Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1720 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 153 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 | 2 | yes | maximal, complemented |
| 3 | D4×C5⋊S4 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #11756896 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×C4⋊(C5⋊S4) | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10619176 | — | 3 | 1 | no | maximal, Hall |
| 7 | C22×C5⋊S4 | C22 | 1 | 6 | yes | complemented |
| 8 | #92100 | — | 4 | 1 | no | maximal |
| 9 | C5×Q8×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C5×D4×A4 | C22 | 1 | 3 | yes | complemented |
| 11 | C2×C4×C5×A4 | C22 | 1 | 3 | yes | complemented |
| 12 | #91958 | C22 | 1 | 6 | yes | complemented |
| 13 | C4⋊(C5⋊S4) | C22 | 1 | 3 | yes | complemented |
| 14 | C4⋊(C5⋊S4) | C22 | 1 | 6 | yes | complemented |
| 15 | C4×C5⋊S4 | C22 | 1 | 6 | yes | complemented |
| 16 | #91948 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #87489 | — | 5 | 1 | no | maximal, Hall |
| 18 | C22×C5×#41 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#4149 | — | 3 | 1 | no | — |
| 20 | #66168 | — | 3 | 2 | no | — |
| 21 | #66167 | — | 3 | 3 | no | — |
| 22 | #66164 | — | 3 | 3 | no | — |
| 23 | #66163 | — | 3 | 6 | no | — |
| 24 | #66161 | — | 3 | 1 | no | — |
| 25 | #66151 | — | 3 | 2 | no | — |
| 26 | D4×C22⋊D5 | — | 3 | 6 | no | — |
| 27 | #66125 | — | 3 | 3 | no | — |
| 28 | C2×#4076 | — | 3 | 3 | no | — |
| 29 | C22×C5×A4 | C23 | 1 | 3 | yes | — |
| 30 | C2×C5⋊S4 | — | 4 | 6 | no | — |
| 31 | C2×C5⋊S4 | C23 | 1 | 6 | yes | — |
| 32 | C3×C5×#41 | — | 4 | 1 | no | — |
| 33 | #6821 | — | 4 | 2 | no | — |
| 34 | D4×D15 | — | 4 | 6 | no | — |
| 35 | #6817 | — | 4 | 3 | no | — |
| 36 | C2×D60 | — | 4 | 3 | no | — |
| 37 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 38 | C4×C5×A4 | C23 | 1 | 3 | yes | — |
| 39 | A4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 40 | A4×#41 | D5 | 1 | 1 | yes | characteristic, complemented |
| 41 | #5919 | — | 5 | 2 | no | — |
| 42 | D4×S4 | — | 5 | 6 | no | — |
| 43 | #5912 | — | 5 | 3 | no | — |
| 44 | C2×C4⋊S4 | — | 5 | 3 | no | — |
| 45 | C2×C5×#41 | — | 3 | 1 | no | — |
| 46 | C2×C5×#41 | — | 3 | 3 | no | — |
| 47 | C2×C5×#41 | — | 3 | 3 | no | — |
| 48 | C2×C5×#41 | — | 3 | 1 | no | — |
| 49 | C22×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | C22×C5×D4 | C2×D3 | 1 | 3 | yes | complemented |
| 51 | C23×C4×C5 | C2×D3 | 1 | 3 | yes | complemented |
| 52 | C22×C22⋊D5 | — | 3 | 6 | no | — |
| 53 | #4149 | — | 6 | 1 | no | — |
| 54 | #4149 | — | 6 | 3 | no | — |
| 55 | #4149 | — | 6 | 3 | no | — |
| 56 | #4149 | — | 6 | 1 | no | — |
| 57 | C2×#713 | — | 3 | 2 | no | — |
| 58 | C2×D4×D5 | — | 3 | 6 | no | — |
| 59 | C2×#709 | — | 3 | 3 | no | — |
| 60 | C22×D20 | — | 3 | 3 | no | — |
| 61 | #4099 | — | 3 | 6 | no | — |
| 62 | #4093 | — | 3 | 6 | no | — |
| 63 | #4092 | — | 3 | 6 | no | — |
| 64 | Q8×Dic5 | — | 3 | 2 | no | — |
| 65 | #4086 | — | 3 | 6 | no | — |
| 66 | #4085 | — | 3 | 12 | no | — |
| 67 | #4084 | — | 3 | 6 | no | — |
| 68 | #4083 | — | 3 | 12 | no | — |
| 69 | D4×Dic5 | — | 3 | 6 | no | — |
| 70 | #4076 | — | 3 | 6 | no | — |
| 71 | #4076 | — | 3 | 6 | no | — |
| 72 | #4076 | — | 3 | 3 | no | — |
| 73 | #4076 | — | 3 | 3 | no | — |
| 74 | #4076 | — | 3 | 6 | no | — |
| 75 | #4075 | — | 3 | 6 | no | — |
| 76 | C4×C22⋊D5 | — | 3 | 6 | no | — |
| 77 | C4×C22⋊D5 | — | 3 | 6 | no | — |
| 78 | C2×#685 | — | 3 | 6 | no | — |
| 79 | #4072 | — | 3 | 3 | no | — |
| 80 | C2×C4⋊Dic5 | — | 3 | 3 | no | — |
| 81 | #4070 | — | 3 | 3 | no | — |
| 82 | #4070 | — | 3 | 1 | no | — |
| 83 | #3488 | — | 15 | 1 | no | Sylow |
| 84 | C22×D15 | — | 4 | 6 | no | — |
| 85 | C2×C5×A4 | — | 2 | 3 | no | — |
| 86 | C2×C5×A4 | C24 | 1 | 1 | yes | characteristic |
| 87 | C5⋊S4 | — | 2 | 6 | no | — |
| 88 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 89 | C3×C5×D4 | — | 4 | 3 | no | — |
| 90 | C2×C3×C4×C5 | — | 4 | 3 | no | — |
| 91 | #1220 | — | 4 | 6 | no | — |
| 92 | D60 | — | 4 | 3 | no | — |
| 93 | D60 | — | 4 | 6 | no | — |
| 94 | C4×D15 | — | 4 | 6 | no | — |
| 95 | Dic30 | — | 4 | 1 | no | — |
| 96 | C22×S4 | — | 5 | 6 | no | — |
| 97 | #1009 | — | 20 | 1 | no | — |
| 98 | Q8×A4 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 99 | D4×A4 | C2×D5 | 1 | 3 | yes | complemented |
| 100 | C2×C4×A4 | C2×D5 | 1 | 3 | yes | complemented |
| 101 | GL(2,ℤ/4) | — | 5 | 6 | no | — |
| 102 | C4⋊S4 | — | 5 | 3 | no | — |
| 103 | C4⋊S4 | — | 5 | 6 | no | — |
| 104 | C4×S4 | — | 5 | 6 | no | — |
| 105 | A4⋊Q8 | — | 5 | 1 | no | — |
| 106 | C24×C5 | C22×D3 | 1 | 3 | yes | — |
| 107 | C23×D5 | — | 3 | 6 | no | — |
| 108 | C5×#41 | — | 3 | 1 | no | — |
| 109 | C5×#41 | — | 3 | 3 | no | — |
| 110 | C5×#41 | — | 3 | 3 | no | — |
| 111 | C5×#41 | — | 6 | 1 | no | — |
| 112 | C5×#41 | — | 6 | 3 | no | — |
| 113 | C5×#41 | — | 6 | 3 | no | — |
| 114 | C5×#41 | S4 | 1 | 1 | yes | characteristic, complemented |
| 115 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 116 | C2×C5×Q8 | — | 3 | 3 | no | — |
| 117 | C2×C5×D4 | — | 3 | 3 | no | — |
| 118 | C2×C5×D4 | — | 3 | 6 | no | — |
| 119 | C2×C5×D4 | — | 3 | 3 | no | — |
| 120 | C22×C4×C5 | — | 3 | 3 | no | — |
| 121 | C22×C4×C5 | — | 3 | 3 | no | — |
| 122 | C22×C4×C5 | — | 3 | 3 | no | — |
| 123 | C22×C4×C5 | — | 3 | 3 | no | — |
| 124 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 125 | C22×C4×C5 | C22×D3 | 1 | 3 | yes | — |
| 126 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 127 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 128 | C2×C22⋊D5 | — | 3 | 6 | no | — |
| 129 | C2×C22⋊D5 | — | 3 | 12 | no | — |
| 130 | C2×C22⋊D5 | — | 12 | 6 | no | — |
| 131 | C2×C22⋊D5 | — | 12 | 6 | no | — |
| 132 | C22×Dic5 | — | 3 | 6 | no | — |
| 133 | #713 | — | 6 | 6 | no | — |
| 134 | #713 | — | 6 | 2 | no | — |
| 135 | D4×D5 | — | 6 | 12 | no | — |
| 136 | D4×D5 | — | 6 | 6 | no | — |
| 137 | D4×D5 | — | 6 | 6 | no | — |
| 138 | #709 | — | 6 | 3 | no | — |
| 139 | #709 | — | 6 | 3 | no | — |
| 140 | #709 | — | 6 | 3 | no | — |
| 141 | #709 | — | 6 | 3 | no | — |
| 142 | C2×D20 | — | 3 | 3 | no | — |
| 143 | C2×D20 | — | 3 | 6 | no | — |
| 144 | C2×D20 | — | 6 | 3 | no | — |
| 145 | C2×D20 | — | 6 | 3 | no | — |
| 146 | C2×D20 | — | 6 | 3 | no | — |
| 147 | C2×D20 | — | 6 | 3 | no | — |
| 148 | C2×C4×D5 | — | 3 | 6 | no | — |
| 149 | C2×Dic10 | — | 3 | 1 | no | — |
| 150 | C22⋊Dic5 | — | 3 | 6 | no | — |
| 151 | C22⋊Dic5 | — | 3 | 6 | no | — |
| 152 | C22⋊Dic5 | — | 3 | 2 | no | — |
| 153 | #685 | — | 3 | 6 | no | — |
| 154 | #685 | — | 3 | 12 | no | — |
| 155 | #685 | — | 3 | 6 | no | — |
| 156 | C4⋊Dic5 | — | 3 | 3 | no | — |
| 157 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 158 | C4⋊Dic5 | — | 3 | 6 | no | — |
| 159 | #683 | — | 3 | 2 | no | — |
| 160 | #683 | — | 3 | 6 | no | — |
| 161 | C4×Dic5 | — | 3 | 6 | no | — |
| 162 | C2×H(5,𝔽2) | — | 15 | 1 | no | — |
| 163 | C22×#41 | D15 | 1 | 1 | yes | characteristic, complemented |
| 164 | #550 | — | 15 | 2 | no | — |
| 165 | #548 | — | 15 | 2 | no | — |
| 166 | #546 | — | 15 | 6 | no | — |
| 167 | D42 | — | 15 | 6 | no | — |
| 168 | #537 | — | 15 | 3 | no | — |
| 169 | #535 | — | 15 | 3 | no | — |
| 170 | #525 | — | 15 | 3 | no | — |
| 171 | C2×#121 | — | 15 | 3 | no | — |
| 172 | #520 | — | 15 | 1 | no | — |
| 173 | C22×C3×C5 | — | 4 | 3 | no | — |
| 174 | C2×D15 | — | 4 | 6 | no | — |
| 175 | C2×D15 | — | 16 | 6 | no | — |
| 176 | C5×A4 | H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 177 | C3×C4×C5 | — | 4 | 1 | no | — |
| 178 | C3×C4×C5 | — | 4 | 3 | no | — |
| 179 | Dic15 | — | 4 | 2 | no | — |
| 180 | C22×A4 | C22×D5 | 1 | 3 | yes | — |
| 181 | C2×S4 | — | 5 | 6 | no | — |
| 182 | C2×S4 | — | 20 | 6 | no | — |
| 183 | C3×#41 | — | 4 | 1 | no | — |
| 184 | #239 | — | 20 | 2 | no | — |
| 185 | D3×D4 | — | 20 | 6 | no | — |
| 186 | #235 | — | 20 | 3 | no | — |
| 187 | C2×D12 | — | 20 | 3 | no | — |
| 188 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 189 | C4×A4 | C22×D5 | 1 | 3 | yes | — |
| 190 | SL(2,ℤ/4) | — | 5 | 2 | no | — |
| 191 | C23×C5 | — | 2 | 3 | no | — |
| 192 | C23×C5 | — | 3 | 3 | no | — |
| 193 | C23×C5 | — | 3 | 3 | no | — |
| 194 | C23×C5 | — | 6 | 3 | no | — |
| 195 | C23×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 196 | C22×D5 | — | 3 | 6 | no | — |
| 197 | C22×D5 | — | 6 | 6 | no | — |
| 198 | C22×D5 | — | 6 | 6 | no | — |
| 199 | C22×D5 | — | 12 | 6 | no | — |
| 200 | C22×D5 | — | 12 | 6 | no | — |
| 201 | C5×Q8 | — | 3 | 3 | no | — |
| 202 | C5×Q8 | — | 6 | 1 | no | — |
| 203 | C5×Q8 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 204 | C5×D4 | — | 3 | 6 | no | — |
| 205 | C5×D4 | — | 3 | 3 | no | — |
| 206 | C5×D4 | — | 6 | 3 | no | — |
| 207 | C5×D4 | C2×S4 | 1 | 3 | yes | complemented |
| 208 | C2×C4×C5 | — | 3 | 3 | no | — |
| 209 | C2×C4×C5 | — | 3 | 3 | no | — |
| 210 | C2×C4×C5 | — | 3 | 1 | no | — |
| 211 | C2×C4×C5 | — | 3 | 3 | no | — |
| 212 | C2×C4×C5 | — | 3 | 3 | no | — |
| 213 | C2×C4×C5 | — | 3 | 1 | no | — |
| 214 | C2×C4×C5 | — | 3 | 3 | no | — |
| 215 | C2×C4×C5 | — | 6 | 3 | no | — |
| 216 | C2×C4×C5 | C2×S4 | 1 | 3 | yes | complemented |
| 217 | C22⋊D5 | — | 6 | 6 | no | — |
| 218 | C22⋊D5 | — | 6 | 6 | no | — |
| 219 | C22⋊D5 | — | 6 | 6 | no | — |
| 220 | C22⋊D5 | — | 6 | 6 | no | — |
| 221 | C22⋊D5 | — | 12 | 6 | no | — |
| 222 | C22⋊D5 | — | 12 | 12 | no | — |
| 223 | C2×Dic5 | — | 3 | 2 | no | — |
| 224 | C2×Dic5 | — | 3 | 6 | no | — |
| 225 | C2×Dic5 | — | 3 | 2 | no | — |
| 226 | C2×Dic5 | — | 12 | 6 | no | — |
| 227 | D20 | — | 6 | 3 | no | — |
| 228 | D20 | — | 6 | 6 | no | — |
| 229 | D20 | — | 6 | 3 | no | — |
| 230 | D20 | — | 6 | 6 | no | — |
| 231 | C4×D5 | — | 6 | 6 | no | — |
| 232 | C4×D5 | — | 6 | 6 | no | — |
| 233 | Dic10 | — | 6 | 1 | no | — |
| 234 | Dic10 | — | 6 | 1 | no | — |
| 235 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 236 | H(5,𝔽2) | — | 30 | 3 | no | — |
| 237 | H(5,𝔽2) | — | 30 | 3 | no | — |
| 238 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 239 | C2×#41 | — | 3 | 1 | no | — |
| 240 | C2×#41 | — | 3 | 3 | no | — |
| 241 | C2×#41 | — | 3 | 3 | no | — |
| 242 | C2×#41 | — | 3 | 1 | no | — |
| 243 | C2×#41 | — | 15 | 3 | no | — |
| 244 | C2×#41 | — | 15 | 2 | no | — |
| 245 | C22×Q8 | C2×D15 | 1 | 1 | yes | characteristic, complemented |
| 246 | C22×D4 | — | 15 | 3 | no | — |
| 247 | C22×D4 | — | 15 | 6 | no | — |
| 248 | C22×D4 | — | 15 | 6 | no | — |
| 249 | C22×D4 | C2×D15 | 1 | 3 | yes | complemented |
| 250 | C23×C4 | C2×D15 | 1 | 3 | yes | complemented |
| 251 | #127 | — | 15 | 6 | no | — |
| 252 | #124 | — | 15 | 6 | no | — |
| 253 | #123 | — | 15 | 6 | no | — |
| 254 | C22⋊Q8 | — | 15 | 3 | no | — |
| 255 | C22⋊Q8 | — | 15 | 6 | no | — |
| 256 | C22⋊Q8 | — | 15 | 1 | no | — |
| 257 | #121 | — | 15 | 6 | no | — |
| 258 | #121 | — | 15 | 6 | no | — |
| 259 | #121 | — | 15 | 3 | no | — |
| 260 | #121 | — | 15 | 12 | no | — |
| 261 | #121 | — | 15 | 6 | no | — |
| 262 | #121 | — | 15 | 3 | no | — |
| 263 | #121 | — | 15 | 6 | no | — |
| 264 | #120 | — | 15 | 12 | no | — |
| 265 | #120 | — | 15 | 6 | no | — |
| 266 | C4×Q8 | — | 15 | 2 | no | — |
| 267 | C4×D4 | — | 15 | 6 | no | — |
| 268 | C4×D4 | — | 15 | 6 | no | — |
| 269 | C4×D4 | — | 15 | 6 | no | — |
| 270 | #117 | — | 15 | 3 | no | — |
| 271 | C2×C4⋊C4 | — | 15 | 3 | no | — |
| 272 | C2×C22⋊C4 | — | 15 | 6 | no | — |
| 273 | C2×C3×C5 | — | 4 | 1 | no | — |
| 274 | C2×C3×C5 | — | 8 | 3 | no | — |
| 275 | D15 | — | 8 | 6 | no | — |
| 276 | C22×D3 | — | 20 | 6 | no | — |
| 277 | C2×A4 | — | 2 | 3 | no | — |
| 278 | C2×A4 | C23×D5 | 1 | 1 | yes | characteristic |
| 279 | S4 | — | 10 | 6 | no | — |
| 280 | C3×Q8 | — | 4 | 1 | no | — |
| 281 | C3×D4 | — | 4 | 3 | no | — |
| 282 | C2×C3×C4 | — | 4 | 3 | no | — |
| 283 | #67 | — | 20 | 6 | no | — |
| 284 | D12 | — | 20 | 3 | no | — |
| 285 | D12 | — | 20 | 6 | no | — |
| 286 | C4×D3 | — | 20 | 6 | no | — |
| 287 | Dic6 | — | 20 | 1 | no | — |
| 288 | C22×C5 | — | 3 | 1 | no | — |
| 289 | C22×C5 | — | 3 | 1 | no | — |
| 290 | C22×C5 | — | 3 | 3 | no | — |
| 291 | C22×C5 | — | 6 | 3 | no | — |
| 292 | C22×C5 | — | 6 | 3 | no | — |
| 293 | C22×C5 | — | 6 | 3 | no | — |
| 294 | C22×C5 | — | 6 | 3 | no | — |
| 295 | C22×C5 | #1009 | 1 | 1 | yes | characteristic, complemented |
| 296 | C22×C5 | C22×S4 | 1 | 3 | yes | — |
| 297 | C2×D5 | — | 6 | 6 | no | — |
| 298 | C2×D5 | — | 6 | 6 | no | — |
| 299 | C2×D5 | — | 6 | 6 | no | — |
| 300 | C2×D5 | — | 24 | 6 | no | — |
| 301 | C2×D5 | — | 24 | 6 | no | — |
| 302 | C4×C5 | — | 3 | 1 | no | — |
| 303 | C4×C5 | — | 3 | 3 | no | — |
| 304 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 305 | C4×C5 | C22×S4 | 1 | 3 | yes | — |
| 306 | Dic5 | — | 6 | 6 | no | — |
| 307 | Dic5 | — | 6 | 2 | no | — |
| 308 | Dic5 | — | 6 | 2 | no | — |
| 309 | C24 | — | 15 | 6 | no | — |
| 310 | C24 | C22×D15 | 1 | 3 | yes | — |
| 311 | #41 | — | 3 | 1 | no | — |
| 312 | #41 | — | 3 | 3 | no | — |
| 313 | #41 | — | 3 | 3 | no | — |
| 314 | #41 | — | 6 | 1 | no | — |
| 315 | #41 | — | 6 | 3 | no | — |
| 316 | #41 | — | 6 | 3 | no | — |
| 317 | #41 | — | 30 | 3 | no | — |
| 318 | #41 | — | 30 | 3 | no | — |
| 319 | #41 | — | 30 | 3 | no | — |
| 320 | #41 | — | 30 | 6 | no | — |
| 321 | #41 | — | 30 | 2 | no | — |
| 322 | #41 | — | 30 | 3 | no | — |
| 323 | #41 | C5⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 324 | C2×Q8 | — | 3 | 1 | no | — |
| 325 | C2×Q8 | — | 3 | 3 | no | — |
| 326 | C2×Q8 | — | 15 | 1 | no | — |
| 327 | C2×D4 | — | 3 | 3 | no | — |
| 328 | C2×D4 | — | 3 | 6 | no | — |
| 329 | C2×D4 | — | 3 | 3 | no | — |
| 330 | C2×D4 | — | 15 | 3 | no | — |
| 331 | C2×D4 | — | 15 | 6 | no | — |
| 332 | C2×D4 | — | 15 | 6 | no | — |
| 333 | C2×D4 | — | 15 | 6 | no | — |
| 334 | C2×D4 | — | 15 | 6 | no | — |
| 335 | C2×D4 | — | 15 | 12 | no | — |
| 336 | C2×D4 | — | 30 | 3 | no | — |
| 337 | C2×D4 | — | 30 | 3 | no | — |
| 338 | C2×D4 | — | 30 | 3 | no | — |
| 339 | C2×D4 | — | 30 | 12 | no | — |
| 340 | C2×D4 | — | 30 | 6 | no | — |
| 341 | C2×D4 | — | 30 | 6 | no | — |
| 342 | C2×D4 | — | 30 | 3 | no | — |
| 343 | C2×D4 | — | 60 | 6 | no | — |
| 344 | C2×D4 | — | 60 | 6 | no | — |
| 345 | C22×C4 | — | 3 | 3 | no | — |
| 346 | C22×C4 | — | 3 | 3 | no | — |
| 347 | C22×C4 | — | 3 | 3 | no | — |
| 348 | C22×C4 | — | 3 | 3 | no | — |
| 349 | C22×C4 | — | 15 | 6 | no | — |
| 350 | C22×C4 | — | 15 | 6 | no | — |
| 351 | C22×C4 | C22×D15 | 1 | 3 | yes | — |
| 352 | C22×C4 | C22×D15 | 1 | 1 | yes | characteristic |
| 353 | C4⋊C4 | — | 15 | 3 | no | — |
| 354 | C4⋊C4 | — | 15 | 6 | no | — |
| 355 | C4⋊C4 | — | 15 | 1 | no | — |
| 356 | C4⋊C4 | — | 15 | 2 | no | — |
| 357 | C4⋊C4 | — | 15 | 6 | no | — |
| 358 | C22⋊C4 | — | 15 | 6 | no | — |
| 359 | C22⋊C4 | — | 15 | 12 | no | — |
| 360 | C22⋊C4 | — | 15 | 6 | no | — |
| 361 | C22⋊C4 | — | 15 | 6 | no | — |
| 362 | C22⋊C4 | — | 15 | 6 | no | — |
| 363 | C22⋊C4 | — | 15 | 2 | no | — |
| 364 | C42 | — | 15 | 6 | no | — |
| 365 | C3×C5 | — | 4 | 1 | no | Hall |
| 366 | C22×C3 | — | 4 | 3 | no | — |
| 367 | C2×D3 | — | 20 | 6 | no | — |
| 368 | C2×D3 | — | 80 | 6 | no | — |
| 369 | A4 | #4149 | 1 | 1 | yes | characteristic, complemented |
| 370 | C3×C4 | — | 4 | 1 | no | — |
| 371 | C3×C4 | — | 4 | 3 | no | — |
| 372 | Dic3 | — | 20 | 2 | no | — |
| 373 | C2×C5 | — | 2 | 3 | no | — |
| 374 | C2×C5 | — | 3 | 1 | no | — |
| 375 | C2×C5 | — | 3 | 1 | no | — |
| 376 | C2×C5 | — | 6 | 3 | no | — |
| 377 | C2×C5 | C23×S4 | 1 | 1 | yes | characteristic |
| 378 | D5 | — | 12 | 6 | no | — |
| 379 | C23 | — | 2 | 3 | no | — |
| 380 | C23 | — | 3 | 3 | no | — |
| 381 | C23 | — | 3 | 3 | no | — |
| 382 | C23 | — | 6 | 3 | no | — |
| 383 | C23 | — | 15 | 6 | no | — |
| 384 | C23 | — | 30 | 6 | no | — |
| 385 | C23 | — | 30 | 6 | no | — |
| 386 | C23 | — | 60 | 6 | no | — |
| 387 | C23 | — | 60 | 6 | no | — |
| 388 | C23 | C23×D15 | 1 | 1 | yes | characteristic |
| 389 | Q8 | — | 3 | 3 | no | — |
| 390 | Q8 | — | 6 | 1 | no | — |
| 391 | Q8 | — | 30 | 1 | no | — |
| 392 | Q8 | — | 30 | 1 | no | — |
| 393 | Q8 | C2×C5⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 394 | D4 | — | 3 | 6 | no | — |
| 395 | D4 | — | 3 | 3 | no | — |
| 396 | D4 | — | 6 | 3 | no | — |
| 397 | D4 | — | 30 | 3 | no | — |
| 398 | D4 | — | 30 | 6 | no | — |
| 399 | D4 | — | 30 | 6 | no | — |
| 400 | D4 | — | 30 | 6 | no | — |
| 401 | D4 | — | 30 | 6 | no | — |
| 402 | D4 | — | 30 | 6 | no | — |
| 403 | D4 | — | 30 | 3 | no | — |
| 404 | D4 | — | 30 | 6 | no | — |
| 405 | D4 | — | 60 | 12 | no | — |
| 406 | D4 | — | 60 | 6 | no | — |
| 407 | D4 | C2×C5⋊S4 | 1 | 3 | yes | complemented |
| 408 | C2×C4 | — | 3 | 3 | no | — |
| 409 | C2×C4 | — | 3 | 3 | no | — |
| 410 | C2×C4 | — | 3 | 1 | no | — |
| 411 | C2×C4 | — | 3 | 3 | no | — |
| 412 | C2×C4 | — | 3 | 3 | no | — |
| 413 | C2×C4 | — | 3 | 1 | no | — |
| 414 | C2×C4 | — | 3 | 3 | no | — |
| 415 | C2×C4 | — | 6 | 3 | no | — |
| 416 | C2×C4 | — | 15 | 2 | no | — |
| 417 | C2×C4 | — | 15 | 6 | no | — |
| 418 | C2×C4 | — | 15 | 2 | no | — |
| 419 | C2×C4 | — | 30 | 6 | no | — |
| 420 | C2×C4 | — | 30 | 6 | no | — |
| 421 | C2×C4 | — | 60 | 6 | no | — |
| 422 | C2×C4 | C2×C5⋊S4 | 1 | 3 | yes | complemented |
| 423 | C2×C3 | — | 4 | 1 | no | — |
| 424 | C2×C3 | — | 8 | 3 | no | — |
| 425 | D3 | — | 40 | 6 | no | — |
| 426 | C5 | #87489 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 427 | C22 | — | 3 | 1 | no | — |
| 428 | C22 | — | 3 | 1 | no | — |
| 429 | C22 | — | 3 | 3 | no | — |
| 430 | C22 | — | 6 | 3 | no | — |
| 431 | C22 | — | 6 | 3 | no | — |
| 432 | C22 | — | 6 | 3 | no | — |
| 433 | C22 | — | 6 | 3 | no | — |
| 434 | C22 | — | 30 | 6 | no | — |
| 435 | C22 | — | 30 | 6 | no | — |
| 436 | C22 | — | 30 | 6 | no | — |
| 437 | C22 | — | 120 | 6 | no | — |
| 438 | C22 | — | 120 | 6 | no | — |
| 439 | C22 | #92100 | 1 | 1 | yes | characteristic, complemented |
| 440 | C22 | C22×C5⋊S4 | 1 | 3 | yes | — |
| 441 | C4 | — | 3 | 1 | no | — |
| 442 | C4 | — | 3 | 3 | no | — |
| 443 | C4 | — | 30 | 6 | no | — |
| 444 | C4 | — | 30 | 2 | no | — |
| 445 | C4 | — | 30 | 2 | no | — |
| 446 | C4 | C22×C5⋊S4 | 1 | 1 | yes | characteristic |
| 447 | C4 | C22×C5⋊S4 | 1 | 3 | yes | — |
| 448 | C3 | — | 4 | 1 | no | Sylow |
| 449 | C2 | — | 2 | 3 | no | — |
| 450 | C2 | — | 3 | 1 | no | — |
| 451 | C2 | — | 3 | 1 | no | — |
| 452 | C2 | — | 6 | 3 | no | — |
| 453 | C2 | — | 60 | 6 | no | — |
| 454 | C2 | C23×C5⋊S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×C5⋊S4 |
| commutator, cosocle | C2×C5×A4 | C24 |
| Fitting | C22×C5×#41 | D3 |
| socle | C23×C5 | C23×D3 |
| hypercenter | #41 | C5⋊S4 |
| hypocenter | C5×A4 | H(5,𝔽2) |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| 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. #11756903 | C2 | semidirect |
| 3. D4×C5⋊S4 | C2 | semidirect |
| 4. #11756896 | C2 | semidirect |
| 5. C2×C4⋊(C5⋊S4) | C2 | semidirect |
| 7. C22×C5⋊S4 | C22 | semidirect |
| 9. C5×Q8×A4 | C22 | semidirect |
| 10. C5×D4×A4 | C22 | semidirect |
| 11. C2×C4×C5×A4 | C22 | semidirect |
| 12. #91958 | C22 | semidirect |
| 13. C4⋊(C5⋊S4) | C22 | semidirect |
| 14. C4⋊(C5⋊S4) | C22 | semidirect |
| 15. C4×C5⋊S4 | C22 | semidirect |
| 16. #91948 | C22 | semidirect |
| 18. C22×C5×#41 | D3 | semidirect |
| 40. A4×#41 | D5 | semidirect |
| 49. C22×C5×Q8 | C2×D3 | semidirect |
| 50. C22×C5×D4 | C2×D3 | semidirect |
| 51. C23×C4×C5 | C2×D3 | semidirect |
| 98. Q8×A4 | C2×D5 | semidirect |
| 99. D4×A4 | C2×D5 | semidirect |
| 100. C2×C4×A4 | C2×D5 | semidirect |
| 114. C5×#41 | S4 | semidirect |
| 163. C22×#41 | D15 | semidirect |
| 176. C5×A4 | H(5,𝔽2) | semidirect |
| 203. C5×Q8 | C2×S4 | semidirect |
| 207. C5×D4 | C2×S4 | semidirect |
| 216. C2×C4×C5 | C2×S4 | semidirect |
| 245. C22×Q8 | C2×D15 | semidirect |
| 249. C22×D4 | C2×D15 | semidirect |
| 250. C23×C4 | C2×D15 | semidirect |
| 295. C22×C5 | #1009 | semidirect |
| 323. #41 | C5⋊S4 | semidirect |
| 369. A4 | #4149 | semidirect |
| 393. Q8 | C2×C5⋊S4 | semidirect |
| 407. D4 | C2×C5⋊S4 | semidirect |
| 422. C2×C4 | C2×C5⋊S4 | semidirect |
| 426. C5 | #87489 | semidirect |
| 439. C22 | #92100 | 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 |
| D4×C5⋊S4 | 2 |
| #11756896 | 2 |
| C2×C4⋊(C5⋊S4) | 2 |
| #10619176 | 3 |
| #92100 | 4 |
| #87489 | 5 |