #11751624 | C2 | semidirect |
| 5. D5×GU(2,𝔽3) | C2 | semidirect |
| 8. D5×#41⋊C3 | C4 | semidirect |
| 9. D5×#41⋊C3 | C4 | semidirect |
| 12. C2×D5×SL(2,𝔽3) | C4 | semidirect |
| 13. C2×C5⋊(#41⋊C3) | C4 | semidirect |
| 15. #91185 | C22 | semidirect |
| 16. C5×GU(2,𝔽3) | C22 | semidirect |
| 30. C5×#41⋊C3 | C2×C4 | semidirect |
| 32. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 34. D5×SL(2,𝔽3) | C2×C4 | semidirect |
| 36. C5⋊(#41⋊C3) | C2×C4 | semidirect |
| 44. #5423 | D5 | direct (N × H) |
| 105. GU(2,𝔽3) | C2×D5 | semidirect |
| 198. #41⋊C3 | C4×D5 | semidirect |
| 202. C2×SL(2,𝔽3) | C4×D5 | semidirect |
| 426. D5 | #5423 | direct (N × H) |
| 487. C5 | C2×#5423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#41⋊C3 | 2 |
| #11752142 | 2 |
| C5×#5423 | 2 |
| #11751624 | 2 |
| D5×GU(2,𝔽3) | 2 |
| D5×#421 | 3 |
| D5×#208 | 4 |
| C2×#5423 | 5 |