← #14319706
Subgroups — #14319706
Order 1920.
1392 conjugacy classes of subgroups.
The subgroup lattice has 460 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#91989 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3×#4130 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×D5×C4⋊Dic3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic3×C22⋊AGL(1,𝔽5) | C2 | 1 | 4 | yes | maximal |
| 5 | #11751846 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | AGL(1,𝔽5)×C4⋊Dic3 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10617098 | — | 3 | 1 | no | maximal, Hall |
| 8 | C22×C3×C4×D5 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×D5×Dic3 | C22 | 1 | 2 | yes | — |
| 10 | C2×#6763 | C22 | 1 | 2 | yes | — |
| 11 | #91989 | C4 | 1 | 8 | yes | complemented |
| 12 | C2×C4⋊ΓL(1,𝔽16) | C22 | 1 | 2 | yes | — |
| 13 | C2×C4×ΓL(1,𝔽16) | C22 | 1 | 2 | yes | — |
| 14 | C2×C3×C22⋊AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 15 | C3×#4130 | C4 | 1 | 8 | yes | complemented |
| 16 | C2×C3×C4⋊AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 17 | C2×C3×C4×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 18 | C2×Dic3×AGL(1,𝔽5) | C22 | 1 | 8 | yes | — |
| 19 | C2×C4⋊Dic15 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×C5×C4⋊Dic3 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#6668 | C4 | 1 | 2 | yes | complemented |
| 22 | D5×C4⋊Dic3 | C4 | 1 | 2 | yes | complemented |
| 23 | D5×C4⋊Dic3 | C4 | 1 | 2 | yes | complemented |
| 24 | D5×C4⋊Dic3 | C22 | 1 | 2 | yes | — |
| 25 | D5×C4⋊Dic3 | C22 | 1 | 2 | yes | — |
| 26 | (C2×AGL(1,𝔽5))⋊Dic3 | C22 | 1 | 8 | yes | — |
| 27 | #82223 | — | 5 | 1 | no | maximal, Hall |
| 28 | C2×#4130 | — | 3 | 1 | no | — |
| 29 | C2×#4130 | D3 | 1 | 1 | yes | characteristic |
| 30 | C2×D5×C4⋊C4 | — | 3 | 1 | no | — |
| 31 | C4×C22⋊AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 32 | C4⋊C4×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 33 | C4⋊C4×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 34 | C23×C3×D5 | C23 | 1 | 1 | yes | characteristic |
| 35 | C22×ΓL(1,𝔽16) | C23 | 1 | 4 | yes | — |
| 36 | C22×C3×AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 37 | C22×C3×C4×C5 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C22×Dic15 | C2×C4 | 1 | 2 | yes | — |
| 39 | C22×C5×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 40 | C22×C3×Dic5 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C2×C3×C4×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C2×C3×C4×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C2×C3×C4×D5 | C2×C4 | 1 | 4 | yes | — |
| 44 | C2×C3×C4×D5 | C2×C4 | 1 | 4 | yes | — |
| 45 | C2×C3×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×C3×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×D5×Dic3 | — | 4 | 4 | no | — |
| 48 | C2×D5×Dic3 | C2×C4 | 1 | 4 | yes | — |
| 49 | C2×D5×Dic3 | C23 | 1 | 4 | yes | — |
| 50 | #6763 | C2×C4 | 1 | 8 | yes | — |
| 51 | C4⋊ΓL(1,𝔽16) | C2×C4 | 1 | 8 | yes | complemented |
| 52 | C4×ΓL(1,𝔽16) | C2×C4 | 1 | 8 | yes | complemented |
| 53 | C3×C22⋊AGL(1,𝔽5) | C2×C4 | 1 | 8 | yes | — |
| 54 | C3×C4⋊AGL(1,𝔽5) | C2×C4 | 1 | 8 | yes | complemented |
| 55 | C3×C4×AGL(1,𝔽5) | C2×C4 | 1 | 8 | yes | complemented |
| 56 | Dic3×AGL(1,𝔽5) | — | 4 | 8 | no | — |
| 57 | C4⋊Dic15 | C2×C4 | 1 | 2 | yes | — |
| 58 | C4⋊Dic15 | C2×C4 | 1 | 2 | yes | — |
| 59 | C5×C4⋊Dic3 | C2×C4 | 1 | 2 | yes | — |
| 60 | C5×C4⋊Dic3 | C2×C4 | 1 | 2 | yes | — |
| 61 | #6668 | C2×C4 | 1 | 4 | yes | — |
| 62 | #6668 | C2×C4 | 1 | 4 | yes | — |
| 63 | C2×C3×#117 | — | 5 | 1 | no | — |
| 64 | C2×#926 | — | 5 | 1 | no | — |
| 65 | C22×C4⋊Dic3 | — | 5 | 1 | no | — |
| 66 | Dic3×C4⋊C4 | — | 5 | 4 | no | — |
| 67 | Dic3×C22⋊C4 | — | 5 | 4 | no | — |
| 68 | C4×C4⋊Dic3 | — | 5 | 4 | no | — |
| 69 | C22×C4×D5 | — | 3 | 2 | no | — |
| 70 | C22×C4×D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 71 | C2×C22⋊AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 72 | C2×C22⋊AGL(1,𝔽5) | C2×D3 | 1 | 2 | yes | — |
| 73 | #4130 | — | 3 | 8 | no | — |
| 74 | #4130 | Dic3 | 1 | 8 | yes | complemented |
| 75 | C2×C4⋊AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 76 | C2×C4⋊AGL(1,𝔽5) | C2×D3 | 1 | 2 | yes | — |
| 77 | C2×C4×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 78 | C2×C4×AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 79 | C2×C4×AGL(1,𝔽5) | C2×D3 | 1 | 2 | yes | — |
| 80 | C2×C5×C4⋊C4 | — | 3 | 1 | no | — |
| 81 | C2×C4⋊Dic5 | — | 3 | 1 | no | — |
| 82 | C2×#683 | — | 3 | 2 | no | — |
| 83 | D5×C4⋊C4 | — | 3 | 2 | no | — |
| 84 | D5×C4⋊C4 | — | 3 | 2 | no | — |
| 85 | D5×C4⋊C4 | — | 3 | 2 | no | — |
| 86 | D5×C4⋊C4 | — | 3 | 2 | no | — |
| 87 | (C2×AGL(1,𝔽5))⋊C4 | — | 3 | 8 | no | — |
| 88 | #2274 | — | 15 | 1 | no | Sylow |
| 89 | C23×C3×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | C22×C3×D5 | — | 2 | 2 | no | — |
| 91 | C22×C3×D5 | — | 2 | 2 | no | — |
| 92 | C22×C3×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 93 | C22×C3×D5 | C22×C4 | 1 | 2 | yes | — |
| 94 | C22×C3×D5 | C22×C4 | 1 | 2 | yes | — |
| 95 | C22×C3×D5 | C24 | 1 | 1 | yes | characteristic |
| 96 | C2×ΓL(1,𝔽16) | — | 2 | 4 | no | — |
| 97 | C2×ΓL(1,𝔽16) | — | 2 | 4 | no | — |
| 98 | C2×ΓL(1,𝔽16) | C22×C4 | 1 | 8 | yes | — |
| 99 | C2×C3×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 100 | C2×C3×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 101 | C2×C3×AGL(1,𝔽5) | C22×C4 | 1 | 8 | yes | — |
| 102 | C2×C3×C4×C5 | C42 | 1 | 4 | yes | complemented |
| 103 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 104 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 105 | C2×Dic15 | — | 4 | 2 | no | — |
| 106 | C2×Dic15 | C22×C4 | 1 | 4 | yes | — |
| 107 | C2×C5×Dic3 | — | 4 | 2 | no | — |
| 108 | C2×C5×Dic3 | C22×C4 | 1 | 4 | yes | — |
| 109 | C2×C3×Dic5 | C42 | 1 | 4 | yes | complemented |
| 110 | C2×C3×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | C2×C3×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 112 | C3×C4×D5 | C42 | 1 | 4 | yes | complemented |
| 113 | C3×C4×D5 | C42 | 1 | 4 | yes | complemented |
| 114 | C3×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 115 | C3×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 116 | C3×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 117 | C3×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 118 | D5×Dic3 | — | 2 | 8 | no | — |
| 119 | D5×Dic3 | — | 4 | 4 | no | — |
| 120 | C23×C3×C4 | — | 5 | 1 | no | — |
| 121 | C23×Dic3 | — | 5 | 2 | no | — |
| 122 | C3×#117 | — | 5 | 8 | no | — |
| 123 | C2×C3×C4⋊C4 | — | 5 | 2 | no | — |
| 124 | C2×C3×C22⋊C4 | — | 5 | 2 | no | — |
| 125 | C2×C3×C42 | — | 5 | 2 | no | — |
| 126 | C2×#217 | — | 5 | 2 | no | — |
| 127 | #926 | — | 5 | 8 | no | — |
| 128 | C2×C4⋊Dic3 | — | 5 | 2 | no | — |
| 129 | C2×C4⋊Dic3 | — | 5 | 1 | no | — |
| 130 | C2×C4⋊Dic3 | — | 5 | 2 | no | — |
| 131 | C2×C4⋊Dic3 | — | 5 | 2 | no | — |
| 132 | C2×C4⋊Dic3 | — | 5 | 2 | no | — |
| 133 | C2×C4⋊Dic3 | — | 5 | 2 | no | — |
| 134 | C2×C4⋊Dic3 | — | 5 | 2 | no | — |
| 135 | C2×C4⋊Dic3 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 136 | C2×C4×Dic3 | — | 5 | 2 | no | — |
| 137 | C2×C4×Dic3 | — | 5 | 8 | no | — |
| 138 | C3⋊#95 | — | 5 | 8 | no | — |
| 139 | C23×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | C22×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 141 | C22×AGL(1,𝔽5) | C22×D3 | 1 | 4 | yes | — |
| 142 | C22×C4×C5 | — | 3 | 2 | no | — |
| 143 | C22×C4×C5 | C4×D3 | 1 | 1 | yes | characteristic |
| 144 | C22×Dic5 | — | 3 | 2 | no | — |
| 145 | C22×Dic5 | C4×D3 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×D5 | — | 3 | 4 | no | — |
| 147 | C2×C4×D5 | — | 3 | 4 | no | — |
| 148 | C2×C4×D5 | — | 12 | 4 | no | — |
| 149 | C2×C4×D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 151 | C2×C4×D5 | C4×D3 | 1 | 4 | yes | — |
| 152 | C2×C4×D5 | C2×Dic3 | 1 | 4 | yes | — |
| 153 | C2×C4×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 155 | C22⋊AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 156 | C22⋊AGL(1,𝔽5) | C2×Dic3 | 1 | 8 | yes | — |
| 157 | C4⋊AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 158 | C4⋊AGL(1,𝔽5) | C2×Dic3 | 1 | 8 | yes | complemented |
| 159 | C4×AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 160 | C4×AGL(1,𝔽5) | — | 12 | 8 | no | — |
| 161 | C4×AGL(1,𝔽5) | C2×Dic3 | 1 | 8 | yes | complemented |
| 162 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 163 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 164 | C4⋊Dic5 | — | 3 | 2 | no | — |
| 165 | C4⋊Dic5 | — | 3 | 2 | no | — |
| 166 | #683 | — | 3 | 4 | no | — |
| 167 | #683 | — | 3 | 4 | no | — |
| 168 | C2×#117 | — | 5 | 1 | no | — |
| 169 | C2×#117 | — | 15 | 1 | no | — |
| 170 | C22×C4⋊C4 | — | 15 | 1 | no | — |
| 171 | C4×C4⋊C4 | — | 15 | 4 | no | — |
| 172 | C4×C4⋊C4 | — | 15 | 4 | no | — |
| 173 | C4×C22⋊C4 | — | 15 | 4 | no | — |
| 174 | C22×C3×C5 | — | 2 | 1 | no | — |
| 175 | C22×C3×C5 | — | 2 | 1 | no | — |
| 176 | C22×C3×C5 | C2×C42 | 1 | 2 | yes | — |
| 177 | C22×C3×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 178 | C2×C3×D5 | — | 2 | 1 | no | — |
| 179 | C2×C3×D5 | — | 2 | 1 | no | — |
| 180 | C2×C3×D5 | — | 2 | 4 | no | — |
| 181 | C2×C3×D5 | — | 2 | 4 | no | — |
| 182 | C2×C3×D5 | C2×C42 | 1 | 2 | yes | — |
| 183 | C2×C3×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 184 | C2×C3×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 185 | C2×C3×D5 | H(5,𝔽2) | 1 | 2 | yes | — |
| 186 | C2×C3×D5 | 2−1+4 | 1 | 2 | yes | — |
| 187 | ΓL(1,𝔽16) | — | 2 | 8 | no | — |
| 188 | C3×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 189 | C3×C4×C5 | C2×C42 | 1 | 2 | yes | — |
| 190 | C3×C4×C5 | C2×C42 | 1 | 2 | yes | — |
| 191 | Dic15 | — | 2 | 4 | no | — |
| 192 | C3×Dic5 | C2×C42 | 1 | 2 | yes | — |
| 193 | C3×Dic5 | C2×C42 | 1 | 2 | yes | — |
| 194 | C5×Dic3 | — | 2 | 4 | no | — |
| 195 | C24×C3 | — | 5 | 1 | no | — |
| 196 | C22×C3×C4 | — | 5 | 1 | no | — |
| 197 | C22×C3×C4 | — | 5 | 4 | no | — |
| 198 | C22×C3×C4 | — | 5 | 4 | no | — |
| 199 | C22×C3×C4 | — | 5 | 1 | no | — |
| 200 | C22×C3×C4 | — | 5 | 1 | no | — |
| 201 | C22×C3×C4 | — | 5 | 1 | no | — |
| 202 | C22×C3×C4 | — | 5 | 1 | no | — |
| 203 | C22×C3×C4 | — | 5 | 4 | no | — |
| 204 | C22×C3×C4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 205 | C22×Dic3 | — | 5 | 4 | no | — |
| 206 | C22×Dic3 | — | 5 | 2 | no | — |
| 207 | C22×Dic3 | — | 5 | 4 | no | — |
| 208 | C22×Dic3 | — | 5 | 4 | no | — |
| 209 | C22×Dic3 | — | 20 | 4 | no | — |
| 210 | C22×Dic3 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 211 | C3×C4⋊C4 | — | 5 | 8 | no | — |
| 212 | C3×C22⋊C4 | — | 5 | 8 | no | — |
| 213 | C3×C42 | — | 5 | 8 | no | — |
| 214 | #217 | — | 5 | 8 | no | — |
| 215 | C4⋊Dic3 | — | 5 | 8 | no | — |
| 216 | C4⋊Dic3 | — | 5 | 2 | no | — |
| 217 | C4⋊Dic3 | — | 5 | 2 | no | — |
| 218 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 219 | C4⋊Dic3 | — | 5 | 4 | no | — |
| 220 | C4⋊Dic3 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 221 | C4⋊Dic3 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 222 | C4×Dic3 | — | 5 | 8 | no | — |
| 223 | C4×Dic3 | — | 20 | 8 | no | — |
| 224 | C23×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 225 | C22×D5 | — | 2 | 2 | no | — |
| 226 | C22×D5 | — | 2 | 2 | no | — |
| 227 | C22×D5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 228 | C22×D5 | C2×C4×D3 | 1 | 2 | yes | — |
| 229 | C22×D5 | C22×Dic3 | 1 | 2 | yes | — |
| 230 | C22×D5 | C23×D3 | 1 | 1 | yes | characteristic |
| 231 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 232 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 233 | C2×AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 234 | C2×AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 235 | C2×AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 236 | C2×AGL(1,𝔽5) | C22×Dic3 | 1 | 8 | yes | — |
| 237 | C2×C4×C5 | — | 3 | 4 | no | — |
| 238 | C2×C4×C5 | — | 12 | 2 | no | — |
| 239 | C2×C4×C5 | C4×Dic3 | 1 | 4 | yes | complemented |
| 240 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 241 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 242 | C2×Dic5 | — | 3 | 4 | no | — |
| 243 | C2×Dic5 | — | 12 | 2 | no | — |
| 244 | C2×Dic5 | C4×Dic3 | 1 | 4 | yes | complemented |
| 245 | C2×Dic5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 246 | C2×Dic5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 247 | C4×D5 | — | 6 | 8 | no | — |
| 248 | C4×D5 | — | 12 | 4 | no | — |
| 249 | C4×D5 | C4×Dic3 | 1 | 4 | yes | complemented |
| 250 | C4×D5 | C4×Dic3 | 1 | 4 | yes | complemented |
| 251 | C4×D5 | C2×C4×D3 | 1 | 2 | yes | — |
| 252 | C4×D5 | C2×C4×D3 | 1 | 2 | yes | — |
| 253 | C4×D5 | C22×Dic3 | 1 | 2 | yes | — |
| 254 | C4×D5 | C22×Dic3 | 1 | 2 | yes | — |
| 255 | C23×C4 | — | 5 | 1 | no | — |
| 256 | C23×C4 | — | 15 | 2 | no | — |
| 257 | #117 | — | 5 | 8 | no | — |
| 258 | #117 | — | 15 | 8 | no | — |
| 259 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 260 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 261 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 262 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 263 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 264 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 265 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 266 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 267 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 268 | C2×C22⋊C4 | — | 5 | 2 | no | — |
| 269 | C2×C22⋊C4 | — | 15 | 2 | no | — |
| 270 | C2×C42 | — | 5 | 2 | no | — |
| 271 | C2×C42 | — | 15 | 2 | no | — |
| 272 | C2×C42 | — | 15 | 8 | no | — |
| 273 | #95 | — | 15 | 8 | no | — |
| 274 | C2×C3×C5 | — | 2 | 2 | no | — |
| 275 | C2×C3×C5 | C22×C42 | 1 | 1 | yes | characteristic |
| 276 | C2×C3×C5 | #518 | 1 | 1 | yes | characteristic |
| 277 | C2×C3×C5 | #519 | 1 | 1 | yes | characteristic |
| 278 | C3×D5 | — | 2 | 2 | no | — |
| 279 | C3×D5 | #520 | 1 | 2 | yes | — |
| 280 | C3×D5 | #520 | 1 | 2 | yes | — |
| 281 | C23×C3 | — | 5 | 1 | no | — |
| 282 | C23×C3 | — | 5 | 2 | no | — |
| 283 | C23×C3 | — | 5 | 2 | no | — |
| 284 | C23×C3 | — | 5 | 1 | no | — |
| 285 | C23×C3 | — | 10 | 2 | no | — |
| 286 | C23×C3 | — | 10 | 2 | no | — |
| 287 | C23×C3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 288 | C2×C3×C4 | — | 5 | 4 | no | — |
| 289 | C2×C3×C4 | — | 5 | 1 | no | — |
| 290 | C2×C3×C4 | — | 5 | 1 | no | — |
| 291 | C2×C3×C4 | — | 5 | 4 | no | — |
| 292 | C2×C3×C4 | — | 5 | 4 | no | — |
| 293 | C2×C3×C4 | — | 5 | 2 | no | — |
| 294 | C2×C3×C4 | — | 5 | 2 | no | — |
| 295 | C2×C3×C4 | — | 5 | 2 | no | — |
| 296 | C2×C3×C4 | — | 5 | 2 | no | — |
| 297 | C2×C3×C4 | — | 5 | 8 | no | — |
| 298 | C2×C3×C4 | — | 10 | 4 | no | — |
| 299 | C2×C3×C4 | — | 10 | 4 | no | — |
| 300 | C2×C3×C4 | C4×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 301 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 302 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 303 | C2×Dic3 | — | 4 | 2 | no | — |
| 304 | C2×Dic3 | — | 5 | 8 | no | — |
| 305 | C2×Dic3 | — | 5 | 4 | no | — |
| 306 | C2×Dic3 | — | 10 | 8 | no | — |
| 307 | C2×Dic3 | — | 10 | 4 | no | — |
| 308 | C2×Dic3 | — | 10 | 4 | no | — |
| 309 | C2×Dic3 | — | 20 | 4 | no | — |
| 310 | C2×Dic3 | — | 20 | 2 | no | — |
| 311 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 312 | C22×C5 | — | 2 | 1 | no | — |
| 313 | C22×C5 | — | 2 | 1 | no | — |
| 314 | C22×C5 | C2×C4×Dic3 | 1 | 2 | yes | — |
| 315 | C22×C5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 316 | C2×D5 | — | 2 | 1 | no | — |
| 317 | C2×D5 | — | 2 | 1 | no | — |
| 318 | C2×D5 | — | 2 | 4 | no | — |
| 319 | C2×D5 | — | 2 | 4 | no | — |
| 320 | C2×D5 | C2×C4×Dic3 | 1 | 2 | yes | — |
| 321 | C2×D5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 322 | C2×D5 | #1009 | 1 | 2 | yes | — |
| 323 | C2×D5 | #1010 | 1 | 2 | yes | — |
| 324 | C2×D5 | C23×Dic3 | 1 | 1 | yes | characteristic |
| 325 | AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 326 | AGL(1,𝔽5) | — | 6 | 8 | no | — |
| 327 | C4×C5 | — | 6 | 4 | no | — |
| 328 | C4×C5 | C2×C4×Dic3 | 1 | 2 | yes | — |
| 329 | C4×C5 | C2×C4×Dic3 | 1 | 2 | yes | — |
| 330 | Dic5 | — | 6 | 4 | no | — |
| 331 | Dic5 | C2×C4×Dic3 | 1 | 2 | yes | — |
| 332 | Dic5 | C2×C4×Dic3 | 1 | 2 | yes | — |
| 333 | C24 | — | 5 | 1 | no | — |
| 334 | C22×C4 | — | 3 | 2 | no | — |
| 335 | C22×C4 | — | 5 | 1 | no | — |
| 336 | C22×C4 | — | 5 | 4 | no | — |
| 337 | C22×C4 | — | 5 | 4 | no | — |
| 338 | C22×C4 | — | 5 | 1 | no | — |
| 339 | C22×C4 | — | 5 | 1 | no | — |
| 340 | C22×C4 | — | 5 | 1 | no | — |
| 341 | C22×C4 | — | 5 | 1 | no | — |
| 342 | C22×C4 | — | 5 | 4 | no | — |
| 343 | C22×C4 | — | 15 | 4 | no | — |
| 344 | C22×C4 | — | 15 | 4 | no | — |
| 345 | C22×C4 | — | 15 | 4 | no | — |
| 346 | C22×C4 | — | 15 | 2 | no | — |
| 347 | C22×C4 | — | 60 | 4 | no | — |
| 348 | C22×C4 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 349 | C4⋊C4 | — | 3 | 2 | no | — |
| 350 | C4⋊C4 | — | 3 | 2 | no | — |
| 351 | C4⋊C4 | — | 5 | 8 | no | — |
| 352 | C4⋊C4 | — | 15 | 4 | no | — |
| 353 | C4⋊C4 | — | 15 | 4 | no | — |
| 354 | C4⋊C4 | — | 15 | 8 | no | — |
| 355 | C4⋊C4 | — | 15 | 2 | no | — |
| 356 | C4⋊C4 | — | 15 | 2 | no | — |
| 357 | C22⋊C4 | — | 5 | 8 | no | — |
| 358 | C22⋊C4 | — | 15 | 8 | no | — |
| 359 | C42 | — | 5 | 8 | no | — |
| 360 | C42 | — | 15 | 8 | no | — |
| 361 | C42 | — | 60 | 8 | no | — |
| 362 | C3×C5 | #2274 | 1 | 1 | yes | characteristic, complemented, Hall |
| 363 | C22×C3 | — | 2 | 1 | no | — |
| 364 | C22×C3 | — | 2 | 1 | no | — |
| 365 | C22×C3 | — | 5 | 1 | no | — |
| 366 | C22×C3 | — | 5 | 1 | no | — |
| 367 | C22×C3 | — | 5 | 2 | no | — |
| 368 | C22×C3 | — | 5 | 2 | no | — |
| 369 | C22×C3 | — | 5 | 2 | no | — |
| 370 | C22×C3 | — | 10 | 4 | no | — |
| 371 | C22×C3 | — | 10 | 4 | no | — |
| 372 | C22×C3 | — | 10 | 1 | no | — |
| 373 | C22×C3 | — | 10 | 1 | no | — |
| 374 | C22×C3 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 375 | C22×C3 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 376 | C3×C4 | — | 5 | 2 | no | — |
| 377 | C3×C4 | — | 5 | 2 | no | — |
| 378 | C3×C4 | — | 10 | 8 | no | — |
| 379 | C3×C4 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 380 | C3×C4 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 381 | Dic3 | — | 2 | 4 | no | — |
| 382 | Dic3 | — | 10 | 8 | no | — |
| 383 | Dic3 | — | 10 | 4 | no | — |
| 384 | C2×C5 | — | 2 | 2 | no | — |
| 385 | C2×C5 | #5516 | 1 | 1 | yes | characteristic |
| 386 | C2×C5 | #5521 | 1 | 1 | yes | characteristic |
| 387 | C2×C5 | C22×C4×Dic3 | 1 | 1 | yes | characteristic |
| 388 | D5 | — | 2 | 2 | no | — |
| 389 | D5 | #5523 | 1 | 2 | yes | — |
| 390 | D5 | #5827 | 1 | 2 | yes | — |
| 391 | C23 | — | 5 | 1 | no | — |
| 392 | C23 | — | 5 | 2 | no | — |
| 393 | C23 | — | 5 | 2 | no | — |
| 394 | C23 | — | 5 | 1 | no | — |
| 395 | C23 | — | 10 | 2 | no | — |
| 396 | C23 | — | 10 | 2 | no | — |
| 397 | C23 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 398 | C2×C4 | — | 3 | 4 | no | — |
| 399 | C2×C4 | — | 5 | 4 | no | — |
| 400 | C2×C4 | — | 5 | 1 | no | — |
| 401 | C2×C4 | — | 5 | 1 | no | — |
| 402 | C2×C4 | — | 5 | 2 | no | — |
| 403 | C2×C4 | — | 5 | 2 | no | — |
| 404 | C2×C4 | — | 5 | 2 | no | — |
| 405 | C2×C4 | — | 5 | 2 | no | — |
| 406 | C2×C4 | — | 5 | 4 | no | — |
| 407 | C2×C4 | — | 5 | 4 | no | — |
| 408 | C2×C4 | — | 5 | 8 | no | — |
| 409 | C2×C4 | — | 10 | 4 | no | — |
| 410 | C2×C4 | — | 10 | 4 | no | — |
| 411 | C2×C4 | — | 12 | 2 | no | — |
| 412 | C2×C4 | — | 15 | 8 | no | — |
| 413 | C2×C4 | — | 15 | 4 | no | — |
| 414 | C2×C4 | — | 30 | 8 | no | — |
| 415 | C2×C4 | — | 30 | 4 | no | — |
| 416 | C2×C4 | — | 30 | 4 | no | — |
| 417 | C2×C4 | — | 60 | 4 | no | — |
| 418 | C2×C4 | — | 60 | 2 | no | — |
| 419 | C2×C4 | Dic3×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 420 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 421 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 422 | C2×C3 | — | 2 | 2 | no | — |
| 423 | C2×C3 | — | 5 | 2 | no | — |
| 424 | C2×C3 | — | 5 | 2 | no | — |
| 425 | C2×C3 | — | 10 | 2 | no | — |
| 426 | C2×C3 | C22×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 427 | C2×C3 | #66258 | 1 | 1 | yes | characteristic |
| 428 | C2×C3 | #66262 | 1 | 1 | yes | characteristic |
| 429 | C5 | #82223 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 430 | C22 | — | 2 | 1 | no | — |
| 431 | C22 | — | 2 | 1 | no | — |
| 432 | C22 | — | 5 | 2 | no | — |
| 433 | C22 | — | 5 | 2 | no | — |
| 434 | C22 | — | 5 | 1 | no | — |
| 435 | C22 | — | 5 | 1 | no | — |
| 436 | C22 | — | 5 | 2 | no | — |
| 437 | C22 | — | 10 | 4 | no | — |
| 438 | C22 | — | 10 | 4 | no | — |
| 439 | C22 | — | 10 | 1 | no | — |
| 440 | C22 | — | 10 | 1 | no | — |
| 441 | C22 | C2×Dic3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 442 | C22 | C22×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 443 | C4 | — | 5 | 2 | no | — |
| 444 | C4 | — | 5 | 2 | no | — |
| 445 | C4 | — | 6 | 4 | no | — |
| 446 | C4 | — | 10 | 8 | no | — |
| 447 | C4 | — | 30 | 8 | no | — |
| 448 | C4 | — | 30 | 4 | no | — |
| 449 | C4 | C2×Dic3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 450 | C4 | C2×Dic3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 451 | C3 | #10617098 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 452 | C2 | — | 2 | 2 | no | — |
| 453 | C2 | — | 5 | 2 | no | — |
| 454 | C2 | — | 5 | 2 | no | — |
| 455 | C2 | — | 10 | 2 | no | — |
| 456 | C2 | #11756812 | 1 | 1 | yes | characteristic |
| 457 | C2 | #11756837 | 1 | 1 | yes | characteristic |
| 458 | 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 |
|---|
| 5. #11751846 | C2 | semidirect |
| 6. AGL(1,𝔽5)×C4⋊Dic3 | C2 | semidirect |
| 11. #91989 | C4 | semidirect |
| 15. C3×#4130 | C4 | semidirect |
| 19. C2×C4⋊Dic15 | C4 | semidirect |
| 20. C2×C5×C4⋊Dic3 | C4 | semidirect |
| 21. C2×#6668 | C4 | semidirect |
| 22. D5×C4⋊Dic3 | C4 | semidirect |
| 23. D5×C4⋊Dic3 | C4 | semidirect |
| 51. C4⋊ΓL(1,𝔽16) | C2×C4 | semidirect |
| 52. C4×ΓL(1,𝔽16) | C2×C4 | semidirect |
| 54. C3×C4⋊AGL(1,𝔽5) | C2×C4 | semidirect |
| 55. C3×C4×AGL(1,𝔽5) | C2×C4 | semidirect |
| 74. #4130 | Dic3 | semidirect |
| 102. C2×C3×C4×C5 | C42 | semidirect |
| 109. C2×C3×Dic5 | C42 | semidirect |
| 112. C3×C4×D5 | C42 | semidirect |
| 113. C3×C4×D5 | C42 | semidirect |
| 135. C2×C4⋊Dic3 | AGL(1,𝔽5) | semidirect |
| 158. C4⋊AGL(1,𝔽5) | C2×Dic3 | semidirect |
| 161. C4×AGL(1,𝔽5) | C2×Dic3 | semidirect |
| 239. C2×C4×C5 | C4×Dic3 | semidirect |
| 244. C2×Dic5 | C4×Dic3 | semidirect |
| 249. C4×D5 | C4×Dic3 | semidirect |
| 250. C4×D5 | C4×Dic3 | semidirect |
| 300. C2×C3×C4 | C4×AGL(1,𝔽5) | semidirect |
| 362. C3×C5 | #2274 | semidirect |
| 419. C2×C4 | Dic3×AGL(1,𝔽5) | semidirect |
| 429. C5 | #82223 | semidirect |
| 451. C3 | #10617098 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta