Finite Group DatabasebetaFinite Group DatabasebetaOrder 14400.
1286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 1286 conjugacy classes of subgroups — too many to draw. Only its 54 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×D15⋊S4 | — | 4 | 2 | no | maximal |
| 2 | C5×#11756799 | — | 3 | 2 | no | maximal |
| 3 | C5×#91905 | — | 3 | 2 | no | — |
| 4 | C5×#91902 | — | 3 | 2 | no | — |
| 5 | C5×#91901 | — | 3 | 2 | no | — |
| 6 | C2×C5×D5×S4 | — | 3 | 2 | no | — |
| 7 | C5×A4×C5⋊S4 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C5×A4×C22⋊D5 | — | 3 | 2 | no | — |
| 9 | C22×C5×C5⋊S4 | D3 | 1 | 2 | yes | complemented |
| 10 | #72231190 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 11 | C5×S42 | — | 5 | 1 | no | maximal |
| 12 | C52×A4⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C52×GL(2,ℤ/4) | — | 3 | 2 | no | — |
| 14 | C52×A42 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C52×#1020 | — | 6 | 1 | no | — |
| 16 | C5×A4×D15 | — | 4 | 2 | no | — |
| 17 | C52×C3⋊S4 | — | 4 | 2 | no | — |
| 18 | C3×C5×C5⋊S4 | — | 4 | 2 | no | — |
| 19 | C5×#65924 | — | 9 | 1 | no | Hall |
| 20 | C5×A4⋊S4 | — | 2 | 2 | no | — |
| 21 | C5×A4⋊S4 | D5 | 1 | 1 | yes | characteristic, complemented |
| 22 | C5×A4⋊S4 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 23 | A4×C5⋊S4 | C2×C5 | 1 | 2 | yes | complemented |
| 24 | C5×A4×S4 | — | 5 | 2 | no | — |
| 25 | C52×C22⋊A4 | — | 2 | 1 | no | — |
| 26 | C22×C52×A4 | C2×D3 | 1 | 2 | yes | complemented |
| 27 | C2×C5×D5×A4 | — | 3 | 2 | no | — |
| 28 | C2×C5×C5⋊S4 | — | 3 | 2 | no | — |
| 29 | C2×C5×C5⋊S4 | — | 3 | 2 | no | — |
| 30 | C2×C52×S4 | — | 3 | 2 | no | — |
| 31 | C5×D5×S4 | — | 6 | 2 | no | — |
| 32 | C5×D5×S4 | — | 6 | 2 | no | — |
| 33 | C5×#6790 | — | 12 | 2 | no | — |
| 34 | C5×A4×Dic5 | — | 3 | 2 | no | — |
| 35 | C52×SL(2,ℤ/4) | — | 3 | 2 | no | — |
| 36 | C5×D4×S4 | — | 15 | 2 | no | — |
| 37 | #11756799 | — | 3 | 2 | no | — |
| 38 | C3×C52×A4 | — | 4 | 2 | no | — |
| 39 | C5×(C3⋊D3)⋊D5 | — | 16 | 1 | no | — |
| 40 | C22×C5×C22⋊D5 | — | 3 | 2 | no | — |
| 41 | C2×C5×D4×D5 | — | 9 | 2 | no | — |
| 42 | C52×#120 | — | 9 | 1 | no | — |
| 43 | C5×#4086 | — | 9 | 1 | no | — |
| 44 | C5×#4085 | — | 9 | 2 | no | — |
| 45 | C5×#4083 | — | 9 | 1 | no | — |
| 46 | C5×#4030 | — | 9 | 2 | no | — |
| 47 | C5×#4028 | — | 9 | 2 | no | — |
| 48 | C5×#4027 | — | 9 | 2 | no | — |
| 49 | C5×A42 | — | 2 | 2 | no | — |
| 50 | C5×A42 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 51 | C5×A42 | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 52 | D15⋊S4 | — | 4 | 2 | no | — |
| 53 | C5×D3×S4 | — | 20 | 2 | no | — |
| 54 | C22×C5×D15 | — | 4 | 2 | no | — |
| 55 | C2×C52×A4 | — | 3 | 2 | no | — |
| 56 | C2×C5×D3×D5 | — | 12 | 2 | no | — |
| 57 | C5×D5×A4 | — | 6 | 2 | no | — |
| 58 | C5×C5⋊S4 | — | 3 | 2 | no | — |
| 59 | C5×C5⋊S4 | S4 | 1 | 2 | yes | complemented |
| 60 | C52×S4 | — | 6 | 2 | no | — |
| 61 | C52×S4 | — | 24 | 2 | no | — |
| 62 | C52×S4 | — | 24 | 1 | no | — |
| 63 | C52×#67 | — | 12 | 2 | no | — |
| 64 | C3×C5×C22⋊D5 | — | 12 | 2 | no | — |
| 65 | C5×#1203 | — | 12 | 2 | no | — |
| 66 | C5×#1202 | — | 12 | 2 | no | — |
| 67 | C5×#1200 | — | 12 | 2 | no | — |
| 68 | S42 | — | 5 | 1 | no | Hall |
| 69 | C5×#1020 | — | 6 | 1 | no | — |
| 70 | C5×#1020 | — | 6 | 1 | no | — |
| 71 | C5×#1020 | — | 6 | 4 | no | — |
| 72 | C22×C5⋊S4 | C5×D3 | 1 | 2 | yes | complemented |
| 73 | C22×C5×S4 | — | 5 | 2 | no | — |
| 74 | C22×C5×S4 | — | 15 | 2 | no | — |
| 75 | C2×D5×S4 | — | 3 | 2 | no | — |
| 76 | C5×D4×A4 | — | 15 | 2 | no | — |
| 77 | A4×C22⋊D5 | — | 3 | 2 | no | — |
| 78 | C5×GL(2,ℤ/4) | — | 3 | 2 | no | — |
| 79 | C5×GL(2,ℤ/4) | — | 3 | 2 | no | — |
| 80 | C5×GL(2,ℤ/4) | — | 6 | 4 | no | — |
| 81 | C5×GL(2,ℤ/4) | — | 15 | 2 | no | — |
| 82 | C5×C4⋊S4 | — | 15 | 2 | no | — |
| 83 | C4×C5×S4 | — | 15 | 2 | no | — |
| 84 | #91905 | — | 3 | 2 | no | — |
| 85 | #91902 | — | 3 | 2 | no | — |
| 86 | #91901 | — | 3 | 2 | no | — |
| 87 | C52×C3⋊D3 | — | 16 | 1 | no | — |
| 88 | C3×C5×D15 | — | 16 | 2 | no | — |
| 89 | C24×C52 | D32 | 1 | 1 | yes | characteristic, complemented |
| 90 | C23×C5×D5 | — | 3 | 2 | no | — |
| 91 | C23×C5×D5 | — | 9 | 1 | no | — |
| 92 | C2×C52×D4 | — | 9 | 2 | no | — |
| 93 | C2×C52×D4 | — | 9 | 1 | no | — |
| 94 | C2×C5×C22⋊D5 | — | 9 | 2 | no | — |
| 95 | C2×C5×C22⋊D5 | — | 9 | 2 | no | — |
| 96 | C2×C5×C22⋊D5 | — | 9 | 2 | no | — |
| 97 | C2×C5×C22⋊D5 | — | 9 | 2 | no | — |
| 98 | C2×C5×C22⋊D5 | — | 9 | 2 | no | — |
| 99 | C22×C5×Dic5 | — | 3 | 2 | no | — |
| 100 | C5×D4×D5 | — | 18 | 2 | no | — |
| 101 | C5×D4×D5 | — | 18 | 2 | no | — |
| 102 | C5×D4×D5 | — | 18 | 2 | no | — |
| 103 | C5×D4×D5 | — | 18 | 2 | no | — |
| 104 | C2×C5×D20 | — | 9 | 2 | no | — |
| 105 | C2×C5×D20 | — | 9 | 1 | no | — |
| 106 | C2×C4×C5×D5 | — | 9 | 2 | no | — |
| 107 | C52×C22⋊C4 | — | 9 | 2 | no | — |
| 108 | C52×C22⋊C4 | — | 9 | 1 | no | — |
| 109 | C5×C22⋊Dic5 | — | 9 | 1 | no | — |
| 110 | C5×#685 | — | 9 | 2 | no | — |
| 111 | C5×#685 | — | 9 | 2 | no | — |
| 112 | C5×#683 | — | 9 | 2 | no | — |
| 113 | C4×C5×Dic5 | — | 9 | 1 | no | — |
| 114 | A4×D15 | — | 4 | 2 | no | — |
| 115 | C5×D3×A4 | — | 20 | 2 | no | — |
| 116 | C5×C3⋊S4 | — | 4 | 2 | no | — |
| 117 | C5×C3⋊S4 | — | 4 | 2 | no | — |
| 118 | C5×C3⋊S4 | — | 8 | 4 | no | — |
| 119 | C3×C5⋊S4 | — | 4 | 2 | no | — |
| 120 | C3×C5×S4 | — | 20 | 2 | no | — |
| 121 | C5×D42 | — | 45 | 1 | no | — |
| 122 | #65924 | — | 9 | 1 | no | — |
| 123 | C22×C3×C52 | — | 4 | 2 | no | — |
| 124 | C2×C5×D15 | — | 12 | 2 | no | — |
| 125 | C2×C5×D15 | — | 12 | 2 | no | — |
| 126 | C2×C52×D3 | — | 12 | 2 | no | — |
| 127 | C2×C3×C5×D5 | — | 12 | 2 | no | — |
| 128 | C52×A4 | — | 8 | 2 | no | — |
| 129 | C52×A4 | — | 24 | 1 | no | — |
| 130 | C52×A4 | C2×S4 | 1 | 2 | yes | complemented |
| 131 | C5×D3×D5 | — | 24 | 2 | no | — |
| 132 | C5×D3×D5 | — | 24 | 2 | no | — |
| 133 | C52×Dic3 | — | 12 | 2 | no | — |
| 134 | C3×C5×Dic5 | — | 12 | 2 | no | — |
| 135 | A4⋊S4 | C5×D5 | 1 | 1 | yes | characteristic, complemented |
| 136 | A4×S4 | — | 5 | 2 | no | — |
| 137 | C5×C22⋊A4 | — | 2 | 4 | no | — |
| 138 | C5×C22⋊A4 | — | 2 | 1 | no | — |
| 139 | C5×C22⋊A4 | — | 2 | 1 | no | — |
| 140 | C22×C5×A4 | — | 2 | 4 | no | — |
| 141 | C22×C5×A4 | — | 15 | 2 | no | — |
| 142 | C22×C5×A4 | D3×D5 | 1 | 2 | yes | complemented |
| 143 | C22×C5×A4 | C2×C5×D3 | 1 | 2 | yes | complemented |
| 144 | C2×D5×A4 | — | 3 | 2 | no | — |
| 145 | C2×C5⋊S4 | — | 3 | 2 | no | — |
| 146 | C2×C5⋊S4 | — | 3 | 2 | no | — |
| 147 | C2×C5×S4 | — | 3 | 2 | no | — |
| 148 | C2×C5×S4 | — | 3 | 2 | no | — |
| 149 | C2×C5×S4 | — | 6 | 4 | no | — |
| 150 | C2×C5×S4 | — | 15 | 2 | no | — |
| 151 | C2×C5×S4 | — | 15 | 2 | no | — |
| 152 | C2×C5×S4 | — | 30 | 2 | no | — |
| 153 | C2×C5×S4 | — | 30 | 2 | no | — |
| 154 | D5×S4 | — | 6 | 2 | no | — |
| 155 | D5×S4 | — | 6 | 2 | no | — |
| 156 | C5×D3×D4 | — | 60 | 2 | no | — |
| 157 | C4×C5×A4 | — | 15 | 2 | no | — |
| 158 | #6790 | — | 12 | 2 | no | — |
| 159 | A4×Dic5 | — | 3 | 2 | no | — |
| 160 | C5×SL(2,ℤ/4) | — | 3 | 2 | no | — |
| 161 | C5×SL(2,ℤ/4) | — | 3 | 2 | no | — |
| 162 | C5×SL(2,ℤ/4) | — | 6 | 4 | no | — |
| 163 | C32×C52 | — | 16 | 1 | no | Hall |
| 164 | C23×C52 | — | 3 | 2 | no | — |
| 165 | C23×C52 | — | 9 | 1 | no | — |
| 166 | C23×C52 | — | 9 | 1 | no | — |
| 167 | C22×C5×D5 | — | 6 | 2 | no | — |
| 168 | C22×C5×D5 | — | 9 | 2 | no | — |
| 169 | C22×C5×D5 | — | 9 | 2 | no | — |
| 170 | C22×C5×D5 | — | 18 | 2 | no | — |
| 171 | C22×C5×D5 | — | 18 | 2 | no | — |
| 172 | C22×C5×D5 | — | 18 | 2 | no | — |
| 173 | C22×C5×D5 | — | 36 | 1 | no | — |
| 174 | C52×D4 | — | 18 | 2 | no | — |
| 175 | C52×D4 | — | 18 | 2 | no | — |
| 176 | C52×D4 | — | 36 | 1 | no | — |
| 177 | C2×C4×C52 | — | 9 | 2 | no | — |
| 178 | C2×C4×C52 | — | 9 | 1 | no | — |
| 179 | C5×C22⋊D5 | — | 3 | 2 | no | — |
| 180 | C5×C22⋊D5 | — | 9 | 2 | no | — |
| 181 | C5×C22⋊D5 | — | 9 | 2 | no | — |
| 182 | C5×C22⋊D5 | — | 9 | 2 | no | — |
| 183 | C5×C22⋊D5 | — | 18 | 2 | no | — |
| 184 | C5×C22⋊D5 | — | 18 | 2 | no | — |
| 185 | C5×C22⋊D5 | — | 18 | 2 | no | — |
| 186 | C2×C5×Dic5 | — | 9 | 2 | no | — |
| 187 | C2×C5×Dic5 | — | 9 | 2 | no | — |
| 188 | C5×D20 | — | 18 | 2 | no | — |
| 189 | C5×D20 | — | 18 | 2 | no | — |
| 190 | C5×D20 | — | 36 | 1 | no | — |
| 191 | C4×C5×D5 | — | 18 | 2 | no | — |
| 192 | C4×C5×D5 | — | 18 | 2 | no | — |
| 193 | D4×S4 | — | 15 | 2 | no | — |
| 194 | C3×C5×A4 | — | 4 | 2 | no | — |
| 195 | C3×C5×A4 | — | 4 | 2 | no | — |
| 196 | C3×C5×A4 | — | 8 | 4 | no | — |
| 197 | (C3⋊D3)⋊D5 | — | 16 | 1 | no | — |
| 198 | C5×D32 | — | 80 | 1 | no | — |
| 199 | C22×C5×D4 | — | 15 | 2 | no | — |
| 200 | C22×C5×D4 | — | 45 | 2 | no | — |
| 201 | C22×C22⋊D5 | — | 3 | 2 | no | — |
| 202 | C2×D4×D5 | — | 9 | 2 | no | — |
| 203 | C5×#127 | — | 45 | 1 | no | — |
| 204 | C5×#121 | — | 45 | 2 | no | — |
| 205 | C5×#121 | — | 45 | 2 | no | — |
| 206 | C5×#120 | — | 9 | 1 | no | — |
| 207 | C5×#120 | — | 9 | 1 | no | — |
| 208 | C5×#120 | — | 18 | 2 | no | — |
| 209 | C5×#120 | — | 45 | 2 | no | — |
| 210 | C5×#120 | — | 45 | 1 | no | — |
| 211 | C4×C5×D4 | — | 45 | 2 | no | — |
| 212 | #4086 | — | 9 | 1 | no | — |
| 213 | #4085 | — | 9 | 2 | no | — |
| 214 | #4083 | — | 9 | 1 | no | — |
| 215 | #4030 | — | 9 | 2 | no | — |
| 216 | #4028 | — | 9 | 2 | no | — |
| 217 | #4027 | — | 9 | 2 | no | — |
| 218 | C2×C3×C52 | — | 12 | 2 | no | — |
| 219 | C5×D15 | — | 4 | 2 | no | — |
| 220 | C5×D15 | — | 12 | 2 | no | — |
| 221 | C52×D3 | — | 24 | 2 | no | — |
| 222 | C52×D3 | — | 96 | 1 | no | — |
| 223 | C3×C5×D5 | — | 24 | 2 | no | — |
| 224 | A42 | C2×C5×D5 | 1 | 1 | yes | characteristic, complemented |
| 225 | D3×S4 | — | 20 | 2 | no | — |
| 226 | C22×D15 | — | 4 | 2 | no | — |
| 227 | C22×C5×D3 | — | 20 | 2 | no | — |
| 228 | C22×C5×D3 | — | 60 | 2 | no | — |
| 229 | C2×C5×A4 | — | 3 | 2 | no | — |
| 230 | C2×C5×A4 | — | 3 | 2 | no | — |
| 231 | C2×C5×A4 | — | 6 | 4 | no | — |
| 232 | C2×C5×A4 | — | 30 | 2 | no | — |
| 233 | C2×D3×D5 | — | 12 | 2 | no | — |
| 234 | D5×A4 | — | 6 | 2 | no | — |
| 235 | C5⋊S4 | — | 3 | 2 | no | — |
| 236 | C5⋊S4 | C5×S4 | 1 | 2 | yes | complemented |
| 237 | C5×S4 | — | 5 | 2 | no | — |
| 238 | C5×S4 | — | 6 | 2 | no | — |
| 239 | C5×S4 | — | 6 | 2 | no | — |
| 240 | C5×S4 | — | 12 | 4 | no | — |
| 241 | C5×S4 | — | 15 | 2 | no | — |
| 242 | C5×S4 | — | 24 | 2 | no | — |
| 243 | C5×S4 | — | 24 | 2 | no | — |
| 244 | C5×S4 | — | 24 | 8 | no | — |
| 245 | C5×S4 | — | 24 | 1 | no | — |
| 246 | C5×S4 | — | 24 | 1 | no | — |
| 247 | C5×S4 | — | 24 | 4 | no | — |
| 248 | C3×C5×D4 | — | 60 | 2 | no | — |
| 249 | C5×#67 | — | 12 | 2 | no | — |
| 250 | C5×#67 | — | 12 | 2 | no | — |
| 251 | C5×#67 | — | 24 | 4 | no | — |
| 252 | C5×#67 | — | 60 | 2 | no | — |
| 253 | C5×D12 | — | 60 | 2 | no | — |
| 254 | C4×C5×D3 | — | 60 | 2 | no | — |
| 255 | C3×C22⋊D5 | — | 12 | 2 | no | — |
| 256 | #1203 | — | 12 | 2 | no | — |
| 257 | #1202 | — | 12 | 2 | no | — |
| 258 | #1200 | — | 12 | 2 | no | — |
| 259 | C22×C52 | — | 6 | 1 | no | — |
| 260 | C22×C52 | — | 9 | 1 | no | — |
| 261 | C22×C52 | — | 9 | 2 | no | — |
| 262 | C22×C52 | — | 18 | 2 | no | — |
| 263 | C22×C52 | — | 18 | 1 | no | — |
| 264 | C22×C52 | D3×S4 | 1 | 2 | yes | complemented |
| 265 | C2×C5×D5 | — | 3 | 2 | no | — |
| 266 | C2×C5×D5 | — | 9 | 2 | no | — |
| 267 | C2×C5×D5 | — | 18 | 2 | no | — |
| 268 | C2×C5×D5 | — | 18 | 2 | no | — |
| 269 | C2×C5×D5 | — | 18 | 2 | no | — |
| 270 | C2×C5×D5 | — | 18 | 2 | no | — |
| 271 | C2×C5×D5 | — | 36 | 1 | no | — |
| 272 | C2×C5×D5 | — | 36 | 2 | no | — |
| 273 | C2×C5×D5 | — | 36 | 1 | no | — |
| 274 | C4×C52 | — | 18 | 2 | no | — |
| 275 | C4×C52 | — | 18 | 1 | no | — |
| 276 | C5×Dic5 | — | 3 | 2 | no | — |
| 277 | C5×Dic5 | — | 9 | 2 | no | — |
| 278 | #1020 | — | 6 | 1 | no | — |
| 279 | C22×S4 | — | 5 | 2 | no | — |
| 280 | C22×S4 | — | 15 | 2 | no | — |
| 281 | D4×A4 | — | 15 | 2 | no | — |
| 282 | GL(2,ℤ/4) | — | 3 | 2 | no | — |
| 283 | GL(2,ℤ/4) | — | 15 | 2 | no | — |
| 284 | C4⋊S4 | — | 15 | 2 | no | — |
| 285 | C4×S4 | — | 15 | 2 | no | — |
| 286 | C5×C3⋊D3 | — | 16 | 1 | no | — |
| 287 | C5×C3⋊D3 | — | 16 | 1 | no | — |
| 288 | C5×C3⋊D3 | — | 32 | 2 | no | — |
| 289 | C3×D15 | — | 16 | 2 | no | — |
| 290 | C3×C5×D3 | — | 80 | 2 | no | — |
| 291 | C24×C5 | — | 2 | 2 | no | — |
| 292 | C24×C5 | — | 15 | 2 | no | — |
| 293 | C24×C5 | — | 45 | 1 | no | — |
| 294 | C24×C5 | C5×D32 | 1 | 1 | yes | characteristic, complemented |
| 295 | C24×C5 | (C3⋊D3)⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 296 | C23×D5 | — | 3 | 2 | no | — |
| 297 | C23×D5 | — | 9 | 1 | no | — |
| 298 | C2×C5×D4 | — | 9 | 2 | no | — |
| 299 | C2×C5×D4 | — | 9 | 2 | no | — |
| 300 | C2×C5×D4 | — | 9 | 1 | no | — |
| 301 | C2×C5×D4 | — | 9 | 1 | no | — |
| 302 | C2×C5×D4 | — | 18 | 4 | no | — |
| 303 | C2×C5×D4 | — | 18 | 2 | no | — |
| 304 | C2×C5×D4 | — | 45 | 2 | no | — |
| 305 | C2×C5×D4 | — | 45 | 1 | no | — |
| 306 | C2×C5×D4 | — | 45 | 2 | no | — |
| 307 | C2×C5×D4 | — | 45 | 2 | no | — |
| 308 | C2×C5×D4 | — | 45 | 2 | no | — |
| 309 | C2×C5×D4 | — | 45 | 2 | no | — |
| 310 | C2×C5×D4 | — | 45 | 2 | no | — |
| 311 | C2×C5×D4 | — | 90 | 2 | no | — |
| 312 | C2×C5×D4 | — | 90 | 2 | no | — |
| 313 | C2×C5×D4 | — | 90 | 2 | no | — |
| 314 | C2×C5×D4 | — | 90 | 2 | no | — |
| 315 | C22×C4×C5 | — | 15 | 2 | no | — |
| 316 | C22×C4×C5 | — | 45 | 2 | no | — |
| 317 | C2×C22⋊D5 | — | 9 | 2 | no | — |
| 318 | C2×C22⋊D5 | — | 9 | 2 | no | — |
| 319 | C2×C22⋊D5 | — | 9 | 2 | no | — |
| 320 | C2×C22⋊D5 | — | 9 | 2 | no | — |
| 321 | C2×C22⋊D5 | — | 9 | 2 | no | — |
| 322 | C22×Dic5 | — | 3 | 2 | no | — |
| 323 | D4×D5 | — | 18 | 2 | no | — |
| 324 | D4×D5 | — | 18 | 2 | no | — |
| 325 | D4×D5 | — | 18 | 2 | no | — |
| 326 | D4×D5 | — | 18 | 2 | no | — |
| 327 | C2×D20 | — | 9 | 2 | no | — |
| 328 | C2×D20 | — | 9 | 1 | no | — |
| 329 | C2×C4×D5 | — | 9 | 2 | no | — |
| 330 | C5×C4⋊C4 | — | 45 | 2 | no | — |
| 331 | C5×C22⋊C4 | — | 9 | 2 | no | — |
| 332 | C5×C22⋊C4 | — | 9 | 2 | no | — |
| 333 | C5×C22⋊C4 | — | 9 | 1 | no | — |
| 334 | C5×C22⋊C4 | — | 9 | 1 | no | — |
| 335 | C5×C22⋊C4 | — | 18 | 4 | no | — |
| 336 | C5×C22⋊C4 | — | 18 | 2 | no | — |
| 337 | C5×C22⋊C4 | — | 45 | 2 | no | — |
| 338 | C5×C22⋊C4 | — | 45 | 2 | no | — |
| 339 | C5×C22⋊C4 | — | 45 | 1 | no | — |
| 340 | C42×C5 | — | 45 | 1 | no | — |
| 341 | C22⋊Dic5 | — | 9 | 1 | no | — |
| 342 | #685 | — | 9 | 2 | no | — |
| 343 | #685 | — | 9 | 2 | no | — |
| 344 | #683 | — | 9 | 2 | no | — |
| 345 | C4×Dic5 | — | 9 | 1 | no | — |
| 346 | C3×C52 | — | 4 | 2 | no | — |
| 347 | C3×C52 | — | 32 | 1 | no | — |
| 348 | D3×A4 | — | 20 | 2 | no | — |
| 349 | C3⋊S4 | — | 4 | 2 | no | — |
| 350 | C3×S4 | — | 20 | 2 | no | — |
| 351 | D42 | — | 45 | 1 | no | Sylow |
| 352 | C22×C3×C5 | — | 4 | 2 | no | — |
| 353 | C22×C3×C5 | — | 4 | 2 | no | — |
| 354 | C22×C3×C5 | — | 8 | 4 | no | — |
| 355 | C22×C3×C5 | — | 60 | 2 | no | — |
| 356 | C2×D15 | — | 12 | 2 | no | — |
| 357 | C2×D15 | — | 12 | 2 | no | — |
| 358 | C2×C5×D3 | — | 12 | 2 | no | — |
| 359 | C2×C5×D3 | — | 12 | 2 | no | — |
| 360 | C2×C5×D3 | — | 24 | 4 | no | — |
| 361 | C2×C5×D3 | — | 60 | 2 | no | — |
| 362 | C2×C5×D3 | — | 60 | 2 | no | — |
| 363 | C2×C5×D3 | — | 120 | 2 | no | — |
| 364 | C2×C5×D3 | — | 120 | 2 | no | — |
| 365 | C2×C3×D5 | — | 12 | 2 | no | — |
| 366 | C5×A4 | — | 2 | 4 | no | — |
| 367 | C5×A4 | — | 8 | 8 | no | — |
| 368 | C5×A4 | — | 8 | 2 | no | — |
| 369 | C5×A4 | — | 8 | 2 | no | — |
| 370 | C5×A4 | — | 24 | 4 | no | — |
| 371 | C5×A4 | — | 24 | 1 | no | — |
| 372 | C5×A4 | — | 24 | 1 | no | — |
| 373 | C5×A4 | D5×S4 | 1 | 2 | yes | complemented |
| 374 | C5×A4 | C2×C5×S4 | 1 | 2 | yes | complemented |
| 375 | D3×D5 | — | 24 | 2 | no | — |
| 376 | D3×D5 | — | 24 | 2 | no | — |
| 377 | C3×C4×C5 | — | 60 | 2 | no | — |
| 378 | C3×Dic5 | — | 12 | 2 | no | — |
| 379 | C5×Dic3 | — | 12 | 2 | no | — |
| 380 | C5×Dic3 | — | 12 | 2 | no | — |
| 381 | C5×Dic3 | — | 24 | 4 | no | — |
| 382 | C2×C52 | — | 3 | 2 | no | — |
| 383 | C2×C52 | — | 9 | 1 | no | — |
| 384 | C2×C52 | — | 36 | 1 | no | — |
| 385 | C5×D5 | — | 6 | 2 | no | — |
| 386 | C5×D5 | — | 18 | 2 | no | — |
| 387 | C22⋊A4 | — | 2 | 1 | no | — |
| 388 | C22×A4 | — | 15 | 2 | no | — |
| 389 | C22×A4 | C5×D3×D5 | 1 | 2 | yes | complemented |
| 390 | C2×S4 | — | 3 | 2 | no | — |
| 391 | C2×S4 | — | 15 | 2 | no | — |
| 392 | C2×S4 | — | 15 | 2 | no | — |
| 393 | C2×S4 | — | 30 | 2 | no | — |
| 394 | C2×S4 | — | 30 | 2 | no | — |
| 395 | D3×D4 | — | 60 | 2 | no | — |
| 396 | C4×A4 | — | 15 | 2 | no | — |
| 397 | SL(2,ℤ/4) | — | 3 | 2 | no | — |
| 398 | C32×C5 | — | 16 | 1 | no | — |
| 399 | C32×C5 | — | 16 | 1 | no | — |
| 400 | C32×C5 | — | 32 | 2 | no | — |
| 401 | C23×C5 | — | 3 | 2 | no | — |
| 402 | C23×C5 | — | 3 | 2 | no | — |
| 403 | C23×C5 | — | 6 | 4 | no | — |
| 404 | C23×C5 | — | 9 | 1 | no | — |
| 405 | C23×C5 | — | 9 | 1 | no | — |
| 406 | C23×C5 | — | 9 | 1 | no | — |
| 407 | C23×C5 | — | 9 | 1 | no | — |
| 408 | C23×C5 | — | 18 | 2 | no | — |
| 409 | C23×C5 | — | 18 | 2 | no | — |
| 410 | C23×C5 | — | 30 | 2 | no | — |
| 411 | C23×C5 | — | 45 | 2 | no | — |
| 412 | C23×C5 | — | 45 | 2 | no | — |
| 413 | C23×C5 | — | 90 | 2 | no | — |
| 414 | C23×C5 | — | 90 | 2 | no | — |
| 415 | C23×C5 | — | 90 | 2 | no | — |
| 416 | C23×C5 | — | 180 | 1 | no | — |
| 417 | C22×D5 | — | 6 | 2 | no | — |
| 418 | C22×D5 | — | 9 | 2 | no | — |
| 419 | C22×D5 | — | 9 | 2 | no | — |
| 420 | C22×D5 | — | 18 | 2 | no | — |
| 421 | C22×D5 | — | 18 | 2 | no | — |
| 422 | C22×D5 | — | 18 | 2 | no | — |
| 423 | C22×D5 | — | 36 | 1 | no | — |
| 424 | C5×D4 | — | 15 | 2 | no | — |
| 425 | C5×D4 | — | 18 | 2 | no | — |
| 426 | C5×D4 | — | 18 | 2 | no | — |
| 427 | C5×D4 | — | 18 | 2 | no | — |
| 428 | C5×D4 | — | 18 | 2 | no | — |
| 429 | C5×D4 | — | 36 | 4 | no | — |
| 430 | C5×D4 | — | 36 | 4 | no | — |
| 431 | C5×D4 | — | 36 | 1 | no | — |
| 432 | C5×D4 | — | 36 | 1 | no | — |
| 433 | C5×D4 | — | 36 | 4 | no | — |
| 434 | C5×D4 | — | 45 | 2 | no | — |
| 435 | C5×D4 | — | 45 | 2 | no | — |
| 436 | C5×D4 | — | 45 | 2 | no | — |
| 437 | C5×D4 | — | 90 | 2 | no | — |
| 438 | C5×D4 | — | 90 | 2 | no | — |
| 439 | C5×D4 | — | 90 | 2 | no | — |
| 440 | C5×D4 | — | 90 | 2 | no | — |
| 441 | C5×D4 | — | 90 | 2 | no | — |
| 442 | C5×D4 | — | 180 | 1 | no | — |
| 443 | C2×C4×C5 | — | 9 | 1 | no | — |
| 444 | C2×C4×C5 | — | 9 | 2 | no | — |
| 445 | C2×C4×C5 | — | 9 | 1 | no | — |
| 446 | C2×C4×C5 | — | 9 | 2 | no | — |
| 447 | C2×C4×C5 | — | 18 | 2 | no | — |
| 448 | C2×C4×C5 | — | 18 | 4 | no | — |
| 449 | C2×C4×C5 | — | 45 | 2 | no | — |
| 450 | C2×C4×C5 | — | 45 | 2 | no | — |
| 451 | C2×C4×C5 | — | 90 | 2 | no | — |
| 452 | C2×C4×C5 | — | 90 | 2 | no | — |
| 453 | C22⋊D5 | — | 3 | 2 | no | — |
| 454 | C22⋊D5 | — | 9 | 2 | no | — |
| 455 | C22⋊D5 | — | 9 | 2 | no | — |
| 456 | C22⋊D5 | — | 9 | 2 | no | — |
| 457 | C22⋊D5 | — | 18 | 2 | no | — |
| 458 | C22⋊D5 | — | 18 | 2 | no | — |
| 459 | C22⋊D5 | — | 18 | 2 | no | — |
| 460 | C2×Dic5 | — | 9 | 2 | no | — |
| 461 | C2×Dic5 | — | 9 | 2 | no | — |
| 462 | D20 | — | 18 | 2 | no | — |
| 463 | D20 | — | 18 | 2 | no | — |
| 464 | D20 | — | 36 | 1 | no | — |
| 465 | C4×D5 | — | 18 | 2 | no | — |
| 466 | C4×D5 | — | 18 | 2 | no | — |
| 467 | C3×A4 | — | 4 | 2 | no | — |
| 468 | D32 | — | 80 | 1 | no | — |
| 469 | C22×D4 | — | 15 | 2 | no | — |
| 470 | C22×D4 | — | 45 | 2 | no | — |
| 471 | #127 | — | 45 | 1 | no | — |
| 472 | #121 | — | 45 | 2 | no | — |
| 473 | #121 | — | 45 | 2 | no | — |
| 474 | #120 | — | 9 | 1 | no | — |
| 475 | #120 | — | 45 | 2 | no | — |
| 476 | #120 | — | 45 | 1 | no | — |
| 477 | C4×D4 | — | 45 | 2 | no | — |
| 478 | C2×C3×C5 | — | 12 | 2 | no | — |
| 479 | C2×C3×C5 | — | 12 | 2 | no | — |
| 480 | C2×C3×C5 | — | 24 | 4 | no | — |
| 481 | C2×C3×C5 | — | 120 | 2 | no | — |
| 482 | D15 | — | 4 | 2 | no | — |
| 483 | D15 | — | 12 | 2 | no | — |
| 484 | C3×D5 | — | 24 | 2 | no | — |
| 485 | C5×D3 | — | 20 | 2 | no | — |
| 486 | C5×D3 | — | 24 | 2 | no | — |
| 487 | C5×D3 | — | 24 | 2 | no | — |
| 488 | C5×D3 | — | 48 | 4 | no | — |
| 489 | C5×D3 | — | 60 | 2 | no | — |
| 490 | C5×D3 | — | 96 | 1 | no | — |
| 491 | C5×D3 | — | 96 | 1 | no | — |
| 492 | C5×D3 | — | 96 | 4 | no | — |
| 493 | C52 | S42 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 494 | C22×D3 | — | 20 | 2 | no | — |
| 495 | C22×D3 | — | 60 | 2 | no | — |
| 496 | C2×A4 | — | 3 | 2 | no | — |
| 497 | C2×A4 | — | 30 | 2 | no | — |
| 498 | S4 | — | 5 | 2 | no | — |
| 499 | S4 | — | 6 | 2 | no | — |
| 500 | S4 | — | 15 | 2 | no | — |
| 501 | S4 | — | 24 | 2 | no | — |
| 502 | S4 | — | 24 | 1 | no | — |
| 503 | C3×D4 | — | 60 | 2 | no | — |
| 504 | #67 | — | 12 | 2 | no | — |
| 505 | #67 | — | 60 | 2 | no | — |
| 506 | D12 | — | 60 | 2 | no | — |
| 507 | C4×D3 | — | 60 | 2 | no | — |
| 508 | C22×C5 | — | 2 | 4 | no | — |
| 509 | C22×C5 | — | 6 | 1 | no | — |
| 510 | C22×C5 | — | 6 | 1 | no | — |
| 511 | C22×C5 | — | 6 | 4 | no | — |
| 512 | C22×C5 | — | 9 | 1 | no | — |
| 513 | C22×C5 | — | 9 | 1 | no | — |
| 514 | C22×C5 | — | 9 | 2 | no | — |
| 515 | C22×C5 | — | 9 | 2 | no | — |
| 516 | C22×C5 | — | 15 | 2 | no | — |
| 517 | C22×C5 | — | 18 | 2 | no | — |
| 518 | C22×C5 | — | 18 | 4 | no | — |
| 519 | C22×C5 | — | 18 | 2 | no | — |
| 520 | C22×C5 | — | 18 | 2 | no | — |
| 521 | C22×C5 | — | 18 | 1 | no | — |
| 522 | C22×C5 | — | 18 | 1 | no | — |
| 523 | C22×C5 | — | 36 | 4 | no | — |
| 524 | C22×C5 | — | 36 | 2 | no | — |
| 525 | C22×C5 | — | 45 | 2 | no | — |
| 526 | C22×C5 | — | 90 | 2 | no | — |
| 527 | C22×C5 | — | 90 | 2 | no | — |
| 528 | C22×C5 | — | 90 | 2 | no | — |
| 529 | C22×C5 | — | 90 | 2 | no | — |
| 530 | C22×C5 | — | 180 | 1 | no | — |
| 531 | C22×C5 | — | 180 | 2 | no | — |
| 532 | C22×C5 | — | 180 | 1 | no | — |
| 533 | C22×C5 | C5×D3×S4 | 1 | 2 | yes | complemented |
| 534 | C22×C5 | D15⋊S4 | 1 | 2 | yes | complemented |
| 535 | C2×D5 | — | 3 | 2 | no | — |
| 536 | C2×D5 | — | 9 | 2 | no | — |
| 537 | C2×D5 | — | 18 | 2 | no | — |
| 538 | C2×D5 | — | 18 | 2 | no | — |
| 539 | C2×D5 | — | 18 | 2 | no | — |
| 540 | C2×D5 | — | 18 | 2 | no | — |
| 541 | C2×D5 | — | 36 | 1 | no | — |
| 542 | C2×D5 | — | 36 | 2 | no | — |
| 543 | C2×D5 | — | 36 | 1 | no | — |
| 544 | C4×C5 | — | 15 | 2 | no | — |
| 545 | C4×C5 | — | 18 | 2 | no | — |
| 546 | C4×C5 | — | 18 | 2 | no | — |
| 547 | C4×C5 | — | 18 | 1 | no | — |
| 548 | C4×C5 | — | 18 | 1 | no | — |
| 549 | C4×C5 | — | 36 | 4 | no | — |
| 550 | C4×C5 | — | 36 | 2 | no | — |
| 551 | C4×C5 | — | 45 | 2 | no | — |
| 552 | Dic5 | — | 3 | 2 | no | — |
| 553 | Dic5 | — | 9 | 2 | no | — |
| 554 | C3⋊D3 | — | 16 | 1 | no | — |
| 555 | C3×D3 | — | 80 | 2 | no | — |
| 556 | C24 | — | 15 | 2 | no | — |
| 557 | C24 | — | 45 | 1 | no | — |
| 558 | C24 | C5×(C3⋊D3)⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 559 | C2×D4 | — | 9 | 2 | no | — |
| 560 | C2×D4 | — | 9 | 1 | no | — |
| 561 | C2×D4 | — | 45 | 2 | no | — |
| 562 | C2×D4 | — | 45 | 1 | no | — |
| 563 | C2×D4 | — | 45 | 2 | no | — |
| 564 | C2×D4 | — | 45 | 2 | no | — |
| 565 | C2×D4 | — | 45 | 2 | no | — |
| 566 | C2×D4 | — | 45 | 2 | no | — |
| 567 | C2×D4 | — | 45 | 2 | no | — |
| 568 | C2×D4 | — | 90 | 2 | no | — |
| 569 | C2×D4 | — | 90 | 2 | no | — |
| 570 | C2×D4 | — | 90 | 2 | no | — |
| 571 | C2×D4 | — | 90 | 2 | no | — |
| 572 | C22×C4 | — | 15 | 2 | no | — |
| 573 | C22×C4 | — | 45 | 2 | no | — |
| 574 | C4⋊C4 | — | 45 | 2 | no | — |
| 575 | C22⋊C4 | — | 9 | 2 | no | — |
| 576 | C22⋊C4 | — | 9 | 1 | no | — |
| 577 | C22⋊C4 | — | 45 | 2 | no | — |
| 578 | C22⋊C4 | — | 45 | 2 | no | — |
| 579 | C22⋊C4 | — | 45 | 1 | no | — |
| 580 | C42 | — | 45 | 1 | no | — |
| 581 | C3×C5 | — | 4 | 2 | no | — |
| 582 | C3×C5 | — | 4 | 2 | no | — |
| 583 | C3×C5 | — | 8 | 4 | no | — |
| 584 | C3×C5 | — | 32 | 4 | no | — |
| 585 | C3×C5 | — | 32 | 1 | no | — |
| 586 | C3×C5 | — | 32 | 1 | no | — |
| 587 | C22×C3 | — | 4 | 2 | no | — |
| 588 | C22×C3 | — | 60 | 2 | no | — |
| 589 | C2×D3 | — | 12 | 2 | no | — |
| 590 | C2×D3 | — | 60 | 2 | no | — |
| 591 | C2×D3 | — | 60 | 2 | no | — |
| 592 | C2×D3 | — | 120 | 2 | no | — |
| 593 | C2×D3 | — | 120 | 2 | no | — |
| 594 | A4 | — | 8 | 2 | no | — |
| 595 | A4 | — | 24 | 1 | no | — |
| 596 | A4 | C5×D5×S4 | 1 | 2 | yes | complemented |
| 597 | C3×C4 | — | 60 | 2 | no | — |
| 598 | Dic3 | — | 12 | 2 | no | — |
| 599 | C2×C5 | — | 3 | 2 | no | — |
| 600 | C2×C5 | — | 3 | 2 | no | — |
| 601 | C2×C5 | — | 6 | 4 | no | — |
| 602 | C2×C5 | — | 9 | 1 | no | — |
| 603 | C2×C5 | — | 9 | 1 | no | — |
| 604 | C2×C5 | — | 18 | 2 | no | — |
| 605 | C2×C5 | — | 30 | 2 | no | — |
| 606 | C2×C5 | — | 36 | 1 | no | — |
| 607 | C2×C5 | — | 36 | 1 | no | — |
| 608 | C2×C5 | — | 72 | 2 | no | — |
| 609 | C2×C5 | — | 90 | 2 | no | — |
| 610 | D5 | — | 6 | 2 | no | — |
| 611 | D5 | — | 18 | 2 | no | — |
| 612 | C32 | — | 16 | 1 | no | Sylow |
| 613 | C23 | — | 3 | 2 | no | — |
| 614 | C23 | — | 9 | 1 | no | — |
| 615 | C23 | — | 9 | 1 | no | — |
| 616 | C23 | — | 30 | 2 | no | — |
| 617 | C23 | — | 45 | 2 | no | — |
| 618 | C23 | — | 45 | 2 | no | — |
| 619 | C23 | — | 90 | 2 | no | — |
| 620 | C23 | — | 90 | 2 | no | — |
| 621 | C23 | — | 90 | 2 | no | — |
| 622 | C23 | — | 180 | 1 | no | — |
| 623 | D4 | — | 15 | 2 | no | — |
| 624 | D4 | — | 18 | 2 | no | — |
| 625 | D4 | — | 18 | 2 | no | — |
| 626 | D4 | — | 36 | 1 | no | — |
| 627 | D4 | — | 45 | 2 | no | — |
| 628 | D4 | — | 45 | 2 | no | — |
| 629 | D4 | — | 45 | 2 | no | — |
| 630 | D4 | — | 90 | 2 | no | — |
| 631 | D4 | — | 90 | 2 | no | — |
| 632 | D4 | — | 90 | 2 | no | — |
| 633 | D4 | — | 90 | 2 | no | — |
| 634 | D4 | — | 90 | 2 | no | — |
| 635 | D4 | — | 180 | 1 | no | — |
| 636 | C2×C4 | — | 9 | 1 | no | — |
| 637 | C2×C4 | — | 9 | 2 | no | — |
| 638 | C2×C4 | — | 45 | 2 | no | — |
| 639 | C2×C4 | — | 45 | 2 | no | — |
| 640 | C2×C4 | — | 90 | 2 | no | — |
| 641 | C2×C4 | — | 90 | 2 | no | — |
| 642 | C2×C3 | — | 12 | 2 | no | — |
| 643 | C2×C3 | — | 120 | 2 | no | — |
| 644 | D3 | — | 20 | 2 | no | — |
| 645 | D3 | — | 24 | 2 | no | — |
| 646 | D3 | — | 60 | 2 | no | — |
| 647 | D3 | — | 96 | 1 | no | — |
| 648 | C5 | — | 2 | 2 | no | — |
| 649 | C5 | C5×S42 | 1 | 1 | yes | characteristic, complemented |
| 650 | C5 | #72231190 | 1 | 1 | yes | characteristic, direct product factor |
| 651 | C22 | — | 6 | 1 | no | — |
| 652 | C22 | — | 9 | 1 | no | — |
| 653 | C22 | — | 9 | 2 | no | — |
| 654 | C22 | — | 15 | 2 | no | — |
| 655 | C22 | — | 18 | 2 | no | — |
| 656 | C22 | — | 18 | 1 | no | — |
| 657 | C22 | — | 45 | 2 | no | — |
| 658 | C22 | — | 90 | 2 | no | — |
| 659 | C22 | — | 90 | 2 | no | — |
| 660 | C22 | — | 90 | 2 | no | — |
| 661 | C22 | — | 90 | 2 | no | — |
| 662 | C22 | — | 180 | 1 | no | — |
| 663 | C22 | — | 180 | 2 | no | — |
| 664 | C22 | — | 180 | 1 | no | — |
| 665 | C22 | C5×D15⋊S4 | 1 | 2 | yes | complemented |
| 666 | C4 | — | 15 | 2 | no | — |
| 667 | C4 | — | 18 | 2 | no | — |
| 668 | C4 | — | 18 | 1 | no | — |
| 669 | C4 | — | 45 | 2 | no | — |
| 670 | C3 | — | 4 | 2 | no | — |
| 671 | C3 | — | 32 | 1 | no | — |
| 672 | C2 | — | 3 | 2 | no | — |
| 673 | C2 | — | 9 | 1 | no | — |
| 674 | C2 | — | 30 | 2 | no | — |
| 675 | C2 | — | 36 | 1 | no | — |
| 676 | C2 | — | 90 | 2 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #72231190 |
| commutator, cosocle, hypocenter | C5×A42 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C24×C52 | D32 |
| LCS | G ▷ C5×A42 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C5×A4×C5⋊S4 | C2 | semidirect |
| 9. C22×C5×C5⋊S4 | D3 | semidirect |
| 10. #72231190 | C5 | direct (N × H) |
| 12. C52×A4⋊S4 | C2 | semidirect |
| 14. C52×A42 | C22 | semidirect |
| 21. C5×A4⋊S4 | D5 | semidirect |
| 22. C5×A4⋊S4 | C2×C5 | semidirect |
| 23. A4×C5⋊S4 | C2×C5 | semidirect |
| 26. C22×C52×A4 | C2×D3 | semidirect |
| 50. C5×A42 | C2×D5 | semidirect |
| 51. C5×A42 | C22×C5 | semidirect |
| 59. C5×C5⋊S4 | S4 | semidirect |
| 72. C22×C5⋊S4 | C5×D3 | semidirect |
| 89. C24×C52 | D32 | semidirect |
| 130. C52×A4 | C2×S4 | semidirect |
| 135. A4⋊S4 | C5×D5 | semidirect |
| 142. C22×C5×A4 | D3×D5 | semidirect |
| 143. C22×C5×A4 | C2×C5×D3 | semidirect |
| 224. A42 | C2×C5×D5 | semidirect |
| 236. C5⋊S4 | C5×S4 | semidirect |
| 264. C22×C52 | D3×S4 | semidirect |
| 294. C24×C5 | C5×D32 | semidirect |
| 295. C24×C5 | (C3⋊D3)⋊D5 | semidirect |
| 373. C5×A4 | D5×S4 | semidirect |
| 374. C5×A4 | C2×C5×S4 | semidirect |
| 389. C22×A4 | C5×D3×D5 | semidirect |
| 493. C52 | S42 | semidirect |
| 533. C22×C5 | C5×D3×S4 | semidirect |
| 534. C22×C5 | D15⋊S4 | semidirect |
| 558. C24 | C5×(C3⋊D3)⋊D5 | semidirect |
| 596. A4 | C5×D5×S4 | semidirect |
| 649. C5 | C5×S42 | semidirect |
| 650. C5 | #72231190 | direct (N × H) |
| 665. C22 | C5×D15⋊S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D15⋊S4 | 4 |
| C5×#11756799 | 3 |
| C5×A4×C5⋊S4 | 2 |
| #72231190 | 5 |
| C5×S42 | 5 |
| C52×A4⋊S4 | 2 |