← #72230021
Subgroups — #72230021
Order 2880.
1548 conjugacy classes of subgroups.
The subgroup lattice has 372 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C23×C3⋊ΓL(1,𝔽16) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C32×C22⋊AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×AGL(1,𝔽5)×C3⋊Dic3 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | D5×#3757 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | (C2×AGL(1,𝔽5))⋊(C3⋊Dic3) | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11752021 | — | 3 | 4 | no | maximal |
| 7 | C23×C32×D5 | C22 | 1 | 1 | yes | characteristic |
| 8 | C22×C3⋊ΓL(1,𝔽16) | — | 2 | 4 | no | — |
| 9 | C22×C3⋊ΓL(1,𝔽16) | C4 | 1 | 4 | yes | complemented |
| 10 | C22×C3⋊ΓL(1,𝔽16) | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×C3⋊ΓL(1,𝔽16) | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×C32×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 13 | C2×D5×C3⋊Dic3 | C22 | 1 | 2 | yes | — |
| 14 | C32×C22⋊AGL(1,𝔽5) | C4 | 1 | 4 | yes | complemented |
| 15 | AGL(1,𝔽5)×C3⋊Dic3 | — | 2 | 4 | no | — |
| 16 | #10623913 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | C5×#3757 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #10623770 | C4 | 1 | 2 | yes | complemented |
| 19 | C22⋊C4×C3⋊Dic3 | — | 5 | 1 | no | maximal, Hall |
| 20 | C23×ΓL(1,𝔽16) | — | 3 | 4 | no | — |
| 21 | C2×C3×C22⋊AGL(1,𝔽5) | D3 | 1 | 4 | yes | — |
| 22 | C2×Dic3×AGL(1,𝔽5) | — | 3 | 8 | no | — |
| 23 | D5×#217 | — | 3 | 4 | no | — |
| 24 | (C2×AGL(1,𝔽5))⋊Dic3 | — | 3 | 8 | no | — |
| 25 | C23×C32×C5 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C22×C32×D5 | — | 2 | 2 | no | — |
| 27 | C22×C32×D5 | — | 2 | 2 | no | — |
| 28 | C22×C32×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C22×C32×D5 | C2×C4 | 1 | 2 | yes | — |
| 30 | C22×C32×D5 | C2×C4 | 1 | 2 | yes | — |
| 31 | C22×C32×D5 | C23 | 1 | 1 | yes | characteristic |
| 32 | C2×C3⋊ΓL(1,𝔽16) | — | 2 | 2 | no | — |
| 33 | C2×C3⋊ΓL(1,𝔽16) | — | 2 | 8 | no | — |
| 34 | C2×C3⋊ΓL(1,𝔽16) | C2×C4 | 1 | 2 | yes | — |
| 35 | C2×C3⋊ΓL(1,𝔽16) | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×C3⋊ΓL(1,𝔽16) | D4 | 1 | 4 | yes | — |
| 37 | C2×C32×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 38 | C2×C32×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 39 | C2×C32×AGL(1,𝔽5) | C2×C4 | 1 | 4 | yes | complemented |
| 40 | C2×C3⋊Dic15 | C2×C4 | 1 | 2 | yes | complemented |
| 41 | C2×C5×C3⋊Dic3 | C2×C4 | 1 | 2 | yes | complemented |
| 42 | D5×C3⋊Dic3 | — | 2 | 2 | no | — |
| 43 | D5×C3⋊Dic3 | — | 2 | 2 | no | — |
| 44 | C22⋊C4×AGL(1,𝔽5) | — | 9 | 1 | no | Hall |
| 45 | C23×C3⋊Dic3 | — | 5 | 1 | no | — |
| 46 | C2×C32×C22⋊C4 | — | 5 | 1 | no | — |
| 47 | C2×#3757 | — | 5 | 1 | no | — |
| 48 | C2×C4×C3⋊Dic3 | — | 5 | 2 | no | — |
| 49 | #63658 | — | 5 | 2 | no | — |
| 50 | C23×C3×D5 | C2×D3 | 1 | 4 | yes | — |
| 51 | C22×ΓL(1,𝔽16) | — | 3 | 4 | no | — |
| 52 | C22×ΓL(1,𝔽16) | — | 3 | 16 | no | — |
| 53 | C22×ΓL(1,𝔽16) | — | 3 | 4 | no | — |
| 54 | C22×ΓL(1,𝔽16) | — | 6 | 16 | no | — |
| 55 | C22×C3×AGL(1,𝔽5) | C2×D3 | 1 | 8 | yes | — |
| 56 | C2×D5×Dic3 | — | 3 | 8 | no | — |
| 57 | C3×C22⋊AGL(1,𝔽5) | Dic3 | 1 | 16 | yes | complemented |
| 58 | Dic3×AGL(1,𝔽5) | — | 6 | 16 | no | — |
| 59 | #6719 | — | 3 | 4 | no | — |
| 60 | C5×#217 | — | 3 | 4 | no | — |
| 61 | #6665 | — | 3 | 8 | no | — |
| 62 | Dic3×C22⋊C4 | — | 15 | 4 | no | — |
| 63 | C22×C32×C5 | — | 2 | 2 | no | — |
| 64 | C22×C32×C5 | C42 | 1 | 2 | yes | complemented |
| 65 | C22×C32×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 66 | C2×C32×D5 | — | 2 | 2 | no | — |
| 67 | C2×C32×D5 | — | 2 | 2 | no | — |
| 68 | C2×C32×D5 | — | 2 | 2 | no | — |
| 69 | C2×C32×D5 | — | 2 | 4 | no | — |
| 70 | C2×C32×D5 | C42 | 1 | 2 | yes | complemented |
| 71 | C2×C32×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 72 | C2×C32×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 73 | C2×C32×D5 | C2×D4 | 1 | 2 | yes | — |
| 74 | C2×C32×D5 | #41 | 1 | 2 | yes | — |
| 75 | C3⋊ΓL(1,𝔽16) | — | 2 | 2 | no | — |
| 76 | C3⋊ΓL(1,𝔽16) | C22⋊C4 | 1 | 4 | yes | complemented |
| 77 | C32×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 78 | C3⋊Dic15 | — | 2 | 2 | no | — |
| 79 | C5×C3⋊Dic3 | — | 2 | 2 | no | — |
| 80 | C23×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 81 | C2×C22⋊AGL(1,𝔽5) | C3⋊D3 | 1 | 1 | yes | characteristic |
| 82 | C2×C4×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 83 | D5×C22⋊C4 | — | 9 | 1 | no | — |
| 84 | (C2×AGL(1,𝔽5))⋊C4 | — | 9 | 2 | no | — |
| 85 | C24×C32 | — | 5 | 1 | no | — |
| 86 | C22×C32×C4 | — | 5 | 2 | no | — |
| 87 | C22×C3⋊Dic3 | — | 5 | 1 | no | — |
| 88 | C22×C3⋊Dic3 | — | 5 | 4 | no | — |
| 89 | C22×C3⋊Dic3 | — | 5 | 1 | no | — |
| 90 | C22×C3⋊Dic3 | — | 5 | 2 | no | — |
| 91 | C22×C3⋊Dic3 | — | 10 | 4 | no | — |
| 92 | C32×C22⋊C4 | — | 5 | 4 | no | — |
| 93 | #3757 | — | 5 | 1 | no | — |
| 94 | #3757 | — | 5 | 2 | no | — |
| 95 | #3757 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 96 | C4×C3⋊Dic3 | — | 10 | 4 | no | — |
| 97 | C23×C3×C5 | C4×D3 | 1 | 4 | yes | — |
| 98 | C22×C3×D5 | — | 2 | 8 | no | — |
| 99 | C22×C3×D5 | — | 2 | 8 | no | — |
| 100 | C22×C3×D5 | C4×D3 | 1 | 4 | yes | — |
| 101 | C22×C3×D5 | C4×D3 | 1 | 8 | yes | — |
| 102 | C22×C3×D5 | C2×Dic3 | 1 | 8 | yes | — |
| 103 | C22×C3×D5 | C22×D3 | 1 | 4 | yes | — |
| 104 | C2×ΓL(1,𝔽16) | — | 3 | 8 | no | — |
| 105 | C2×ΓL(1,𝔽16) | — | 3 | 16 | no | — |
| 106 | C2×ΓL(1,𝔽16) | — | 3 | 8 | no | — |
| 107 | C2×ΓL(1,𝔽16) | — | 6 | 32 | no | — |
| 108 | C2×ΓL(1,𝔽16) | — | 6 | 8 | no | — |
| 109 | C2×C3×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 110 | C2×C3×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 111 | C2×C3×AGL(1,𝔽5) | C2×Dic3 | 1 | 16 | yes | complemented |
| 112 | C2×Dic15 | — | 3 | 8 | no | — |
| 113 | C2×C5×Dic3 | — | 3 | 8 | no | — |
| 114 | D5×Dic3 | — | 6 | 8 | no | — |
| 115 | D5×Dic3 | — | 6 | 8 | no | — |
| 116 | C23×Dic3 | — | 15 | 4 | no | — |
| 117 | C2×C3×C22⋊C4 | — | 5 | 4 | no | — |
| 118 | C2×#217 | — | 15 | 4 | no | — |
| 119 | C2×C4×Dic3 | — | 15 | 8 | no | — |
| 120 | C3⋊#95 | — | 15 | 8 | no | — |
| 121 | C2×C32×C5 | — | 2 | 2 | no | — |
| 122 | C2×C32×C5 | C2×C42 | 1 | 1 | yes | characteristic |
| 123 | C2×C32×C5 | C4×D4 | 1 | 2 | yes | — |
| 124 | C32×D5 | — | 2 | 2 | no | — |
| 125 | C32×D5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 126 | C32×D5 | #117 | 1 | 1 | yes | characteristic |
| 127 | C32×D5 | C4×D4 | 1 | 2 | yes | — |
| 128 | C23×D5 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 129 | C22×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 130 | C22×AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 131 | C22×AGL(1,𝔽5) | — | 9 | 1 | no | — |
| 132 | C22×AGL(1,𝔽5) | — | 18 | 4 | no | — |
| 133 | C22×AGL(1,𝔽5) | C2×C3⋊D3 | 1 | 2 | yes | — |
| 134 | C2×C4×D5 | — | 9 | 2 | no | — |
| 135 | C22⋊AGL(1,𝔽5) | C3⋊Dic3 | 1 | 4 | yes | complemented |
| 136 | C4×AGL(1,𝔽5) | — | 18 | 4 | no | — |
| 137 | C5×C22⋊C4 | — | 9 | 1 | no | — |
| 138 | C22⋊Dic5 | — | 9 | 1 | no | — |
| 139 | #685 | — | 9 | 2 | no | — |
| 140 | C23×C32 | — | 5 | 1 | no | — |
| 141 | C23×C32 | — | 5 | 2 | no | — |
| 142 | C23×C32 | — | 5 | 2 | no | — |
| 143 | C23×C32 | — | 5 | 1 | no | — |
| 144 | C23×C32 | — | 10 | 2 | no | — |
| 145 | C23×C32 | — | 10 | 2 | no | — |
| 146 | C23×C32 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 147 | C2×C32×C4 | — | 5 | 4 | no | — |
| 148 | C2×C32×C4 | — | 10 | 2 | no | — |
| 149 | C2×C32×C4 | — | 10 | 2 | no | — |
| 150 | C2×C3⋊Dic3 | — | 5 | 2 | no | — |
| 151 | C2×C3⋊Dic3 | — | 5 | 4 | no | — |
| 152 | C2×C3⋊Dic3 | — | 5 | 2 | no | — |
| 153 | C2×C3⋊Dic3 | — | 5 | 2 | no | — |
| 154 | C2×C3⋊Dic3 | — | 10 | 2 | no | — |
| 155 | C2×C3⋊Dic3 | — | 10 | 2 | no | — |
| 156 | C2×C3⋊Dic3 | — | 10 | 8 | no | — |
| 157 | C2×C3⋊Dic3 | — | 10 | 2 | no | — |
| 158 | C2×C3⋊Dic3 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 159 | C4×C22⋊C4 | — | 45 | 1 | no | Sylow |
| 160 | C22×C3×C5 | — | 2 | 8 | no | — |
| 161 | C22×C3×C5 | C4×Dic3 | 1 | 8 | yes | complemented |
| 162 | C22×C3×C5 | C2×C4×D3 | 1 | 4 | yes | — |
| 163 | C2×C3×D5 | — | 2 | 8 | no | — |
| 164 | C2×C3×D5 | — | 2 | 8 | no | — |
| 165 | C2×C3×D5 | — | 2 | 8 | no | — |
| 166 | C2×C3×D5 | — | 2 | 16 | no | — |
| 167 | C2×C3×D5 | C4×Dic3 | 1 | 8 | yes | complemented |
| 168 | C2×C3×D5 | C2×C4×D3 | 1 | 4 | yes | — |
| 169 | C2×C3×D5 | D3×D4 | 1 | 8 | yes | — |
| 170 | C2×C3×D5 | #237 | 1 | 8 | yes | — |
| 171 | C2×C3×D5 | C22×Dic3 | 1 | 4 | yes | — |
| 172 | ΓL(1,𝔽16) | — | 3 | 16 | no | — |
| 173 | ΓL(1,𝔽16) | — | 6 | 8 | no | — |
| 174 | C3×AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 175 | Dic15 | — | 6 | 8 | no | — |
| 176 | C5×Dic3 | — | 6 | 8 | no | — |
| 177 | C24×C3 | — | 5 | 4 | no | — |
| 178 | C22×C3×C4 | — | 5 | 8 | no | — |
| 179 | C22×Dic3 | — | 15 | 8 | no | — |
| 180 | C22×Dic3 | — | 15 | 4 | no | — |
| 181 | C22×Dic3 | — | 15 | 4 | no | — |
| 182 | C22×Dic3 | — | 15 | 16 | no | — |
| 183 | C22×Dic3 | — | 30 | 16 | no | — |
| 184 | C3×C22⋊C4 | — | 5 | 16 | no | — |
| 185 | #217 | — | 3 | 4 | no | — |
| 186 | #217 | — | 15 | 8 | no | — |
| 187 | #217 | — | 15 | 4 | no | — |
| 188 | C4×Dic3 | — | 30 | 16 | no | — |
| 189 | C32×C5 | C4×C22⋊C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 190 | C23×C5 | C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 191 | C22×D5 | — | 2 | 2 | no | — |
| 192 | C22×D5 | — | 2 | 2 | no | — |
| 193 | C22×D5 | C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 194 | C22×D5 | C4×C3⋊D3 | 1 | 2 | yes | — |
| 195 | C22×D5 | C2×C3⋊Dic3 | 1 | 2 | yes | — |
| 196 | C22×D5 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 197 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 198 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 199 | C2×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 200 | C2×AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 201 | C2×AGL(1,𝔽5) | — | 9 | 2 | no | — |
| 202 | C2×AGL(1,𝔽5) | — | 18 | 8 | no | — |
| 203 | C2×AGL(1,𝔽5) | — | 18 | 2 | no | — |
| 204 | C2×AGL(1,𝔽5) | C2×C3⋊Dic3 | 1 | 4 | yes | complemented |
| 205 | C2×C4×C5 | — | 9 | 2 | no | — |
| 206 | C2×Dic5 | — | 9 | 2 | no | — |
| 207 | C4×D5 | — | 18 | 2 | no | — |
| 208 | C4×D5 | — | 18 | 2 | no | — |
| 209 | C22×C32 | — | 2 | 2 | no | — |
| 210 | C22×C32 | — | 5 | 1 | no | — |
| 211 | C22×C32 | — | 5 | 1 | no | — |
| 212 | C22×C32 | — | 5 | 2 | no | — |
| 213 | C22×C32 | — | 5 | 2 | no | — |
| 214 | C22×C32 | — | 5 | 2 | no | — |
| 215 | C22×C32 | — | 10 | 2 | no | — |
| 216 | C22×C32 | — | 10 | 2 | no | — |
| 217 | C22×C32 | — | 10 | 4 | no | — |
| 218 | C22×C32 | — | 10 | 2 | no | — |
| 219 | C22×C32 | C4×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 220 | C22×C32 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 221 | C32×C4 | — | 10 | 4 | no | — |
| 222 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 223 | C3⋊Dic3 | — | 5 | 4 | no | — |
| 224 | C3⋊Dic3 | — | 10 | 2 | no | — |
| 225 | C3⋊Dic3 | — | 10 | 2 | no | — |
| 226 | C23×C4 | — | 45 | 1 | no | — |
| 227 | C2×C22⋊C4 | — | 5 | 1 | no | — |
| 228 | C2×C22⋊C4 | — | 45 | 1 | no | — |
| 229 | C2×C42 | — | 45 | 2 | no | — |
| 230 | #95 | — | 45 | 2 | no | — |
| 231 | C2×C3×C5 | — | 2 | 8 | no | — |
| 232 | C2×C3×C5 | #67⋊C4 | 1 | 8 | yes | — |
| 233 | C2×C3×C5 | C2×C4×Dic3 | 1 | 4 | yes | — |
| 234 | C3×D5 | — | 2 | 8 | no | — |
| 235 | C3×D5 | #877 | 1 | 4 | yes | — |
| 236 | C3×D5 | D3×C22⋊C4 | 1 | 4 | yes | — |
| 237 | C3×D5 | D4×Dic3 | 1 | 8 | yes | — |
| 238 | C23×C3 | — | 5 | 4 | no | — |
| 239 | C23×C3 | — | 5 | 8 | no | — |
| 240 | C23×C3 | — | 5 | 8 | no | — |
| 241 | C23×C3 | — | 5 | 4 | no | — |
| 242 | C23×C3 | — | 10 | 8 | no | — |
| 243 | C23×C3 | — | 10 | 8 | no | — |
| 244 | C23×C3 | D3×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 245 | C2×C3×C4 | — | 5 | 16 | no | — |
| 246 | C2×C3×C4 | — | 10 | 8 | no | — |
| 247 | C2×C3×C4 | — | 10 | 8 | no | — |
| 248 | C2×Dic3 | — | 3 | 8 | no | — |
| 249 | C2×Dic3 | — | 15 | 16 | no | — |
| 250 | C2×Dic3 | — | 15 | 8 | no | — |
| 251 | C2×Dic3 | — | 15 | 8 | no | — |
| 252 | C2×Dic3 | — | 15 | 8 | no | — |
| 253 | C2×Dic3 | — | 30 | 8 | no | — |
| 254 | C2×Dic3 | — | 30 | 8 | no | — |
| 255 | C2×Dic3 | — | 30 | 32 | no | — |
| 256 | C2×Dic3 | — | 30 | 8 | no | — |
| 257 | C22×C5 | — | 2 | 2 | no | — |
| 258 | C22×C5 | C4×C3⋊Dic3 | 1 | 2 | yes | complemented |
| 259 | C22×C5 | C2×C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 260 | C2×D5 | — | 2 | 2 | no | — |
| 261 | C2×D5 | — | 2 | 2 | no | — |
| 262 | C2×D5 | — | 2 | 2 | no | — |
| 263 | C2×D5 | — | 2 | 4 | no | — |
| 264 | C2×D5 | C4×C3⋊Dic3 | 1 | 2 | yes | complemented |
| 265 | C2×D5 | C2×C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 266 | C2×D5 | D4×C3⋊D3 | 1 | 2 | yes | — |
| 267 | C2×D5 | #3830 | 1 | 2 | yes | — |
| 268 | C2×D5 | C22×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 269 | AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 270 | AGL(1,𝔽5) | — | 9 | 4 | no | — |
| 271 | AGL(1,𝔽5) | — | 18 | 2 | no | — |
| 272 | C4×C5 | — | 18 | 2 | no | — |
| 273 | Dic5 | — | 18 | 2 | no | — |
| 274 | C2×C32 | — | 2 | 2 | no | — |
| 275 | C2×C32 | — | 5 | 1 | no | — |
| 276 | C2×C32 | — | 5 | 1 | no | — |
| 277 | C2×C32 | — | 5 | 2 | no | — |
| 278 | C2×C32 | — | 10 | 2 | no | — |
| 279 | C2×C32 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 280 | C2×C32 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 281 | C24 | — | 5 | 1 | no | — |
| 282 | C22×C4 | — | 5 | 2 | no | — |
| 283 | C22×C4 | — | 45 | 2 | no | — |
| 284 | C22×C4 | — | 45 | 1 | no | — |
| 285 | C22×C4 | — | 45 | 1 | no | — |
| 286 | C22×C4 | — | 45 | 4 | no | — |
| 287 | C22×C4 | — | 90 | 4 | no | — |
| 288 | C22⋊C4 | — | 5 | 4 | no | — |
| 289 | C22⋊C4 | — | 9 | 1 | no | — |
| 290 | C22⋊C4 | — | 45 | 2 | no | — |
| 291 | C22⋊C4 | — | 45 | 1 | no | — |
| 292 | C42 | — | 90 | 4 | no | — |
| 293 | C3×C5 | Dic3×C22⋊C4 | 1 | 4 | yes | complemented |
| 294 | C22×C3 | — | 2 | 8 | no | — |
| 295 | C22×C3 | — | 5 | 4 | no | — |
| 296 | C22×C3 | — | 5 | 4 | no | — |
| 297 | C22×C3 | — | 5 | 8 | no | — |
| 298 | C22×C3 | — | 5 | 8 | no | — |
| 299 | C22×C3 | — | 5 | 8 | no | — |
| 300 | C22×C3 | — | 10 | 8 | no | — |
| 301 | C22×C3 | — | 10 | 16 | no | — |
| 302 | C22×C3 | — | 10 | 8 | no | — |
| 303 | C22×C3 | — | 10 | 8 | no | — |
| 304 | C22×C3 | Dic3×AGL(1,𝔽5) | 1 | 8 | yes | complemented |
| 305 | C22×C3 | C2×D3×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 306 | C3×C4 | — | 10 | 16 | no | — |
| 307 | Dic3 | — | 6 | 8 | no | — |
| 308 | Dic3 | — | 15 | 16 | no | — |
| 309 | Dic3 | — | 30 | 8 | no | — |
| 310 | Dic3 | — | 30 | 8 | no | — |
| 311 | C2×C5 | — | 2 | 2 | no | — |
| 312 | C2×C5 | #64090 | 1 | 2 | yes | — |
| 313 | C2×C5 | C2×C4×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 314 | D5 | — | 2 | 2 | no | — |
| 315 | D5 | #64086 | 1 | 1 | yes | characteristic |
| 316 | D5 | C22⋊C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 317 | D5 | D4×C3⋊Dic3 | 1 | 2 | yes | — |
| 318 | C32 | C22⋊C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 319 | C23 | — | 5 | 1 | no | — |
| 320 | C23 | — | 5 | 1 | no | — |
| 321 | C23 | — | 5 | 2 | no | — |
| 322 | C23 | — | 5 | 2 | no | — |
| 323 | C23 | — | 10 | 2 | no | — |
| 324 | C23 | — | 10 | 2 | no | — |
| 325 | C23 | C3⋊D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 326 | C2×C4 | — | 5 | 4 | no | — |
| 327 | C2×C4 | — | 9 | 2 | no | — |
| 328 | C2×C4 | — | 10 | 2 | no | — |
| 329 | C2×C4 | — | 10 | 2 | no | — |
| 330 | C2×C4 | — | 45 | 4 | no | — |
| 331 | C2×C4 | — | 45 | 2 | no | — |
| 332 | C2×C4 | — | 45 | 2 | no | — |
| 333 | C2×C4 | — | 45 | 2 | no | — |
| 334 | C2×C4 | — | 90 | 2 | no | — |
| 335 | C2×C4 | — | 90 | 2 | no | — |
| 336 | C2×C4 | — | 90 | 8 | no | — |
| 337 | C2×C4 | — | 90 | 2 | no | — |
| 338 | C2×C3 | — | 2 | 8 | no | — |
| 339 | C2×C3 | — | 5 | 4 | no | — |
| 340 | C2×C3 | — | 5 | 8 | no | — |
| 341 | C2×C3 | — | 5 | 4 | no | — |
| 342 | C2×C3 | — | 10 | 8 | no | — |
| 343 | C2×C3 | C2×Dic3×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 344 | C2×C3 | #67⋊AGL(1,𝔽5) | 1 | 8 | yes | — |
| 345 | C5 | C22⋊C4×C3⋊Dic3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 346 | C22 | — | 2 | 2 | no | — |
| 347 | C22 | — | 5 | 1 | no | — |
| 348 | C22 | — | 5 | 1 | no | — |
| 349 | C22 | — | 5 | 2 | no | — |
| 350 | C22 | — | 5 | 2 | no | — |
| 351 | C22 | — | 5 | 2 | no | — |
| 352 | C22 | — | 10 | 2 | no | — |
| 353 | C22 | — | 10 | 4 | no | — |
| 354 | C22 | — | 10 | 2 | no | — |
| 355 | C22 | — | 10 | 2 | no | — |
| 356 | C22 | AGL(1,𝔽5)×C3⋊Dic3 | 1 | 2 | yes | complemented |
| 357 | C22 | C2×C3⋊D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 358 | C4 | — | 10 | 4 | no | — |
| 359 | C4 | — | 18 | 2 | no | — |
| 360 | C4 | — | 45 | 4 | no | — |
| 361 | C4 | — | 90 | 2 | no | — |
| 362 | C4 | — | 90 | 2 | no | — |
| 363 | C3 | #11752021 | 1 | 4 | yes | complemented |
| 364 | C2 | — | 2 | 2 | no | — |
| 365 | C2 | — | 5 | 2 | no | — |
| 366 | C2 | — | 5 | 1 | no | — |
| 367 | C2 | — | 5 | 1 | no | — |
| 368 | C2 | — | 10 | 2 | no | — |
| 369 | C2 | C2×AGL(1,𝔽5)×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 370 | C2 | #13088690 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 3. C2×AGL(1,𝔽5)×C3⋊Dic3 | C2 | semidirect |
| 5. (C2×AGL(1,𝔽5))⋊(C3⋊Dic3) | C2 | semidirect |
| 9. C22×C3⋊ΓL(1,𝔽16) | C4 | semidirect |
| 14. C32×C22⋊AGL(1,𝔽5) | C4 | semidirect |
| 16. #10623913 | C4 | semidirect |
| 17. C5×#3757 | C4 | semidirect |
| 18. #10623770 | C4 | semidirect |
| 39. C2×C32×AGL(1,𝔽5) | C2×C4 | semidirect |
| 40. C2×C3⋊Dic15 | C2×C4 | semidirect |
| 41. C2×C5×C3⋊Dic3 | C2×C4 | semidirect |
| 57. C3×C22⋊AGL(1,𝔽5) | Dic3 | semidirect |
| 64. C22×C32×C5 | C42 | semidirect |
| 70. C2×C32×D5 | C42 | semidirect |
| 76. C3⋊ΓL(1,𝔽16) | C22⋊C4 | semidirect |
| 95. #3757 | AGL(1,𝔽5) | semidirect |
| 111. C2×C3×AGL(1,𝔽5) | C2×Dic3 | semidirect |
| 135. C22⋊AGL(1,𝔽5) | C3⋊Dic3 | semidirect |
| 158. C2×C3⋊Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 161. C22×C3×C5 | C4×Dic3 | semidirect |
| 167. C2×C3×D5 | C4×Dic3 | semidirect |
| 189. C32×C5 | C4×C22⋊C4 | semidirect |
| 204. C2×AGL(1,𝔽5) | C2×C3⋊Dic3 | semidirect |
| 219. C22×C32 | C4×AGL(1,𝔽5) | semidirect |
| 258. C22×C5 | C4×C3⋊Dic3 | semidirect |
| 264. C2×D5 | C4×C3⋊Dic3 | semidirect |
| 293. C3×C5 | Dic3×C22⋊C4 | semidirect |
| 304. C22×C3 | Dic3×AGL(1,𝔽5) | semidirect |
| 318. C32 | C22⋊C4×AGL(1,𝔽5) | semidirect |
| 345. C5 | C22⋊C4×C3⋊Dic3 | semidirect |
| 356. C22 | AGL(1,𝔽5)×C3⋊Dic3 | semidirect |
| 363. C3 | #11752021 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta