Finite Group DatabasebetaFinite Group DatabasebetaOrder 7200.
660 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 42 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 | A4×C3⋊#1044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×A4⋊#1044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72231060 | — | 3 | 1 | no | maximal |
| 4 | C5⋊D5×C3⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | S4×#1044 | — | 3 | 1 | no | maximal |
| 6 | C3×A4×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 7 | C3⋊(C5⋊(C5⋊S4)) | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C52×C3⋊S4 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | #14268436 | — | 4 | 1 | no | maximal |
| 10 | ΓL(1,𝔽16)⋊S4 | — | 5 | 2 | no | maximal |
| 11 | C22×C3⋊#1044 | D3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×D3×#1044 | — | 3 | 1 | no | — |
| 13 | S4×C5⋊D5 | — | 3 | 1 | no | — |
| 14 | S4×C5⋊D5 | — | 6 | 1 | no | — |
| 15 | A4×#1044 | — | 3 | 1 | no | — |
| 16 | A4⋊#1044 | D3 | 1 | 1 | yes | characteristic, complemented |
| 17 | #67×C5⋊D5 | — | 3 | 1 | no | — |
| 18 | C3×C22⋊#1044 | — | 3 | 1 | no | — |
| 19 | Dic3⋊#1044 | — | 3 | 1 | no | — |
| 20 | (C2×D3)⋊#1044 | — | 3 | 1 | no | — |
| 21 | Dic3×#1044 | — | 3 | 1 | no | — |
| 22 | C3×C52×A4 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3⋊D3×C5⋊D5 | — | 4 | 1 | no | — |
| 24 | C3×C3⋊#1044 | — | 4 | 1 | no | — |
| 25 | C3×C3⋊#1044 | — | 4 | 1 | no | — |
| 26 | D4×#1044 | — | 9 | 1 | no | Hall |
| 27 | D5×C3⋊S4 | — | 5 | 2 | no | — |
| 28 | D5×C3⋊S4 | — | 10 | 2 | no | — |
| 29 | A4×ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 30 | C3×A4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 31 | C22×C3×C5⋊D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 32 | C2×D3×C5⋊D5 | — | 3 | 1 | no | — |
| 33 | C2×C3⋊#1044 | — | 3 | 1 | no | — |
| 34 | C2×C3⋊#1044 | — | 3 | 1 | no | — |
| 35 | C2×C3×#1044 | — | 3 | 1 | no | — |
| 36 | C2×C3×#1044 | — | 3 | 1 | no | — |
| 37 | A4×C5⋊D5 | — | 2 | 1 | no | — |
| 38 | A4×C5⋊D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 39 | C5⋊(C5⋊S4) | — | 3 | 1 | no | — |
| 40 | C5⋊(C5⋊S4) | — | 6 | 1 | no | — |
| 41 | C52×S4 | — | 3 | 1 | no | — |
| 42 | C52×S4 | — | 6 | 1 | no | — |
| 43 | D3×#1044 | — | 6 | 1 | no | — |
| 44 | D3×#1044 | — | 6 | 1 | no | — |
| 45 | D3×#1044 | — | 12 | 1 | no | — |
| 46 | #10597159 | — | 3 | 1 | no | — |
| 47 | C52×#67 | — | 3 | 1 | no | — |
| 48 | #10597115 | — | 3 | 1 | no | — |
| 49 | #10597114 | — | 3 | 1 | no | — |
| 50 | Dic3×C5⋊D5 | — | 3 | 1 | no | — |
| 51 | AGL(1,𝔽5)×S4 | — | 15 | 2 | no | — |
| 52 | #67⋊AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 53 | C3⋊(C3⋊(C5⋊D5)) | — | 4 | 1 | no | — |
| 54 | C52×C3⋊D3 | — | 4 | 1 | no | — |
| 55 | C32×C5⋊D5 | — | 4 | 1 | no | — |
| 56 | C22×#1044 | — | 3 | 1 | no | — |
| 57 | C22×#1044 | — | 9 | 1 | no | — |
| 58 | D4×C5⋊D5 | — | 9 | 1 | no | — |
| 59 | C22⋊#1044 | — | 3 | 1 | no | — |
| 60 | C22⋊#1044 | — | 9 | 1 | no | — |
| 61 | C4⋊#1044 | — | 9 | 1 | no | — |
| 62 | C4×#1044 | — | 9 | 1 | no | — |
| 63 | C3×D5×A4 | — | 5 | 2 | no | — |
| 64 | C3×D5×A4 | — | 10 | 2 | no | — |
| 65 | C3⋊(C5⋊S4) | — | 5 | 2 | no | — |
| 66 | C3⋊(C5⋊S4) | — | 10 | 2 | no | — |
| 67 | C5×C3⋊S4 | — | 2 | 2 | no | — |
| 68 | C5×C3⋊S4 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 69 | ΓL(1,𝔽16)⋊D3 | — | 20 | 2 | no | — |
| 70 | C22×C3×C52 | C4×D3 | 1 | 1 | yes | characteristic, complemented |
| 71 | C2×C3⋊(C5⋊D5) | — | 3 | 1 | no | — |
| 72 | C2×C52×D3 | — | 3 | 1 | no | — |
| 73 | C2×C3×C5⋊D5 | — | 3 | 1 | no | — |
| 74 | C2×C3×C5⋊D5 | — | 3 | 1 | no | — |
| 75 | C52×A4 | — | 2 | 1 | no | — |
| 76 | C52×A4 | C4×D3 | 1 | 1 | yes | characteristic, complemented |
| 77 | D3×C5⋊D5 | — | 6 | 1 | no | — |
| 78 | D3×C5⋊D5 | — | 6 | 1 | no | — |
| 79 | D3×C5⋊D5 | — | 12 | 1 | no | — |
| 80 | D3×C5⋊D5 | — | 24 | 1 | no | — |
| 81 | C3⋊#1044 | — | 3 | 1 | no | — |
| 82 | C3⋊#1044 | — | 4 | 1 | no | — |
| 83 | C3⋊#1044 | S4 | 1 | 1 | yes | characteristic, complemented |
| 84 | C3×#1044 | — | 6 | 1 | no | — |
| 85 | C3×#1044 | — | 6 | 1 | no | — |
| 86 | C3×#1044 | — | 12 | 1 | no | — |
| 87 | C3⋊#1039 | — | 3 | 1 | no | — |
| 88 | C52×Dic3 | — | 3 | 1 | no | — |
| 89 | (C3⋊S4)⋊C4 | — | 25 | 1 | no | Hall |
| 90 | C22×ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 91 | C2×D3×AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 92 | D5×S4 | — | 15 | 2 | no | — |
| 93 | D5×S4 | — | 30 | 2 | no | — |
| 94 | D5×S4 | — | 30 | 2 | no | — |
| 95 | D5×S4 | — | 30 | 4 | no | — |
| 96 | A4×AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 97 | A4⋊AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 98 | D5×#67 | — | 15 | 2 | no | — |
| 99 | D5×#67 | — | 30 | 2 | no | — |
| 100 | C3×C22⋊AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 101 | Dic3⋊AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 102 | (C2×D3)⋊AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 103 | Dic3×AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 104 | C32×C52 | — | 4 | 1 | no | Hall |
| 105 | C22×C5⋊D5 | — | 9 | 1 | no | — |
| 106 | C22×C5⋊D5 | D32 | 1 | 1 | yes | characteristic |
| 107 | C2×#1044 | — | 3 | 1 | no | — |
| 108 | C2×#1044 | — | 3 | 1 | no | — |
| 109 | C2×#1044 | — | 9 | 1 | no | — |
| 110 | C2×#1044 | — | 9 | 1 | no | — |
| 111 | C2×#1044 | — | 18 | 1 | no | — |
| 112 | C2×#1044 | — | 18 | 1 | no | — |
| 113 | C52×D4 | — | 9 | 1 | no | — |
| 114 | C22⋊(C5⋊D5) | — | 9 | 1 | no | — |
| 115 | C22⋊(C5⋊D5) | — | 9 | 1 | no | — |
| 116 | C4⋊(C5⋊D5) | — | 9 | 1 | no | — |
| 117 | C4×C5⋊D5 | — | 9 | 1 | no | — |
| 118 | C3×C5×A4 | — | 2 | 2 | no | — |
| 119 | C3×C5×A4 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 120 | D5×C3⋊D3 | — | 20 | 2 | no | — |
| 121 | D5×C3⋊D3 | — | 40 | 2 | no | — |
| 122 | C3×ΓL(1,𝔽16) | — | 20 | 2 | no | — |
| 123 | C3×ΓL(1,𝔽16) | — | 20 | 2 | no | — |
| 124 | D4×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 125 | C2×C3×C52 | — | 3 | 1 | no | — |
| 126 | C3⋊(C5⋊D5) | — | 6 | 1 | no | — |
| 127 | C3⋊(C5⋊D5) | — | 12 | 1 | no | — |
| 128 | C3⋊(C5⋊D5) | — | 24 | 1 | no | — |
| 129 | C52×D3 | — | 6 | 1 | no | — |
| 130 | C52×D3 | — | 12 | 1 | no | — |
| 131 | C52×D3 | — | 24 | 1 | no | — |
| 132 | C3×C5⋊D5 | — | 3 | 1 | no | — |
| 133 | C3×C5⋊D5 | — | 4 | 1 | no | — |
| 134 | C3×C5⋊D5 | — | 8 | 1 | no | — |
| 135 | C3×C5⋊D5 | C2×S4 | 1 | 1 | yes | characteristic |
| 136 | C2×C3⋊S4 | — | 25 | 1 | no | — |
| 137 | Dic3×A4 | — | 25 | 1 | no | — |
| 138 | C3×SL(2,ℤ/4) | — | 25 | 1 | no | — |
| 139 | C22×C3×D5 | — | 5 | 2 | no | — |
| 140 | C22×C3×D5 | — | 10 | 2 | no | — |
| 141 | C2×D3×D5 | — | 15 | 2 | no | — |
| 142 | C2×D3×D5 | — | 30 | 2 | no | — |
| 143 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 144 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 145 | C2×C3×AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 146 | C2×C3×AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 147 | D5×A4 | — | 5 | 2 | no | — |
| 148 | D5×A4 | — | 10 | 2 | no | — |
| 149 | D5×A4 | — | 10 | 2 | no | — |
| 150 | D5×A4 | — | 10 | 4 | no | — |
| 151 | C5⋊S4 | — | 15 | 2 | no | — |
| 152 | C5⋊S4 | — | 30 | 2 | no | — |
| 153 | C5⋊S4 | — | 30 | 2 | no | — |
| 154 | C5⋊S4 | — | 30 | 4 | no | — |
| 155 | C5×S4 | — | 3 | 2 | no | — |
| 156 | C5×S4 | — | 6 | 2 | no | — |
| 157 | C5×S4 | — | 6 | 2 | no | — |
| 158 | C5×S4 | — | 6 | 4 | no | — |
| 159 | D3×AGL(1,𝔽5) | — | 30 | 2 | no | — |
| 160 | D3×AGL(1,𝔽5) | — | 30 | 2 | no | — |
| 161 | D3×AGL(1,𝔽5) | — | 60 | 2 | no | — |
| 162 | #1220 | — | 15 | 2 | no | — |
| 163 | #1220 | — | 30 | 2 | no | — |
| 164 | C5×#67 | — | 3 | 2 | no | — |
| 165 | C5×#67 | — | 6 | 2 | no | — |
| 166 | #1202 | — | 15 | 2 | no | — |
| 167 | #1202 | — | 30 | 2 | no | — |
| 168 | #1201 | — | 15 | 2 | no | — |
| 169 | #1201 | — | 30 | 2 | no | — |
| 170 | D5×Dic3 | — | 15 | 2 | no | — |
| 171 | D5×Dic3 | — | 30 | 2 | no | — |
| 172 | C22×C52 | — | 9 | 1 | no | — |
| 173 | C22×C52 | #624 | 1 | 1 | yes | characteristic, complemented |
| 174 | C2×C5⋊D5 | — | 3 | 1 | no | — |
| 175 | C2×C5⋊D5 | — | 3 | 1 | no | — |
| 176 | C2×C5⋊D5 | — | 9 | 1 | no | — |
| 177 | C2×C5⋊D5 | — | 18 | 1 | no | — |
| 178 | C2×C5⋊D5 | — | 18 | 1 | no | — |
| 179 | #1044 | — | 3 | 1 | no | — |
| 180 | #1044 | — | 6 | 1 | no | — |
| 181 | #1044 | — | 6 | 1 | no | — |
| 182 | #1044 | — | 9 | 1 | no | — |
| 183 | C4×C52 | — | 9 | 1 | no | — |
| 184 | #1039 | — | 9 | 1 | no | — |
| 185 | C4×S4 | — | 75 | 1 | no | — |
| 186 | #67⋊C4 | — | 75 | 1 | no | — |
| 187 | C3⋊D15 | — | 20 | 2 | no | — |
| 188 | C3⋊D15 | — | 40 | 2 | no | — |
| 189 | C5×C3⋊D3 | — | 4 | 2 | no | — |
| 190 | C5×C3⋊D3 | — | 8 | 2 | no | — |
| 191 | C32×D5 | — | 20 | 2 | no | — |
| 192 | C32×D5 | — | 40 | 2 | no | — |
| 193 | C22×AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 194 | C22×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 195 | D4×D5 | — | 45 | 2 | no | — |
| 196 | D4×D5 | — | 90 | 2 | no | — |
| 197 | C22⋊AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 198 | C22⋊AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 199 | C4⋊AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 200 | C4×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 201 | C3×C52 | — | 4 | 1 | no | — |
| 202 | C3×C52 | — | 8 | 1 | no | — |
| 203 | C3×C52 | C4×S4 | 1 | 1 | yes | characteristic, complemented |
| 204 | C2×C3×A4 | — | 25 | 1 | no | — |
| 205 | C3⋊S4 | — | 25 | 1 | no | — |
| 206 | C3⋊S4 | #1044 | 1 | 1 | yes | characteristic, complemented |
| 207 | #624 | — | 100 | 1 | no | — |
| 208 | C22×C3×C5 | — | 2 | 2 | no | — |
| 209 | C22×C3×C5 | D3×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 210 | C2×D15 | — | 15 | 2 | no | — |
| 211 | C2×D15 | — | 30 | 2 | no | — |
| 212 | C2×C5×D3 | — | 3 | 2 | no | — |
| 213 | C2×C5×D3 | — | 6 | 2 | no | — |
| 214 | C2×C3×D5 | — | 15 | 2 | no | — |
| 215 | C2×C3×D5 | — | 15 | 2 | no | — |
| 216 | C2×C3×D5 | — | 30 | 2 | no | — |
| 217 | C2×C3×D5 | — | 30 | 2 | no | — |
| 218 | C5×A4 | — | 2 | 4 | no | — |
| 219 | C5×A4 | — | 2 | 2 | no | — |
| 220 | C5×A4 | — | 2 | 2 | no | — |
| 221 | C5×A4 | D3×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 222 | D3×D5 | — | 30 | 2 | no | — |
| 223 | D3×D5 | — | 30 | 2 | no | — |
| 224 | D3×D5 | — | 60 | 2 | no | — |
| 225 | D3×D5 | — | 60 | 2 | no | — |
| 226 | D3×D5 | — | 60 | 2 | no | — |
| 227 | D3×D5 | — | 120 | 2 | no | — |
| 228 | D3×D5 | — | 120 | 2 | no | — |
| 229 | D3×D5 | — | 120 | 4 | no | — |
| 230 | ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 231 | ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 232 | ΓL(1,𝔽16) | — | 20 | 2 | no | — |
| 233 | C3×AGL(1,𝔽5) | — | 30 | 2 | no | — |
| 234 | C3×AGL(1,𝔽5) | — | 30 | 2 | no | — |
| 235 | C3×AGL(1,𝔽5) | — | 60 | 2 | no | — |
| 236 | Dic15 | — | 15 | 2 | no | — |
| 237 | Dic15 | — | 30 | 2 | no | — |
| 238 | C5×Dic3 | — | 3 | 2 | no | — |
| 239 | C5×Dic3 | — | 6 | 2 | no | — |
| 240 | C2×C52 | — | 3 | 1 | no | — |
| 241 | C2×C52 | — | 18 | 1 | no | — |
| 242 | C5⋊D5 | — | 3 | 1 | no | — |
| 243 | C5⋊D5 | — | 18 | 1 | no | — |
| 244 | C5⋊D5 | D3×S4 | 1 | 1 | yes | characteristic |
| 245 | C2×S4 | — | 75 | 1 | no | — |
| 246 | C2×S4 | — | 150 | 1 | no | — |
| 247 | C2×#67 | — | 75 | 1 | no | — |
| 248 | C22×Dic3 | — | 25 | 1 | no | — |
| 249 | C2×C4×D3 | — | 75 | 1 | no | — |
| 250 | C4×A4 | — | 75 | 1 | no | — |
| 251 | SL(2,ℤ/4) | — | 25 | 1 | no | — |
| 252 | C3×C22⋊C4 | — | 75 | 1 | no | — |
| 253 | (C2×D3)⋊C4 | — | 75 | 1 | no | — |
| 254 | Dic3⋊C4 | — | 75 | 1 | no | — |
| 255 | C4×Dic3 | — | 75 | 1 | no | — |
| 256 | C32×C5 | — | 4 | 2 | no | — |
| 257 | C32×C5 | — | 8 | 2 | no | — |
| 258 | C22×D5 | — | 5 | 2 | no | — |
| 259 | C22×D5 | — | 10 | 2 | no | — |
| 260 | C22×D5 | — | 45 | 2 | no | — |
| 261 | C22×D5 | — | 90 | 2 | no | — |
| 262 | C2×AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 263 | C2×AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 264 | C2×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 265 | C2×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 266 | C2×AGL(1,𝔽5) | — | 90 | 2 | no | — |
| 267 | C2×AGL(1,𝔽5) | — | 90 | 2 | no | — |
| 268 | C5×D4 | — | 9 | 2 | no | — |
| 269 | C5×D4 | — | 18 | 2 | no | — |
| 270 | C22⋊D5 | — | 45 | 2 | no | — |
| 271 | C22⋊D5 | — | 45 | 2 | no | — |
| 272 | C22⋊D5 | — | 90 | 2 | no | — |
| 273 | C22⋊D5 | — | 90 | 2 | no | — |
| 274 | D20 | — | 45 | 2 | no | — |
| 275 | D20 | — | 90 | 2 | no | — |
| 276 | C4×D5 | — | 45 | 2 | no | — |
| 277 | C4×D5 | — | 90 | 2 | no | — |
| 278 | C2×C3⋊D3 | — | 100 | 1 | no | — |
| 279 | C3×A4 | C2×#1044 | 1 | 1 | yes | characteristic, complemented |
| 280 | C3×Dic3 | — | 100 | 1 | no | — |
| 281 | C3×Dic3 | — | 100 | 1 | no | — |
| 282 | C4×D4 | — | 225 | 1 | no | Sylow |
| 283 | C2×C3×C5 | — | 3 | 2 | no | — |
| 284 | C2×C3×C5 | — | 6 | 2 | no | — |
| 285 | D15 | — | 30 | 2 | no | — |
| 286 | D15 | — | 60 | 2 | no | — |
| 287 | D15 | — | 60 | 2 | no | — |
| 288 | D15 | — | 120 | 2 | no | — |
| 289 | D15 | — | 120 | 2 | no | — |
| 290 | D15 | — | 120 | 4 | no | — |
| 291 | C3×D5 | — | 5 | 2 | no | — |
| 292 | C3×D5 | — | 10 | 2 | no | — |
| 293 | C3×D5 | — | 15 | 2 | no | — |
| 294 | C3×D5 | — | 20 | 2 | no | — |
| 295 | C3×D5 | — | 30 | 2 | no | — |
| 296 | C3×D5 | — | 40 | 2 | no | — |
| 297 | C3×D5 | — | 40 | 2 | no | — |
| 298 | C3×D5 | — | 40 | 4 | no | — |
| 299 | C5×D3 | — | 6 | 2 | no | — |
| 300 | C5×D3 | — | 12 | 2 | no | — |
| 301 | C5×D3 | — | 12 | 2 | no | — |
| 302 | C5×D3 | — | 24 | 2 | no | — |
| 303 | C5×D3 | — | 24 | 2 | no | — |
| 304 | C5×D3 | — | 24 | 4 | no | — |
| 305 | C52 | (C3⋊S4)⋊C4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 306 | C23×C3 | — | 25 | 1 | no | — |
| 307 | C22×D3 | — | 75 | 1 | no | — |
| 308 | C2×A4 | — | 25 | 1 | no | — |
| 309 | C2×A4 | — | 50 | 1 | no | — |
| 310 | S4 | — | 3 | 1 | no | — |
| 311 | S4 | — | 6 | 1 | no | — |
| 312 | S4 | — | 75 | 1 | no | — |
| 313 | S4 | — | 150 | 1 | no | — |
| 314 | C2×C3×C4 | — | 75 | 1 | no | — |
| 315 | C2×C3×C4 | — | 75 | 1 | no | — |
| 316 | #67 | — | 3 | 1 | no | — |
| 317 | #67 | — | 75 | 1 | no | — |
| 318 | #67 | — | 75 | 1 | no | — |
| 319 | #67 | — | 75 | 1 | no | — |
| 320 | C2×Dic3 | — | 75 | 1 | no | — |
| 321 | C2×Dic3 | — | 75 | 1 | no | — |
| 322 | C2×Dic3 | — | 75 | 1 | no | — |
| 323 | C4×D3 | — | 300 | 1 | no | — |
| 324 | C4×D3 | — | 150 | 1 | no | — |
| 325 | C4×D3 | — | 150 | 1 | no | — |
| 326 | C22×C5 | — | 2 | 2 | no | — |
| 327 | C22×C5 | — | 9 | 2 | no | — |
| 328 | C22×C5 | — | 18 | 2 | no | — |
| 329 | C22×C5 | ΓL(1,𝔽16)⋊D3 | 1 | 2 | yes | complemented |
| 330 | C2×D5 | — | 15 | 2 | no | — |
| 331 | C2×D5 | — | 15 | 2 | no | — |
| 332 | C2×D5 | — | 30 | 2 | no | — |
| 333 | C2×D5 | — | 30 | 2 | no | — |
| 334 | C2×D5 | — | 45 | 2 | no | — |
| 335 | C2×D5 | — | 90 | 2 | no | — |
| 336 | C2×D5 | — | 90 | 2 | no | — |
| 337 | C2×D5 | — | 90 | 2 | no | — |
| 338 | C2×D5 | — | 180 | 2 | no | — |
| 339 | C2×D5 | — | 180 | 2 | no | — |
| 340 | AGL(1,𝔽5) | — | 15 | 2 | no | — |
| 341 | AGL(1,𝔽5) | — | 30 | 2 | no | — |
| 342 | AGL(1,𝔽5) | — | 30 | 2 | no | — |
| 343 | AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 344 | C4×C5 | — | 9 | 2 | no | — |
| 345 | C4×C5 | — | 18 | 2 | no | — |
| 346 | Dic5 | — | 45 | 2 | no | — |
| 347 | Dic5 | — | 90 | 2 | no | — |
| 348 | C2×C32 | — | 100 | 1 | no | — |
| 349 | C3⋊D3 | — | 4 | 1 | no | — |
| 350 | C3⋊D3 | — | 100 | 1 | no | — |
| 351 | C2×D4 | — | 225 | 1 | no | — |
| 352 | C22×C4 | — | 75 | 1 | no | — |
| 353 | C22×C4 | — | 225 | 1 | no | — |
| 354 | C4⋊C4 | — | 225 | 1 | no | — |
| 355 | C22⋊C4 | — | 75 | 1 | no | — |
| 356 | C22⋊C4 | — | 225 | 1 | no | — |
| 357 | C42 | — | 225 | 1 | no | — |
| 358 | C3×C5 | — | 2 | 2 | no | — |
| 359 | C3×C5 | — | 4 | 2 | no | — |
| 360 | C3×C5 | — | 8 | 2 | no | — |
| 361 | C3×C5 | — | 8 | 4 | no | — |
| 362 | C3×C5 | — | 8 | 2 | no | — |
| 363 | C3×C5 | AGL(1,𝔽5)×S4 | 1 | 2 | yes | complemented |
| 364 | C22×C3 | — | 75 | 1 | no | — |
| 365 | C22×C3 | — | 75 | 1 | no | — |
| 366 | C22×C3 | D3×#1044 | 1 | 1 | yes | characteristic, complemented |
| 367 | C2×D3 | — | 3 | 1 | no | — |
| 368 | C2×D3 | — | 300 | 1 | no | — |
| 369 | C2×D3 | — | 75 | 1 | no | — |
| 370 | C2×D3 | — | 600 | 1 | no | — |
| 371 | C2×D3 | — | 150 | 1 | no | — |
| 372 | C2×D3 | — | 150 | 1 | no | — |
| 373 | A4 | — | 2 | 1 | no | — |
| 374 | A4 | D3×#1044 | 1 | 1 | yes | characteristic, complemented |
| 375 | C3×C4 | — | 300 | 1 | no | — |
| 376 | C3×C4 | — | 150 | 1 | no | — |
| 377 | C3×C4 | — | 150 | 1 | no | — |
| 378 | Dic3 | — | 3 | 1 | no | — |
| 379 | Dic3 | — | 25 | 1 | no | — |
| 380 | Dic3 | — | 75 | 1 | no | — |
| 381 | Dic3 | — | 75 | 1 | no | — |
| 382 | Dic3 | — | 100 | 1 | no | — |
| 383 | C2×C5 | — | 3 | 2 | no | — |
| 384 | C2×C5 | — | 6 | 2 | no | — |
| 385 | C2×C5 | — | 18 | 2 | no | — |
| 386 | C2×C5 | — | 36 | 2 | no | — |
| 387 | D5 | — | 5 | 2 | no | — |
| 388 | D5 | — | 10 | 2 | no | — |
| 389 | D5 | — | 15 | 2 | no | — |
| 390 | D5 | — | 30 | 2 | no | — |
| 391 | D5 | — | 90 | 2 | no | — |
| 392 | D5 | — | 180 | 2 | no | — |
| 393 | C32 | — | 4 | 1 | no | Sylow |
| 394 | C23 | — | 25 | 1 | no | — |
| 395 | C23 | — | 225 | 1 | no | — |
| 396 | D4 | — | 9 | 1 | no | — |
| 397 | D4 | — | 225 | 1 | no | — |
| 398 | D4 | — | 225 | 1 | no | — |
| 399 | D4 | — | 225 | 1 | no | — |
| 400 | C2×C4 | — | 75 | 1 | no | — |
| 401 | C2×C4 | — | 75 | 1 | no | — |
| 402 | C2×C4 | — | 450 | 1 | no | — |
| 403 | C2×C4 | — | 450 | 1 | no | — |
| 404 | C2×C4 | — | 225 | 1 | no | — |
| 405 | C2×C4 | — | 225 | 1 | no | — |
| 406 | C2×C4 | — | 225 | 1 | no | — |
| 407 | C2×C3 | — | 3 | 1 | no | — |
| 408 | C2×C3 | — | 25 | 1 | no | — |
| 409 | C2×C3 | — | 75 | 1 | no | — |
| 410 | C2×C3 | — | 100 | 1 | no | — |
| 411 | C2×C3 | — | 200 | 1 | no | — |
| 412 | D3 | — | 6 | 1 | no | — |
| 413 | D3 | — | 12 | 1 | no | — |
| 414 | D3 | — | 24 | 1 | no | — |
| 415 | D3 | — | 300 | 1 | no | — |
| 416 | D3 | — | 600 | 1 | no | — |
| 417 | D3 | — | 150 | 1 | no | — |
| 418 | C5 | — | 2 | 2 | no | — |
| 419 | C5 | ΓL(1,𝔽16)⋊S4 | 1 | 2 | yes | complemented |
| 420 | C22 | — | 9 | 1 | no | — |
| 421 | C22 | — | 75 | 1 | no | — |
| 422 | C22 | — | 75 | 1 | no | — |
| 423 | C22 | — | 450 | 1 | no | — |
| 424 | C22 | — | 450 | 1 | no | — |
| 425 | C22 | — | 225 | 1 | no | — |
| 426 | C22 | #14268436 | 1 | 1 | yes | characteristic, complemented |
| 427 | C4 | — | 9 | 1 | no | — |
| 428 | C4 | — | 75 | 1 | no | — |
| 429 | C4 | — | 150 | 1 | no | — |
| 430 | C4 | — | 150 | 1 | no | — |
| 431 | C4 | — | 225 | 1 | no | — |
| 432 | C4 | — | 225 | 1 | no | — |
| 433 | C3 | — | 4 | 1 | no | — |
| 434 | C3 | — | 8 | 1 | no | — |
| 435 | C3 | S4×#1044 | 1 | 1 | yes | characteristic, complemented |
| 436 | C2 | — | 3 | 1 | no | — |
| 437 | C2 | — | 18 | 1 | no | — |
| 438 | C2 | — | 25 | 1 | no | — |
| 439 | C2 | — | 75 | 1 | no | — |
| 440 | C2 | — | 450 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C52×A4 | C2×C4 |
| Fitting, socle | C22×C3×C52 | C4×D3 |
| prime radical | C5⋊D5×C3⋊S4 | C2 |
| cosocle | C3×A4×C5⋊D5 | C22 |
| LCS | G ▷ C3×C52×A4 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×C3⋊#1044 | C2 | semidirect |
| 2. C3×A4⋊#1044 | C2 | semidirect |
| 7. C3⋊(C5⋊(C5⋊S4)) | C4 | semidirect |
| 8. C52×C3⋊S4 | C4 | semidirect |
| 11. C22×C3⋊#1044 | D3 | semidirect |
| 16. A4⋊#1044 | D3 | semidirect |
| 22. C3×C52×A4 | C2×C4 | semidirect |
| 68. C5×C3⋊S4 | AGL(1,𝔽5) | semidirect |
| 70. C22×C3×C52 | C4×D3 | semidirect |
| 76. C52×A4 | C4×D3 | semidirect |
| 83. C3⋊#1044 | S4 | semidirect |
| 119. C3×C5×A4 | C2×AGL(1,𝔽5) | semidirect |
| 173. C22×C52 | #624 | semidirect |
| 203. C3×C52 | C4×S4 | semidirect |
| 206. C3⋊S4 | #1044 | semidirect |
| 209. C22×C3×C5 | D3×AGL(1,𝔽5) | semidirect |
| 221. C5×A4 | D3×AGL(1,𝔽5) | semidirect |
| 279. C3×A4 | C2×#1044 | semidirect |
| 305. C52 | (C3⋊S4)⋊C4 | semidirect |
| 329. C22×C5 | ΓL(1,𝔽16)⋊D3 | semidirect |
| 363. C3×C5 | AGL(1,𝔽5)×S4 | semidirect |
| 366. C22×C3 | D3×#1044 | semidirect |
| 374. A4 | D3×#1044 | semidirect |
| 419. C5 | ΓL(1,𝔽16)⋊S4 | semidirect |
| 426. C22 | #14268436 | semidirect |
| 435. C3 | S4×#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×C3⋊#1044 | 2 |
| C3×A4⋊#1044 | 2 |
| #72231060 | 3 |
| C5⋊D5×C3⋊S4 | 2 |
| S4×#1044 | 3 |
| #14268436 | 4 |
| ΓL(1,𝔽16)⋊S4 | 5 |