← AGL(1,𝔽5)×#559 #13044011
Order 1280.
2564 conjugacy classes of subgroups.
The subgroup lattice has 580 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D5×#559 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617369 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | AGL(1,𝔽5)×#127 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10617326 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | AGL(1,𝔽5)×#124 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10617307 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | AGL(1,𝔽5)×#123 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10617213 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C4×Q8×AGL(1,𝔽5) | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10617182 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | C4×D4×AGL(1,𝔽5) | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | C2×Q8×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 13 | C2×Q8×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 14 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 15 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 16 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 17 | C22×C4×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 18 | C5×#559 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | D5×#127 | C22 | 1 | 1 | yes | characteristic |
| 20 | #66047 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | #66015 | C4 | 1 | 4 | yes | complemented |
| 22 | D5×#124 | C22 | 1 | 4 | yes | — |
| 23 | #65998 | C4 | 1 | 4 | yes | complemented |
| 24 | D5×#123 | C22 | 1 | 4 | yes | — |
| 25 | #65919 | C4 | 1 | 2 | yes | complemented |
| 26 | C4×Q8×D5 | C22 | 1 | 2 | yes | — |
| 27 | #65893 | C4 | 1 | 4 | yes | complemented |
| 28 | C4×D4×D5 | C22 | 1 | 4 | yes | — |
| 29 | (C2×AGL(1,𝔽5))⋊Q8 | C22 | 1 | 4 | yes | — |
| 30 | #65780 | C22 | 1 | 4 | yes | — |
| 31 | #65780 | C22 | 1 | 2 | yes | — |
| 32 | #65780 | C22 | 1 | 4 | yes | — |
| 33 | #65779 | C22 | 1 | 4 | yes | — |
| 34 | #65764 | C22 | 1 | 4 | yes | — |
| 35 | C4×C22⋊AGL(1,𝔽5) | C22 | 1 | 8 | yes | — |
| 36 | #65711 | C22 | 1 | 8 | yes | — |
| 37 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 38 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 39 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 40 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 41 | C4⋊C4×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 42 | #65700 | C22 | 1 | 8 | yes | — |
| 43 | #65700 | C22 | 1 | 8 | yes | — |
| 44 | #65700 | C22 | 1 | 8 | yes | — |
| 45 | #65699 | C22 | 1 | 4 | yes | — |
| 46 | C22⋊C4×AGL(1,𝔽5) | C22 | 1 | 8 | yes | — |
| 47 | C22⋊C4×AGL(1,𝔽5) | C22 | 1 | 8 | yes | — |
| 48 | C22⋊C4×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 49 | #65689 | C22 | 1 | 4 | yes | — |
| 50 | #65688 | C22 | 1 | 1 | yes | characteristic |
| 51 | C4×C4⋊AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 52 | C4×C4⋊AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 53 | C4×C4⋊AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 54 | C42×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 55 | C42×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 56 | C4×#559 | — | 5 | 1 | no | maximal, Sylow |
| 57 | C23×AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 58 | C23×AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 59 | C2×Q8×D5 | C23 | 1 | 2 | yes | — |
| 60 | C2×D4×D5 | C23 | 1 | 4 | yes | — |
| 61 | C2×D4×D5 | C23 | 1 | 2 | yes | — |
| 62 | C22×C4×D5 | C23 | 1 | 4 | yes | — |
| 63 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 8 | yes | — |
| 64 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 8 | yes | — |
| 65 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 66 | C2×C22⋊AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 67 | Q8×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 68 | Q8×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 69 | D4×AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 70 | D4×AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 71 | D4×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 72 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 73 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 74 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 75 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 76 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 77 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 78 | C2×C4×AGL(1,𝔽5) | — | 4 | 8 | no | — |
| 79 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 80 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 81 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 82 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 83 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 84 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 4 | yes | — |
| 86 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 8 | yes | — |
| 88 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 89 | C5×#127 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | C5×#124 | C2×C4 | 1 | 4 | yes | complemented |
| 91 | C5×#123 | C2×C4 | 1 | 4 | yes | complemented |
| 92 | C4×C5×Q8 | C2×C4 | 1 | 2 | yes | complemented |
| 93 | C4×C5×D4 | C2×C4 | 1 | 4 | yes | complemented |
| 94 | #4093 | C2×C4 | 1 | 4 | yes | complemented |
| 95 | Q8×Dic5 | C2×C4 | 1 | 2 | yes | complemented |
| 96 | #4086 | C2×C4 | 1 | 4 | yes | — |
| 97 | #4086 | C2×C4 | 1 | 2 | yes | — |
| 98 | #4082 | C2×C4 | 1 | 4 | yes | complemented |
| 99 | #4081 | C2×C4 | 1 | 4 | yes | complemented |
| 100 | D4×Dic5 | C2×C4 | 1 | 4 | yes | complemented |
| 101 | #4075 | C2×C4 | 1 | 4 | yes | complemented |
| 102 | C4×C22⋊D5 | C2×C4 | 1 | 8 | yes | complemented |
| 103 | #4040 | C2×C4 | 1 | 8 | yes | complemented |
| 104 | #4039 | C2×C4 | 1 | 4 | yes | complemented |
| 105 | D5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 106 | D5×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 107 | #4033 | C2×C4 | 1 | 2 | yes | complemented |
| 108 | #4033 | C2×C4 | 1 | 4 | yes | complemented |
| 109 | #4032 | C2×C4 | 1 | 4 | yes | complemented |
| 110 | #4031 | C2×C4 | 1 | 8 | yes | complemented |
| 111 | #4031 | C2×C4 | 1 | 8 | yes | complemented |
| 112 | #4029 | C2×C4 | 1 | 8 | yes | complemented |
| 113 | #4027 | C2×C4 | 1 | 8 | yes | complemented |
| 114 | D5×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 115 | D5×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 116 | #4021 | C2×C4 | 1 | 4 | yes | complemented |
| 117 | #4020 | C2×C4 | 1 | 1 | yes | characteristic |
| 118 | C4×D20 | C2×C4 | 1 | 4 | yes | complemented |
| 119 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 120 | C42×D5 | C23 | 1 | 4 | yes | — |
| 121 | C4×Dic10 | C2×C4 | 1 | 4 | yes | complemented |
| 122 | C4×Dic10 | C2×C4 | 1 | 2 | yes | complemented |
| 123 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 8 | yes | — |
| 124 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 4 | yes | — |
| 125 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 4 | yes | — |
| 126 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 4 | yes | — |
| 127 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 8 | yes | — |
| 128 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 8 | yes | — |
| 129 | C2×#559 | — | 5 | 1 | no | — |
| 130 | #2374 | — | 5 | 4 | no | — |
| 131 | #2367 | — | 5 | 4 | no | — |
| 132 | #2366 | — | 5 | 1 | no | — |
| 133 | #2357 | — | 5 | 4 | no | — |
| 134 | #2355 | — | 5 | 2 | no | — |
| 135 | C4×#127 | — | 5 | 1 | no | — |
| 136 | C4×#124 | — | 5 | 4 | no | — |
| 137 | C4×#123 | — | 5 | 4 | no | — |
| 138 | C42×Q8 | — | 5 | 2 | no | — |
| 139 | C42×D4 | — | 5 | 4 | no | — |
| 140 | C23×D5 | C24 | 1 | 4 | yes | — |
| 141 | C22×AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 142 | C22×AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 143 | C22×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 144 | C22×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 145 | C22×AGL(1,𝔽5) | C24 | 1 | 1 | yes | characteristic |
| 146 | C22×AGL(1,𝔽5) | C24 | 1 | 4 | yes | — |
| 147 | C22×AGL(1,𝔽5) | C24 | 1 | 4 | yes | — |
| 148 | C22×AGL(1,𝔽5) | C24 | 1 | 2 | yes | — |
| 149 | C22×AGL(1,𝔽5) | C24 | 1 | 4 | yes | — |
| 150 | C22×AGL(1,𝔽5) | C24 | 1 | 1 | yes | characteristic |
| 151 | C2×C5×Q8 | C22×C4 | 1 | 2 | yes | — |
| 152 | C2×C5×D4 | C22×C4 | 1 | 4 | yes | — |
| 153 | C2×C5×D4 | C22×C4 | 1 | 2 | yes | — |
| 154 | C22×C4×C5 | C22×C4 | 1 | 4 | yes | — |
| 155 | C2×C22⋊D5 | C22×C4 | 1 | 8 | yes | — |
| 156 | C2×C22⋊D5 | C22×C4 | 1 | 4 | yes | — |
| 157 | C22×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 158 | Q8×D5 | — | 2 | 4 | no | — |
| 159 | Q8×D5 | — | 2 | 4 | no | — |
| 160 | D4×D5 | — | 2 | 8 | no | — |
| 161 | D4×D5 | — | 2 | 8 | no | — |
| 162 | D4×D5 | — | 4 | 2 | no | — |
| 163 | D4×D5 | — | 4 | 2 | no | — |
| 164 | C2×D20 | C22×C4 | 1 | 4 | yes | — |
| 165 | C2×D20 | C22×C4 | 1 | 2 | yes | — |
| 166 | C2×C4×D5 | — | 4 | 4 | no | — |
| 167 | C2×C4×D5 | — | 4 | 4 | no | — |
| 168 | C2×C4×D5 | C22×C4 | 1 | 8 | yes | — |
| 169 | C2×C4×D5 | C24 | 1 | 4 | yes | — |
| 170 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 171 | C2×C4×D5 | C24 | 1 | 4 | yes | — |
| 172 | C2×C4×D5 | C24 | 1 | 2 | yes | — |
| 173 | C2×Dic10 | C22×C4 | 1 | 2 | yes | — |
| 174 | C2×Dic10 | C22×C4 | 1 | 4 | yes | — |
| 175 | C22⋊AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 176 | C22⋊AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 177 | C22⋊AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 178 | C22⋊AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 179 | C4⋊AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 180 | C4⋊AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 181 | C4⋊AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 182 | C4⋊AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 183 | C4⋊AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 184 | C4⋊AGL(1,𝔽5) | #41 | 1 | 8 | yes | — |
| 185 | C4×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 186 | C4×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 187 | C4×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 188 | C4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 189 | C4×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 190 | C4×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 191 | C4×AGL(1,𝔽5) | — | 4 | 8 | no | — |
| 192 | C4×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 193 | C4×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 194 | C4×AGL(1,𝔽5) | #41 | 1 | 8 | yes | — |
| 195 | C5×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 196 | C5×C4⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 197 | C5×C22⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 198 | C5×C22⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 199 | C42×C5 | C22×C4 | 1 | 4 | yes | — |
| 200 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 201 | C22⋊Dic5 | C22×C4 | 1 | 8 | yes | — |
| 202 | C22⋊Dic5 | C22×C4 | 1 | 4 | yes | — |
| 203 | #685 | C22×C4 | 1 | 8 | yes | — |
| 204 | #685 | C22×C4 | 1 | 8 | yes | — |
| 205 | #685 | C22×C4 | 1 | 8 | yes | — |
| 206 | C4⋊Dic5 | C22×C4 | 1 | 2 | yes | — |
| 207 | C4⋊Dic5 | C22×C4 | 1 | 4 | yes | — |
| 208 | #683 | C22×C4 | 1 | 4 | yes | — |
| 209 | #683 | C22×C4 | 1 | 4 | yes | — |
| 210 | #683 | C22×C4 | 1 | 4 | yes | — |
| 211 | C4×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 212 | C4×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 213 | C4×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 214 | C4×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 215 | C4×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 216 | #559 | — | 5 | 1 | no | — |
| 217 | #559 | — | 5 | 4 | no | — |
| 218 | #559 | — | 5 | 4 | no | — |
| 219 | #559 | — | 5 | 2 | no | — |
| 220 | #559 | — | 5 | 4 | no | — |
| 221 | #559 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 222 | C2×#127 | — | 5 | 1 | no | — |
| 223 | C2×#124 | — | 5 | 4 | no | — |
| 224 | C2×#123 | — | 5 | 4 | no | — |
| 225 | C2×C4×Q8 | — | 5 | 2 | no | — |
| 226 | C2×C4×Q8 | — | 5 | 2 | no | — |
| 227 | C2×C4×Q8 | — | 5 | 2 | no | — |
| 228 | C2×C4×D4 | — | 5 | 4 | no | — |
| 229 | C2×C4×D4 | — | 5 | 4 | no | — |
| 230 | C2×C4×D4 | — | 5 | 4 | no | — |
| 231 | C2×C4×D4 | — | 5 | 2 | no | — |
| 232 | C22×C42 | — | 5 | 4 | no | — |
| 233 | #391 | — | 5 | 4 | no | — |
| 234 | #390 | — | 5 | 4 | no | — |
| 235 | #390 | — | 5 | 2 | no | — |
| 236 | #390 | — | 5 | 4 | no | — |
| 237 | #388 | — | 5 | 8 | no | — |
| 238 | #388 | — | 5 | 8 | no | — |
| 239 | #388 | — | 5 | 8 | no | — |
| 240 | #387 | — | 5 | 8 | no | — |
| 241 | #386 | — | 5 | 4 | no | — |
| 242 | #385 | — | 5 | 4 | no | — |
| 243 | #384 | — | 5 | 1 | no | — |
| 244 | #382 | — | 5 | 4 | no | — |
| 245 | #381 | — | 5 | 4 | no | — |
| 246 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 247 | C4×C4⋊C4 | — | 5 | 2 | no | — |
| 248 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 249 | C4×C4⋊C4 | — | 5 | 2 | no | — |
| 250 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 251 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 252 | C4×C4⋊C4 | — | 5 | 2 | no | — |
| 253 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 254 | C4×C22⋊C4 | — | 5 | 8 | no | — |
| 255 | C4×C22⋊C4 | — | 5 | 8 | no | — |
| 256 | C4×C22⋊C4 | — | 5 | 8 | no | — |
| 257 | C4×C22⋊C4 | — | 5 | 4 | no | — |
| 258 | C43 | — | 5 | 1 | no | — |
| 259 | C43 | — | 5 | 4 | no | — |
| 260 | C23×C5 | C23×C4 | 1 | 4 | yes | — |
| 261 | C22×D5 | — | 2 | 8 | no | — |
| 262 | C22×D5 | — | 2 | 8 | no | — |
| 263 | C22×D5 | — | 2 | 4 | no | — |
| 264 | C22×D5 | — | 2 | 4 | no | — |
| 265 | C22×D5 | C23×C4 | 1 | 4 | yes | — |
| 266 | C22×D5 | C25 | 1 | 1 | yes | characteristic |
| 267 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 268 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 269 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 270 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 271 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 272 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 273 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 274 | C2×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 275 | C2×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 276 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 277 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 278 | C2×AGL(1,𝔽5) | — | 4 | 16 | no | — |
| 279 | C2×AGL(1,𝔽5) | — | 4 | 16 | no | — |
| 280 | C2×AGL(1,𝔽5) | C2×#41 | 1 | 8 | yes | — |
| 281 | C2×AGL(1,𝔽5) | C2×#41 | 1 | 4 | yes | — |
| 282 | C2×AGL(1,𝔽5) | C2×#41 | 1 | 4 | yes | — |
| 283 | C2×AGL(1,𝔽5) | H(5,𝔽2) | 1 | 2 | yes | — |
| 284 | C5×Q8 | — | 2 | 4 | no | — |
| 285 | C5×D4 | — | 2 | 8 | no | — |
| 286 | C5×D4 | — | 4 | 2 | no | — |
| 287 | C2×C4×C5 | — | 4 | 4 | no | — |
| 288 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 289 | C2×C4×C5 | C23×C4 | 1 | 4 | yes | — |
| 290 | C2×C4×C5 | C23×C4 | 1 | 4 | yes | — |
| 291 | C2×C4×C5 | C23×C4 | 1 | 2 | yes | — |
| 292 | C22⋊D5 | — | 2 | 16 | no | — |
| 293 | C22⋊D5 | — | 4 | 4 | no | — |
| 294 | C2×Dic5 | — | 4 | 4 | no | — |
| 295 | C2×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 296 | C2×Dic5 | C23×C4 | 1 | 4 | yes | — |
| 297 | C2×Dic5 | C23×C4 | 1 | 4 | yes | — |
| 298 | C2×Dic5 | C23×C4 | 1 | 2 | yes | — |
| 299 | D20 | — | 2 | 8 | no | — |
| 300 | D20 | — | 4 | 2 | no | — |
| 301 | C4×D5 | — | 2 | 4 | no | — |
| 302 | C4×D5 | — | 2 | 4 | no | — |
| 303 | C4×D5 | — | 2 | 4 | no | — |
| 304 | C4×D5 | — | 2 | 1 | no | — |
| 305 | C4×D5 | — | 2 | 4 | no | — |
| 306 | C4×D5 | — | 2 | 1 | no | — |
| 307 | C4×D5 | — | 4 | 8 | no | — |
| 308 | C4×D5 | C2×#41 | 1 | 4 | yes | — |
| 309 | C4×D5 | C2×#41 | 1 | 4 | yes | — |
| 310 | Dic10 | — | 2 | 4 | no | — |
| 311 | Dic10 | — | 2 | 8 | no | — |
| 312 | C22×Q8 | — | 5 | 2 | no | — |
| 313 | C22×D4 | — | 5 | 4 | no | — |
| 314 | C22×D4 | — | 5 | 2 | no | — |
| 315 | C23×C4 | — | 5 | 4 | no | — |
| 316 | C23×C4 | — | 5 | 4 | no | — |
| 317 | C23×C4 | — | 5 | 4 | no | — |
| 318 | #127 | — | 5 | 2 | no | — |
| 319 | #127 | — | 5 | 4 | no | — |
| 320 | #127 | — | 5 | 1 | no | — |
| 321 | #127 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 322 | #124 | — | 5 | 4 | no | — |
| 323 | #124 | — | 5 | 4 | no | — |
| 324 | #124 | — | 5 | 8 | no | — |
| 325 | #124 | — | 5 | 8 | no | — |
| 326 | #124 | — | 5 | 4 | no | — |
| 327 | #124 | C2×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 328 | #123 | — | 5 | 4 | no | — |
| 329 | #123 | — | 5 | 4 | no | — |
| 330 | #123 | — | 5 | 8 | no | — |
| 331 | #123 | — | 5 | 8 | no | — |
| 332 | #123 | — | 5 | 4 | no | — |
| 333 | #123 | C2×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 334 | C4×Q8 | — | 5 | 2 | no | — |
| 335 | C4×Q8 | — | 5 | 4 | no | — |
| 336 | C4×Q8 | — | 5 | 2 | no | — |
| 337 | C4×Q8 | — | 5 | 2 | no | — |
| 338 | C4×Q8 | — | 5 | 4 | no | — |
| 339 | C4×Q8 | — | 10 | 8 | no | — |
| 340 | C4×Q8 | — | 10 | 8 | no | — |
| 341 | C4×Q8 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 342 | C4×D4 | — | 5 | 4 | no | — |
| 343 | C4×D4 | — | 5 | 8 | no | — |
| 344 | C4×D4 | — | 5 | 4 | no | — |
| 345 | C4×D4 | — | 5 | 8 | no | — |
| 346 | C4×D4 | — | 5 | 4 | no | — |
| 347 | C4×D4 | — | 10 | 16 | no | — |
| 348 | C4×D4 | — | 10 | 16 | no | — |
| 349 | C4×D4 | — | 20 | 4 | no | — |
| 350 | C4×D4 | C2×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 351 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 352 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 353 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 354 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 355 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 356 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 357 | C2×C4⋊C4 | — | 5 | 4 | no | — |
| 358 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 359 | C2×C22⋊C4 | — | 5 | 8 | no | — |
| 360 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 361 | C2×C22⋊C4 | — | 5 | 8 | no | — |
| 362 | C2×C22⋊C4 | — | 5 | 8 | no | — |
| 363 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 364 | C2×C22⋊C4 | — | 5 | 4 | no | — |
| 365 | C2×C42 | — | 5 | 2 | no | — |
| 366 | C2×C42 | — | 5 | 4 | no | — |
| 367 | C2×C42 | — | 5 | 1 | no | — |
| 368 | C2×C42 | — | 5 | 1 | no | — |
| 369 | C2×C42 | — | 5 | 4 | no | — |
| 370 | C2×C42 | — | 5 | 4 | no | — |
| 371 | C2×C42 | — | 5 | 4 | no | — |
| 372 | C2×C42 | — | 5 | 2 | no | — |
| 373 | C2×C42 | — | 5 | 4 | no | — |
| 374 | C2×C42 | — | 5 | 4 | no | — |
| 375 | C2×C42 | — | 5 | 1 | no | — |
| 376 | C2×C42 | — | 5 | 8 | no | — |
| 377 | C2×C42 | — | 20 | 8 | no | — |
| 378 | #95 | — | 5 | 4 | no | — |
| 379 | #95 | — | 5 | 8 | no | — |
| 380 | #95 | — | 5 | 8 | no | — |
| 381 | #95 | — | 5 | 8 | no | — |
| 382 | #95 | — | 5 | 4 | no | — |
| 383 | #95 | — | 5 | 4 | no | — |
| 384 | C22×C5 | — | 2 | 8 | no | — |
| 385 | C22×C5 | — | 2 | 4 | no | — |
| 386 | C22×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 387 | C2×D5 | — | 2 | 8 | no | — |
| 388 | C2×D5 | — | 2 | 4 | no | — |
| 389 | C2×D5 | — | 4 | 4 | no | — |
| 390 | C2×D5 | — | 4 | 8 | no | — |
| 391 | C2×D5 | — | 4 | 4 | no | — |
| 392 | C2×D5 | C22×#41 | 1 | 2 | yes | — |
| 393 | C2×D5 | C22×#41 | 1 | 2 | yes | — |
| 394 | C2×D5 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 395 | C2×D5 | #585 | 1 | 1 | yes | characteristic |
| 396 | AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 397 | AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 398 | AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 399 | AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 400 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 401 | AGL(1,𝔽5) | #559 | 1 | 4 | yes | direct product factor |
| 402 | C4×C5 | — | 2 | 4 | no | — |
| 403 | C4×C5 | — | 2 | 4 | no | — |
| 404 | C4×C5 | — | 2 | 1 | no | — |
| 405 | C4×C5 | C4×#41 | 1 | 4 | yes | — |
| 406 | Dic5 | — | 2 | 4 | no | — |
| 407 | Dic5 | — | 2 | 4 | no | — |
| 408 | Dic5 | — | 2 | 1 | no | — |
| 409 | Dic5 | C4×#41 | 1 | 4 | yes | — |
| 410 | C24 | — | 5 | 4 | no | — |
| 411 | C2×Q8 | — | 5 | 4 | no | — |
| 412 | C2×Q8 | — | 5 | 2 | no | — |
| 413 | C2×Q8 | — | 10 | 4 | no | — |
| 414 | C2×Q8 | — | 10 | 4 | no | — |
| 415 | C2×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 416 | C2×D4 | — | 5 | 8 | no | — |
| 417 | C2×D4 | — | 5 | 4 | no | — |
| 418 | C2×D4 | — | 5 | 4 | no | — |
| 419 | C2×D4 | — | 5 | 2 | no | — |
| 420 | C2×D4 | — | 10 | 8 | no | — |
| 421 | C2×D4 | — | 10 | 8 | no | — |
| 422 | C2×D4 | — | 20 | 2 | no | — |
| 423 | C2×D4 | — | 20 | 2 | no | — |
| 424 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 425 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 426 | C22×C4 | — | 5 | 1 | no | — |
| 427 | C22×C4 | — | 5 | 2 | no | — |
| 428 | C22×C4 | — | 5 | 4 | no | — |
| 429 | C22×C4 | — | 5 | 2 | no | — |
| 430 | C22×C4 | — | 5 | 4 | no | — |
| 431 | C22×C4 | — | 5 | 4 | no | — |
| 432 | C22×C4 | — | 5 | 4 | no | — |
| 433 | C22×C4 | — | 5 | 1 | no | — |
| 434 | C22×C4 | — | 5 | 8 | no | — |
| 435 | C22×C4 | — | 5 | 4 | no | — |
| 436 | C22×C4 | — | 5 | 4 | no | — |
| 437 | C22×C4 | — | 5 | 1 | no | — |
| 438 | C22×C4 | — | 10 | 8 | no | — |
| 439 | C22×C4 | — | 10 | 16 | no | — |
| 440 | C22×C4 | — | 10 | 16 | no | — |
| 441 | C22×C4 | — | 20 | 4 | no | — |
| 442 | C22×C4 | — | 20 | 4 | no | — |
| 443 | C22×C4 | — | 20 | 4 | no | — |
| 444 | C22×C4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 445 | C4⋊C4 | — | 5 | 8 | no | — |
| 446 | C4⋊C4 | — | 5 | 4 | no | — |
| 447 | C4⋊C4 | — | 5 | 2 | no | — |
| 448 | C4⋊C4 | — | 5 | 4 | no | — |
| 449 | C4⋊C4 | — | 5 | 4 | no | — |
| 450 | C4⋊C4 | — | 5 | 4 | no | — |
| 451 | C4⋊C4 | — | 10 | 8 | no | — |
| 452 | C4⋊C4 | — | 10 | 4 | no | — |
| 453 | C4⋊C4 | — | 10 | 8 | no | — |
| 454 | C4⋊C4 | — | 10 | 8 | no | — |
| 455 | C4⋊C4 | — | 20 | 2 | no | — |
| 456 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 457 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 458 | C22⋊C4 | — | 5 | 8 | no | — |
| 459 | C22⋊C4 | — | 5 | 4 | no | — |
| 460 | C22⋊C4 | — | 5 | 8 | no | — |
| 461 | C22⋊C4 | — | 5 | 8 | no | — |
| 462 | C22⋊C4 | — | 5 | 8 | no | — |
| 463 | C22⋊C4 | — | 10 | 16 | no | — |
| 464 | C22⋊C4 | — | 10 | 16 | no | — |
| 465 | C22⋊C4 | — | 20 | 4 | no | — |
| 466 | C22⋊C4 | — | 20 | 4 | no | — |
| 467 | C22⋊C4 | C22×AGL(1,𝔽5) | 1 | 8 | yes | — |
| 468 | C22⋊C4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 469 | C42 | — | 5 | 8 | no | — |
| 470 | C42 | — | 5 | 4 | no | — |
| 471 | C42 | — | 5 | 4 | no | — |
| 472 | C42 | — | 5 | 4 | no | — |
| 473 | C42 | — | 5 | 1 | no | — |
| 474 | C42 | — | 5 | 2 | no | — |
| 475 | C42 | — | 10 | 8 | no | — |
| 476 | C42 | — | 10 | 8 | no | — |
| 477 | C42 | — | 10 | 2 | no | — |
| 478 | C42 | — | 10 | 8 | no | — |
| 479 | C42 | — | 10 | 4 | no | — |
| 480 | C42 | — | 10 | 8 | no | — |
| 481 | C42 | — | 20 | 8 | no | — |
| 482 | C42 | — | 20 | 4 | no | — |
| 483 | C42 | — | 20 | 1 | no | — |
| 484 | C42 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 485 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 486 | C2×C5 | — | 4 | 4 | no | — |
| 487 | C2×C5 | C2×C4×#41 | 1 | 2 | yes | — |
| 488 | C2×C5 | C4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 489 | D5 | — | 4 | 4 | no | — |
| 490 | D5 | C2×#559 | 1 | 1 | yes | characteristic |
| 491 | D5 | #3480 | 1 | 2 | yes | — |
| 492 | D5 | #3481 | 1 | 1 | yes | characteristic |
| 493 | C23 | — | 5 | 1 | no | — |
| 494 | C23 | — | 5 | 4 | no | — |
| 495 | C23 | — | 10 | 8 | no | — |
| 496 | C23 | — | 10 | 8 | no | — |
| 497 | C23 | — | 10 | 4 | no | — |
| 498 | C23 | — | 10 | 4 | no | — |
| 499 | C23 | C23×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 500 | Q8 | — | 2 | 4 | no | — |
| 501 | Q8 | — | 10 | 8 | no | — |
| 502 | Q8 | — | 10 | 4 | no | — |
| 503 | D4 | — | 2 | 8 | no | — |
| 504 | D4 | — | 4 | 2 | no | — |
| 505 | D4 | — | 10 | 16 | no | — |
| 506 | D4 | — | 10 | 8 | no | — |
| 507 | D4 | — | 20 | 2 | no | — |
| 508 | D4 | — | 20 | 4 | no | — |
| 509 | C2×C4 | — | 4 | 4 | no | — |
| 510 | C2×C4 | — | 5 | 4 | no | — |
| 511 | C2×C4 | — | 5 | 2 | no | — |
| 512 | C2×C4 | — | 5 | 2 | no | — |
| 513 | C2×C4 | — | 5 | 4 | no | — |
| 514 | C2×C4 | — | 5 | 4 | no | — |
| 515 | C2×C4 | — | 5 | 4 | no | — |
| 516 | C2×C4 | — | 5 | 8 | no | — |
| 517 | C2×C4 | — | 5 | 4 | no | — |
| 518 | C2×C4 | — | 5 | 4 | no | — |
| 519 | C2×C4 | — | 5 | 1 | no | — |
| 520 | C2×C4 | — | 10 | 4 | no | — |
| 521 | C2×C4 | — | 10 | 4 | no | — |
| 522 | C2×C4 | — | 10 | 4 | no | — |
| 523 | C2×C4 | — | 10 | 1 | no | — |
| 524 | C2×C4 | — | 10 | 4 | no | — |
| 525 | C2×C4 | — | 10 | 1 | no | — |
| 526 | C2×C4 | — | 10 | 2 | no | — |
| 527 | C2×C4 | — | 10 | 4 | no | — |
| 528 | C2×C4 | — | 10 | 4 | no | — |
| 529 | C2×C4 | — | 10 | 2 | no | — |
| 530 | C2×C4 | — | 10 | 4 | no | — |
| 531 | C2×C4 | — | 10 | 1 | no | — |
| 532 | C2×C4 | — | 10 | 4 | no | — |
| 533 | C2×C4 | — | 10 | 2 | no | — |
| 534 | C2×C4 | — | 10 | 4 | no | — |
| 535 | C2×C4 | — | 10 | 4 | no | — |
| 536 | C2×C4 | — | 10 | 8 | no | — |
| 537 | C2×C4 | — | 20 | 8 | no | — |
| 538 | C2×C4 | — | 20 | 16 | no | — |
| 539 | C2×C4 | — | 20 | 4 | no | — |
| 540 | C2×C4 | — | 20 | 16 | no | — |
| 541 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 542 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 543 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 544 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 545 | C5 | C4×#559 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 546 | C22 | — | 2 | 8 | no | — |
| 547 | C22 | — | 2 | 4 | no | — |
| 548 | C22 | — | 5 | 2 | no | — |
| 549 | C22 | — | 5 | 2 | no | — |
| 550 | C22 | — | 5 | 1 | no | — |
| 551 | C22 | — | 5 | 1 | no | — |
| 552 | C22 | — | 10 | 8 | no | — |
| 553 | C22 | — | 10 | 4 | no | — |
| 554 | C22 | — | 20 | 4 | no | — |
| 555 | C22 | — | 20 | 4 | no | — |
| 556 | C22 | — | 20 | 8 | no | — |
| 557 | C22 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 558 | C4 | — | 2 | 4 | no | — |
| 559 | C4 | — | 2 | 4 | no | — |
| 560 | C4 | — | 2 | 1 | no | — |
| 561 | C4 | — | 5 | 4 | no | — |
| 562 | C4 | — | 5 | 4 | no | — |
| 563 | C4 | — | 10 | 8 | no | — |
| 564 | C4 | — | 10 | 4 | no | — |
| 565 | C4 | — | 10 | 4 | no | — |
| 566 | C4 | — | 10 | 4 | no | — |
| 567 | C4 | — | 10 | 1 | no | — |
| 568 | C4 | — | 20 | 4 | no | — |
| 569 | C4 | — | 20 | 1 | no | — |
| 570 | C4 | — | 20 | 4 | no | — |
| 571 | C4 | #41×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 572 | C2 | — | 4 | 4 | no | — |
| 573 | C2 | — | 5 | 1 | no | — |
| 574 | C2 | — | 5 | 1 | no | — |
| 575 | C2 | — | 5 | 2 | no | — |
| 576 | C2 | — | 20 | 4 | no | — |
| 577 | C2 | C2×#41×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 578 | C2 | AGL(1,𝔽5)×H(5,𝔽2) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 4. #10617326 | C2 | semidirect |
| 5. AGL(1,𝔽5)×#124 | C2 | semidirect |
| 6. #10617307 | C2 | semidirect |
| 7. AGL(1,𝔽5)×#123 | C2 | semidirect |
| 8. #10617213 | C2 | semidirect |
| 9. C4×Q8×AGL(1,𝔽5) | C2 | semidirect |
| 10. #10617182 | C2 | semidirect |
| 11. C4×D4×AGL(1,𝔽5) | C2 | semidirect |
| 18. C5×#559 | C4 | semidirect |
| 20. #66047 | C4 | semidirect |
| 21. #66015 | C4 | semidirect |
| 23. #65998 | C4 | semidirect |
| 25. #65919 | C4 | semidirect |
| 27. #65893 | C4 | semidirect |
| 90. C5×#124 | C2×C4 | semidirect |
| 91. C5×#123 | C2×C4 | semidirect |
| 92. C4×C5×Q8 | C2×C4 | semidirect |
| 93. C4×C5×D4 | C2×C4 | semidirect |
| 94. #4093 | C2×C4 | semidirect |
| 95. Q8×Dic5 | C2×C4 | semidirect |
| 98. #4082 | C2×C4 | semidirect |
| 99. #4081 | C2×C4 | semidirect |
| 100. D4×Dic5 | C2×C4 | semidirect |
| 101. #4075 | C2×C4 | semidirect |
| 102. C4×C22⋊D5 | C2×C4 | semidirect |
| 103. #4040 | C2×C4 | semidirect |
| 104. #4039 | C2×C4 | semidirect |
| 107. #4033 | C2×C4 | semidirect |
| 108. #4033 | C2×C4 | semidirect |
| 109. #4032 | C2×C4 | semidirect |
| 110. #4031 | C2×C4 | semidirect |
| 111. #4031 | C2×C4 | semidirect |
| 112. #4029 | C2×C4 | semidirect |
| 113. #4027 | C2×C4 | semidirect |
| 116. #4021 | C2×C4 | semidirect |
| 118. C4×D20 | C2×C4 | semidirect |
| 121. C4×Dic10 | C2×C4 | semidirect |
| 122. C4×Dic10 | C2×C4 | semidirect |
| 221. #559 | AGL(1,𝔽5) | direct (N × H) |
| 327. #124 | C2×AGL(1,𝔽5) | semidirect |
| 333. #123 | C2×AGL(1,𝔽5) | semidirect |
| 341. C4×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 350. C4×D4 | C2×AGL(1,𝔽5) | semidirect |
| 401. AGL(1,𝔽5) | #559 | direct (N × H) |
| 545. C5 | C4×#559 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta