← #72230298
Subgroups — #72230298
Order 2880.
1284 conjugacy classes of subgroups.
The subgroup lattice has 562 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D5×#3797 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×ΓL(1,𝔽16)⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | Dic6×ΓL(1,𝔽16) | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3⋊D3×C4⋊AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×ΓL(1,𝔽16)⋊Q8 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13088419 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #13088407 | C2 | 1 | 2 | yes | maximal |
| 8 | AGL(1,𝔽5)×#624 | C2 | 1 | 2 | yes | maximal |
| 9 | D3×Q8×AGL(1,𝔽5) | — | 3 | 2 | no | maximal |
| 10 | C2×ΓL(1,𝔽16)⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×ΓL(1,𝔽16)⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3⋊D3×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 13 | #10624222 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #10624198 | C4 | 1 | 2 | yes | complemented |
| 15 | C5×#3797 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | C4×D5×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×D5×Dic6 | C22 | 1 | 2 | yes | — |
| 18 | C4⋊(C3⋊ΓL(1,𝔽16)) | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×C4×ΓL(1,𝔽16) | C22 | 1 | 2 | yes | — |
| 20 | C32×C4⋊AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 21 | #10624040 | C4 | 1 | 2 | yes | complemented |
| 22 | #10624039 | C4 | 1 | 2 | yes | complemented |
| 23 | D5×#627 | C22 | 1 | 2 | yes | — |
| 24 | D5×#624 | C22 | 1 | 2 | yes | — |
| 25 | ΓL(1,𝔽16)⋊Dic3 | C22 | 1 | 2 | yes | — |
| 26 | Dic3⋊ΓL(1,𝔽16) | C22 | 1 | 4 | yes | — |
| 27 | Dic3×ΓL(1,𝔽16) | C22 | 1 | 4 | yes | — |
| 28 | #10623965 | C22 | 1 | 2 | yes | — |
| 29 | C3×Dic3⋊AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 30 | C3×Dic3×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 31 | #10594363 | — | 5 | 1 | no | maximal, Hall |
| 32 | D3×Q8×D5 | — | 3 | 2 | no | — |
| 33 | Q8×ΓL(1,𝔽16) | — | 3 | 2 | no | — |
| 34 | C3×Q8×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 35 | D3×C4⋊AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 36 | D3×C4⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 37 | D3×C4⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 38 | C4×D3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 39 | C4×D3×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 40 | ΓL(1,𝔽16)⋊Q8 | — | 3 | 4 | no | — |
| 41 | ΓL(1,𝔽16)⋊Q8 | D3 | 1 | 2 | yes | complemented |
| 42 | AGL(1,𝔽5)×Dic6 | — | 3 | 2 | no | — |
| 43 | AGL(1,𝔽5)×Dic6 | — | 3 | 4 | no | — |
| 44 | C2×D5×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×C3⋊ΓL(1,𝔽16) | C23 | 1 | 2 | yes | — |
| 46 | C2×C3×ΓL(1,𝔽16) | C23 | 1 | 2 | yes | — |
| 47 | C2×C3×ΓL(1,𝔽16) | C23 | 1 | 2 | yes | — |
| 48 | C2×C32×AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 49 | ΓL(1,𝔽16)⋊D3 | — | 2 | 2 | no | — |
| 50 | ΓL(1,𝔽16)⋊D3 | Q8 | 1 | 4 | yes | complemented |
| 51 | C3⋊D3×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 52 | C4×C3⋊D15 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C4×C5×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C3×Dic30 | C2×C4 | 1 | 2 | yes | complemented |
| 55 | C3×C5×Dic6 | C2×C4 | 1 | 2 | yes | complemented |
| 56 | C32×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 57 | #67158 | C2×C4 | 1 | 2 | yes | complemented |
| 58 | #67155 | C2×C4 | 1 | 2 | yes | — |
| 59 | #67153 | C2×C4 | 1 | 4 | yes | complemented |
| 60 | #67149 | C2×C4 | 1 | 4 | yes | — |
| 61 | C5×#627 | C2×C4 | 1 | 2 | yes | complemented |
| 62 | C5×#624 | C2×C4 | 1 | 2 | yes | — |
| 63 | #67137 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | C3⋊D3×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | D5×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 66 | C3×#1204 | C2×C4 | 1 | 4 | yes | complemented |
| 67 | C3×D5×Dic3 | C23 | 1 | 4 | yes | — |
| 68 | C2×Q8×AGL(1,𝔽5) | — | 9 | 1 | no | Hall |
| 69 | C2×#3797 | — | 5 | 1 | no | — |
| 70 | C4⋊C4×C3⋊D3 | — | 5 | 1 | no | — |
| 71 | C3×#887 | — | 5 | 2 | no | — |
| 72 | #63883 | — | 5 | 2 | no | — |
| 73 | C4×#624 | — | 5 | 2 | no | — |
| 74 | C4×#624 | — | 5 | 1 | no | — |
| 75 | Dic3×Dic6 | — | 5 | 2 | no | — |
| 76 | #63837 | — | 5 | 4 | no | — |
| 77 | C2×D3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 78 | C2×D3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 79 | C2×D3×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 80 | C2×D3×AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 81 | Q8×D15 | — | 3 | 2 | no | — |
| 82 | C5×D3×Q8 | — | 3 | 2 | no | — |
| 83 | C3×Q8×D5 | — | 3 | 2 | no | — |
| 84 | C4×D3×D5 | — | 3 | 2 | no | — |
| 85 | C4×D3×D5 | — | 3 | 4 | no | — |
| 86 | C4×D3×D5 | — | 6 | 1 | no | — |
| 87 | D15⋊Q8 | — | 3 | 2 | no | — |
| 88 | D15⋊Q8 | — | 3 | 4 | no | — |
| 89 | D3×Dic10 | — | 3 | 2 | no | — |
| 90 | D3×Dic10 | — | 3 | 4 | no | — |
| 91 | D5×Dic6 | — | 3 | 4 | no | — |
| 92 | D5×Dic6 | C2×D3 | 1 | 2 | yes | — |
| 93 | C4⋊ΓL(1,𝔽16) | — | 3 | 4 | no | — |
| 94 | C4⋊ΓL(1,𝔽16) | — | 3 | 2 | no | — |
| 95 | C4⋊ΓL(1,𝔽16) | — | 6 | 1 | no | — |
| 96 | C4×ΓL(1,𝔽16) | — | 3 | 4 | no | — |
| 97 | C4×ΓL(1,𝔽16) | C2×D3 | 1 | 2 | yes | — |
| 98 | C3×C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 99 | C3×C4⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 100 | C3×C4⋊AGL(1,𝔽5) | C2×D3 | 1 | 2 | yes | — |
| 101 | C3×C4×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 102 | C3×C4×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 103 | Dic3⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 104 | Dic3⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 105 | Dic3⋊AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 106 | Dic3⋊AGL(1,𝔽5) | C2×D3 | 1 | 4 | yes | — |
| 107 | Dic3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 108 | Dic3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 109 | Dic3×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 110 | Dic3×AGL(1,𝔽5) | C2×D3 | 1 | 4 | yes | — |
| 111 | C4×D3×Q8 | — | 15 | 2 | no | — |
| 112 | C2×C3⋊D15 | C22×C4 | 1 | 1 | yes | characteristic |
| 113 | C2×C5×C3⋊D3 | C22×C4 | 1 | 1 | yes | characteristic |
| 114 | C2×C32×D5 | C24 | 1 | 1 | yes | characteristic |
| 115 | D5×C3⋊D3 | C2×Q8 | 1 | 2 | yes | — |
| 116 | D5×C3⋊D3 | #41 | 1 | 2 | yes | — |
| 117 | C3⋊ΓL(1,𝔽16) | — | 2 | 2 | no | — |
| 118 | C3×ΓL(1,𝔽16) | — | 2 | 2 | no | — |
| 119 | C3×ΓL(1,𝔽16) | C2×Q8 | 1 | 4 | yes | complemented |
| 120 | C32×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 121 | C32×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 122 | C3⋊Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C5×C3⋊Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 124 | C3×Dic15 | C22×C4 | 1 | 4 | yes | — |
| 125 | C3×C5×Dic3 | C22×C4 | 1 | 4 | yes | — |
| 126 | C32×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 127 | C2×Q8×D5 | — | 9 | 1 | no | — |
| 128 | Q8×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 129 | Q8×AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 130 | Q8×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 131 | C2×C4⋊AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 132 | C2×C4⋊AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 133 | C2×C4×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 134 | C2×C4×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 135 | C2×C4×C3⋊D3 | — | 5 | 1 | no | — |
| 136 | C2×C4×C3⋊D3 | — | 5 | 2 | no | — |
| 137 | C2×C3×Dic6 | — | 5 | 2 | no | — |
| 138 | C2×#627 | — | 5 | 2 | no | — |
| 139 | C2×#624 | — | 5 | 1 | no | — |
| 140 | C2×#624 | — | 5 | 2 | no | — |
| 141 | C2×#624 | — | 5 | 1 | no | — |
| 142 | #3797 | — | 5 | 1 | no | — |
| 143 | #3797 | — | 5 | 2 | no | — |
| 144 | #3797 | — | 5 | 2 | no | — |
| 145 | #3797 | — | 5 | 2 | no | — |
| 146 | #3797 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 147 | C32×C4⋊C4 | — | 5 | 1 | no | — |
| 148 | C4⋊(C3⋊Dic3) | — | 5 | 1 | no | — |
| 149 | #3750 | — | 5 | 2 | no | — |
| 150 | C3×Dic3⋊C4 | — | 5 | 4 | no | — |
| 151 | C3×C4×Dic3 | — | 5 | 2 | no | — |
| 152 | C3×C4×Dic3 | — | 5 | 4 | no | — |
| 153 | Dic3⋊Dic3 | — | 5 | 4 | no | — |
| 154 | Dic32 | — | 5 | 2 | no | — |
| 155 | Dic32 | — | 5 | 4 | no | — |
| 156 | C2×D3×D5 | — | 3 | 2 | no | — |
| 157 | C2×D3×D5 | — | 6 | 1 | no | — |
| 158 | C2×ΓL(1,𝔽16) | — | 3 | 4 | no | — |
| 159 | C2×ΓL(1,𝔽16) | — | 6 | 2 | no | — |
| 160 | C2×ΓL(1,𝔽16) | C22×D3 | 1 | 2 | yes | — |
| 161 | C2×ΓL(1,𝔽16) | C22×D3 | 1 | 2 | yes | — |
| 162 | C2×C3×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 163 | C2×C3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 164 | C2×C3×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 165 | C2×C3×AGL(1,𝔽5) | C22×D3 | 1 | 4 | yes | — |
| 166 | D3×AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 167 | D3×AGL(1,𝔽5) | — | 6 | 8 | no | — |
| 168 | D3×AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 169 | D3×AGL(1,𝔽5) | — | 12 | 4 | no | — |
| 170 | C3×C5×Q8 | — | 3 | 2 | no | — |
| 171 | C4×D15 | — | 3 | 2 | no | — |
| 172 | C4×D15 | — | 3 | 4 | no | — |
| 173 | C4×D15 | — | 6 | 1 | no | — |
| 174 | Dic30 | — | 3 | 4 | no | — |
| 175 | Dic30 | C4×D3 | 1 | 2 | yes | complemented |
| 176 | C4×C5×D3 | — | 3 | 2 | no | — |
| 177 | C4×C5×D3 | — | 3 | 4 | no | — |
| 178 | C4×C5×D3 | — | 6 | 1 | no | — |
| 179 | C5×Dic6 | — | 3 | 4 | no | — |
| 180 | C5×Dic6 | C4×D3 | 1 | 2 | yes | complemented |
| 181 | C3×C4×D5 | — | 2 | 1 | no | — |
| 182 | C3×C4×D5 | — | 3 | 4 | no | — |
| 183 | C3×C4×D5 | C22×D3 | 1 | 2 | yes | — |
| 184 | C3×Dic10 | — | 3 | 2 | no | — |
| 185 | C3×Dic10 | — | 3 | 4 | no | — |
| 186 | #1204 | — | 3 | 4 | no | — |
| 187 | #1204 | — | 3 | 4 | no | — |
| 188 | #1204 | C4×D3 | 1 | 4 | yes | complemented |
| 189 | #1200 | — | 3 | 2 | no | — |
| 190 | #1200 | — | 3 | 4 | no | — |
| 191 | #1200 | — | 6 | 1 | no | — |
| 192 | D3×Dic5 | — | 3 | 4 | no | — |
| 193 | D3×Dic5 | — | 3 | 2 | no | — |
| 194 | D3×Dic5 | — | 6 | 1 | no | — |
| 195 | D5×Dic3 | — | 3 | 2 | no | — |
| 196 | D5×Dic3 | — | 6 | 1 | no | — |
| 197 | D5×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 198 | C2×D3×Q8 | — | 15 | 2 | no | — |
| 199 | C3×C4×Q8 | — | 15 | 2 | no | — |
| 200 | Q8×Dic3 | — | 15 | 2 | no | — |
| 201 | D3×C4⋊C4 | — | 15 | 4 | no | — |
| 202 | D3×C4⋊C4 | — | 15 | 2 | no | — |
| 203 | D3×C4⋊C4 | — | 30 | 1 | no | — |
| 204 | #887 | — | 5 | 2 | no | — |
| 205 | #887 | — | 15 | 4 | no | — |
| 206 | C42×D3 | — | 15 | 4 | no | — |
| 207 | C42×D3 | — | 15 | 2 | no | — |
| 208 | C4×Dic6 | — | 15 | 4 | no | — |
| 209 | C4×Dic6 | — | 15 | 2 | no | — |
| 210 | C2×C32×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 211 | C3⋊D15 | C4×Q8 | 1 | 2 | yes | complemented |
| 212 | C5×C3⋊D3 | C4×Q8 | 1 | 2 | yes | complemented |
| 213 | C32×D5 | C22×Q8 | 1 | 1 | yes | characteristic |
| 214 | C32×D5 | C2×#41 | 1 | 1 | yes | characteristic |
| 215 | C22×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 216 | C22×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 217 | C22×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 218 | C2×C5×Q8 | — | 9 | 1 | no | — |
| 219 | Q8×D5 | — | 3 | 2 | no | — |
| 220 | Q8×D5 | — | 9 | 2 | no | — |
| 221 | Q8×D5 | — | 9 | 2 | no | — |
| 222 | Q8×D5 | — | 9 | 2 | no | — |
| 223 | C2×C4×D5 | — | 9 | 2 | no | — |
| 224 | C2×C4×D5 | — | 9 | 1 | no | — |
| 225 | C2×Dic10 | — | 9 | 1 | no | — |
| 226 | C2×Dic10 | — | 9 | 2 | no | — |
| 227 | C4⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 228 | C4⋊AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 229 | C4⋊AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 230 | C4⋊AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 231 | C4⋊AGL(1,𝔽5) | D32 | 1 | 1 | yes | characteristic |
| 232 | C4×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 233 | C4×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 234 | C4×AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 235 | C4×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 236 | C22×C3⋊D3 | — | 5 | 1 | no | — |
| 237 | C2×C32×C4 | — | 5 | 1 | no | — |
| 238 | C2×C32×C4 | — | 5 | 2 | no | — |
| 239 | C2×C3⋊Dic3 | — | 5 | 1 | no | — |
| 240 | C2×C3⋊Dic3 | — | 5 | 2 | no | — |
| 241 | C4×C3⋊D3 | — | 5 | 1 | no | — |
| 242 | C4×C3⋊D3 | — | 5 | 1 | no | — |
| 243 | C4×C3⋊D3 | — | 5 | 1 | no | — |
| 244 | C4×C3⋊D3 | — | 10 | 4 | no | — |
| 245 | C4×C3⋊D3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 246 | C2×C3×Dic3 | — | 5 | 2 | no | — |
| 247 | C2×C3×Dic3 | — | 5 | 4 | no | — |
| 248 | C2×C3×Dic3 | — | 5 | 2 | no | — |
| 249 | C3×Dic6 | — | 5 | 2 | no | — |
| 250 | C3×Dic6 | — | 5 | 4 | no | — |
| 251 | C3×Dic6 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 252 | #627 | — | 5 | 2 | no | — |
| 253 | #627 | — | 5 | 4 | no | — |
| 254 | #627 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 255 | #624 | — | 5 | 4 | no | — |
| 256 | #624 | — | 5 | 2 | no | — |
| 257 | #624 | — | 5 | 4 | no | — |
| 258 | #624 | — | 10 | 2 | no | — |
| 259 | #624 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 260 | C2×C4×Q8 | — | 45 | 1 | no | Sylow |
| 261 | C2×D15 | — | 3 | 2 | no | — |
| 262 | C2×D15 | — | 6 | 1 | no | — |
| 263 | C2×C5×D3 | — | 3 | 2 | no | — |
| 264 | C2×C5×D3 | — | 6 | 1 | no | — |
| 265 | C2×C3×D5 | — | 2 | 1 | no | — |
| 266 | C2×C3×D5 | C23×D3 | 1 | 2 | yes | — |
| 267 | D3×D5 | — | 3 | 4 | no | — |
| 268 | D3×D5 | — | 3 | 4 | no | — |
| 269 | D3×D5 | — | 6 | 2 | no | — |
| 270 | D3×D5 | — | 6 | 2 | no | — |
| 271 | ΓL(1,𝔽16) | — | 2 | 2 | no | — |
| 272 | ΓL(1,𝔽16) | — | 6 | 4 | no | — |
| 273 | ΓL(1,𝔽16) | — | 12 | 2 | no | — |
| 274 | ΓL(1,𝔽16) | D3×Q8 | 1 | 4 | yes | complemented |
| 275 | C3×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 276 | C3×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 277 | C3×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 278 | C3×AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 279 | C3×C4×C5 | — | 2 | 1 | no | — |
| 280 | C3×C4×C5 | — | 3 | 4 | no | — |
| 281 | C3×C4×C5 | C2×C4×D3 | 1 | 2 | yes | — |
| 282 | Dic15 | — | 3 | 2 | no | — |
| 283 | Dic15 | — | 6 | 1 | no | — |
| 284 | Dic15 | C2×C4×D3 | 1 | 4 | yes | — |
| 285 | C3×Dic5 | — | 2 | 1 | no | — |
| 286 | C3×Dic5 | — | 3 | 4 | no | — |
| 287 | C3×Dic5 | C2×C4×D3 | 1 | 2 | yes | — |
| 288 | C5×Dic3 | — | 3 | 2 | no | — |
| 289 | C5×Dic3 | — | 6 | 1 | no | — |
| 290 | C5×Dic3 | C2×C4×D3 | 1 | 4 | yes | — |
| 291 | C2×C3×Q8 | — | 15 | 2 | no | — |
| 292 | D3×Q8 | — | 3 | 2 | no | — |
| 293 | D3×Q8 | — | 15 | 4 | no | — |
| 294 | D3×Q8 | — | 15 | 2 | no | — |
| 295 | D3×Q8 | — | 15 | 4 | no | — |
| 296 | D3×Q8 | — | 15 | 2 | no | — |
| 297 | D3×Q8 | — | 15 | 2 | no | — |
| 298 | C2×C4×D3 | — | 15 | 4 | no | — |
| 299 | C2×C4×D3 | — | 15 | 2 | no | — |
| 300 | C2×C4×D3 | — | 15 | 2 | no | — |
| 301 | C2×C4×D3 | — | 15 | 2 | no | — |
| 302 | C2×C4×D3 | — | 15 | 4 | no | — |
| 303 | C2×C4×D3 | — | 30 | 1 | no | — |
| 304 | C2×C4×D3 | — | 30 | 2 | no | — |
| 305 | C2×Dic6 | — | 5 | 2 | no | — |
| 306 | C2×Dic6 | — | 15 | 4 | no | — |
| 307 | C3×C4⋊C4 | — | 5 | 2 | no | — |
| 308 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 309 | C3×C4⋊C4 | — | 15 | 4 | no | — |
| 310 | C3×C42 | — | 15 | 2 | no | — |
| 311 | C3×C42 | — | 15 | 4 | no | — |
| 312 | C4⋊Dic3 | — | 15 | 4 | no | — |
| 313 | C4⋊Dic3 | — | 15 | 2 | no | — |
| 314 | C4⋊Dic3 | — | 30 | 1 | no | — |
| 315 | Dic3⋊C4 | — | 5 | 4 | no | — |
| 316 | Dic3⋊C4 | — | 15 | 4 | no | — |
| 317 | Dic3⋊C4 | — | 15 | 4 | no | — |
| 318 | Dic3⋊C4 | — | 30 | 2 | no | — |
| 319 | C4×Dic3 | — | 5 | 4 | no | — |
| 320 | C4×Dic3 | — | 5 | 2 | no | — |
| 321 | C4×Dic3 | — | 15 | 4 | no | — |
| 322 | C4×Dic3 | — | 15 | 2 | no | — |
| 323 | C4×Dic3 | — | 15 | 2 | no | — |
| 324 | C4×Dic3 | — | 15 | 4 | no | — |
| 325 | C32×C5 | C2×C4×Q8 | 1 | 1 | yes | characteristic, complemented, Hall |
| 326 | C22×D5 | — | 9 | 1 | no | — |
| 327 | C2×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 328 | C2×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 329 | C2×AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 330 | C2×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 331 | C2×AGL(1,𝔽5) | — | 18 | 4 | no | — |
| 332 | C2×AGL(1,𝔽5) | — | 18 | 2 | no | — |
| 333 | C2×AGL(1,𝔽5) | C2×D32 | 1 | 2 | yes | — |
| 334 | C5×Q8 | — | 3 | 2 | no | — |
| 335 | C5×Q8 | — | 9 | 2 | no | — |
| 336 | C2×C4×C5 | — | 9 | 2 | no | — |
| 337 | C2×C4×C5 | — | 9 | 1 | no | — |
| 338 | C2×Dic5 | — | 9 | 2 | no | — |
| 339 | C2×Dic5 | — | 9 | 1 | no | — |
| 340 | C4×D5 | — | 3 | 4 | no | — |
| 341 | C4×D5 | — | 9 | 4 | no | — |
| 342 | C4×D5 | — | 9 | 1 | no | — |
| 343 | C4×D5 | — | 9 | 1 | no | — |
| 344 | C4×D5 | — | 9 | 1 | no | — |
| 345 | C4×D5 | C2×D32 | 1 | 1 | yes | characteristic |
| 346 | Dic10 | — | 3 | 2 | no | — |
| 347 | Dic10 | — | 3 | 4 | no | — |
| 348 | Dic10 | — | 9 | 2 | no | — |
| 349 | Dic10 | — | 9 | 4 | no | — |
| 350 | C22×C32 | — | 5 | 1 | no | — |
| 351 | C2×C3⋊D3 | — | 5 | 1 | no | — |
| 352 | C2×C3⋊D3 | — | 5 | 2 | no | — |
| 353 | C2×C3⋊D3 | — | 5 | 2 | no | — |
| 354 | C2×C3⋊D3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 355 | C32×C4 | — | 5 | 1 | no | — |
| 356 | C32×C4 | — | 10 | 2 | no | — |
| 357 | C32×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 358 | C3⋊Dic3 | — | 5 | 1 | no | — |
| 359 | C3⋊Dic3 | — | 10 | 2 | no | — |
| 360 | C3⋊Dic3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 361 | C3×Dic3 | — | 5 | 4 | no | — |
| 362 | C3×Dic3 | — | 5 | 4 | no | — |
| 363 | C3×Dic3 | — | 10 | 2 | no | — |
| 364 | C3×Dic3 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 365 | C22×Q8 | — | 45 | 1 | no | — |
| 366 | C4×Q8 | — | 15 | 2 | no | — |
| 367 | C4×Q8 | — | 45 | 4 | no | — |
| 368 | C4×Q8 | — | 45 | 2 | no | — |
| 369 | C2×C4⋊C4 | — | 45 | 1 | no | — |
| 370 | C2×C4⋊C4 | — | 45 | 2 | no | — |
| 371 | C2×C42 | — | 45 | 1 | no | — |
| 372 | C2×C42 | — | 45 | 2 | no | — |
| 373 | C2×C3×C5 | — | 2 | 1 | no | — |
| 374 | C2×C3×C5 | C22×C4×D3 | 1 | 2 | yes | — |
| 375 | D15 | — | 3 | 4 | no | — |
| 376 | D15 | — | 6 | 2 | no | — |
| 377 | C3×D5 | — | 2 | 1 | no | — |
| 378 | C3×D5 | — | 2 | 1 | no | — |
| 379 | C3×D5 | C2×D3×Q8 | 1 | 2 | yes | — |
| 380 | C3×D5 | D3×#41 | 1 | 2 | yes | — |
| 381 | C5×D3 | — | 3 | 4 | no | — |
| 382 | C5×D3 | — | 6 | 2 | no | — |
| 383 | C22×D3 | — | 15 | 2 | no | — |
| 384 | C22×D3 | — | 30 | 1 | no | — |
| 385 | C3×Q8 | — | 3 | 2 | no | — |
| 386 | C3×Q8 | — | 15 | 4 | no | — |
| 387 | C3×Q8 | — | 15 | 2 | no | — |
| 388 | C2×C3×C4 | — | 5 | 2 | no | — |
| 389 | C2×C3×C4 | — | 5 | 4 | no | — |
| 390 | C2×C3×C4 | — | 10 | 1 | no | — |
| 391 | C2×C3×C4 | — | 10 | 2 | no | — |
| 392 | C2×C3×C4 | — | 15 | 4 | no | — |
| 393 | C2×C3×C4 | — | 15 | 2 | no | — |
| 394 | C2×C3×C4 | — | 15 | 2 | no | — |
| 395 | C2×Dic3 | — | 5 | 2 | no | — |
| 396 | C2×Dic3 | — | 5 | 4 | no | — |
| 397 | C2×Dic3 | — | 5 | 2 | no | — |
| 398 | C2×Dic3 | — | 15 | 2 | no | — |
| 399 | C2×Dic3 | — | 15 | 4 | no | — |
| 400 | C2×Dic3 | — | 30 | 1 | no | — |
| 401 | C2×Dic3 | — | 30 | 2 | no | — |
| 402 | C4×D3 | — | 3 | 2 | no | — |
| 403 | C4×D3 | — | 3 | 4 | no | — |
| 404 | C4×D3 | — | 6 | 1 | no | — |
| 405 | C4×D3 | — | 15 | 2 | no | — |
| 406 | C4×D3 | — | 15 | 4 | no | — |
| 407 | C4×D3 | — | 15 | 4 | no | — |
| 408 | C4×D3 | — | 15 | 8 | no | — |
| 409 | C4×D3 | — | 15 | 2 | no | — |
| 410 | C4×D3 | — | 15 | 2 | no | — |
| 411 | C4×D3 | — | 15 | 4 | no | — |
| 412 | C4×D3 | — | 30 | 1 | no | — |
| 413 | C4×D3 | — | 30 | 1 | no | — |
| 414 | C4×D3 | — | 30 | 1 | no | — |
| 415 | C4×D3 | — | 30 | 4 | no | — |
| 416 | C4×D3 | — | 30 | 8 | no | — |
| 417 | C4×D3 | — | 60 | 4 | no | — |
| 418 | Dic6 | — | 3 | 4 | no | — |
| 419 | Dic6 | — | 5 | 2 | no | — |
| 420 | Dic6 | — | 5 | 4 | no | — |
| 421 | Dic6 | — | 15 | 4 | no | — |
| 422 | Dic6 | — | 15 | 4 | no | — |
| 423 | Dic6 | — | 15 | 4 | no | — |
| 424 | Dic6 | D3×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 425 | C22×C5 | — | 9 | 1 | no | — |
| 426 | C2×D5 | — | 9 | 1 | no | — |
| 427 | C2×D5 | — | 9 | 2 | no | — |
| 428 | C2×D5 | — | 9 | 2 | no | — |
| 429 | C2×D5 | C22×D32 | 1 | 1 | yes | characteristic |
| 430 | AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 431 | AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 432 | AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 433 | AGL(1,𝔽5) | — | 18 | 2 | no | — |
| 434 | C4×C5 | — | 3 | 4 | no | — |
| 435 | C4×C5 | — | 9 | 1 | no | — |
| 436 | C4×C5 | C4×D32 | 1 | 1 | yes | characteristic |
| 437 | Dic5 | — | 3 | 4 | no | — |
| 438 | Dic5 | — | 9 | 1 | no | — |
| 439 | Dic5 | C4×D32 | 1 | 1 | yes | characteristic |
| 440 | C2×C32 | — | 5 | 1 | no | — |
| 441 | C2×C32 | — | 5 | 1 | no | — |
| 442 | C2×C32 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 443 | C3⋊D3 | — | 5 | 2 | no | — |
| 444 | C3⋊D3 | Q8×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 445 | C2×Q8 | — | 9 | 1 | no | — |
| 446 | C2×Q8 | — | 15 | 2 | no | — |
| 447 | C2×Q8 | — | 45 | 2 | no | — |
| 448 | C2×Q8 | — | 45 | 1 | no | — |
| 449 | C2×Q8 | — | 45 | 2 | no | — |
| 450 | C2×Q8 | — | 45 | 2 | no | — |
| 451 | C2×Q8 | — | 45 | 2 | no | — |
| 452 | C22×C4 | — | 45 | 1 | no | — |
| 453 | C22×C4 | — | 45 | 2 | no | — |
| 454 | C22×C4 | — | 45 | 2 | no | — |
| 455 | C22×C4 | — | 45 | 1 | no | — |
| 456 | C22×C4 | — | 45 | 1 | no | — |
| 457 | C4⋊C4 | — | 5 | 1 | no | — |
| 458 | C4⋊C4 | — | 15 | 4 | no | — |
| 459 | C4⋊C4 | — | 45 | 2 | no | — |
| 460 | C4⋊C4 | — | 45 | 1 | no | — |
| 461 | C4⋊C4 | — | 45 | 4 | no | — |
| 462 | C42 | — | 15 | 2 | no | — |
| 463 | C42 | — | 15 | 4 | no | — |
| 464 | C42 | — | 45 | 4 | no | — |
| 465 | C42 | — | 45 | 2 | no | — |
| 466 | C3×C5 | — | 2 | 1 | no | — |
| 467 | C3×C5 | C4×D3×Q8 | 1 | 2 | yes | complemented |
| 468 | C22×C3 | — | 5 | 2 | no | — |
| 469 | C22×C3 | — | 10 | 1 | no | — |
| 470 | C2×D3 | — | 3 | 2 | no | — |
| 471 | C2×D3 | — | 6 | 1 | no | — |
| 472 | C2×D3 | — | 15 | 4 | no | — |
| 473 | C2×D3 | — | 15 | 4 | no | — |
| 474 | C2×D3 | — | 15 | 2 | no | — |
| 475 | C2×D3 | — | 30 | 2 | no | — |
| 476 | C2×D3 | — | 30 | 2 | no | — |
| 477 | C2×D3 | — | 30 | 1 | no | — |
| 478 | C3×C4 | — | 2 | 1 | no | — |
| 479 | C3×C4 | — | 3 | 4 | no | — |
| 480 | C3×C4 | — | 5 | 2 | no | — |
| 481 | C3×C4 | — | 10 | 1 | no | — |
| 482 | C3×C4 | — | 10 | 4 | no | — |
| 483 | C3×C4 | — | 15 | 4 | no | — |
| 484 | C3×C4 | — | 15 | 4 | no | — |
| 485 | C3×C4 | — | 20 | 2 | no | — |
| 486 | C3×C4 | — | 30 | 2 | no | — |
| 487 | C3×C4 | C2×D3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 488 | Dic3 | — | 3 | 2 | no | — |
| 489 | Dic3 | — | 5 | 4 | no | — |
| 490 | Dic3 | — | 5 | 4 | no | — |
| 491 | Dic3 | — | 6 | 1 | no | — |
| 492 | Dic3 | — | 10 | 2 | no | — |
| 493 | Dic3 | — | 15 | 2 | no | — |
| 494 | Dic3 | — | 30 | 1 | no | — |
| 495 | Dic3 | — | 30 | 4 | no | — |
| 496 | Dic3 | — | 60 | 2 | no | — |
| 497 | Dic3 | C2×D3×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 498 | C2×C5 | — | 9 | 2 | no | — |
| 499 | C2×C5 | C2×C4×D32 | 1 | 1 | yes | characteristic |
| 500 | D5 | — | 9 | 2 | no | — |
| 501 | D5 | #64312 | 1 | 1 | yes | characteristic |
| 502 | D5 | D32×Q8 | 1 | 1 | yes | characteristic |
| 503 | C32 | C2×Q8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 504 | C23 | — | 45 | 1 | no | — |
| 505 | Q8 | — | 3 | 2 | no | — |
| 506 | Q8 | — | 9 | 2 | no | — |
| 507 | Q8 | — | 15 | 4 | no | — |
| 508 | Q8 | — | 15 | 2 | no | — |
| 509 | Q8 | — | 45 | 4 | no | — |
| 510 | Q8 | — | 45 | 2 | no | — |
| 511 | C2×C4 | — | 5 | 1 | no | — |
| 512 | C2×C4 | — | 5 | 2 | no | — |
| 513 | C2×C4 | — | 9 | 2 | no | — |
| 514 | C2×C4 | — | 9 | 1 | no | — |
| 515 | C2×C4 | — | 15 | 4 | no | — |
| 516 | C2×C4 | — | 15 | 2 | no | — |
| 517 | C2×C4 | — | 15 | 2 | no | — |
| 518 | C2×C4 | — | 45 | 4 | no | — |
| 519 | C2×C4 | — | 45 | 1 | no | — |
| 520 | C2×C4 | — | 45 | 1 | no | — |
| 521 | C2×C4 | — | 45 | 1 | no | — |
| 522 | C2×C4 | — | 45 | 2 | no | — |
| 523 | C2×C4 | — | 45 | 4 | no | — |
| 524 | C2×C4 | — | 45 | 1 | no | — |
| 525 | C2×C4 | — | 45 | 2 | no | — |
| 526 | C2×C4 | — | 90 | 4 | no | — |
| 527 | C2×C4 | — | 90 | 2 | no | — |
| 528 | C2×C3 | — | 2 | 1 | no | — |
| 529 | C2×C3 | — | 5 | 2 | no | — |
| 530 | C2×C3 | — | 5 | 2 | no | — |
| 531 | C2×C3 | — | 10 | 1 | no | — |
| 532 | C2×C3 | — | 10 | 1 | no | — |
| 533 | C2×C3 | C22×D3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 534 | D3 | — | 3 | 4 | no | — |
| 535 | D3 | — | 6 | 2 | no | — |
| 536 | D3 | — | 15 | 4 | no | — |
| 537 | D3 | — | 30 | 2 | no | — |
| 538 | C5 | #10594363 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 539 | C22 | — | 5 | 1 | no | — |
| 540 | C22 | — | 9 | 1 | no | — |
| 541 | C22 | — | 45 | 2 | no | — |
| 542 | C22 | — | 45 | 2 | no | — |
| 543 | C22 | — | 45 | 1 | no | — |
| 544 | C4 | — | 3 | 4 | no | — |
| 545 | C4 | — | 5 | 1 | no | — |
| 546 | C4 | — | 9 | 1 | no | — |
| 547 | C4 | — | 10 | 2 | no | — |
| 548 | C4 | — | 15 | 4 | no | — |
| 549 | C4 | — | 15 | 4 | no | — |
| 550 | C4 | — | 30 | 2 | no | — |
| 551 | C4 | — | 45 | 1 | no | — |
| 552 | C4 | — | 90 | 2 | no | — |
| 553 | C4 | D32×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 554 | C3 | — | 2 | 1 | no | — |
| 555 | C3 | D3×Q8×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 556 | C2 | — | 5 | 1 | no | — |
| 557 | C2 | — | 5 | 1 | no | — |
| 558 | C2 | — | 9 | 2 | no | — |
| 559 | C2 | — | 45 | 2 | no | — |
| 560 | C2 | C2×D32×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 3. Dic6×ΓL(1,𝔽16) | C2 | semidirect |
| 5. C3×ΓL(1,𝔽16)⋊Q8 | C2 | semidirect |
| 6. #13088419 | C2 | semidirect |
| 13. #10624222 | C4 | semidirect |
| 14. #10624198 | C4 | semidirect |
| 15. C5×#3797 | C4 | semidirect |
| 21. #10624040 | C4 | semidirect |
| 22. #10624039 | C4 | semidirect |
| 41. ΓL(1,𝔽16)⋊Q8 | D3 | semidirect |
| 50. ΓL(1,𝔽16)⋊D3 | Q8 | semidirect |
| 54. C3×Dic30 | C2×C4 | semidirect |
| 55. C3×C5×Dic6 | C2×C4 | semidirect |
| 57. #67158 | C2×C4 | semidirect |
| 59. #67153 | C2×C4 | semidirect |
| 61. C5×#627 | C2×C4 | semidirect |
| 66. C3×#1204 | C2×C4 | semidirect |
| 119. C3×ΓL(1,𝔽16) | C2×Q8 | semidirect |
| 146. #3797 | AGL(1,𝔽5) | semidirect |
| 175. Dic30 | C4×D3 | semidirect |
| 180. C5×Dic6 | C4×D3 | semidirect |
| 188. #1204 | C4×D3 | semidirect |
| 211. C3⋊D15 | C4×Q8 | semidirect |
| 212. C5×C3⋊D3 | C4×Q8 | semidirect |
| 251. C3×Dic6 | C2×AGL(1,𝔽5) | semidirect |
| 254. #627 | C2×AGL(1,𝔽5) | semidirect |
| 274. ΓL(1,𝔽16) | D3×Q8 | semidirect |
| 325. C32×C5 | C2×C4×Q8 | semidirect |
| 424. Dic6 | D3×AGL(1,𝔽5) | semidirect |
| 444. C3⋊D3 | Q8×AGL(1,𝔽5) | semidirect |
| 467. C3×C5 | C4×D3×Q8 | semidirect |
| 503. C32 | C2×Q8×AGL(1,𝔽5) | semidirect |
| 538. C5 | #10594363 | semidirect |
| 555. C3 | D3×Q8×AGL(1,𝔽5) | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta