← C2×AGL(1,𝔽5)×H(5,𝔽2) #13046016
Order 1280.
12378 conjugacy classes of subgroups.
The subgroup lattice has 346 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×D5×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | AGL(1,𝔽5)×H(5,𝔽2) | C2 | 1 | 32 | yes | maximal, direct product factor |
| 3 | C2×#66266 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C2×#41×AGL(1,𝔽5) | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C2×#66258 | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | C22×D4×AGL(1,𝔽5) | C2 | 1 | 9 | yes | maximal, complemented |
| 7 | C24×AGL(1,𝔽5) | C22 | 1 | 6 | yes | complemented |
| 8 | C2×C5×H(5,𝔽2) | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | D5×H(5,𝔽2) | C4 | 1 | 16 | yes | complemented |
| 10 | D5×H(5,𝔽2) | C22 | 1 | 16 | yes | — |
| 11 | C2×#4149 | C4 | 1 | 6 | yes | complemented |
| 12 | C2×D5×#41 | C22 | 1 | 6 | yes | — |
| 13 | C2×#4144 | C4 | 1 | 9 | yes | complemented |
| 14 | C22×D4×D5 | C22 | 1 | 9 | yes | — |
| 15 | C22×C22⋊AGL(1,𝔽5) | C22 | 1 | 18 | yes | complemented |
| 16 | #66266 | C22 | 1 | 96 | yes | complemented |
| 17 | #41×AGL(1,𝔽5) | C22 | 1 | 96 | yes | complemented |
| 18 | C2×Q8×AGL(1,𝔽5) | C22 | 1 | 2 | yes | complemented |
| 19 | C2×Q8×AGL(1,𝔽5) | C22 | 1 | 6 | yes | complemented |
| 20 | #66258 | C22 | 1 | 144 | yes | complemented |
| 21 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 18 | yes | complemented |
| 22 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 36 | yes | complemented |
| 23 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 18 | yes | complemented |
| 24 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 144 | yes | complemented |
| 25 | C2×#4130 | C22 | 1 | 18 | yes | complemented |
| 26 | C22×C4⋊AGL(1,𝔽5) | C22 | 1 | 9 | yes | complemented |
| 27 | C22×C4×AGL(1,𝔽5) | C22 | 1 | 9 | yes | complemented |
| 28 | C2×C4×H(5,𝔽2) | — | 5 | 1 | no | maximal, Sylow |
| 29 | C24×D5 | C23 | 1 | 6 | yes | — |
| 30 | C23×AGL(1,𝔽5) | — | 4 | 24 | no | — |
| 31 | C23×AGL(1,𝔽5) | C23 | 1 | 9 | yes | — |
| 32 | C23×AGL(1,𝔽5) | C23 | 1 | 9 | yes | — |
| 33 | C23×AGL(1,𝔽5) | C23 | 1 | 18 | yes | — |
| 34 | C23×AGL(1,𝔽5) | C23 | 1 | 48 | yes | complemented |
| 35 | C5×H(5,𝔽2) | C2×C4 | 1 | 16 | yes | complemented |
| 36 | C2×C5×#41 | C2×C4 | 1 | 6 | yes | complemented |
| 37 | C22×C5×D4 | C2×C4 | 1 | 9 | yes | complemented |
| 38 | C22×C22⋊D5 | C2×C4 | 1 | 18 | yes | complemented |
| 39 | #4149 | C2×C4 | 1 | 96 | yes | complemented |
| 40 | D5×#41 | C2×C4 | 1 | 48 | yes | complemented |
| 41 | D5×#41 | C23 | 1 | 48 | yes | — |
| 42 | C2×#713 | C2×C4 | 1 | 6 | yes | complemented |
| 43 | C2×Q8×D5 | C23 | 1 | 2 | yes | — |
| 44 | #4144 | C2×C4 | 1 | 144 | yes | complemented |
| 45 | C2×#711 | C2×C4 | 1 | 18 | yes | complemented |
| 46 | C2×D4×D5 | C2×C4 | 1 | 36 | yes | complemented |
| 47 | C2×D4×D5 | C2×C4 | 1 | 72 | yes | complemented |
| 48 | C2×D4×D5 | C23 | 1 | 18 | yes | — |
| 49 | C2×D4×D5 | C23 | 1 | 72 | yes | — |
| 50 | C2×#709 | C2×C4 | 1 | 18 | yes | complemented |
| 51 | C22×D20 | C2×C4 | 1 | 9 | yes | complemented |
| 52 | C22×C4×D5 | C23 | 1 | 9 | yes | — |
| 53 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 36 | yes | — |
| 54 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 144 | yes | complemented |
| 55 | Q8×AGL(1,𝔽5) | C23 | 1 | 16 | yes | complemented |
| 56 | Q8×AGL(1,𝔽5) | C23 | 1 | 48 | yes | complemented |
| 57 | D4×AGL(1,𝔽5) | C23 | 1 | 144 | yes | complemented |
| 58 | D4×AGL(1,𝔽5) | C23 | 1 | 288 | yes | complemented |
| 59 | D4×AGL(1,𝔽5) | C23 | 1 | 144 | yes | complemented |
| 60 | #4130 | C23 | 1 | 144 | yes | complemented |
| 61 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 18 | yes | — |
| 62 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 63 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 72 | yes | complemented |
| 64 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 65 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 18 | yes | — |
| 66 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 72 | yes | complemented |
| 67 | C22×H(5,𝔽2) | — | 5 | 1 | no | — |
| 68 | C4×H(5,𝔽2) | — | 5 | 32 | no | — |
| 69 | C2×#520 | — | 5 | 6 | no | — |
| 70 | C2×#518 | — | 5 | 9 | no | — |
| 71 | C2×C4×#41 | — | 5 | 6 | no | — |
| 72 | C22×C4×D4 | — | 5 | 9 | no | — |
| 73 | C24×C5 | C22×C4 | 1 | 6 | yes | complemented |
| 74 | C23×D5 | — | 4 | 12 | no | — |
| 75 | C23×D5 | — | 4 | 12 | no | — |
| 76 | C23×D5 | C22×C4 | 1 | 24 | yes | complemented |
| 77 | C23×D5 | C22×C4 | 1 | 18 | yes | complemented |
| 78 | C23×D5 | C24 | 1 | 9 | yes | — |
| 79 | C23×D5 | C24 | 1 | 24 | yes | — |
| 80 | C22×AGL(1,𝔽5) | — | 2 | 36 | no | — |
| 81 | C22×AGL(1,𝔽5) | — | 4 | 96 | no | — |
| 82 | C22×AGL(1,𝔽5) | — | 4 | 36 | no | — |
| 83 | C22×AGL(1,𝔽5) | — | 4 | 18 | no | — |
| 84 | C22×AGL(1,𝔽5) | C24 | 1 | 6 | yes | — |
| 85 | C22×AGL(1,𝔽5) | C24 | 1 | 9 | yes | — |
| 86 | C22×AGL(1,𝔽5) | C24 | 1 | 36 | yes | — |
| 87 | C22×AGL(1,𝔽5) | C24 | 1 | 36 | yes | — |
| 88 | C22×AGL(1,𝔽5) | C24 | 1 | 72 | yes | — |
| 89 | C22×AGL(1,𝔽5) | C24 | 1 | 1 | yes | characteristic |
| 90 | C5×#41 | C22×C4 | 1 | 48 | yes | complemented |
| 91 | C2×C5×Q8 | C22×C4 | 1 | 2 | yes | complemented |
| 92 | C2×C5×D4 | C22×C4 | 1 | 18 | yes | complemented |
| 93 | C2×C5×D4 | C22×C4 | 1 | 72 | yes | complemented |
| 94 | C22×C4×C5 | C22×C4 | 1 | 9 | yes | complemented |
| 95 | C2×C22⋊D5 | C22×C4 | 1 | 36 | yes | complemented |
| 96 | C2×C22⋊D5 | C22×C4 | 1 | 144 | yes | complemented |
| 97 | C22×Dic5 | C22×C4 | 1 | 9 | yes | complemented |
| 98 | #713 | C22×C4 | 1 | 48 | yes | complemented |
| 99 | Q8×D5 | C22×C4 | 1 | 8 | yes | complemented |
| 100 | Q8×D5 | C24 | 1 | 8 | yes | — |
| 101 | #711 | C22×C4 | 1 | 144 | yes | complemented |
| 102 | D4×D5 | C22×C4 | 1 | 72 | yes | complemented |
| 103 | D4×D5 | C22×C4 | 1 | 288 | yes | complemented |
| 104 | D4×D5 | C24 | 1 | 72 | yes | — |
| 105 | #709 | C22×C4 | 1 | 144 | yes | complemented |
| 106 | C2×D20 | C22×C4 | 1 | 18 | yes | complemented |
| 107 | C2×D20 | C22×C4 | 1 | 72 | yes | complemented |
| 108 | C2×C4×D5 | C22×C4 | 1 | 36 | yes | complemented |
| 109 | C2×C4×D5 | C22×C4 | 1 | 18 | yes | complemented |
| 110 | C2×C4×D5 | C24 | 1 | 6 | yes | — |
| 111 | C2×C4×D5 | C24 | 1 | 36 | yes | — |
| 112 | C2×Dic10 | C22×C4 | 1 | 6 | yes | complemented |
| 113 | C22⋊AGL(1,𝔽5) | C24 | 1 | 144 | yes | — |
| 114 | C4⋊AGL(1,𝔽5) | C24 | 1 | 72 | yes | — |
| 115 | C4⋊AGL(1,𝔽5) | C24 | 1 | 24 | yes | — |
| 116 | C4×AGL(1,𝔽5) | C24 | 1 | 24 | yes | — |
| 117 | C4×AGL(1,𝔽5) | C24 | 1 | 72 | yes | — |
| 118 | C2×H(5,𝔽2) | — | 5 | 16 | no | — |
| 119 | C2×H(5,𝔽2) | — | 5 | 16 | no | — |
| 120 | C2×H(5,𝔽2) | — | 5 | 6 | no | — |
| 121 | C2×H(5,𝔽2) | — | 5 | 9 | no | — |
| 122 | C2×H(5,𝔽2) | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 123 | C22×#41 | — | 5 | 6 | no | — |
| 124 | C23×D4 | — | 5 | 9 | no | — |
| 125 | C24×C4 | — | 5 | 6 | no | — |
| 126 | #520 | — | 5 | 96 | no | — |
| 127 | #518 | — | 5 | 144 | no | — |
| 128 | C4×#41 | — | 5 | 96 | no | — |
| 129 | C2×C4×Q8 | — | 5 | 2 | no | — |
| 130 | C2×C4×Q8 | — | 5 | 6 | no | — |
| 131 | C2×C4×D4 | — | 5 | 18 | no | — |
| 132 | C2×C4×D4 | — | 5 | 36 | no | — |
| 133 | C2×C4×D4 | — | 5 | 144 | no | — |
| 134 | C2×C4×D4 | — | 5 | 18 | no | — |
| 135 | C2×#117 | — | 5 | 18 | no | — |
| 136 | C22×C4⋊C4 | — | 5 | 9 | no | — |
| 137 | C22×C22⋊C4 | — | 5 | 18 | no | — |
| 138 | C22×C42 | — | 5 | 9 | no | — |
| 139 | C23×C5 | — | 4 | 12 | no | — |
| 140 | C23×C5 | C23×C4 | 1 | 9 | yes | — |
| 141 | C23×C5 | C23×C4 | 1 | 24 | yes | complemented |
| 142 | C22×D5 | — | 2 | 18 | no | — |
| 143 | C22×D5 | — | 2 | 18 | no | — |
| 144 | C22×D5 | — | 4 | 24 | no | — |
| 145 | C22×D5 | — | 4 | 48 | no | — |
| 146 | C22×D5 | — | 4 | 24 | no | — |
| 147 | C22×D5 | — | 4 | 36 | no | — |
| 148 | C22×D5 | C23×C4 | 1 | 9 | yes | — |
| 149 | C22×D5 | C23×C4 | 1 | 18 | yes | — |
| 150 | C22×D5 | C23×C4 | 1 | 72 | yes | complemented |
| 151 | C22×D5 | C25 | 1 | 18 | yes | — |
| 152 | C22×D5 | C25 | 1 | 1 | yes | characteristic |
| 153 | C2×AGL(1,𝔽5) | — | 2 | 18 | no | — |
| 154 | C2×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 155 | C2×AGL(1,𝔽5) | — | 2 | 72 | no | — |
| 156 | C2×AGL(1,𝔽5) | — | 4 | 72 | no | — |
| 157 | C2×AGL(1,𝔽5) | — | 4 | 36 | no | — |
| 158 | C2×AGL(1,𝔽5) | H(5,𝔽2) | 1 | 4 | yes | direct product factor |
| 159 | C2×AGL(1,𝔽5) | C25 | 1 | 12 | yes | — |
| 160 | C2×AGL(1,𝔽5) | C25 | 1 | 18 | yes | — |
| 161 | C2×AGL(1,𝔽5) | C25 | 1 | 2 | yes | — |
| 162 | C5×Q8 | C23×C4 | 1 | 8 | yes | complemented |
| 163 | C5×D4 | C23×C4 | 1 | 72 | yes | complemented |
| 164 | C2×C4×C5 | C23×C4 | 1 | 6 | yes | — |
| 165 | C2×C4×C5 | C23×C4 | 1 | 36 | yes | complemented |
| 166 | C22⋊D5 | C23×C4 | 1 | 144 | yes | complemented |
| 167 | C2×Dic5 | C23×C4 | 1 | 6 | yes | — |
| 168 | C2×Dic5 | C23×C4 | 1 | 36 | yes | complemented |
| 169 | D20 | C23×C4 | 1 | 72 | yes | complemented |
| 170 | C4×D5 | C23×C4 | 1 | 12 | yes | — |
| 171 | C4×D5 | C23×C4 | 1 | 72 | yes | complemented |
| 172 | C4×D5 | C25 | 1 | 12 | yes | — |
| 173 | Dic10 | C23×C4 | 1 | 24 | yes | complemented |
| 174 | C25 | — | 5 | 6 | no | — |
| 175 | H(5,𝔽2) | — | 5 | 96 | no | — |
| 176 | H(5,𝔽2) | — | 5 | 144 | no | — |
| 177 | H(5,𝔽2) | C2×AGL(1,𝔽5) | 1 | 16 | yes | direct product factor |
| 178 | C2×#41 | — | 5 | 48 | no | — |
| 179 | C2×#41 | — | 5 | 48 | no | — |
| 180 | C2×#41 | — | 5 | 6 | no | — |
| 181 | C2×#41 | — | 5 | 18 | no | — |
| 182 | C2×#41 | — | 5 | 18 | no | — |
| 183 | C2×#41 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 184 | C22×Q8 | — | 5 | 2 | no | — |
| 185 | C22×D4 | — | 5 | 18 | no | — |
| 186 | C22×D4 | — | 5 | 18 | no | — |
| 187 | C22×D4 | — | 5 | 72 | no | — |
| 188 | C22×D4 | — | 5 | 36 | no | — |
| 189 | C22×D4 | — | 5 | 72 | no | — |
| 190 | C22×D4 | — | 5 | 9 | no | — |
| 191 | C22×D4 | C2×AGL(1,𝔽5) | 1 | 9 | yes | complemented |
| 192 | C23×C4 | — | 5 | 9 | no | — |
| 193 | C23×C4 | — | 5 | 9 | no | — |
| 194 | C23×C4 | — | 5 | 9 | no | — |
| 195 | C23×C4 | — | 5 | 18 | no | — |
| 196 | C23×C4 | — | 5 | 48 | no | — |
| 197 | C23×C4 | — | 20 | 24 | no | — |
| 198 | C4×Q8 | — | 5 | 16 | no | — |
| 199 | C4×Q8 | — | 5 | 48 | no | — |
| 200 | C4×D4 | — | 5 | 144 | no | — |
| 201 | C4×D4 | — | 5 | 288 | no | — |
| 202 | C4×D4 | — | 5 | 144 | no | — |
| 203 | #117 | — | 5 | 144 | no | — |
| 204 | C2×C4⋊C4 | — | 5 | 18 | no | — |
| 205 | C2×C4⋊C4 | — | 5 | 72 | no | — |
| 206 | C2×C4⋊C4 | — | 5 | 6 | no | — |
| 207 | C2×C22⋊C4 | — | 5 | 36 | no | — |
| 208 | C2×C22⋊C4 | — | 5 | 144 | no | — |
| 209 | C2×C42 | — | 5 | 18 | no | — |
| 210 | C2×C42 | — | 5 | 6 | no | — |
| 211 | C2×C42 | — | 5 | 72 | no | — |
| 212 | C22×C5 | — | 2 | 18 | no | — |
| 213 | C22×C5 | — | 4 | 24 | no | — |
| 214 | C22×C5 | C24×C4 | 1 | 18 | yes | — |
| 215 | C22×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 216 | C2×D5 | — | 2 | 18 | no | — |
| 217 | C2×D5 | — | 2 | 18 | no | — |
| 218 | C2×D5 | — | 2 | 18 | no | — |
| 219 | C2×D5 | — | 2 | 36 | no | — |
| 220 | C2×D5 | — | 4 | 72 | no | — |
| 221 | C2×D5 | C24×C4 | 1 | 18 | yes | — |
| 222 | C2×D5 | C24×C4 | 1 | 1 | yes | characteristic |
| 223 | C2×D5 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 224 | C2×D5 | #585 | 1 | 2 | yes | — |
| 225 | C2×D5 | C26 | 1 | 1 | yes | characteristic |
| 226 | AGL(1,𝔽5) | — | 2 | 18 | no | — |
| 227 | AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 228 | AGL(1,𝔽5) | C2×H(5,𝔽2) | 1 | 4 | yes | direct product factor |
| 229 | C4×C5 | C24×C4 | 1 | 12 | yes | — |
| 230 | Dic5 | C24×C4 | 1 | 12 | yes | — |
| 231 | C24 | — | 5 | 9 | no | — |
| 232 | C24 | — | 5 | 18 | no | — |
| 233 | C24 | — | 5 | 24 | no | — |
| 234 | C24 | — | 5 | 24 | no | — |
| 235 | C24 | — | 20 | 12 | no | — |
| 236 | C24 | — | 20 | 12 | no | — |
| 237 | C24 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 238 | #41 | — | 5 | 48 | no | — |
| 239 | #41 | — | 5 | 144 | no | — |
| 240 | #41 | — | 5 | 144 | no | — |
| 241 | #41 | C22×AGL(1,𝔽5) | 1 | 48 | yes | complemented |
| 242 | C2×Q8 | — | 5 | 8 | no | — |
| 243 | C2×Q8 | — | 5 | 8 | no | — |
| 244 | C2×Q8 | — | 5 | 6 | no | — |
| 245 | C2×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 246 | C2×D4 | — | 5 | 36 | no | — |
| 247 | C2×D4 | — | 5 | 144 | no | — |
| 248 | C2×D4 | — | 5 | 72 | no | — |
| 249 | C2×D4 | — | 5 | 72 | no | — |
| 250 | C2×D4 | — | 5 | 288 | no | — |
| 251 | C2×D4 | — | 5 | 18 | no | — |
| 252 | C2×D4 | — | 5 | 72 | no | — |
| 253 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 18 | yes | complemented |
| 254 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 72 | yes | complemented |
| 255 | C22×C4 | — | 5 | 1 | no | — |
| 256 | C22×C4 | — | 5 | 9 | no | — |
| 257 | C22×C4 | — | 5 | 6 | no | — |
| 258 | C22×C4 | — | 5 | 18 | no | — |
| 259 | C22×C4 | — | 5 | 36 | no | — |
| 260 | C22×C4 | — | 5 | 36 | no | — |
| 261 | C22×C4 | — | 5 | 6 | no | — |
| 262 | C22×C4 | — | 5 | 9 | no | — |
| 263 | C22×C4 | — | 5 | 36 | no | — |
| 264 | C22×C4 | — | 5 | 36 | no | — |
| 265 | C22×C4 | — | 5 | 72 | no | — |
| 266 | C22×C4 | — | 10 | 36 | no | — |
| 267 | C22×C4 | — | 20 | 96 | no | — |
| 268 | C22×C4 | — | 20 | 36 | no | — |
| 269 | C22×C4 | — | 20 | 18 | no | — |
| 270 | C22×C4 | C22×AGL(1,𝔽5) | 1 | 9 | yes | complemented |
| 271 | C4⋊C4 | — | 5 | 72 | no | — |
| 272 | C4⋊C4 | — | 5 | 24 | no | — |
| 273 | C22⋊C4 | — | 5 | 144 | no | — |
| 274 | C42 | — | 5 | 24 | no | — |
| 275 | C42 | — | 5 | 72 | no | — |
| 276 | C2×C5 | — | 2 | 18 | no | — |
| 277 | C2×C5 | C4×H(5,𝔽2) | 1 | 2 | yes | complemented |
| 278 | C2×C5 | C25×C4 | 1 | 1 | yes | characteristic |
| 279 | D5 | — | 2 | 18 | no | — |
| 280 | D5 | C4×H(5,𝔽2) | 1 | 2 | yes | complemented |
| 281 | D5 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 282 | D5 | C2×#585 | 1 | 1 | yes | characteristic |
| 283 | C23 | — | 4 | 12 | no | — |
| 284 | C23 | — | 5 | 1 | no | — |
| 285 | C23 | — | 5 | 18 | no | — |
| 286 | C23 | — | 5 | 18 | no | — |
| 287 | C23 | — | 5 | 9 | no | — |
| 288 | C23 | — | 5 | 72 | no | — |
| 289 | C23 | — | 10 | 18 | no | — |
| 290 | C23 | — | 10 | 18 | no | — |
| 291 | C23 | — | 20 | 36 | no | — |
| 292 | C23 | — | 20 | 24 | no | — |
| 293 | C23 | — | 20 | 24 | no | — |
| 294 | C23 | — | 20 | 48 | no | — |
| 295 | C23 | C23×AGL(1,𝔽5) | 1 | 9 | yes | — |
| 296 | C23 | C23×AGL(1,𝔽5) | 1 | 24 | yes | complemented |
| 297 | Q8 | — | 5 | 24 | no | — |
| 298 | Q8 | C23×AGL(1,𝔽5) | 1 | 8 | yes | complemented |
| 299 | D4 | — | 5 | 144 | no | — |
| 300 | D4 | — | 5 | 72 | no | — |
| 301 | D4 | C23×AGL(1,𝔽5) | 1 | 72 | yes | complemented |
| 302 | C2×C4 | — | 5 | 2 | no | — |
| 303 | C2×C4 | — | 5 | 4 | no | — |
| 304 | C2×C4 | — | 5 | 36 | no | — |
| 305 | C2×C4 | — | 5 | 6 | no | — |
| 306 | C2×C4 | — | 5 | 12 | no | — |
| 307 | C2×C4 | — | 5 | 12 | no | — |
| 308 | C2×C4 | — | 5 | 72 | no | — |
| 309 | C2×C4 | — | 5 | 12 | no | — |
| 310 | C2×C4 | — | 5 | 18 | no | — |
| 311 | C2×C4 | — | 10 | 72 | no | — |
| 312 | C2×C4 | — | 10 | 18 | no | — |
| 313 | C2×C4 | — | 10 | 12 | no | — |
| 314 | C2×C4 | — | 20 | 72 | no | — |
| 315 | C2×C4 | — | 20 | 36 | no | — |
| 316 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 317 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 36 | yes | complemented |
| 318 | C5 | C2×C4×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 319 | C22 | — | 2 | 18 | no | — |
| 320 | C22 | — | 4 | 24 | no | — |
| 321 | C22 | — | 5 | 2 | no | — |
| 322 | C22 | — | 5 | 2 | no | — |
| 323 | C22 | — | 5 | 1 | no | — |
| 324 | C22 | — | 5 | 1 | no | — |
| 325 | C22 | — | 5 | 18 | no | — |
| 326 | C22 | — | 10 | 18 | no | — |
| 327 | C22 | — | 10 | 18 | no | — |
| 328 | C22 | — | 10 | 36 | no | — |
| 329 | C22 | — | 10 | 18 | no | — |
| 330 | C22 | — | 20 | 72 | no | — |
| 331 | C22 | C24×AGL(1,𝔽5) | 1 | 18 | yes | — |
| 332 | C22 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 333 | C4 | — | 5 | 4 | no | — |
| 334 | C4 | — | 5 | 12 | no | — |
| 335 | C4 | — | 10 | 18 | no | — |
| 336 | C4 | — | 10 | 12 | no | — |
| 337 | C4 | C24×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 338 | C2 | — | 2 | 18 | no | — |
| 339 | C2 | — | 5 | 1 | no | — |
| 340 | C2 | — | 5 | 1 | no | — |
| 341 | C2 | — | 5 | 2 | no | — |
| 342 | C2 | — | 10 | 18 | no | — |
| 343 | C2 | AGL(1,𝔽5)×H(5,𝔽2) | 1 | 2 | yes | direct product factor |
| 344 | C2 | C25×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 2. AGL(1,𝔽5)×H(5,𝔽2) | C2 | direct (N × H) |
| 3. C2×#66266 | C2 | semidirect |
| 4. C2×#41×AGL(1,𝔽5) | C2 | semidirect |
| 5. C2×#66258 | C2 | semidirect |
| 6. C22×D4×AGL(1,𝔽5) | C2 | semidirect |
| 7. C24×AGL(1,𝔽5) | C22 | semidirect |
| 8. C2×C5×H(5,𝔽2) | C4 | semidirect |
| 9. D5×H(5,𝔽2) | C4 | semidirect |
| 11. C2×#4149 | C4 | semidirect |
| 13. C2×#4144 | C4 | semidirect |
| 15. C22×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 16. #66266 | C22 | semidirect |
| 17. #41×AGL(1,𝔽5) | C22 | semidirect |
| 18. C2×Q8×AGL(1,𝔽5) | C22 | semidirect |
| 19. C2×Q8×AGL(1,𝔽5) | C22 | semidirect |
| 20. #66258 | C22 | semidirect |
| 21. C2×D4×AGL(1,𝔽5) | C22 | semidirect |
| 22. C2×D4×AGL(1,𝔽5) | C22 | semidirect |
| 23. C2×D4×AGL(1,𝔽5) | C22 | semidirect |
| 24. C2×D4×AGL(1,𝔽5) | C22 | semidirect |
| 25. C2×#4130 | C22 | semidirect |
| 26. C22×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 27. C22×C4×AGL(1,𝔽5) | C22 | semidirect |
| 34. C23×AGL(1,𝔽5) | C23 | semidirect |
| 35. C5×H(5,𝔽2) | C2×C4 | semidirect |
| 36. C2×C5×#41 | C2×C4 | semidirect |
| 37. C22×C5×D4 | C2×C4 | semidirect |
| 38. C22×C22⋊D5 | C2×C4 | semidirect |
| 39. #4149 | C2×C4 | semidirect |
| 40. D5×#41 | C2×C4 | semidirect |
| 42. C2×#713 | C2×C4 | semidirect |
| 44. #4144 | C2×C4 | semidirect |
| 45. C2×#711 | C2×C4 | semidirect |
| 46. C2×D4×D5 | C2×C4 | semidirect |
| 47. C2×D4×D5 | C2×C4 | semidirect |
| 50. C2×#709 | C2×C4 | semidirect |
| 51. C22×D20 | C2×C4 | semidirect |
| 54. C2×C22⋊AGL(1,𝔽5) | C23 | semidirect |
| 55. Q8×AGL(1,𝔽5) | C23 | semidirect |
| 56. Q8×AGL(1,𝔽5) | C23 | semidirect |
| 57. D4×AGL(1,𝔽5) | C23 | semidirect |
| 58. D4×AGL(1,𝔽5) | C23 | semidirect |
| 59. D4×AGL(1,𝔽5) | C23 | semidirect |
| 60. #4130 | C23 | semidirect |
| 63. C2×C4⋊AGL(1,𝔽5) | C23 | semidirect |
| 66. C2×C4×AGL(1,𝔽5) | C23 | semidirect |
| 73. C24×C5 | C22×C4 | semidirect |
| 76. C23×D5 | C22×C4 | semidirect |
| 77. C23×D5 | C22×C4 | semidirect |
| 90. C5×#41 | C22×C4 | semidirect |
| 91. C2×C5×Q8 | C22×C4 | semidirect |
| 92. C2×C5×D4 | C22×C4 | semidirect |
| 93. C2×C5×D4 | C22×C4 | semidirect |
| 94. C22×C4×C5 | C22×C4 | semidirect |
| 95. C2×C22⋊D5 | C22×C4 | semidirect |
| 96. C2×C22⋊D5 | C22×C4 | semidirect |
| 97. C22×Dic5 | C22×C4 | semidirect |
| 98. #713 | C22×C4 | semidirect |
| 99. Q8×D5 | C22×C4 | semidirect |
| 101. #711 | C22×C4 | semidirect |
| 102. D4×D5 | C22×C4 | semidirect |
| 103. D4×D5 | C22×C4 | semidirect |
| 105. #709 | C22×C4 | semidirect |
| 106. C2×D20 | C22×C4 | semidirect |
| 107. C2×D20 | C22×C4 | semidirect |
| 108. C2×C4×D5 | C22×C4 | semidirect |
| 109. C2×C4×D5 | C22×C4 | semidirect |
| 112. C2×Dic10 | C22×C4 | semidirect |
| 122. C2×H(5,𝔽2) | AGL(1,𝔽5) | direct (N × H) |
| 141. C23×C5 | C23×C4 | semidirect |
| 150. C22×D5 | C23×C4 | semidirect |
| 158. C2×AGL(1,𝔽5) | H(5,𝔽2) | direct (N × H) |
| 162. C5×Q8 | C23×C4 | semidirect |
| 163. C5×D4 | C23×C4 | semidirect |
| 165. C2×C4×C5 | C23×C4 | semidirect |
| 166. C22⋊D5 | C23×C4 | semidirect |
| 168. C2×Dic5 | C23×C4 | semidirect |
| 169. D20 | C23×C4 | semidirect |
| 171. C4×D5 | C23×C4 | semidirect |
| 173. Dic10 | C23×C4 | semidirect |
| 177. H(5,𝔽2) | C2×AGL(1,𝔽5) | direct (N × H) |
| 183. C2×#41 | C2×AGL(1,𝔽5) | semidirect |
| 191. C22×D4 | C2×AGL(1,𝔽5) | semidirect |
| 228. AGL(1,𝔽5) | C2×H(5,𝔽2) | direct (N × H) |
| 237. C24 | C22×AGL(1,𝔽5) | semidirect |
| 241. #41 | C22×AGL(1,𝔽5) | semidirect |
| 245. C2×Q8 | C22×AGL(1,𝔽5) | semidirect |
| 253. C2×D4 | C22×AGL(1,𝔽5) | semidirect |
| 254. C2×D4 | C22×AGL(1,𝔽5) | semidirect |
| 270. C22×C4 | C22×AGL(1,𝔽5) | semidirect |
| 277. C2×C5 | C4×H(5,𝔽2) | semidirect |
| 280. D5 | C4×H(5,𝔽2) | semidirect |
| 296. C23 | C23×AGL(1,𝔽5) | semidirect |
| 298. Q8 | C23×AGL(1,𝔽5) | semidirect |
| 301. D4 | C23×AGL(1,𝔽5) | semidirect |
| 317. C2×C4 | C23×AGL(1,𝔽5) | semidirect |
| 318. C5 | C2×C4×H(5,𝔽2) | semidirect |
| 343. C2 | AGL(1,𝔽5)×H(5,𝔽2) | direct (N × H) |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta