← Q8×Dic3×AGL(1,𝔽5) #14319637
Order 1920.
1368 conjugacy classes of subgroups.
The subgroup lattice has 416 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×Q8×ΓL(1,𝔽16) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3×Q8×AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | Q8×D5×Dic3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11751846 | C2 | 1 | 3 | yes | maximal |
| 5 | Dic3×C4⋊AGL(1,𝔽5) | C2 | 1 | 3 | yes | maximal |
| 6 | AGL(1,𝔽5)×C4⋊Dic3 | C2 | 1 | 3 | yes | maximal |
| 7 | C4×Dic3×AGL(1,𝔽5) | C2 | 1 | 3 | yes | maximal |
| 8 | C4×Q8×AGL(1,𝔽5) | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×C3×Q8×D5 | C22 | 1 | 1 | yes | characteristic |
| 10 | Q8×ΓL(1,𝔽16) | C4 | 1 | 8 | yes | complemented |
| 11 | C2×C4⋊ΓL(1,𝔽16) | C22 | 1 | 3 | yes | — |
| 12 | C2×C4×ΓL(1,𝔽16) | C22 | 1 | 3 | yes | — |
| 13 | C3×Q8×AGL(1,𝔽5) | C4 | 1 | 8 | yes | complemented |
| 14 | C2×C3×C4⋊AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 15 | C2×C3×C4×AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 16 | C2×Dic3×AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 17 | C2×Dic3×AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 18 | C2×Dic3×AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 19 | C2×Dic3×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 20 | Q8×Dic15 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C5×Q8×Dic3 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | D5×C4⋊Dic3 | C22 | 1 | 3 | yes | — |
| 23 | C4×D5×Dic3 | C22 | 1 | 3 | yes | — |
| 24 | #91331 | C4 | 1 | 3 | yes | complemented |
| 25 | Dic3×Dic10 | C4 | 1 | 3 | yes | complemented |
| 26 | (C2×AGL(1,𝔽5))⋊Dic3 | C22 | 1 | 6 | yes | — |
| 27 | C4×Q8×Dic3 | — | 5 | 1 | no | maximal, Hall |
| 28 | C2×Q8×AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 29 | C2×Q8×AGL(1,𝔽5) | D3 | 1 | 1 | yes | characteristic |
| 30 | C4×Q8×D5 | — | 3 | 1 | no | — |
| 31 | C4⋊C4×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 32 | C4⋊C4×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 33 | C4×C4⋊AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 34 | C42×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 35 | C22×ΓL(1,𝔽16) | C23 | 1 | 3 | yes | — |
| 36 | C22×ΓL(1,𝔽16) | C23 | 1 | 1 | yes | characteristic |
| 37 | C22×C3×AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 38 | C22×C3×AGL(1,𝔽5) | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×C3×C5×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C3×Q8×D5 | C2×C4 | 1 | 4 | yes | — |
| 41 | C3×Q8×D5 | C2×C4 | 1 | 4 | yes | — |
| 42 | C2×C3×C4×D5 | C23 | 1 | 3 | yes | — |
| 43 | C2×C3×Dic10 | C2×C4 | 1 | 3 | yes | — |
| 44 | C2×D5×Dic3 | C23 | 1 | 3 | yes | — |
| 45 | C2×D5×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 46 | C4⋊ΓL(1,𝔽16) | C2×C4 | 1 | 12 | yes | — |
| 47 | C4×ΓL(1,𝔽16) | C2×C4 | 1 | 12 | yes | — |
| 48 | C3×C4⋊AGL(1,𝔽5) | C2×C4 | 1 | 12 | yes | — |
| 49 | C3×C4×AGL(1,𝔽5) | C2×C4 | 1 | 12 | yes | — |
| 50 | Dic3×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 51 | Dic3×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 52 | Dic3×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 53 | Dic3×AGL(1,𝔽5) | Q8 | 1 | 4 | yes | direct product factor |
| 54 | C4⋊Dic15 | C2×C4 | 1 | 3 | yes | — |
| 55 | C4×Dic15 | C2×C4 | 1 | 3 | yes | — |
| 56 | C5×C4⋊Dic3 | C2×C4 | 1 | 3 | yes | — |
| 57 | C4×C5×Dic3 | C2×C4 | 1 | 3 | yes | — |
| 58 | #6668 | C2×C4 | 1 | 6 | yes | — |
| 59 | Dic3×Dic5 | C2×C4 | 1 | 3 | yes | — |
| 60 | Dic3×Dic5 | C2×C4 | 1 | 3 | yes | — |
| 61 | C2×C3×C4×Q8 | — | 5 | 1 | no | — |
| 62 | C2×Q8×Dic3 | — | 5 | 1 | no | — |
| 63 | C2×Q8×Dic3 | — | 5 | 1 | no | — |
| 64 | Dic3×C4⋊C4 | — | 5 | 3 | no | — |
| 65 | Dic3×C4⋊C4 | — | 5 | 3 | no | — |
| 66 | C4×C4⋊Dic3 | — | 5 | 3 | no | — |
| 67 | C42×Dic3 | — | 5 | 3 | no | — |
| 68 | C2×Q8×D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 69 | Q8×AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 70 | Q8×AGL(1,𝔽5) | Dic3 | 1 | 8 | yes | direct product factor |
| 71 | C2×C4⋊AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 72 | C2×C4⋊AGL(1,𝔽5) | C2×D3 | 1 | 3 | yes | — |
| 73 | C2×C4×AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 74 | C2×C4×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 75 | C2×C4×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 76 | C2×C4×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 77 | C2×C4×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 78 | C2×C4×AGL(1,𝔽5) | C2×D3 | 1 | 3 | yes | — |
| 79 | C4×C5×Q8 | — | 3 | 1 | no | — |
| 80 | Q8×Dic5 | — | 3 | 1 | no | — |
| 81 | D5×C4⋊C4 | — | 3 | 3 | no | — |
| 82 | #4033 | — | 3 | 3 | no | — |
| 83 | C42×D5 | — | 3 | 3 | no | — |
| 84 | C4×Dic10 | — | 3 | 3 | no | — |
| 85 | (C2×AGL(1,𝔽5))⋊C4 | — | 3 | 6 | no | — |
| 86 | C42×Q8 | — | 15 | 1 | no | Sylow |
| 87 | C22×C3×D5 | C24 | 1 | 1 | yes | characteristic |
| 88 | C2×ΓL(1,𝔽16) | — | 2 | 3 | no | — |
| 89 | C2×ΓL(1,𝔽16) | — | 2 | 3 | no | — |
| 90 | C2×ΓL(1,𝔽16) | C22×C4 | 1 | 6 | yes | — |
| 91 | C2×ΓL(1,𝔽16) | C22×C4 | 1 | 2 | yes | — |
| 92 | C2×ΓL(1,𝔽16) | C2×Q8 | 1 | 2 | yes | — |
| 93 | C2×ΓL(1,𝔽16) | #41 | 1 | 2 | yes | — |
| 94 | C2×C3×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 95 | C2×C3×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 96 | C2×C3×AGL(1,𝔽5) | C22×C4 | 1 | 6 | yes | — |
| 97 | C2×C3×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 98 | C2×C3×AGL(1,𝔽5) | C2×Q8 | 1 | 2 | yes | — |
| 99 | C2×C3×AGL(1,𝔽5) | #41 | 1 | 2 | yes | — |
| 100 | C3×C5×Q8 | C42 | 1 | 4 | yes | complemented |
| 101 | C2×C3×C4×C5 | C22×C4 | 1 | 3 | yes | — |
| 102 | C2×Dic15 | C22×C4 | 1 | 3 | yes | — |
| 103 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 104 | C2×C5×Dic3 | C22×C4 | 1 | 3 | yes | — |
| 105 | C2×C5×Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 106 | C2×C3×Dic5 | C22×C4 | 1 | 3 | yes | — |
| 107 | C3×C4×D5 | C22×C4 | 1 | 6 | yes | — |
| 108 | C3×C4×D5 | C22×C4 | 1 | 6 | yes | — |
| 109 | C3×Dic10 | C42 | 1 | 12 | yes | complemented |
| 110 | D5×Dic3 | — | 2 | 3 | no | — |
| 111 | D5×Dic3 | — | 2 | 3 | no | — |
| 112 | D5×Dic3 | C2×Q8 | 1 | 2 | yes | — |
| 113 | D5×Dic3 | #41 | 1 | 2 | yes | — |
| 114 | C22×C3×Q8 | — | 5 | 1 | no | — |
| 115 | C3×C4×Q8 | — | 5 | 8 | no | — |
| 116 | C2×C3×C4⋊C4 | — | 5 | 3 | no | — |
| 117 | C2×C3×C42 | — | 5 | 3 | no | — |
| 118 | Q8×Dic3 | — | 5 | 8 | no | — |
| 119 | Q8×Dic3 | — | 5 | 1 | no | — |
| 120 | Q8×Dic3 | — | 5 | 3 | no | — |
| 121 | Q8×Dic3 | — | 5 | 3 | no | — |
| 122 | Q8×Dic3 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 123 | C2×C4⋊Dic3 | — | 5 | 3 | no | — |
| 124 | C2×C4⋊Dic3 | — | 5 | 3 | no | — |
| 125 | C2×C4×Dic3 | — | 5 | 1 | no | — |
| 126 | C2×C4×Dic3 | — | 5 | 3 | no | — |
| 127 | C2×C4×Dic3 | — | 5 | 3 | no | — |
| 128 | C2×C4×Dic3 | — | 5 | 3 | no | — |
| 129 | C2×C4×Dic3 | — | 5 | 3 | no | — |
| 130 | C2×C4×Dic3 | — | 5 | 3 | no | — |
| 131 | C3⋊#95 | — | 5 | 6 | no | — |
| 132 | C22×AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 133 | C22×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 134 | C22×AGL(1,𝔽5) | C22×D3 | 1 | 3 | yes | — |
| 135 | C22×AGL(1,𝔽5) | C22×D3 | 1 | 1 | yes | characteristic |
| 136 | C2×C5×Q8 | C4×D3 | 1 | 1 | yes | characteristic |
| 137 | Q8×D5 | C4×D3 | 1 | 4 | yes | — |
| 138 | Q8×D5 | C2×Dic3 | 1 | 4 | yes | — |
| 139 | C2×C4×D5 | — | 3 | 1 | no | — |
| 140 | C2×C4×D5 | — | 3 | 3 | no | — |
| 141 | C2×C4×D5 | C22×D3 | 1 | 3 | yes | — |
| 142 | C2×Dic10 | C4×D3 | 1 | 3 | yes | — |
| 143 | C4⋊AGL(1,𝔽5) | — | 3 | 12 | no | — |
| 144 | C4⋊AGL(1,𝔽5) | C2×Dic3 | 1 | 12 | yes | — |
| 145 | C4×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 146 | C4×AGL(1,𝔽5) | — | 3 | 12 | no | — |
| 147 | C4×AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 148 | C4×AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 149 | C4×AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 150 | C4×AGL(1,𝔽5) | C2×Dic3 | 1 | 12 | yes | — |
| 151 | C5×C4⋊C4 | — | 3 | 3 | no | — |
| 152 | C42×C5 | — | 3 | 3 | no | — |
| 153 | C4⋊Dic5 | — | 3 | 3 | no | — |
| 154 | #683 | — | 3 | 6 | no | — |
| 155 | C4×Dic5 | — | 3 | 3 | no | — |
| 156 | C4×Dic5 | — | 3 | 3 | no | — |
| 157 | C4×Dic5 | — | 3 | 3 | no | — |
| 158 | C2×C4×Q8 | — | 5 | 1 | no | — |
| 159 | C2×C4×Q8 | — | 15 | 1 | no | — |
| 160 | C2×C4×Q8 | — | 15 | 1 | no | — |
| 161 | C4×C4⋊C4 | — | 15 | 3 | no | — |
| 162 | C4×C4⋊C4 | — | 15 | 3 | no | — |
| 163 | C4×C4⋊C4 | — | 15 | 3 | no | — |
| 164 | C43 | — | 15 | 3 | no | — |
| 165 | C22×C3×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 166 | C2×C3×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 167 | C2×C3×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 168 | C2×C3×D5 | C22×Q8 | 1 | 1 | yes | characteristic |
| 169 | C2×C3×D5 | C2×#41 | 1 | 1 | yes | characteristic |
| 170 | C2×C3×D5 | C2×#41 | 1 | 1 | yes | characteristic |
| 171 | C2×C3×D5 | C2×#41 | 1 | 1 | yes | characteristic |
| 172 | ΓL(1,𝔽16) | — | 2 | 6 | no | — |
| 173 | ΓL(1,𝔽16) | C4×Q8 | 1 | 4 | yes | complemented |
| 174 | C3×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 175 | C3×AGL(1,𝔽5) | C4×Q8 | 1 | 4 | yes | complemented |
| 176 | C3×C4×C5 | C2×C42 | 1 | 6 | yes | — |
| 177 | Dic15 | — | 2 | 3 | no | — |
| 178 | Dic15 | C4×Q8 | 1 | 2 | yes | complemented |
| 179 | C3×Dic5 | C2×C42 | 1 | 6 | yes | — |
| 180 | C5×Dic3 | — | 2 | 3 | no | — |
| 181 | C5×Dic3 | C4×Q8 | 1 | 2 | yes | complemented |
| 182 | C2×C3×Q8 | — | 5 | 4 | no | — |
| 183 | C2×C3×Q8 | — | 5 | 4 | no | — |
| 184 | C2×C3×Q8 | — | 5 | 3 | no | — |
| 185 | C2×C3×Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 186 | C22×C3×C4 | — | 5 | 1 | no | — |
| 187 | C22×C3×C4 | — | 5 | 3 | no | — |
| 188 | C22×C3×C4 | — | 5 | 3 | no | — |
| 189 | C22×Dic3 | — | 5 | 1 | no | — |
| 190 | C22×Dic3 | — | 5 | 1 | no | — |
| 191 | C22×Dic3 | — | 5 | 3 | no | — |
| 192 | C22×Dic3 | — | 5 | 3 | no | — |
| 193 | C3×C4⋊C4 | — | 5 | 12 | no | — |
| 194 | C3×C42 | — | 5 | 12 | no | — |
| 195 | C4⋊Dic3 | — | 5 | 12 | no | — |
| 196 | C4⋊Dic3 | — | 5 | 3 | no | — |
| 197 | C4⋊Dic3 | — | 5 | 6 | no | — |
| 198 | C4⋊Dic3 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 199 | C4×Dic3 | — | 5 | 4 | no | — |
| 200 | C4×Dic3 | — | 5 | 12 | no | — |
| 201 | C4×Dic3 | — | 5 | 3 | no | — |
| 202 | C4×Dic3 | — | 5 | 3 | no | — |
| 203 | C4×Dic3 | — | 5 | 3 | no | — |
| 204 | C4×Dic3 | — | 10 | 6 | no | — |
| 205 | C4×Dic3 | — | 10 | 6 | no | — |
| 206 | C4×Dic3 | — | 10 | 6 | no | — |
| 207 | C4×Dic3 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 208 | C22×D5 | C23×D3 | 1 | 1 | yes | characteristic |
| 209 | C2×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 210 | C2×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 211 | C2×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 212 | C2×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 213 | C2×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 214 | C2×AGL(1,𝔽5) | — | 3 | 6 | no | — |
| 215 | C2×AGL(1,𝔽5) | — | 6 | 3 | no | — |
| 216 | C2×AGL(1,𝔽5) | — | 6 | 3 | no | — |
| 217 | C2×AGL(1,𝔽5) | D3×Q8 | 1 | 2 | yes | — |
| 218 | C2×AGL(1,𝔽5) | #239 | 1 | 2 | yes | — |
| 219 | C2×AGL(1,𝔽5) | C22×Dic3 | 1 | 6 | yes | — |
| 220 | C2×AGL(1,𝔽5) | C22×Dic3 | 1 | 2 | yes | — |
| 221 | C5×Q8 | C4×Dic3 | 1 | 4 | yes | complemented |
| 222 | C2×C4×C5 | — | 3 | 1 | no | — |
| 223 | C2×C4×C5 | — | 3 | 3 | no | — |
| 224 | C2×C4×C5 | C2×C4×D3 | 1 | 3 | yes | — |
| 225 | C2×Dic5 | — | 3 | 1 | no | — |
| 226 | C2×Dic5 | — | 3 | 3 | no | — |
| 227 | C2×Dic5 | C2×C4×D3 | 1 | 3 | yes | — |
| 228 | C4×D5 | — | 3 | 2 | no | — |
| 229 | C4×D5 | — | 3 | 2 | no | — |
| 230 | C4×D5 | — | 6 | 3 | no | — |
| 231 | C4×D5 | — | 6 | 3 | no | — |
| 232 | C4×D5 | C2×C4×D3 | 1 | 6 | yes | — |
| 233 | C4×D5 | C22×Dic3 | 1 | 6 | yes | — |
| 234 | Dic10 | C4×Dic3 | 1 | 12 | yes | complemented |
| 235 | C22×Q8 | — | 5 | 1 | no | — |
| 236 | C4×Q8 | — | 3 | 1 | no | — |
| 237 | C4×Q8 | — | 5 | 8 | no | — |
| 238 | C4×Q8 | — | 15 | 3 | no | — |
| 239 | C4×Q8 | — | 15 | 3 | no | — |
| 240 | C4×Q8 | — | 15 | 8 | no | — |
| 241 | C4×Q8 | — | 15 | 1 | no | — |
| 242 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 243 | C2×C4⋊C4 | — | 15 | 3 | no | — |
| 244 | C2×C4⋊C4 | — | 15 | 3 | no | — |
| 245 | C2×C42 | — | 5 | 3 | no | — |
| 246 | C2×C42 | — | 15 | 3 | no | — |
| 247 | C2×C42 | — | 15 | 3 | no | — |
| 248 | C2×C42 | — | 15 | 1 | no | — |
| 249 | C2×C42 | — | 15 | 3 | no | — |
| 250 | C2×C42 | — | 15 | 3 | no | — |
| 251 | C2×C42 | — | 15 | 3 | no | — |
| 252 | #95 | — | 15 | 6 | no | — |
| 253 | C2×C3×C5 | C22×C42 | 1 | 1 | yes | characteristic |
| 254 | C2×C3×C5 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 255 | C2×C3×C5 | C4×#41 | 1 | 1 | yes | characteristic |
| 256 | C3×D5 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 257 | C3×D5 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 258 | C3×D5 | C4×#41 | 1 | 1 | yes | characteristic |
| 259 | C3×D5 | C4×#41 | 1 | 1 | yes | characteristic |
| 260 | C23×C3 | — | 5 | 1 | no | — |
| 261 | C3×Q8 | — | 5 | 12 | no | — |
| 262 | C3×Q8 | C4×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 263 | C2×C3×C4 | — | 5 | 2 | no | — |
| 264 | C2×C3×C4 | — | 5 | 2 | no | — |
| 265 | C2×C3×C4 | — | 5 | 2 | no | — |
| 266 | C2×C3×C4 | — | 5 | 3 | no | — |
| 267 | C2×C3×C4 | — | 5 | 6 | no | — |
| 268 | C2×C3×C4 | — | 5 | 6 | no | — |
| 269 | C2×C3×C4 | — | 5 | 6 | no | — |
| 270 | C2×C3×C4 | — | 10 | 3 | no | — |
| 271 | C2×C3×C4 | — | 10 | 3 | no | — |
| 272 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 273 | C2×Dic3 | — | 5 | 2 | no | — |
| 274 | C2×Dic3 | — | 5 | 2 | no | — |
| 275 | C2×Dic3 | — | 5 | 2 | no | — |
| 276 | C2×Dic3 | — | 5 | 1 | no | — |
| 277 | C2×Dic3 | — | 5 | 2 | no | — |
| 278 | C2×Dic3 | — | 5 | 2 | no | — |
| 279 | C2×Dic3 | — | 5 | 6 | no | — |
| 280 | C2×Dic3 | — | 5 | 3 | no | — |
| 281 | C2×Dic3 | — | 10 | 3 | no | — |
| 282 | C2×Dic3 | — | 10 | 3 | no | — |
| 283 | C2×Dic3 | — | 10 | 3 | no | — |
| 284 | C2×Dic3 | — | 10 | 3 | no | — |
| 285 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 286 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 287 | C22×C5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 288 | C2×D5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 289 | C2×D5 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 290 | C2×D5 | C2×#239 | 1 | 1 | yes | characteristic |
| 291 | C2×D5 | D3×#41 | 1 | 1 | yes | characteristic |
| 292 | C2×D5 | D3×#41 | 1 | 1 | yes | characteristic |
| 293 | C2×D5 | C23×Dic3 | 1 | 1 | yes | characteristic |
| 294 | AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 295 | AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 296 | AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 297 | AGL(1,𝔽5) | Q8×Dic3 | 1 | 4 | yes | direct product factor |
| 298 | C4×C5 | — | 3 | 2 | no | — |
| 299 | C4×C5 | — | 6 | 3 | no | — |
| 300 | C4×C5 | C2×C4×Dic3 | 1 | 6 | yes | — |
| 301 | Dic5 | — | 3 | 2 | no | — |
| 302 | Dic5 | — | 6 | 3 | no | — |
| 303 | Dic5 | C2×C4×Dic3 | 1 | 6 | yes | — |
| 304 | C2×Q8 | — | 5 | 4 | no | — |
| 305 | C2×Q8 | — | 5 | 4 | no | — |
| 306 | C2×Q8 | — | 5 | 3 | no | — |
| 307 | C2×Q8 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 308 | C22×C4 | — | 5 | 1 | no | — |
| 309 | C22×C4 | — | 5 | 3 | no | — |
| 310 | C22×C4 | — | 5 | 3 | no | — |
| 311 | C22×C4 | — | 15 | 1 | no | — |
| 312 | C22×C4 | — | 15 | 3 | no | — |
| 313 | C22×C4 | — | 15 | 1 | no | — |
| 314 | C22×C4 | — | 15 | 3 | no | — |
| 315 | C4⋊C4 | — | 3 | 3 | no | — |
| 316 | C4⋊C4 | — | 5 | 12 | no | — |
| 317 | C4⋊C4 | — | 15 | 6 | no | — |
| 318 | C4⋊C4 | — | 15 | 12 | no | — |
| 319 | C4⋊C4 | — | 15 | 3 | no | — |
| 320 | C42 | — | 3 | 3 | no | — |
| 321 | C42 | — | 5 | 12 | no | — |
| 322 | C42 | — | 15 | 3 | no | — |
| 323 | C42 | — | 15 | 3 | no | — |
| 324 | C42 | — | 15 | 12 | no | — |
| 325 | C42 | — | 15 | 4 | no | — |
| 326 | C42 | — | 15 | 3 | no | — |
| 327 | C42 | — | 30 | 6 | no | — |
| 328 | C42 | — | 30 | 6 | no | — |
| 329 | C42 | — | 30 | 6 | no | — |
| 330 | C3×C5 | C42×Q8 | 1 | 1 | yes | characteristic, complemented, Hall |
| 331 | C22×C3 | — | 5 | 1 | no | — |
| 332 | C22×C3 | — | 5 | 1 | no | — |
| 333 | C22×C3 | — | 5 | 1 | no | — |
| 334 | C22×C3 | — | 5 | 1 | no | — |
| 335 | C22×C3 | — | 5 | 1 | no | — |
| 336 | C22×C3 | — | 5 | 1 | no | — |
| 337 | C22×C3 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 338 | C3×C4 | — | 5 | 4 | no | — |
| 339 | C3×C4 | — | 5 | 6 | no | — |
| 340 | C3×C4 | — | 10 | 6 | no | — |
| 341 | C3×C4 | C2×C4×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 342 | Dic3 | — | 2 | 3 | no | — |
| 343 | Dic3 | — | 5 | 4 | no | — |
| 344 | Dic3 | — | 5 | 2 | no | — |
| 345 | Dic3 | — | 10 | 6 | no | — |
| 346 | Dic3 | — | 10 | 3 | no | — |
| 347 | Dic3 | Q8×AGL(1,𝔽5) | 1 | 2 | yes | direct product factor |
| 348 | C2×C5 | C4×D3×Q8 | 1 | 1 | yes | characteristic |
| 349 | C2×C5 | C4×#239 | 1 | 1 | yes | characteristic |
| 350 | C2×C5 | C22×C4×Dic3 | 1 | 1 | yes | characteristic |
| 351 | D5 | C4×D3×Q8 | 1 | 1 | yes | characteristic |
| 352 | D5 | C4×#239 | 1 | 1 | yes | characteristic |
| 353 | D5 | C2×Q8×Dic3 | 1 | 1 | yes | characteristic |
| 354 | D5 | Dic3×#41 | 1 | 1 | yes | characteristic |
| 355 | C23 | — | 5 | 1 | no | — |
| 356 | Q8 | — | 5 | 12 | no | — |
| 357 | Q8 | Dic3×AGL(1,𝔽5) | 1 | 4 | yes | direct product factor |
| 358 | C2×C4 | — | 3 | 1 | no | — |
| 359 | C2×C4 | — | 3 | 3 | no | — |
| 360 | C2×C4 | — | 5 | 2 | no | — |
| 361 | C2×C4 | — | 5 | 2 | no | — |
| 362 | C2×C4 | — | 5 | 2 | no | — |
| 363 | C2×C4 | — | 5 | 3 | no | — |
| 364 | C2×C4 | — | 5 | 6 | no | — |
| 365 | C2×C4 | — | 5 | 6 | no | — |
| 366 | C2×C4 | — | 5 | 6 | no | — |
| 367 | C2×C4 | — | 10 | 3 | no | — |
| 368 | C2×C4 | — | 10 | 3 | no | — |
| 369 | C2×C4 | — | 15 | 2 | no | — |
| 370 | C2×C4 | — | 15 | 2 | no | — |
| 371 | C2×C4 | — | 15 | 2 | no | — |
| 372 | C2×C4 | — | 15 | 2 | no | — |
| 373 | C2×C4 | — | 15 | 2 | no | — |
| 374 | C2×C4 | — | 15 | 1 | no | — |
| 375 | C2×C4 | — | 15 | 6 | no | — |
| 376 | C2×C4 | — | 15 | 3 | no | — |
| 377 | C2×C4 | — | 30 | 3 | no | — |
| 378 | C2×C4 | — | 30 | 3 | no | — |
| 379 | C2×C4 | — | 30 | 3 | no | — |
| 380 | C2×C4 | — | 30 | 3 | no | — |
| 381 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 382 | C2×C3 | — | 5 | 1 | no | — |
| 383 | C2×C3 | — | 5 | 1 | no | — |
| 384 | C2×C3 | — | 5 | 1 | no | — |
| 385 | C2×C3 | — | 5 | 1 | no | — |
| 386 | C2×C3 | C22×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 387 | C2×C3 | C2×Q8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 388 | C2×C3 | #41×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 389 | C5 | C4×Q8×Dic3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 390 | C22 | — | 5 | 1 | no | — |
| 391 | C22 | — | 5 | 1 | no | — |
| 392 | C22 | — | 5 | 1 | no | — |
| 393 | C22 | — | 5 | 1 | no | — |
| 394 | C22 | — | 5 | 1 | no | — |
| 395 | C22 | — | 5 | 1 | no | — |
| 396 | C22 | C22×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 397 | C4 | — | 3 | 2 | no | — |
| 398 | C4 | — | 5 | 4 | no | — |
| 399 | C4 | — | 5 | 6 | no | — |
| 400 | C4 | — | 6 | 3 | no | — |
| 401 | C4 | — | 10 | 6 | no | — |
| 402 | C4 | — | 15 | 4 | no | — |
| 403 | C4 | — | 15 | 2 | no | — |
| 404 | C4 | — | 30 | 6 | no | — |
| 405 | C4 | — | 30 | 3 | no | — |
| 406 | C4 | C2×Dic3×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 407 | C3 | C4×Q8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 408 | C2 | — | 5 | 1 | no | — |
| 409 | C2 | — | 5 | 1 | no | — |
| 410 | C2 | — | 5 | 1 | no | — |
| 411 | C2 | — | 5 | 1 | no | — |
| 412 | C2 | D3×Q8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 413 | C2 | AGL(1,𝔽5)×#239 | 1 | 1 | yes | characteristic |
| 414 | C2 | C22×Dic3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 10. Q8×ΓL(1,𝔽16) | C4 | semidirect |
| 13. C3×Q8×AGL(1,𝔽5) | C4 | semidirect |
| 20. Q8×Dic15 | C4 | semidirect |
| 21. C5×Q8×Dic3 | C4 | semidirect |
| 24. #91331 | C4 | semidirect |
| 25. Dic3×Dic10 | C4 | semidirect |
| 53. Dic3×AGL(1,𝔽5) | Q8 | direct (N × H) |
| 70. Q8×AGL(1,𝔽5) | Dic3 | direct (N × H) |
| 100. C3×C5×Q8 | C42 | semidirect |
| 109. C3×Dic10 | C42 | semidirect |
| 122. Q8×Dic3 | AGL(1,𝔽5) | direct (N × H) |
| 173. ΓL(1,𝔽16) | C4×Q8 | semidirect |
| 175. C3×AGL(1,𝔽5) | C4×Q8 | semidirect |
| 178. Dic15 | C4×Q8 | semidirect |
| 181. C5×Dic3 | C4×Q8 | semidirect |
| 221. C5×Q8 | C4×Dic3 | semidirect |
| 234. Dic10 | C4×Dic3 | semidirect |
| 262. C3×Q8 | C4×AGL(1,𝔽5) | semidirect |
| 297. AGL(1,𝔽5) | Q8×Dic3 | direct (N × H) |
| 330. C3×C5 | C42×Q8 | semidirect |
| 347. Dic3 | Q8×AGL(1,𝔽5) | direct (N × H) |
| 357. Q8 | Dic3×AGL(1,𝔽5) | direct (N × H) |
| 389. C5 | C4×Q8×Dic3 | semidirect |
| 407. C3 | C4×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