Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1706 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1706 conjugacy classes of subgroups — too many to draw. Only its 155 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 | #11756903 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×C5⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11756898 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | D4×C5⋊S4 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11756896 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×C4×C5⋊S4 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #41×C22⋊D5 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×C5⋊S4 | C22 | 1 | 3 | yes | — |
| 10 | #41×D15 | — | 4 | 1 | no | maximal |
| 11 | C5×Q8×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C5×D4×A4 | C22 | 1 | 3 | yes | complemented |
| 13 | C2×C4×C5×A4 | C22 | 1 | 3 | yes | complemented |
| 14 | #91958 | C22 | 1 | 6 | yes | complemented |
| 15 | C2×A4⋊Dic5 | C22 | 1 | 3 | yes | complemented |
| 16 | C4⋊(C5⋊S4) | C22 | 1 | 3 | yes | complemented |
| 17 | C4×C5⋊S4 | C22 | 1 | 1 | yes | characteristic |
| 18 | C4×C5⋊S4 | C22 | 1 | 3 | yes | — |
| 19 | C4×C5⋊S4 | C22 | 1 | 3 | yes | complemented |
| 20 | C4×C5⋊S4 | C22 | 1 | 3 | yes | complemented |
| 21 | #91948 | C22 | 1 | 3 | yes | complemented |
| 22 | #41×S4 | — | 5 | 1 | no | maximal, Hall |
| 23 | C22×C5×#41 | D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×D5×#41 | — | 3 | 1 | no | — |
| 25 | #66168 | — | 3 | 1 | no | — |
| 26 | #66166 | — | 3 | 3 | no | — |
| 27 | #66165 | — | 3 | 1 | no | — |
| 28 | #66163 | — | 3 | 3 | no | — |
| 29 | #66162 | — | 3 | 3 | no | — |
| 30 | #41×Dic5 | — | 3 | 1 | no | — |
| 31 | #66158 | — | 3 | 3 | no | — |
| 32 | #66151 | — | 3 | 1 | no | — |
| 33 | Q8×C22⋊D5 | — | 3 | 1 | no | — |
| 34 | #66140 | — | 3 | 3 | no | — |
| 35 | D4×C22⋊D5 | — | 3 | 3 | no | — |
| 36 | #66125 | — | 3 | 3 | no | — |
| 37 | C2×C4×C22⋊D5 | — | 3 | 3 | no | — |
| 38 | C22×C5×A4 | C23 | 1 | 3 | yes | — |
| 39 | C2×C5⋊S4 | — | 2 | 6 | no | — |
| 40 | C2×C5⋊S4 | C23 | 1 | 3 | yes | — |
| 41 | C2×C5⋊S4 | C23 | 1 | 1 | yes | characteristic |
| 42 | C3×C5×#41 | — | 4 | 1 | no | — |
| 43 | #6821 | — | 4 | 1 | no | — |
| 44 | Q8×D15 | — | 4 | 1 | no | — |
| 45 | #6819 | — | 4 | 3 | no | — |
| 46 | D4×D15 | — | 4 | 3 | no | — |
| 47 | #6817 | — | 4 | 3 | no | — |
| 48 | C2×C4×D15 | — | 4 | 3 | no | — |
| 49 | C4×C5×A4 | C23 | 1 | 3 | yes | — |
| 50 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 51 | A4⋊Dic5 | C23 | 1 | 3 | yes | — |
| 52 | A4⋊Dic5 | C23 | 1 | 1 | yes | characteristic |
| 53 | A4×#41 | D5 | 1 | 1 | yes | characteristic, complemented |
| 54 | #5919 | — | 5 | 1 | no | — |
| 55 | Q8×S4 | — | 5 | 1 | no | — |
| 56 | #5914 | — | 5 | 3 | no | — |
| 57 | D4×S4 | — | 5 | 3 | no | — |
| 58 | #5912 | — | 5 | 3 | no | — |
| 59 | C2×C4×S4 | — | 5 | 3 | no | — |
| 60 | C2×C5×#41 | — | 3 | 1 | no | — |
| 61 | C2×C5×#41 | — | 3 | 3 | no | — |
| 62 | C2×C5×#41 | — | 3 | 3 | no | — |
| 63 | C2×C5×#41 | — | 3 | 1 | no | — |
| 64 | C22×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 65 | C22×C5×D4 | C2×D3 | 1 | 3 | yes | complemented |
| 66 | C23×C4×C5 | C2×D3 | 1 | 3 | yes | complemented |
| 67 | C22×C22⋊D5 | — | 3 | 3 | no | — |
| 68 | D5×#41 | — | 6 | 1 | no | — |
| 69 | D5×#41 | — | 6 | 3 | no | — |
| 70 | D5×#41 | — | 6 | 3 | no | — |
| 71 | D5×#41 | — | 6 | 1 | no | — |
| 72 | C2×#713 | — | 3 | 1 | no | — |
| 73 | C2×Q8×D5 | — | 3 | 1 | no | — |
| 74 | C2×#711 | — | 3 | 3 | no | — |
| 75 | C2×D4×D5 | — | 3 | 3 | no | — |
| 76 | C2×#709 | — | 3 | 3 | no | — |
| 77 | C22×C4×D5 | — | 3 | 3 | no | — |
| 78 | #4099 | — | 3 | 6 | no | — |
| 79 | C2×C22⋊Dic5 | — | 3 | 3 | no | — |
| 80 | #4093 | — | 3 | 3 | no | — |
| 81 | #4092 | — | 3 | 3 | no | — |
| 82 | #4092 | — | 3 | 3 | no | — |
| 83 | Q8×Dic5 | — | 3 | 1 | no | — |
| 84 | Q8×Dic5 | — | 3 | 1 | no | — |
| 85 | #4090 | — | 3 | 3 | no | — |
| 86 | #4086 | — | 3 | 3 | no | — |
| 87 | #4085 | — | 3 | 6 | no | — |
| 88 | #4085 | — | 3 | 6 | no | — |
| 89 | #4084 | — | 3 | 3 | no | — |
| 90 | #4084 | — | 3 | 3 | no | — |
| 91 | #4083 | — | 3 | 6 | no | — |
| 92 | #4082 | — | 3 | 3 | no | — |
| 93 | #4081 | — | 3 | 6 | no | — |
| 94 | D4×Dic5 | — | 3 | 3 | no | — |
| 95 | D4×Dic5 | — | 3 | 3 | no | — |
| 96 | #4076 | — | 3 | 3 | no | — |
| 97 | #4076 | — | 3 | 3 | no | — |
| 98 | #4075 | — | 3 | 6 | no | — |
| 99 | C4×C22⋊D5 | — | 3 | 3 | no | — |
| 100 | C4×C22⋊D5 | — | 3 | 3 | no | — |
| 101 | C4×C22⋊D5 | — | 3 | 3 | no | — |
| 102 | C4×C22⋊D5 | — | 3 | 3 | no | — |
| 103 | C4×C22⋊D5 | — | 3 | 6 | no | — |
| 104 | C4×C22⋊D5 | — | 3 | 1 | no | — |
| 105 | C4×C22⋊D5 | — | 3 | 3 | no | — |
| 106 | C4×C22⋊D5 | — | 3 | 3 | no | — |
| 107 | C4×C22⋊D5 | — | 3 | 3 | no | — |
| 108 | C2×#685 | — | 3 | 3 | no | — |
| 109 | #4072 | — | 3 | 3 | no | — |
| 110 | #4070 | — | 3 | 3 | no | — |
| 111 | #4070 | — | 3 | 3 | no | — |
| 112 | C2×#683 | — | 3 | 3 | no | — |
| 113 | C2×C4×Dic5 | — | 3 | 3 | no | — |
| 114 | D4×#41 | — | 15 | 1 | no | Sylow |
| 115 | C22×D15 | — | 4 | 3 | no | — |
| 116 | C2×C5×A4 | — | 2 | 3 | no | — |
| 117 | C2×C5×A4 | C24 | 1 | 1 | yes | characteristic |
| 118 | C5⋊S4 | — | 2 | 3 | no | — |
| 119 | C5⋊S4 | #41 | 1 | 2 | yes | direct product factor |
| 120 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 121 | C3×C5×D4 | — | 4 | 3 | no | — |
| 122 | C2×C3×C4×C5 | — | 4 | 3 | no | — |
| 123 | #1220 | — | 4 | 6 | no | — |
| 124 | C2×Dic15 | — | 4 | 3 | no | — |
| 125 | D60 | — | 4 | 3 | no | — |
| 126 | C4×D15 | — | 4 | 1 | no | — |
| 127 | C4×D15 | — | 4 | 3 | no | — |
| 128 | C4×D15 | — | 4 | 3 | no | — |
| 129 | C4×D15 | — | 4 | 3 | no | — |
| 130 | Dic30 | — | 4 | 3 | no | — |
| 131 | C22×S4 | — | 5 | 3 | no | — |
| 132 | D3×#41 | — | 20 | 1 | no | — |
| 133 | Q8×A4 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 134 | D4×A4 | C2×D5 | 1 | 3 | yes | complemented |
| 135 | C2×C4×A4 | C2×D5 | 1 | 3 | yes | complemented |
| 136 | GL(2,ℤ/4) | — | 5 | 6 | no | — |
| 137 | C2×SL(2,ℤ/4) | — | 5 | 3 | no | — |
| 138 | C4⋊S4 | — | 5 | 3 | no | — |
| 139 | C4×S4 | — | 5 | 1 | no | — |
| 140 | C4×S4 | — | 5 | 3 | no | — |
| 141 | C4×S4 | — | 5 | 3 | no | — |
| 142 | C4×S4 | — | 5 | 3 | no | — |
| 143 | A4⋊Q8 | — | 5 | 3 | no | — |
| 144 | C24×C5 | C22×D3 | 1 | 3 | yes | — |
| 145 | C23×D5 | — | 3 | 3 | no | — |
| 146 | C5×#41 | — | 3 | 1 | no | — |
| 147 | C5×#41 | — | 3 | 3 | no | — |
| 148 | C5×#41 | — | 3 | 3 | no | — |
| 149 | C5×#41 | — | 6 | 1 | no | — |
| 150 | C5×#41 | — | 6 | 3 | no | — |
| 151 | C5×#41 | — | 6 | 3 | no | — |
| 152 | C5×#41 | S4 | 1 | 1 | yes | characteristic, complemented |
| 153 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 154 | C2×C5×Q8 | — | 3 | 3 | no | — |
| 155 | C2×C5×D4 | — | 3 | 3 | no | — |
| 156 | C2×C5×D4 | — | 3 | 6 | no | — |
| 157 | C2×C5×D4 | — | 3 | 3 | no | — |
| 158 | C22×C4×C5 | — | 3 | 3 | no | — |
| 159 | C22×C4×C5 | — | 3 | 3 | no | — |
| 160 | C22×C4×C5 | — | 3 | 3 | no | — |
| 161 | C22×C4×C5 | — | 3 | 3 | no | — |
| 162 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 163 | C22×C4×C5 | C22×D3 | 1 | 3 | yes | — |
| 164 | C2×C22⋊D5 | — | 3 | 1 | no | — |
| 165 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 166 | C2×C22⋊D5 | — | 3 | 3 | no | — |
| 167 | C2×C22⋊D5 | — | 3 | 3 | no | — |
| 168 | C2×C22⋊D5 | — | 3 | 3 | no | — |
| 169 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 170 | C2×C22⋊D5 | — | 6 | 6 | no | — |
| 171 | C2×C22⋊D5 | — | 6 | 6 | no | — |
| 172 | C22×Dic5 | — | 3 | 3 | no | — |
| 173 | C22×Dic5 | — | 3 | 3 | no | — |
| 174 | C22×Dic5 | — | 3 | 3 | no | — |
| 175 | #713 | — | 6 | 3 | no | — |
| 176 | #713 | — | 6 | 1 | no | — |
| 177 | Q8×D5 | — | 6 | 3 | no | — |
| 178 | Q8×D5 | — | 6 | 1 | no | — |
| 179 | #711 | — | 6 | 6 | no | — |
| 180 | #711 | — | 6 | 3 | no | — |
| 181 | #711 | — | 6 | 3 | no | — |
| 182 | D4×D5 | — | 6 | 6 | no | — |
| 183 | D4×D5 | — | 6 | 3 | no | — |
| 184 | D4×D5 | — | 6 | 3 | no | — |
| 185 | #709 | — | 6 | 3 | no | — |
| 186 | #709 | — | 6 | 3 | no | — |
| 187 | #709 | — | 6 | 3 | no | — |
| 188 | #709 | — | 6 | 3 | no | — |
| 189 | C2×D20 | — | 3 | 3 | no | — |
| 190 | C2×C4×D5 | — | 3 | 1 | no | — |
| 191 | C2×C4×D5 | — | 3 | 3 | no | — |
| 192 | C2×C4×D5 | — | 3 | 3 | no | — |
| 193 | C2×C4×D5 | — | 3 | 3 | no | — |
| 194 | C2×C4×D5 | — | 6 | 3 | no | — |
| 195 | C2×C4×D5 | — | 6 | 3 | no | — |
| 196 | C2×C4×D5 | — | 6 | 3 | no | — |
| 197 | C2×C4×D5 | — | 6 | 3 | no | — |
| 198 | C2×Dic10 | — | 3 | 3 | no | — |
| 199 | C22⋊Dic5 | — | 3 | 3 | no | — |
| 200 | C22⋊Dic5 | — | 3 | 3 | no | — |
| 201 | C22⋊Dic5 | — | 3 | 6 | no | — |
| 202 | C22⋊Dic5 | — | 3 | 6 | no | — |
| 203 | C22⋊Dic5 | — | 3 | 1 | no | — |
| 204 | C22⋊Dic5 | — | 3 | 3 | no | — |
| 205 | #685 | — | 3 | 1 | no | — |
| 206 | #685 | — | 3 | 3 | no | — |
| 207 | #685 | — | 3 | 3 | no | — |
| 208 | #685 | — | 3 | 3 | no | — |
| 209 | #685 | — | 3 | 6 | no | — |
| 210 | C4⋊Dic5 | — | 3 | 3 | no | — |
| 211 | C4⋊Dic5 | — | 3 | 3 | no | — |
| 212 | #683 | — | 3 | 1 | no | — |
| 213 | #683 | — | 3 | 3 | no | — |
| 214 | #683 | — | 3 | 3 | no | — |
| 215 | #683 | — | 3 | 3 | no | — |
| 216 | #683 | — | 3 | 6 | no | — |
| 217 | C4×Dic5 | — | 3 | 1 | no | — |
| 218 | C4×Dic5 | — | 3 | 3 | no | — |
| 219 | C4×Dic5 | — | 3 | 3 | no | — |
| 220 | C4×Dic5 | — | 3 | 3 | no | — |
| 221 | C22×#41 | — | 15 | 1 | no | — |
| 222 | C22×#41 | D15 | 1 | 1 | yes | characteristic, complemented |
| 223 | #550 | — | 15 | 1 | no | — |
| 224 | D4×Q8 | — | 15 | 1 | no | — |
| 225 | #548 | — | 15 | 1 | no | — |
| 226 | #548 | — | 15 | 1 | no | — |
| 227 | #547 | — | 15 | 3 | no | — |
| 228 | #546 | — | 15 | 3 | no | — |
| 229 | #546 | — | 15 | 3 | no | — |
| 230 | D42 | — | 15 | 3 | no | — |
| 231 | #532 | — | 15 | 3 | no | — |
| 232 | #525 | — | 15 | 3 | no | — |
| 233 | #525 | — | 15 | 3 | no | — |
| 234 | C4×#41 | — | 15 | 1 | no | — |
| 235 | C2×C4×D4 | — | 15 | 3 | no | — |
| 236 | C22×C3×C5 | — | 4 | 3 | no | — |
| 237 | C2×D15 | — | 4 | 1 | no | — |
| 238 | C2×D15 | — | 4 | 3 | no | — |
| 239 | C2×D15 | — | 8 | 6 | no | — |
| 240 | C5×A4 | C2×#41 | 1 | 1 | yes | characteristic, complemented |
| 241 | C3×C4×C5 | — | 4 | 3 | no | — |
| 242 | C3×C4×C5 | — | 4 | 1 | no | — |
| 243 | Dic15 | — | 4 | 3 | no | — |
| 244 | Dic15 | — | 4 | 1 | no | — |
| 245 | C22×A4 | C22×D5 | 1 | 3 | yes | — |
| 246 | C2×S4 | — | 5 | 1 | no | — |
| 247 | C2×S4 | — | 5 | 3 | no | — |
| 248 | C2×S4 | — | 10 | 6 | no | — |
| 249 | C3×#41 | — | 4 | 1 | no | — |
| 250 | #239 | — | 20 | 1 | no | — |
| 251 | D3×Q8 | — | 20 | 1 | no | — |
| 252 | #237 | — | 20 | 3 | no | — |
| 253 | D3×D4 | — | 20 | 3 | no | — |
| 254 | #235 | — | 20 | 3 | no | — |
| 255 | C2×C4×D3 | — | 20 | 3 | no | — |
| 256 | C4×A4 | C22×D5 | 1 | 3 | yes | — |
| 257 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 258 | SL(2,ℤ/4) | — | 5 | 3 | no | — |
| 259 | SL(2,ℤ/4) | — | 5 | 1 | no | — |
| 260 | C23×C5 | — | 2 | 3 | no | — |
| 261 | C23×C5 | — | 3 | 3 | no | — |
| 262 | C23×C5 | — | 3 | 3 | no | — |
| 263 | C23×C5 | — | 6 | 3 | no | — |
| 264 | C23×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 265 | C22×D5 | — | 3 | 1 | no | — |
| 266 | C22×D5 | — | 3 | 3 | no | — |
| 267 | C22×D5 | — | 6 | 6 | no | — |
| 268 | C22×D5 | — | 6 | 3 | no | — |
| 269 | C22×D5 | — | 6 | 3 | no | — |
| 270 | C22×D5 | — | 12 | 3 | no | — |
| 271 | C5×Q8 | — | 3 | 3 | no | — |
| 272 | C5×Q8 | — | 6 | 1 | no | — |
| 273 | C5×Q8 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 274 | C5×D4 | — | 3 | 6 | no | — |
| 275 | C5×D4 | — | 3 | 3 | no | — |
| 276 | C5×D4 | — | 6 | 3 | no | — |
| 277 | C5×D4 | C2×S4 | 1 | 3 | yes | complemented |
| 278 | C2×C4×C5 | — | 3 | 3 | no | — |
| 279 | C2×C4×C5 | — | 3 | 1 | no | — |
| 280 | C2×C4×C5 | — | 3 | 3 | no | — |
| 281 | C2×C4×C5 | — | 3 | 3 | no | — |
| 282 | C2×C4×C5 | — | 3 | 3 | no | — |
| 283 | C2×C4×C5 | — | 3 | 1 | no | — |
| 284 | C2×C4×C5 | — | 3 | 3 | no | — |
| 285 | C2×C4×C5 | — | 6 | 3 | no | — |
| 286 | C2×C4×C5 | C2×S4 | 1 | 3 | yes | complemented |
| 287 | C22⋊D5 | — | 3 | 2 | no | — |
| 288 | C22⋊D5 | — | 3 | 2 | no | — |
| 289 | C22⋊D5 | — | 6 | 6 | no | — |
| 290 | C22⋊D5 | — | 6 | 6 | no | — |
| 291 | C22⋊D5 | — | 6 | 6 | no | — |
| 292 | C22⋊D5 | — | 6 | 3 | no | — |
| 293 | C22⋊D5 | — | 6 | 3 | no | — |
| 294 | C22⋊D5 | — | 6 | 6 | no | — |
| 295 | C22⋊D5 | — | 12 | 6 | no | — |
| 296 | C2×Dic5 | — | 3 | 1 | no | — |
| 297 | C2×Dic5 | — | 3 | 1 | no | — |
| 298 | C2×Dic5 | — | 3 | 3 | no | — |
| 299 | C2×Dic5 | — | 3 | 3 | no | — |
| 300 | C2×Dic5 | — | 3 | 3 | no | — |
| 301 | C2×Dic5 | — | 3 | 1 | no | — |
| 302 | C2×Dic5 | — | 6 | 6 | no | — |
| 303 | C2×Dic5 | — | 6 | 3 | no | — |
| 304 | C2×Dic5 | — | 6 | 3 | no | — |
| 305 | C2×Dic5 | — | 12 | 3 | no | — |
| 306 | D20 | — | 6 | 3 | no | — |
| 307 | D20 | — | 6 | 3 | no | — |
| 308 | C4×D5 | — | 6 | 1 | no | — |
| 309 | C4×D5 | — | 6 | 3 | no | — |
| 310 | C4×D5 | — | 6 | 3 | no | — |
| 311 | C4×D5 | — | 6 | 3 | no | — |
| 312 | C4×D5 | — | 6 | 1 | no | — |
| 313 | C4×D5 | — | 6 | 3 | no | — |
| 314 | C4×D5 | — | 6 | 3 | no | — |
| 315 | C4×D5 | — | 6 | 3 | no | — |
| 316 | Dic10 | — | 6 | 3 | no | — |
| 317 | Dic10 | — | 6 | 3 | no | — |
| 318 | C2×#41 | — | 3 | 1 | no | — |
| 319 | C2×#41 | — | 3 | 3 | no | — |
| 320 | C2×#41 | — | 3 | 3 | no | — |
| 321 | C2×#41 | — | 3 | 1 | no | — |
| 322 | C2×#41 | — | 15 | 3 | no | — |
| 323 | C2×#41 | — | 15 | 3 | no | — |
| 324 | C2×#41 | — | 15 | 1 | no | — |
| 325 | C2×#41 | — | 30 | 1 | no | — |
| 326 | C2×#41 | — | 30 | 3 | no | — |
| 327 | C2×#41 | — | 30 | 3 | no | — |
| 328 | C2×#41 | — | 30 | 1 | no | — |
| 329 | C22×Q8 | — | 15 | 1 | no | — |
| 330 | C22×Q8 | C2×D15 | 1 | 1 | yes | characteristic, complemented |
| 331 | C22×D4 | — | 15 | 3 | no | — |
| 332 | C22×D4 | — | 15 | 3 | no | — |
| 333 | C22×D4 | C2×D15 | 1 | 3 | yes | complemented |
| 334 | C23×C4 | — | 15 | 3 | no | — |
| 335 | C23×C4 | C2×D15 | 1 | 3 | yes | complemented |
| 336 | C4⋊Q8 | — | 15 | 3 | no | — |
| 337 | #127 | — | 15 | 3 | no | — |
| 338 | #124 | — | 15 | 3 | no | — |
| 339 | #124 | — | 15 | 3 | no | — |
| 340 | #123 | — | 15 | 6 | no | — |
| 341 | #123 | — | 15 | 6 | no | — |
| 342 | C22⋊Q8 | — | 15 | 3 | no | — |
| 343 | C22⋊Q8 | — | 15 | 3 | no | — |
| 344 | C22⋊Q8 | — | 15 | 3 | no | — |
| 345 | C22⋊Q8 | — | 15 | 3 | no | — |
| 346 | #121 | — | 15 | 3 | no | — |
| 347 | #121 | — | 15 | 3 | no | — |
| 348 | #121 | — | 15 | 3 | no | — |
| 349 | #121 | — | 15 | 6 | no | — |
| 350 | #121 | — | 15 | 6 | no | — |
| 351 | #121 | — | 15 | 3 | no | — |
| 352 | #120 | — | 15 | 6 | no | — |
| 353 | #120 | — | 15 | 6 | no | — |
| 354 | C4×Q8 | — | 15 | 1 | no | — |
| 355 | C4×Q8 | — | 15 | 1 | no | — |
| 356 | C4×D4 | — | 15 | 3 | no | — |
| 357 | C4×D4 | — | 15 | 3 | no | — |
| 358 | C4×D4 | — | 15 | 3 | no | — |
| 359 | C4×D4 | — | 15 | 3 | no | — |
| 360 | C4×D4 | — | 15 | 6 | no | — |
| 361 | C4×D4 | — | 15 | 3 | no | — |
| 362 | C4×D4 | — | 15 | 3 | no | — |
| 363 | C4×D4 | — | 15 | 1 | no | — |
| 364 | C4×D4 | — | 15 | 3 | no | — |
| 365 | C4×D4 | — | 15 | 3 | no | — |
| 366 | C4×D4 | — | 15 | 3 | no | — |
| 367 | #117 | — | 15 | 3 | no | — |
| 368 | C2×C4⋊C4 | — | 15 | 3 | no | — |
| 369 | C2×C22⋊C4 | — | 15 | 3 | no | — |
| 370 | C2×C22⋊C4 | — | 15 | 3 | no | — |
| 371 | C2×C42 | — | 15 | 3 | no | — |
| 372 | C2×C3×C5 | — | 4 | 1 | no | — |
| 373 | C2×C3×C5 | — | 8 | 3 | no | — |
| 374 | D15 | — | 4 | 2 | no | — |
| 375 | D15 | — | 8 | 3 | no | — |
| 376 | C22×D3 | — | 20 | 3 | no | — |
| 377 | C2×A4 | — | 2 | 3 | no | — |
| 378 | C2×A4 | C23×D5 | 1 | 1 | yes | characteristic |
| 379 | S4 | — | 5 | 2 | no | — |
| 380 | S4 | — | 10 | 3 | no | — |
| 381 | C3×Q8 | — | 4 | 1 | no | — |
| 382 | C3×D4 | — | 4 | 3 | no | — |
| 383 | C2×C3×C4 | — | 4 | 3 | no | — |
| 384 | #67 | — | 20 | 6 | no | — |
| 385 | C2×Dic3 | — | 20 | 3 | no | — |
| 386 | D12 | — | 20 | 3 | no | — |
| 387 | C4×D3 | — | 20 | 1 | no | — |
| 388 | C4×D3 | — | 20 | 3 | no | — |
| 389 | C4×D3 | — | 20 | 3 | no | — |
| 390 | C4×D3 | — | 20 | 3 | no | — |
| 391 | Dic6 | — | 20 | 3 | no | — |
| 392 | C22×C5 | — | 3 | 1 | no | — |
| 393 | C22×C5 | — | 3 | 1 | no | — |
| 394 | C22×C5 | — | 3 | 3 | no | — |
| 395 | C22×C5 | — | 6 | 3 | no | — |
| 396 | C22×C5 | — | 6 | 3 | no | — |
| 397 | C22×C5 | — | 6 | 3 | no | — |
| 398 | C22×C5 | — | 6 | 3 | no | — |
| 399 | C22×C5 | D3×#41 | 1 | 1 | yes | characteristic, complemented |
| 400 | C22×C5 | C22×S4 | 1 | 3 | yes | — |
| 401 | C2×D5 | — | 3 | 2 | no | — |
| 402 | C2×D5 | — | 6 | 1 | no | — |
| 403 | C2×D5 | — | 6 | 1 | no | — |
| 404 | C2×D5 | — | 6 | 3 | no | — |
| 405 | C2×D5 | — | 6 | 3 | no | — |
| 406 | C2×D5 | — | 6 | 3 | no | — |
| 407 | C2×D5 | — | 12 | 6 | no | — |
| 408 | C2×D5 | — | 12 | 6 | no | — |
| 409 | C4×C5 | — | 3 | 3 | no | — |
| 410 | C4×C5 | — | 3 | 1 | no | — |
| 411 | C4×C5 | C22×S4 | 1 | 3 | yes | — |
| 412 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 413 | Dic5 | — | 3 | 2 | no | — |
| 414 | Dic5 | — | 6 | 3 | no | — |
| 415 | Dic5 | — | 6 | 1 | no | — |
| 416 | Dic5 | — | 6 | 3 | no | — |
| 417 | Dic5 | — | 6 | 3 | no | — |
| 418 | Dic5 | — | 6 | 1 | no | — |
| 419 | C24 | — | 15 | 3 | no | — |
| 420 | C24 | C22×D15 | 1 | 3 | yes | — |
| 421 | #41 | — | 3 | 1 | no | — |
| 422 | #41 | — | 3 | 3 | no | — |
| 423 | #41 | — | 3 | 3 | no | — |
| 424 | #41 | — | 6 | 1 | no | — |
| 425 | #41 | — | 6 | 3 | no | — |
| 426 | #41 | — | 6 | 3 | no | — |
| 427 | #41 | — | 30 | 3 | no | — |
| 428 | #41 | — | 30 | 3 | no | — |
| 429 | #41 | — | 30 | 3 | no | — |
| 430 | #41 | — | 30 | 6 | no | — |
| 431 | #41 | — | 30 | 3 | no | — |
| 432 | #41 | — | 30 | 3 | no | — |
| 433 | #41 | — | 30 | 1 | no | — |
| 434 | #41 | — | 30 | 3 | no | — |
| 435 | #41 | — | 30 | 3 | no | — |
| 436 | #41 | C5⋊S4 | 1 | 1 | yes | characteristic, direct product factor |
| 437 | C2×Q8 | — | 3 | 1 | no | — |
| 438 | C2×Q8 | — | 3 | 3 | no | — |
| 439 | C2×Q8 | — | 15 | 3 | no | — |
| 440 | C2×Q8 | — | 30 | 3 | no | — |
| 441 | C2×Q8 | — | 30 | 1 | no | — |
| 442 | C2×D4 | — | 3 | 3 | no | — |
| 443 | C2×D4 | — | 3 | 6 | no | — |
| 444 | C2×D4 | — | 3 | 3 | no | — |
| 445 | C2×D4 | — | 15 | 3 | no | — |
| 446 | C2×D4 | — | 15 | 1 | no | — |
| 447 | C2×D4 | — | 15 | 3 | no | — |
| 448 | C2×D4 | — | 15 | 3 | no | — |
| 449 | C2×D4 | — | 15 | 6 | no | — |
| 450 | C2×D4 | — | 15 | 3 | no | — |
| 451 | C2×D4 | — | 15 | 6 | no | — |
| 452 | C2×D4 | — | 30 | 6 | no | — |
| 453 | C2×D4 | — | 30 | 3 | no | — |
| 454 | C2×D4 | — | 30 | 6 | no | — |
| 455 | C2×D4 | — | 30 | 6 | no | — |
| 456 | C2×D4 | — | 30 | 3 | no | — |
| 457 | C22×C4 | — | 3 | 3 | no | — |
| 458 | C22×C4 | — | 3 | 3 | no | — |
| 459 | C22×C4 | — | 3 | 3 | no | — |
| 460 | C22×C4 | — | 3 | 3 | no | — |
| 461 | C22×C4 | — | 15 | 1 | no | — |
| 462 | C22×C4 | — | 15 | 3 | no | — |
| 463 | C22×C4 | — | 15 | 3 | no | — |
| 464 | C22×C4 | — | 15 | 3 | no | — |
| 465 | C22×C4 | — | 15 | 3 | no | — |
| 466 | C22×C4 | — | 15 | 3 | no | — |
| 467 | C22×C4 | — | 15 | 3 | no | — |
| 468 | C22×C4 | — | 30 | 3 | no | — |
| 469 | C22×C4 | — | 30 | 3 | no | — |
| 470 | C22×C4 | — | 30 | 3 | no | — |
| 471 | C22×C4 | — | 30 | 3 | no | — |
| 472 | C22×C4 | C22×D15 | 1 | 1 | yes | characteristic |
| 473 | C22×C4 | C22×D15 | 1 | 3 | yes | — |
| 474 | C4⋊C4 | — | 15 | 1 | no | — |
| 475 | C4⋊C4 | — | 15 | 3 | no | — |
| 476 | C4⋊C4 | — | 15 | 3 | no | — |
| 477 | C4⋊C4 | — | 15 | 3 | no | — |
| 478 | C4⋊C4 | — | 15 | 3 | no | — |
| 479 | C4⋊C4 | — | 15 | 3 | no | — |
| 480 | C4⋊C4 | — | 15 | 6 | no | — |
| 481 | C22⋊C4 | — | 15 | 1 | no | — |
| 482 | C22⋊C4 | — | 15 | 3 | no | — |
| 483 | C22⋊C4 | — | 15 | 3 | no | — |
| 484 | C22⋊C4 | — | 15 | 3 | no | — |
| 485 | C22⋊C4 | — | 15 | 6 | no | — |
| 486 | C22⋊C4 | — | 15 | 3 | no | — |
| 487 | C22⋊C4 | — | 15 | 3 | no | — |
| 488 | C22⋊C4 | — | 15 | 6 | no | — |
| 489 | C22⋊C4 | — | 15 | 6 | no | — |
| 490 | C22⋊C4 | — | 15 | 1 | no | — |
| 491 | C22⋊C4 | — | 15 | 3 | no | — |
| 492 | C42 | — | 15 | 1 | no | — |
| 493 | C42 | — | 15 | 3 | no | — |
| 494 | C42 | — | 15 | 3 | no | — |
| 495 | C42 | — | 15 | 3 | no | — |
| 496 | C3×C5 | — | 4 | 1 | no | Hall |
| 497 | C22×C3 | — | 4 | 3 | no | — |
| 498 | C2×D3 | — | 20 | 1 | no | — |
| 499 | C2×D3 | — | 20 | 3 | no | — |
| 500 | C2×D3 | — | 40 | 6 | no | — |
| 501 | A4 | D5×#41 | 1 | 1 | yes | characteristic, complemented |
| 502 | C3×C4 | — | 4 | 3 | no | — |
| 503 | C3×C4 | — | 4 | 1 | no | — |
| 504 | Dic3 | — | 20 | 3 | no | — |
| 505 | Dic3 | — | 20 | 1 | no | — |
| 506 | C2×C5 | — | 2 | 3 | no | — |
| 507 | C2×C5 | — | 3 | 1 | no | — |
| 508 | C2×C5 | — | 3 | 1 | no | — |
| 509 | C2×C5 | — | 6 | 3 | no | — |
| 510 | C2×C5 | C23×S4 | 1 | 1 | yes | characteristic |
| 511 | D5 | — | 6 | 2 | no | — |
| 512 | D5 | — | 12 | 3 | no | — |
| 513 | C23 | — | 2 | 3 | no | — |
| 514 | C23 | — | 3 | 3 | no | — |
| 515 | C23 | — | 3 | 3 | no | — |
| 516 | C23 | — | 6 | 3 | no | — |
| 517 | C23 | — | 15 | 1 | no | — |
| 518 | C23 | — | 15 | 3 | no | — |
| 519 | C23 | — | 30 | 3 | no | — |
| 520 | C23 | — | 30 | 6 | no | — |
| 521 | C23 | — | 30 | 3 | no | — |
| 522 | C23 | — | 60 | 3 | no | — |
| 523 | C23 | C23×D15 | 1 | 1 | yes | characteristic |
| 524 | Q8 | — | 3 | 3 | no | — |
| 525 | Q8 | — | 6 | 1 | no | — |
| 526 | Q8 | — | 30 | 3 | no | — |
| 527 | Q8 | — | 30 | 3 | no | — |
| 528 | Q8 | C2×C5⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 529 | D4 | — | 3 | 6 | no | — |
| 530 | D4 | — | 3 | 3 | no | — |
| 531 | D4 | — | 6 | 3 | no | — |
| 532 | D4 | — | 15 | 2 | no | — |
| 533 | D4 | — | 15 | 2 | no | — |
| 534 | D4 | — | 30 | 3 | no | — |
| 535 | D4 | — | 30 | 6 | no | — |
| 536 | D4 | — | 30 | 6 | no | — |
| 537 | D4 | — | 30 | 3 | no | — |
| 538 | D4 | — | 30 | 6 | no | — |
| 539 | D4 | — | 30 | 3 | no | — |
| 540 | D4 | — | 30 | 6 | no | — |
| 541 | D4 | — | 30 | 3 | no | — |
| 542 | D4 | — | 60 | 6 | no | — |
| 543 | D4 | C2×C5⋊S4 | 1 | 3 | yes | complemented |
| 544 | C2×C4 | — | 3 | 3 | no | — |
| 545 | C2×C4 | — | 3 | 3 | no | — |
| 546 | C2×C4 | — | 3 | 3 | no | — |
| 547 | C2×C4 | — | 3 | 1 | no | — |
| 548 | C2×C4 | — | 3 | 3 | no | — |
| 549 | C2×C4 | — | 3 | 1 | no | — |
| 550 | C2×C4 | — | 3 | 3 | no | — |
| 551 | C2×C4 | — | 6 | 3 | no | — |
| 552 | C2×C4 | — | 15 | 1 | no | — |
| 553 | C2×C4 | — | 15 | 1 | no | — |
| 554 | C2×C4 | — | 15 | 3 | no | — |
| 555 | C2×C4 | — | 15 | 3 | no | — |
| 556 | C2×C4 | — | 15 | 1 | no | — |
| 557 | C2×C4 | — | 15 | 3 | no | — |
| 558 | C2×C4 | — | 30 | 1 | no | — |
| 559 | C2×C4 | — | 30 | 3 | no | — |
| 560 | C2×C4 | — | 30 | 3 | no | — |
| 561 | C2×C4 | — | 30 | 3 | no | — |
| 562 | C2×C4 | — | 30 | 6 | no | — |
| 563 | C2×C4 | — | 30 | 3 | no | — |
| 564 | C2×C4 | — | 30 | 3 | no | — |
| 565 | C2×C4 | — | 30 | 3 | no | — |
| 566 | C2×C4 | — | 30 | 3 | no | — |
| 567 | C2×C4 | — | 30 | 1 | no | — |
| 568 | C2×C4 | — | 30 | 3 | no | — |
| 569 | C2×C4 | — | 60 | 3 | no | — |
| 570 | C2×C4 | C2×C5⋊S4 | 1 | 3 | yes | complemented |
| 571 | C2×C3 | — | 4 | 1 | no | — |
| 572 | C2×C3 | — | 8 | 3 | no | — |
| 573 | D3 | — | 20 | 2 | no | — |
| 574 | D3 | — | 40 | 3 | no | — |
| 575 | C5 | #41×S4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 576 | C22 | — | 3 | 1 | no | — |
| 577 | C22 | — | 3 | 1 | no | — |
| 578 | C22 | — | 3 | 3 | no | — |
| 579 | C22 | — | 6 | 3 | no | — |
| 580 | C22 | — | 6 | 3 | no | — |
| 581 | C22 | — | 6 | 3 | no | — |
| 582 | C22 | — | 6 | 3 | no | — |
| 583 | C22 | — | 15 | 2 | no | — |
| 584 | C22 | — | 30 | 1 | no | — |
| 585 | C22 | — | 30 | 3 | no | — |
| 586 | C22 | — | 30 | 3 | no | — |
| 587 | C22 | — | 30 | 1 | no | — |
| 588 | C22 | — | 30 | 3 | no | — |
| 589 | C22 | — | 60 | 6 | no | — |
| 590 | C22 | — | 60 | 6 | no | — |
| 591 | C22 | #41×D15 | 1 | 1 | yes | characteristic, complemented |
| 592 | C22 | C22×C5⋊S4 | 1 | 3 | yes | — |
| 593 | C4 | — | 3 | 1 | no | — |
| 594 | C4 | — | 3 | 3 | no | — |
| 595 | C4 | — | 15 | 2 | no | — |
| 596 | C4 | — | 30 | 3 | no | — |
| 597 | C4 | — | 30 | 1 | no | — |
| 598 | C4 | — | 30 | 3 | no | — |
| 599 | C4 | — | 30 | 1 | no | — |
| 600 | C4 | — | 30 | 3 | no | — |
| 601 | C4 | C22×C5⋊S4 | 1 | 3 | yes | — |
| 602 | C4 | C22×C5⋊S4 | 1 | 1 | yes | characteristic |
| 603 | C3 | — | 4 | 1 | no | Sylow |
| 604 | C2 | — | 2 | 3 | no | — |
| 605 | C2 | — | 3 | 1 | no | — |
| 606 | C2 | — | 3 | 1 | no | — |
| 607 | C2 | — | 6 | 3 | no | — |
| 608 | C2 | — | 30 | 2 | no | — |
| 609 | C2 | — | 60 | 3 | no | — |
| 610 | C2 | C23×C5⋊S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×C5⋊S4 |
| commutator, cosocle | C2×C5×A4 | C24 |
| Frattini | C2 | C23×C5⋊S4 |
| Fitting | C22×C5×#41 | D3 |
| socle | C23×C5 | C23×D3 |
| hypercenter | #41 | C5⋊S4 |
| hypocenter | C5×A4 | C2×#41 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×A4×#41 | C2 | semidirect |
| 2. #11756903 | C2 | semidirect |
| 3. Q8×C5⋊S4 | C2 | semidirect |
| 4. #11756898 | C2 | semidirect |
| 5. D4×C5⋊S4 | C2 | semidirect |
| 6. #11756896 | C2 | semidirect |
| 7. C2×C4×C5⋊S4 | C2 | semidirect |
| 11. C5×Q8×A4 | C22 | semidirect |
| 12. C5×D4×A4 | C22 | semidirect |
| 13. C2×C4×C5×A4 | C22 | semidirect |
| 14. #91958 | C22 | semidirect |
| 15. C2×A4⋊Dic5 | C22 | semidirect |
| 16. C4⋊(C5⋊S4) | C22 | semidirect |
| 19. C4×C5⋊S4 | C22 | semidirect |
| 20. C4×C5⋊S4 | C22 | semidirect |
| 21. #91948 | C22 | semidirect |
| 23. C22×C5×#41 | D3 | semidirect |
| 53. A4×#41 | D5 | semidirect |
| 64. C22×C5×Q8 | C2×D3 | semidirect |
| 65. C22×C5×D4 | C2×D3 | semidirect |
| 66. C23×C4×C5 | C2×D3 | semidirect |
| 119. C5⋊S4 | #41 | direct (N × H) |
| 133. Q8×A4 | C2×D5 | semidirect |
| 134. D4×A4 | C2×D5 | semidirect |
| 135. C2×C4×A4 | C2×D5 | semidirect |
| 152. C5×#41 | S4 | semidirect |
| 222. C22×#41 | D15 | semidirect |
| 240. C5×A4 | C2×#41 | semidirect |
| 273. C5×Q8 | C2×S4 | semidirect |
| 277. C5×D4 | C2×S4 | semidirect |
| 286. C2×C4×C5 | C2×S4 | semidirect |
| 330. C22×Q8 | C2×D15 | semidirect |
| 333. C22×D4 | C2×D15 | semidirect |
| 335. C23×C4 | C2×D15 | semidirect |
| 399. C22×C5 | D3×#41 | semidirect |
| 436. #41 | C5⋊S4 | direct (N × H) |
| 501. A4 | D5×#41 | semidirect |
| 528. Q8 | C2×C5⋊S4 | semidirect |
| 543. D4 | C2×C5⋊S4 | semidirect |
| 570. C2×C4 | C2×C5⋊S4 | semidirect |
| 575. C5 | #41×S4 | semidirect |
| 591. C22 | #41×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×#41 | 2 |
| #11756903 | 2 |
| Q8×C5⋊S4 | 2 |
| #11756898 | 2 |
| D4×C5⋊S4 | 2 |
| #11756896 | 2 |
| C2×C4×C5⋊S4 | 2 |
| #41×C22⋊D5 | 3 |
| #41×D15 | 4 |
| #41×S4 | 5 |