Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2444 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 2444 conjugacy classes of subgroups — too many to draw. Only its 255 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 | C5×A4×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | Q8×D5×A4 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | A4×#711 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | A4×#709 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×A4×Dic10 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C22×#4150 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 7 | C3×#4150 | — | 4 | 1 | no | maximal |
| 8 | C5×Q8×A4 | C22 | 1 | 1 | yes | characteristic |
| 9 | C5×D4×A4 | C22 | 1 | 3 | yes | — |
| 10 | C2×C4×C5×A4 | C22 | 1 | 3 | yes | — |
| 11 | A4×C22⋊D5 | C22 | 1 | 6 | yes | — |
| 12 | C2×A4×Dic5 | C22 | 1 | 6 | yes | — |
| 13 | A4×D20 | C22 | 1 | 1 | yes | characteristic |
| 14 | C4×D5×A4 | C22 | 1 | 6 | yes | — |
| 15 | A4×Dic10 | C22 | 1 | 3 | yes | — |
| 16 | A4×Dic10 | C22 | 1 | 6 | yes | — |
| 17 | A4×2−1+4 | — | 5 | 1 | no | maximal, Hall |
| 18 | C22×C5×#41 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#4150 | — | 3 | 1 | no | — |
| 20 | C2×#4150 | — | 3 | 3 | no | — |
| 21 | C2×#4150 | — | 3 | 3 | no | — |
| 22 | C2×#4150 | — | 3 | 6 | no | — |
| 23 | C2×#4150 | — | 3 | 2 | no | — |
| 24 | C2×#4150 | — | 3 | 1 | no | — |
| 25 | C22×Q8×D5 | C2×C3 | 1 | 2 | yes | complemented |
| 26 | C22×#711 | C2×C3 | 1 | 6 | yes | complemented |
| 27 | C22×#709 | C2×C3 | 1 | 3 | yes | complemented |
| 28 | C23×Dic10 | C2×C3 | 1 | 3 | yes | complemented |
| 29 | C22×C5×A4 | C23 | 1 | 3 | yes | — |
| 30 | C2×D5×A4 | C23 | 1 | 2 | yes | — |
| 31 | C3×C5×#41 | — | 4 | 1 | no | — |
| 32 | C3×Q8×D5 | — | 4 | 2 | no | — |
| 33 | C3×#711 | — | 4 | 6 | no | — |
| 34 | C3×#709 | — | 4 | 3 | no | — |
| 35 | C2×C3×Dic10 | — | 4 | 3 | no | — |
| 36 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 37 | C4×C5×A4 | C23 | 1 | 3 | yes | — |
| 38 | A4×Dic5 | C23 | 1 | 6 | yes | — |
| 39 | A4×#41 | — | 5 | 6 | no | — |
| 40 | A4×#41 | — | 5 | 3 | no | — |
| 41 | A4×#41 | D5 | 1 | 1 | yes | characteristic, complemented |
| 42 | C2×Q8×A4 | — | 5 | 2 | no | — |
| 43 | C2×Q8×A4 | — | 5 | 3 | no | — |
| 44 | C2×C5×#41 | — | 3 | 3 | no | — |
| 45 | C2×C5×#41 | — | 3 | 3 | no | — |
| 46 | C2×C5×#41 | — | 3 | 1 | no | — |
| 47 | C2×C5×#41 | — | 3 | 1 | no | — |
| 48 | C22×C5×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 49 | C22×C5×D4 | C22×C3 | 1 | 3 | yes | — |
| 50 | C23×C4×C5 | C22×C3 | 1 | 3 | yes | — |
| 51 | C22×C22⋊D5 | C22×C3 | 1 | 6 | yes | — |
| 52 | C23×Dic5 | C22×C3 | 1 | 6 | yes | — |
| 53 | #4150 | — | 3 | 2 | no | — |
| 54 | #4150 | — | 3 | 6 | no | — |
| 55 | #4150 | — | 3 | 12 | no | — |
| 56 | #4150 | — | 3 | 12 | no | — |
| 57 | #4150 | — | 3 | 2 | no | — |
| 58 | #4150 | — | 3 | 6 | no | — |
| 59 | #4150 | — | 3 | 12 | no | — |
| 60 | #4150 | — | 3 | 12 | no | — |
| 61 | #4150 | — | 3 | 6 | no | — |
| 62 | #4150 | — | 3 | 1 | no | — |
| 63 | #4150 | — | 3 | 2 | no | — |
| 64 | #4150 | — | 3 | 6 | no | — |
| 65 | #4150 | — | 3 | 3 | no | — |
| 66 | #4150 | — | 3 | 3 | no | — |
| 67 | #4150 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 68 | C2×Q8×D5 | — | 3 | 2 | no | — |
| 69 | C2×Q8×D5 | — | 3 | 6 | no | — |
| 70 | C2×Q8×D5 | — | 3 | 6 | no | — |
| 71 | C2×Q8×D5 | — | 3 | 2 | no | — |
| 72 | C2×#711 | — | 3 | 6 | no | — |
| 73 | C2×#711 | — | 3 | 6 | no | — |
| 74 | C2×#711 | — | 3 | 6 | no | — |
| 75 | C2×#711 | — | 3 | 6 | no | — |
| 76 | C2×#711 | — | 3 | 12 | no | — |
| 77 | C2×#711 | — | 3 | 12 | no | — |
| 78 | C2×#709 | — | 3 | 3 | no | — |
| 79 | C2×#709 | — | 3 | 3 | no | — |
| 80 | C2×#709 | — | 3 | 6 | no | — |
| 81 | C2×#709 | — | 3 | 3 | no | — |
| 82 | C2×#709 | — | 3 | 3 | no | — |
| 83 | C2×#709 | — | 3 | 6 | no | — |
| 84 | C22×D20 | C22×C3 | 1 | 1 | yes | characteristic |
| 85 | C22×C4×D5 | C22×C3 | 1 | 6 | yes | — |
| 86 | C22×Dic10 | — | 3 | 3 | no | — |
| 87 | C22×Dic10 | — | 3 | 3 | no | — |
| 88 | C22×Dic10 | — | 3 | 6 | no | — |
| 89 | C22×Dic10 | — | 3 | 6 | no | — |
| 90 | C22×Dic10 | — | 3 | 6 | no | — |
| 91 | C22×Dic10 | C22×C3 | 1 | 3 | yes | — |
| 92 | C22×Dic10 | C22×C3 | 1 | 6 | yes | — |
| 93 | C22×2−1+4 | — | 5 | 1 | no | Sylow |
| 94 | C2×C5×A4 | — | 2 | 3 | no | — |
| 95 | C2×C5×A4 | C24 | 1 | 1 | yes | characteristic |
| 96 | D5×A4 | — | 2 | 2 | no | — |
| 97 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 98 | C3×C5×D4 | — | 4 | 3 | no | — |
| 99 | C2×C3×C4×C5 | — | 4 | 3 | no | — |
| 100 | C3×C22⋊D5 | — | 4 | 6 | no | — |
| 101 | C2×C3×Dic5 | — | 4 | 6 | no | — |
| 102 | C3×D20 | — | 4 | 1 | no | — |
| 103 | C3×C4×D5 | — | 4 | 6 | no | — |
| 104 | C3×Dic10 | — | 4 | 3 | no | — |
| 105 | C3×Dic10 | — | 4 | 6 | no | — |
| 106 | C3×2−1+4 | — | 20 | 1 | no | — |
| 107 | Q8×A4 | — | 5 | 6 | no | — |
| 108 | Q8×A4 | — | 5 | 3 | no | — |
| 109 | Q8×A4 | C2×D5 | 1 | 1 | yes | characteristic |
| 110 | D4×A4 | — | 5 | 6 | no | — |
| 111 | D4×A4 | — | 5 | 1 | no | — |
| 112 | D4×A4 | C2×D5 | 1 | 3 | yes | — |
| 113 | C2×C4×A4 | — | 5 | 6 | no | — |
| 114 | C2×C4×A4 | — | 5 | 6 | no | — |
| 115 | C2×C4×A4 | C2×D5 | 1 | 3 | yes | — |
| 116 | C24×C5 | C23×C3 | 1 | 3 | yes | — |
| 117 | C23×D5 | C23×C3 | 1 | 2 | yes | — |
| 118 | C5×#41 | — | 3 | 6 | no | — |
| 119 | C5×#41 | — | 3 | 6 | no | — |
| 120 | C5×#41 | — | 3 | 2 | no | — |
| 121 | C5×#41 | — | 3 | 1 | no | — |
| 122 | C5×#41 | — | 3 | 3 | no | — |
| 123 | C5×#41 | — | 3 | 3 | no | — |
| 124 | C5×#41 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 125 | C2×C5×Q8 | — | 3 | 3 | no | — |
| 126 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 127 | C2×C5×D4 | — | 3 | 3 | no | — |
| 128 | C2×C5×D4 | — | 3 | 3 | no | — |
| 129 | C2×C5×D4 | — | 3 | 6 | no | — |
| 130 | C22×C4×C5 | — | 3 | 3 | no | — |
| 131 | C22×C4×C5 | — | 3 | 3 | no | — |
| 132 | C22×C4×C5 | — | 3 | 3 | no | — |
| 133 | C22×C4×C5 | — | 3 | 3 | no | — |
| 134 | C22×C4×C5 | C23×C3 | 1 | 1 | yes | characteristic |
| 135 | C22×C4×C5 | C23×C3 | 1 | 3 | yes | — |
| 136 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 137 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 138 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 139 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 140 | C22×Dic5 | — | 3 | 6 | no | — |
| 141 | C22×Dic5 | — | 3 | 6 | no | — |
| 142 | C22×Dic5 | — | 3 | 12 | no | — |
| 143 | C22×Dic5 | C23×C3 | 1 | 6 | yes | — |
| 144 | Q8×D5 | — | 3 | 4 | no | — |
| 145 | Q8×D5 | — | 3 | 12 | no | — |
| 146 | Q8×D5 | — | 3 | 12 | no | — |
| 147 | Q8×D5 | — | 3 | 2 | no | — |
| 148 | Q8×D5 | — | 3 | 6 | no | — |
| 149 | Q8×D5 | — | 3 | 6 | no | — |
| 150 | Q8×D5 | C2×A4 | 1 | 2 | yes | complemented |
| 151 | #711 | — | 3 | 24 | no | — |
| 152 | #711 | — | 3 | 12 | no | — |
| 153 | #711 | — | 3 | 12 | no | — |
| 154 | #711 | — | 3 | 12 | no | — |
| 155 | #711 | — | 3 | 24 | no | — |
| 156 | #711 | — | 3 | 6 | no | — |
| 157 | #711 | — | 3 | 12 | no | — |
| 158 | #711 | — | 3 | 12 | no | — |
| 159 | #711 | — | 3 | 6 | no | — |
| 160 | #711 | — | 3 | 6 | no | — |
| 161 | #711 | C2×A4 | 1 | 6 | yes | complemented |
| 162 | #709 | — | 3 | 6 | no | — |
| 163 | #709 | — | 3 | 12 | no | — |
| 164 | #709 | — | 3 | 6 | no | — |
| 165 | #709 | — | 3 | 6 | no | — |
| 166 | #709 | — | 3 | 12 | no | — |
| 167 | #709 | — | 3 | 3 | no | — |
| 168 | #709 | — | 3 | 6 | no | — |
| 169 | #709 | — | 3 | 3 | no | — |
| 170 | #709 | — | 3 | 6 | no | — |
| 171 | #709 | — | 3 | 3 | no | — |
| 172 | #709 | C2×A4 | 1 | 3 | yes | complemented |
| 173 | C2×D20 | — | 3 | 1 | no | — |
| 174 | C2×D20 | — | 3 | 2 | no | — |
| 175 | C2×D20 | — | 3 | 1 | no | — |
| 176 | C2×C4×D5 | — | 3 | 6 | no | — |
| 177 | C2×C4×D5 | — | 3 | 6 | no | — |
| 178 | C2×C4×D5 | — | 3 | 6 | no | — |
| 179 | C2×C4×D5 | — | 3 | 6 | no | — |
| 180 | C2×Dic10 | — | 3 | 6 | no | — |
| 181 | C2×Dic10 | — | 3 | 6 | no | — |
| 182 | C2×Dic10 | — | 3 | 24 | no | — |
| 183 | C2×Dic10 | — | 3 | 6 | no | — |
| 184 | C2×Dic10 | — | 3 | 3 | no | — |
| 185 | C2×Dic10 | — | 3 | 6 | no | — |
| 186 | C2×Dic10 | — | 3 | 3 | no | — |
| 187 | C2×Dic10 | — | 3 | 6 | no | — |
| 188 | C2×Dic10 | — | 3 | 6 | no | — |
| 189 | C2×Dic10 | — | 3 | 6 | no | — |
| 190 | C2×Dic10 | — | 3 | 3 | no | — |
| 191 | C2×Dic10 | — | 3 | 6 | no | — |
| 192 | C2×Dic10 | — | 3 | 6 | no | — |
| 193 | C2×Dic10 | — | 3 | 12 | no | — |
| 194 | C2×Dic10 | C2×A4 | 1 | 3 | yes | complemented |
| 195 | C2×2−1+4 | — | 15 | 1 | no | — |
| 196 | C2×2−1+4 | — | 15 | 3 | no | — |
| 197 | C2×2−1+4 | — | 15 | 2 | no | — |
| 198 | C2×2−1+4 | — | 15 | 3 | no | — |
| 199 | C2×2−1+4 | — | 15 | 6 | no | — |
| 200 | C2×2−1+4 | — | 15 | 1 | no | — |
| 201 | C22×#41 | — | 5 | 6 | no | — |
| 202 | C22×#41 | — | 5 | 3 | no | — |
| 203 | C22×#41 | C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 204 | C23×Q8 | — | 5 | 2 | no | — |
| 205 | C23×Q8 | — | 5 | 3 | no | — |
| 206 | C22×C3×C5 | — | 4 | 3 | no | — |
| 207 | C2×C3×D5 | — | 4 | 2 | no | — |
| 208 | C5×A4 | 2−1+4 | 1 | 1 | yes | characteristic, complemented |
| 209 | C3×C4×C5 | — | 4 | 1 | no | — |
| 210 | C3×C4×C5 | — | 4 | 3 | no | — |
| 211 | C3×Dic5 | — | 4 | 6 | no | — |
| 212 | C22×A4 | — | 5 | 2 | no | — |
| 213 | C22×A4 | C22×D5 | 1 | 3 | yes | — |
| 214 | C3×#41 | — | 4 | 1 | no | — |
| 215 | C3×#41 | — | 20 | 3 | no | — |
| 216 | C3×#41 | — | 20 | 6 | no | — |
| 217 | C2×C3×Q8 | — | 20 | 3 | no | — |
| 218 | C2×C3×Q8 | — | 20 | 2 | no | — |
| 219 | C4×A4 | — | 5 | 6 | no | — |
| 220 | C4×A4 | C22×D5 | 1 | 3 | yes | — |
| 221 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 222 | C23×C5 | — | 2 | 3 | no | — |
| 223 | C23×C5 | — | 3 | 3 | no | — |
| 224 | C23×C5 | — | 3 | 3 | no | — |
| 225 | C23×C5 | — | 6 | 3 | no | — |
| 226 | C23×C5 | C24×C3 | 1 | 1 | yes | characteristic |
| 227 | C22×D5 | — | 2 | 2 | no | — |
| 228 | C22×D5 | — | 3 | 2 | no | — |
| 229 | C22×D5 | — | 3 | 2 | no | — |
| 230 | C22×D5 | — | 6 | 2 | no | — |
| 231 | C5×Q8 | — | 3 | 2 | no | — |
| 232 | C5×Q8 | — | 3 | 3 | no | — |
| 233 | C5×Q8 | C22×A4 | 1 | 1 | yes | characteristic |
| 234 | C5×D4 | — | 3 | 6 | no | — |
| 235 | C5×D4 | — | 3 | 6 | no | — |
| 236 | C5×D4 | — | 3 | 3 | no | — |
| 237 | C5×D4 | C22×A4 | 1 | 3 | yes | — |
| 238 | C2×C4×C5 | — | 3 | 6 | no | — |
| 239 | C2×C4×C5 | — | 3 | 3 | no | — |
| 240 | C2×C4×C5 | — | 3 | 1 | no | — |
| 241 | C2×C4×C5 | — | 3 | 3 | no | — |
| 242 | C2×C4×C5 | — | 3 | 3 | no | — |
| 243 | C2×C4×C5 | — | 3 | 3 | no | — |
| 244 | C2×C4×C5 | — | 3 | 1 | no | — |
| 245 | C2×C4×C5 | — | 3 | 3 | no | — |
| 246 | C2×C4×C5 | C22×A4 | 1 | 3 | yes | — |
| 247 | C22⋊D5 | — | 3 | 12 | no | — |
| 248 | C22⋊D5 | — | 3 | 6 | no | — |
| 249 | C22⋊D5 | — | 3 | 6 | no | — |
| 250 | C22⋊D5 | — | 3 | 6 | no | — |
| 251 | C22⋊D5 | C22×A4 | 1 | 6 | yes | — |
| 252 | C2×Dic5 | — | 3 | 12 | no | — |
| 253 | C2×Dic5 | — | 3 | 6 | no | — |
| 254 | C2×Dic5 | — | 3 | 6 | no | — |
| 255 | C2×Dic5 | — | 3 | 12 | no | — |
| 256 | C2×Dic5 | — | 3 | 6 | no | — |
| 257 | C2×Dic5 | C22×A4 | 1 | 6 | yes | — |
| 258 | D20 | — | 3 | 2 | no | — |
| 259 | D20 | — | 3 | 2 | no | — |
| 260 | D20 | — | 3 | 1 | no | — |
| 261 | D20 | C22×A4 | 1 | 1 | yes | characteristic |
| 262 | C4×D5 | — | 3 | 12 | no | — |
| 263 | C4×D5 | — | 3 | 6 | no | — |
| 264 | C4×D5 | — | 3 | 6 | no | — |
| 265 | C4×D5 | — | 3 | 6 | no | — |
| 266 | C4×D5 | C22×A4 | 1 | 6 | yes | — |
| 267 | Dic10 | — | 3 | 6 | no | — |
| 268 | Dic10 | — | 3 | 12 | no | — |
| 269 | Dic10 | — | 3 | 3 | no | — |
| 270 | Dic10 | — | 3 | 6 | no | — |
| 271 | Dic10 | — | 3 | 6 | no | — |
| 272 | Dic10 | — | 3 | 12 | no | — |
| 273 | Dic10 | C22×A4 | 1 | 3 | yes | — |
| 274 | Dic10 | C22×A4 | 1 | 6 | yes | — |
| 275 | 2−1+4 | — | 5 | 1 | no | — |
| 276 | 2−1+4 | — | 15 | 2 | no | — |
| 277 | 2−1+4 | — | 15 | 3 | no | — |
| 278 | 2−1+4 | — | 15 | 6 | no | — |
| 279 | 2−1+4 | — | 15 | 3 | no | — |
| 280 | 2−1+4 | — | 15 | 12 | no | — |
| 281 | 2−1+4 | — | 15 | 6 | no | — |
| 282 | 2−1+4 | — | 15 | 12 | no | — |
| 283 | 2−1+4 | — | 15 | 12 | no | — |
| 284 | 2−1+4 | — | 15 | 2 | no | — |
| 285 | 2−1+4 | — | 15 | 12 | no | — |
| 286 | 2−1+4 | — | 15 | 6 | no | — |
| 287 | 2−1+4 | — | 15 | 2 | no | — |
| 288 | 2−1+4 | — | 15 | 6 | no | — |
| 289 | 2−1+4 | — | 15 | 1 | no | — |
| 290 | C2×#41 | — | 3 | 3 | no | — |
| 291 | C2×#41 | — | 3 | 3 | no | — |
| 292 | C2×#41 | — | 3 | 1 | no | — |
| 293 | C2×#41 | — | 3 | 1 | no | — |
| 294 | C2×#41 | — | 15 | 3 | no | — |
| 295 | C2×#41 | — | 15 | 3 | no | — |
| 296 | C2×#41 | — | 15 | 6 | no | — |
| 297 | C2×#41 | — | 15 | 3 | no | — |
| 298 | C2×#41 | — | 15 | 6 | no | — |
| 299 | C2×#41 | — | 15 | 3 | no | — |
| 300 | C2×#41 | — | 15 | 6 | no | — |
| 301 | C2×#41 | — | 15 | 6 | no | — |
| 302 | C2×#41 | — | 15 | 12 | no | — |
| 303 | C2×#41 | — | 15 | 6 | no | — |
| 304 | C2×#41 | — | 15 | 12 | no | — |
| 305 | C2×#41 | — | 15 | 6 | no | — |
| 306 | C22×Q8 | — | 5 | 6 | no | — |
| 307 | C22×Q8 | — | 5 | 3 | no | — |
| 308 | C22×Q8 | — | 15 | 3 | no | — |
| 309 | C22×Q8 | — | 15 | 3 | no | — |
| 310 | C22×Q8 | — | 15 | 6 | no | — |
| 311 | C22×Q8 | — | 15 | 6 | no | — |
| 312 | C22×Q8 | — | 15 | 6 | no | — |
| 313 | C22×Q8 | — | 15 | 2 | no | — |
| 314 | C22×Q8 | — | 15 | 6 | no | — |
| 315 | C22×Q8 | — | 15 | 6 | no | — |
| 316 | C22×Q8 | — | 15 | 2 | no | — |
| 317 | C22×Q8 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 318 | C22×D4 | — | 5 | 6 | no | — |
| 319 | C22×D4 | — | 5 | 1 | no | — |
| 320 | C22×D4 | C2×C3×D5 | 1 | 3 | yes | — |
| 321 | C23×C4 | — | 5 | 6 | no | — |
| 322 | C23×C4 | — | 5 | 6 | no | — |
| 323 | C23×C4 | C2×C3×D5 | 1 | 3 | yes | — |
| 324 | C2×C3×C5 | — | 4 | 1 | no | — |
| 325 | C2×C3×C5 | — | 8 | 3 | no | — |
| 326 | C3×D5 | — | 8 | 2 | no | — |
| 327 | C2×A4 | — | 2 | 3 | no | — |
| 328 | C2×A4 | — | 10 | 2 | no | — |
| 329 | C2×A4 | C23×D5 | 1 | 1 | yes | characteristic |
| 330 | C3×Q8 | — | 4 | 1 | no | — |
| 331 | C3×Q8 | — | 20 | 3 | no | — |
| 332 | C3×Q8 | — | 20 | 6 | no | — |
| 333 | C3×D4 | — | 4 | 3 | no | — |
| 334 | C3×D4 | — | 20 | 1 | no | — |
| 335 | C3×D4 | — | 20 | 6 | no | — |
| 336 | C2×C3×C4 | — | 4 | 3 | no | — |
| 337 | C2×C3×C4 | — | 20 | 6 | no | — |
| 338 | C2×C3×C4 | — | 20 | 6 | no | — |
| 339 | C22×C5 | — | 3 | 1 | no | — |
| 340 | C22×C5 | — | 3 | 1 | no | — |
| 341 | C22×C5 | — | 3 | 3 | no | — |
| 342 | C22×C5 | — | 6 | 3 | no | — |
| 343 | C22×C5 | — | 6 | 3 | no | — |
| 344 | C22×C5 | — | 6 | 3 | no | — |
| 345 | C22×C5 | — | 6 | 3 | no | — |
| 346 | C22×C5 | C3×2−1+4 | 1 | 1 | yes | characteristic, complemented |
| 347 | C22×C5 | C23×A4 | 1 | 3 | yes | — |
| 348 | C2×D5 | — | 3 | 2 | no | — |
| 349 | C2×D5 | — | 6 | 2 | no | — |
| 350 | C2×D5 | — | 6 | 2 | no | — |
| 351 | C2×D5 | — | 6 | 2 | no | — |
| 352 | C2×D5 | — | 6 | 2 | no | — |
| 353 | C2×D5 | C23×A4 | 1 | 2 | yes | — |
| 354 | C4×C5 | — | 3 | 1 | no | — |
| 355 | C4×C5 | — | 3 | 3 | no | — |
| 356 | C4×C5 | C23×A4 | 1 | 1 | yes | characteristic |
| 357 | C4×C5 | C23×A4 | 1 | 3 | yes | — |
| 358 | Dic5 | — | 3 | 6 | no | — |
| 359 | Dic5 | C23×A4 | 1 | 6 | yes | — |
| 360 | C24 | — | 5 | 2 | no | — |
| 361 | C24 | C22×C3×D5 | 1 | 3 | yes | — |
| 362 | #41 | — | 3 | 6 | no | — |
| 363 | #41 | — | 3 | 6 | no | — |
| 364 | #41 | — | 3 | 2 | no | — |
| 365 | #41 | — | 3 | 1 | no | — |
| 366 | #41 | — | 3 | 3 | no | — |
| 367 | #41 | — | 3 | 3 | no | — |
| 368 | #41 | — | 5 | 6 | no | — |
| 369 | #41 | — | 5 | 3 | no | — |
| 370 | #41 | — | 15 | 6 | no | — |
| 371 | #41 | — | 15 | 6 | no | — |
| 372 | #41 | — | 15 | 3 | no | — |
| 373 | #41 | — | 15 | 3 | no | — |
| 374 | #41 | — | 15 | 12 | no | — |
| 375 | #41 | — | 15 | 12 | no | — |
| 376 | #41 | — | 15 | 6 | no | — |
| 377 | #41 | — | 15 | 6 | no | — |
| 378 | #41 | — | 15 | 6 | no | — |
| 379 | #41 | — | 15 | 12 | no | — |
| 380 | #41 | — | 15 | 6 | no | — |
| 381 | #41 | — | 15 | 12 | no | — |
| 382 | #41 | — | 15 | 6 | no | — |
| 383 | #41 | — | 15 | 12 | no | — |
| 384 | #41 | — | 15 | 12 | no | — |
| 385 | #41 | — | 15 | 24 | no | — |
| 386 | #41 | — | 15 | 24 | no | — |
| 387 | #41 | — | 15 | 12 | no | — |
| 388 | #41 | — | 15 | 6 | no | — |
| 389 | #41 | — | 15 | 3 | no | — |
| 390 | #41 | D5×A4 | 1 | 1 | yes | characteristic, complemented |
| 391 | C2×Q8 | — | 3 | 3 | no | — |
| 392 | C2×Q8 | — | 3 | 1 | no | — |
| 393 | C2×Q8 | — | 5 | 2 | no | — |
| 394 | C2×Q8 | — | 5 | 3 | no | — |
| 395 | C2×Q8 | — | 15 | 6 | no | — |
| 396 | C2×Q8 | — | 15 | 3 | no | — |
| 397 | C2×Q8 | — | 15 | 6 | no | — |
| 398 | C2×Q8 | — | 15 | 6 | no | — |
| 399 | C2×Q8 | — | 15 | 6 | no | — |
| 400 | C2×Q8 | — | 15 | 3 | no | — |
| 401 | C2×Q8 | — | 15 | 6 | no | — |
| 402 | C2×Q8 | — | 15 | 6 | no | — |
| 403 | C2×Q8 | — | 15 | 12 | no | — |
| 404 | C2×Q8 | — | 15 | 24 | no | — |
| 405 | C2×Q8 | — | 15 | 6 | no | — |
| 406 | C2×Q8 | — | 15 | 6 | no | — |
| 407 | C2×Q8 | — | 15 | 6 | no | — |
| 408 | C2×Q8 | — | 15 | 6 | no | — |
| 409 | C2×Q8 | — | 15 | 6 | no | — |
| 410 | C2×Q8 | — | 15 | 12 | no | — |
| 411 | C2×Q8 | — | 15 | 4 | no | — |
| 412 | C2×Q8 | — | 15 | 12 | no | — |
| 413 | C2×Q8 | — | 15 | 2 | no | — |
| 414 | C2×Q8 | — | 15 | 3 | no | — |
| 415 | C2×D4 | — | 3 | 3 | no | — |
| 416 | C2×D4 | — | 3 | 3 | no | — |
| 417 | C2×D4 | — | 3 | 6 | no | — |
| 418 | C2×D4 | — | 15 | 1 | no | — |
| 419 | C2×D4 | — | 15 | 1 | no | — |
| 420 | C2×D4 | — | 15 | 2 | no | — |
| 421 | C2×D4 | — | 15 | 6 | no | — |
| 422 | C2×D4 | — | 15 | 6 | no | — |
| 423 | C2×D4 | — | 15 | 6 | no | — |
| 424 | C2×D4 | — | 15 | 6 | no | — |
| 425 | C22×C4 | — | 3 | 3 | no | — |
| 426 | C22×C4 | — | 3 | 3 | no | — |
| 427 | C22×C4 | — | 3 | 3 | no | — |
| 428 | C22×C4 | — | 3 | 3 | no | — |
| 429 | C22×C4 | — | 5 | 6 | no | — |
| 430 | C22×C4 | — | 15 | 6 | no | — |
| 431 | C22×C4 | — | 15 | 6 | no | — |
| 432 | C22×C4 | — | 15 | 6 | no | — |
| 433 | C22×C4 | — | 15 | 6 | no | — |
| 434 | C22×C4 | — | 15 | 6 | no | — |
| 435 | C22×C4 | — | 15 | 12 | no | — |
| 436 | C22×C4 | — | 15 | 6 | no | — |
| 437 | C22×C4 | C22×C3×D5 | 1 | 3 | yes | — |
| 438 | C22×C4 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 439 | C3×C5 | — | 4 | 1 | no | Hall |
| 440 | C22×C3 | — | 4 | 3 | no | — |
| 441 | C22×C3 | — | 20 | 2 | no | — |
| 442 | A4 | #4150 | 1 | 1 | yes | characteristic, direct product factor |
| 443 | C3×C4 | — | 4 | 1 | no | — |
| 444 | C3×C4 | — | 4 | 3 | no | — |
| 445 | C3×C4 | — | 20 | 6 | no | — |
| 446 | C2×C5 | — | 2 | 3 | no | — |
| 447 | C2×C5 | — | 3 | 1 | no | — |
| 448 | C2×C5 | — | 3 | 1 | no | — |
| 449 | C2×C5 | — | 6 | 3 | no | — |
| 450 | C2×C5 | C24×A4 | 1 | 1 | yes | characteristic |
| 451 | D5 | — | 2 | 2 | no | — |
| 452 | D5 | — | 6 | 2 | no | — |
| 453 | C23 | — | 2 | 3 | no | — |
| 454 | C23 | — | 3 | 3 | no | — |
| 455 | C23 | — | 3 | 3 | no | — |
| 456 | C23 | — | 6 | 3 | no | — |
| 457 | C23 | — | 10 | 2 | no | — |
| 458 | C23 | — | 15 | 2 | no | — |
| 459 | C23 | — | 15 | 2 | no | — |
| 460 | C23 | — | 30 | 2 | no | — |
| 461 | C23 | C23×C3×D5 | 1 | 1 | yes | characteristic |
| 462 | Q8 | — | 3 | 2 | no | — |
| 463 | Q8 | — | 3 | 3 | no | — |
| 464 | Q8 | — | 5 | 3 | no | — |
| 465 | Q8 | — | 5 | 6 | no | — |
| 466 | Q8 | — | 15 | 6 | no | — |
| 467 | Q8 | — | 15 | 12 | no | — |
| 468 | Q8 | — | 15 | 6 | no | — |
| 469 | Q8 | — | 15 | 12 | no | — |
| 470 | Q8 | — | 15 | 3 | no | — |
| 471 | Q8 | — | 15 | 6 | no | — |
| 472 | Q8 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 473 | D4 | — | 3 | 6 | no | — |
| 474 | D4 | — | 3 | 6 | no | — |
| 475 | D4 | — | 3 | 3 | no | — |
| 476 | D4 | — | 5 | 6 | no | — |
| 477 | D4 | — | 5 | 1 | no | — |
| 478 | D4 | — | 15 | 2 | no | — |
| 479 | D4 | — | 15 | 2 | no | — |
| 480 | D4 | — | 15 | 6 | no | — |
| 481 | D4 | — | 15 | 6 | no | — |
| 482 | D4 | — | 15 | 12 | no | — |
| 483 | D4 | — | 15 | 6 | no | — |
| 484 | D4 | — | 15 | 1 | no | — |
| 485 | D4 | C2×D5×A4 | 1 | 3 | yes | — |
| 486 | C2×C4 | — | 3 | 6 | no | — |
| 487 | C2×C4 | — | 3 | 3 | no | — |
| 488 | C2×C4 | — | 3 | 1 | no | — |
| 489 | C2×C4 | — | 3 | 3 | no | — |
| 490 | C2×C4 | — | 3 | 3 | no | — |
| 491 | C2×C4 | — | 3 | 3 | no | — |
| 492 | C2×C4 | — | 3 | 1 | no | — |
| 493 | C2×C4 | — | 3 | 3 | no | — |
| 494 | C2×C4 | — | 5 | 6 | no | — |
| 495 | C2×C4 | — | 5 | 6 | no | — |
| 496 | C2×C4 | — | 15 | 6 | no | — |
| 497 | C2×C4 | — | 15 | 6 | no | — |
| 498 | C2×C4 | — | 15 | 12 | no | — |
| 499 | C2×C4 | — | 15 | 6 | no | — |
| 500 | C2×C4 | — | 15 | 12 | no | — |
| 501 | C2×C4 | — | 15 | 12 | no | — |
| 502 | C2×C4 | — | 15 | 6 | no | — |
| 503 | C2×C4 | — | 15 | 6 | no | — |
| 504 | C2×C4 | — | 15 | 6 | no | — |
| 505 | C2×C4 | C2×D5×A4 | 1 | 3 | yes | — |
| 506 | C2×C3 | — | 4 | 1 | no | — |
| 507 | C2×C3 | — | 8 | 3 | no | — |
| 508 | C2×C3 | — | 40 | 2 | no | — |
| 509 | C5 | A4×2−1+4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 510 | C22 | — | 3 | 1 | no | — |
| 511 | C22 | — | 3 | 1 | no | — |
| 512 | C22 | — | 3 | 3 | no | — |
| 513 | C22 | — | 5 | 2 | no | — |
| 514 | C22 | — | 6 | 3 | no | — |
| 515 | C22 | — | 6 | 3 | no | — |
| 516 | C22 | — | 6 | 3 | no | — |
| 517 | C22 | — | 6 | 3 | no | — |
| 518 | C22 | — | 15 | 2 | no | — |
| 519 | C22 | — | 30 | 2 | no | — |
| 520 | C22 | — | 30 | 2 | no | — |
| 521 | C22 | — | 30 | 2 | no | — |
| 522 | C22 | — | 30 | 2 | no | — |
| 523 | C22 | C3×#4150 | 1 | 1 | yes | characteristic, complemented |
| 524 | C22 | C22×D5×A4 | 1 | 3 | yes | — |
| 525 | C4 | — | 3 | 1 | no | — |
| 526 | C4 | — | 3 | 3 | no | — |
| 527 | C4 | — | 5 | 6 | no | — |
| 528 | C4 | — | 15 | 6 | no | — |
| 529 | C4 | C22×D5×A4 | 1 | 1 | yes | characteristic |
| 530 | C4 | C22×D5×A4 | 1 | 3 | yes | — |
| 531 | C3 | — | 4 | 1 | no | Sylow |
| 532 | C2 | — | 2 | 3 | no | — |
| 533 | C2 | — | 3 | 1 | no | — |
| 534 | C2 | — | 3 | 1 | no | — |
| 535 | C2 | — | 6 | 3 | no | — |
| 536 | C2 | — | 10 | 2 | no | — |
| 537 | C2 | — | 30 | 2 | no | — |
| 538 | C2 | C23×D5×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D5×A4 |
| commutator, socle, cosocle | C23×C5 | C24×C3 |
| Fitting | C22×C5×#41 | C2×C3 |
| hypercenter | #41 | D5×A4 |
| hypocenter | C22×C5 | C3×2−1+4 |
| LCS | G ▷ C23×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×A4×#41 | C2 | semidirect |
| 2. Q8×D5×A4 | C2 | semidirect |
| 3. A4×#711 | C2 | semidirect |
| 4. A4×#709 | C2 | semidirect |
| 5. C2×A4×Dic10 | C2 | semidirect |
| 6. C22×#4150 | C3 | semidirect |
| 18. C22×C5×#41 | C2×C3 | semidirect |
| 25. C22×Q8×D5 | C2×C3 | semidirect |
| 26. C22×#711 | C2×C3 | semidirect |
| 27. C22×#709 | C2×C3 | semidirect |
| 28. C23×Dic10 | C2×C3 | semidirect |
| 41. A4×#41 | D5 | semidirect |
| 67. #4150 | A4 | direct (N × H) |
| 124. C5×#41 | C2×A4 | semidirect |
| 150. Q8×D5 | C2×A4 | semidirect |
| 161. #711 | C2×A4 | semidirect |
| 172. #709 | C2×A4 | semidirect |
| 194. C2×Dic10 | C2×A4 | semidirect |
| 203. C22×#41 | C3×D5 | semidirect |
| 208. C5×A4 | 2−1+4 | semidirect |
| 346. C22×C5 | C3×2−1+4 | semidirect |
| 390. #41 | D5×A4 | semidirect |
| 442. A4 | #4150 | direct (N × H) |
| 509. C5 | A4×2−1+4 | semidirect |
| 523. C22 | C3×#4150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×#41 | 2 |
| Q8×D5×A4 | 2 |
| A4×#711 | 2 |
| A4×#709 | 2 |
| C2×A4×Dic10 | 2 |
| C22×#4150 | 3 |
| C3×#4150 | 4 |
| A4×2−1+4 | 5 |