← AGL(1,𝔽5)×#405 #13033113
Order 1280.
1526 conjugacy classes of subgroups.
The subgroup lattice has 510 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#65728 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×M16×AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#65718 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C22×C8×AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | AGL(1,𝔽5)×#117 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10617105 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | D5×#405 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #10603877 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | AGL(1,𝔽5)×#97 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10603838 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C4×C8×AGL(1,𝔽5) | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#4130 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×C4×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×D5⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×D5⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×D5×M16 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×C8×D5 | C22 | 1 | 1 | yes | characteristic |
| 18 | D5×#117 | C22 | 1 | 1 | yes | characteristic |
| 19 | #65728 | C4 | 1 | 8 | yes | complemented |
| 20 | M16×AGL(1,𝔽5) | C4 | 1 | 8 | yes | complemented |
| 21 | #65718 | C4 | 1 | 8 | yes | complemented |
| 22 | C2×#3992 | C22 | 1 | 2 | yes | — |
| 23 | C2×#3992 | C22 | 1 | 2 | yes | — |
| 24 | C2×#3992 | C22 | 1 | 2 | yes | — |
| 25 | C2×C8×AGL(1,𝔽5) | C4 | 1 | 8 | yes | complemented |
| 26 | C2×C8×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×C8×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C8×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×C8×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×C8×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 31 | C2×C8×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 32 | C2×C8×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 33 | C4⋊C4×AGL(1,𝔽5) | C4 | 1 | 4 | yes | — |
| 34 | #65701 | C4 | 1 | 4 | yes | complemented |
| 35 | C22⋊C4×AGL(1,𝔽5) | C4 | 1 | 4 | yes | — |
| 36 | #65691 | C4 | 1 | 4 | yes | complemented |
| 37 | #65686 | C22 | 1 | 2 | yes | — |
| 38 | C42×AGL(1,𝔽5) | C22 | 1 | 2 | yes | — |
| 39 | #65676 | C22 | 1 | 2 | yes | — |
| 40 | C4×D5⋊C8 | C22 | 1 | 2 | yes | — |
| 41 | C5×#405 | C4 | 1 | 1 | yes | characteristic, complemented |
| 42 | #65411 | C4 | 1 | 1 | yes | characteristic, complemented |
| 43 | #65390 | C4 | 1 | 1 | yes | characteristic, complemented |
| 44 | #65286 | C4 | 1 | 1 | yes | characteristic, complemented |
| 45 | #64997 | C4 | 1 | 2 | yes | complemented |
| 46 | D5×#97 | C22 | 1 | 2 | yes | — |
| 47 | #64978 | C4 | 1 | 2 | yes | complemented |
| 48 | C4×C8×D5 | C22 | 1 | 2 | yes | — |
| 49 | C4×#405 | — | 5 | 1 | no | maximal, Sylow |
| 50 | C23×AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 51 | C22×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×C22⋊AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 53 | C2×#704 | C2×C4 | 1 | 2 | yes | — |
| 54 | C22×#170 | C2×C4 | 1 | 2 | yes | — |
| 55 | #4130 | C2×C4 | 1 | 4 | yes | — |
| 56 | #4130 | C2×C4 | 1 | 4 | yes | — |
| 57 | C2×C4⋊AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 58 | C2×C4×AGL(1,𝔽5) | C2×C4 | 1 | 8 | yes | — |
| 59 | C2×C4×AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 60 | C2×C4×AGL(1,𝔽5) | C2×C4 | 1 | 4 | yes | — |
| 61 | C2×C4×AGL(1,𝔽5) | C2×C4 | 1 | 4 | yes | — |
| 62 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 64 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 1 | yes | characteristic |
| 65 | D5⋊M16 | C2×C4 | 1 | 4 | yes | — |
| 66 | D5⋊M16 | C2×C4 | 1 | 4 | yes | — |
| 67 | C2×#700 | C2×C4 | 1 | 2 | yes | — |
| 68 | C2×D5⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 69 | C2×D5⋊C8 | C2×C4 | 1 | 4 | yes | — |
| 70 | C2×D5⋊C8 | C2×C4 | 1 | 4 | yes | — |
| 71 | C2×D5⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×D5⋊C8 | C23 | 1 | 2 | yes | — |
| 73 | C2×D5⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C5×M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | C22×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 76 | C5×#117 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | #4072 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | C2×#681 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C22×#168 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | D5×M16 | C2×C4 | 1 | 4 | yes | — |
| 81 | D5×M16 | C2×C4 | 1 | 4 | yes | — |
| 82 | C2×#676 | C2×C4 | 1 | 2 | yes | — |
| 83 | C2×C8×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C2×C8×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C2×C8×D5 | C2×C4 | 1 | 4 | yes | — |
| 86 | C2×C8×D5 | C2×C4 | 1 | 4 | yes | — |
| 87 | C2×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×C8×D5 | C23 | 1 | 2 | yes | — |
| 90 | #4038 | C2×C4 | 1 | 2 | yes | — |
| 91 | D5×C4⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 92 | D5×C22⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 93 | #4023 | C2×C4 | 1 | 2 | yes | — |
| 94 | #4018 | C2×C4 | 1 | 2 | yes | — |
| 95 | C42×D5 | C23 | 1 | 2 | yes | — |
| 96 | (C2×AGL(1,𝔽5))⋊C4 | C2×C4 | 1 | 8 | yes | — |
| 97 | #4002 | C2×C4 | 1 | 8 | yes | complemented |
| 98 | C4×#170 | C2×C4 | 1 | 8 | yes | complemented |
| 99 | #3992 | C2×C4 | 1 | 8 | yes | — |
| 100 | #3992 | C2×C4 | 1 | 8 | yes | complemented |
| 101 | #3992 | C2×C4 | 1 | 8 | yes | complemented |
| 102 | C8×AGL(1,𝔽5) | C2×C4 | 1 | 4 | yes | — |
| 103 | C8×AGL(1,𝔽5) | C2×C4 | 1 | 4 | yes | — |
| 104 | C8×AGL(1,𝔽5) | C2×C4 | 1 | 4 | yes | — |
| 105 | C8×AGL(1,𝔽5) | C2×C4 | 1 | 4 | yes | — |
| 106 | C8×AGL(1,𝔽5) | C2×C4 | 1 | 8 | yes | — |
| 107 | C8×AGL(1,𝔽5) | C2×C4 | 1 | 8 | yes | complemented |
| 108 | C8×AGL(1,𝔽5) | C2×C4 | 1 | 8 | yes | complemented |
| 109 | C5×#97 | C2×C4 | 1 | 2 | yes | complemented |
| 110 | C4×C5×C8 | C2×C4 | 1 | 2 | yes | complemented |
| 111 | #3947 | C2×C4 | 1 | 2 | yes | complemented |
| 112 | #3947 | C2×C4 | 1 | 2 | yes | complemented |
| 113 | C8×Dic5 | C2×C4 | 1 | 2 | yes | complemented |
| 114 | C8×Dic5 | C2×C4 | 1 | 2 | yes | complemented |
| 115 | #3935 | C2×C4 | 1 | 2 | yes | complemented |
| 116 | C4×#168 | C2×C4 | 1 | 2 | yes | complemented |
| 117 | C2×#405 | — | 5 | 1 | no | — |
| 118 | C2×#405 | — | 5 | 1 | no | — |
| 119 | C2×#405 | — | 5 | 1 | no | — |
| 120 | C2×#405 | — | 5 | 1 | no | — |
| 121 | C2×C4×M16 | — | 5 | 1 | no | — |
| 122 | C22×C4×C8 | — | 5 | 1 | no | — |
| 123 | C4×#117 | — | 5 | 1 | no | — |
| 124 | #1726 | — | 5 | 2 | no | — |
| 125 | #1726 | — | 5 | 2 | no | — |
| 126 | C4×#97 | — | 5 | 2 | no | — |
| 127 | C42×C8 | — | 5 | 2 | no | — |
| 128 | C23×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 129 | C22×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 130 | C22×AGL(1,𝔽5) | C42 | 1 | 8 | yes | — |
| 131 | C22×AGL(1,𝔽5) | C22×C4 | 1 | 4 | yes | — |
| 132 | C22×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 133 | C22×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 134 | C22×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 135 | C22×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×D5 | C22×C4 | 1 | 4 | yes | — |
| 137 | C2×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 141 | C2×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 142 | C2×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 143 | C2×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 144 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 145 | C22⋊AGL(1,𝔽5) | C42 | 1 | 8 | yes | — |
| 146 | #704 | C42 | 1 | 8 | yes | complemented |
| 147 | C2×#170 | C42 | 1 | 8 | yes | complemented |
| 148 | C2×#170 | C22×C4 | 1 | 2 | yes | — |
| 149 | C2×#170 | C22×C4 | 1 | 2 | yes | — |
| 150 | C2×#170 | C22×C4 | 1 | 4 | yes | — |
| 151 | C4⋊AGL(1,𝔽5) | C42 | 1 | 8 | yes | — |
| 152 | C4×AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 153 | C4×AGL(1,𝔽5) | C42 | 1 | 8 | yes | — |
| 154 | C4×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 155 | C4×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 156 | C4×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 157 | C4×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 158 | C4×AGL(1,𝔽5) | C22×C4 | 1 | 4 | yes | — |
| 159 | C4×AGL(1,𝔽5) | C22×C4 | 1 | 4 | yes | — |
| 160 | #700 | C42 | 1 | 8 | yes | complemented |
| 161 | D5⋊C8 | C42 | 1 | 8 | yes | complemented |
| 162 | D5⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 163 | D5⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 164 | D5⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 165 | D5⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 166 | D5⋊C8 | C22×C4 | 1 | 4 | yes | — |
| 167 | D5⋊C8 | C22×C4 | 1 | 4 | yes | — |
| 168 | C5×M16 | C42 | 1 | 4 | yes | complemented |
| 169 | C2×C5×C8 | C42 | 1 | 4 | yes | complemented |
| 170 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 171 | C2×C5×C8 | C22×C4 | 1 | 2 | yes | — |
| 172 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 173 | C5×C4⋊C4 | C42 | 1 | 2 | yes | — |
| 174 | C5×C22⋊C4 | C42 | 1 | 2 | yes | — |
| 175 | C42×C5 | C22×C4 | 1 | 2 | yes | — |
| 176 | C22⋊Dic5 | C42 | 1 | 2 | yes | — |
| 177 | #685 | C42 | 1 | 4 | yes | — |
| 178 | C4⋊Dic5 | C42 | 1 | 2 | yes | — |
| 179 | #683 | C42 | 1 | 4 | yes | — |
| 180 | C4×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 181 | C4×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 182 | #681 | C42 | 1 | 4 | yes | complemented |
| 183 | C2×#168 | C42 | 1 | 4 | yes | complemented |
| 184 | C2×#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 185 | C2×#168 | C22×C4 | 1 | 2 | yes | — |
| 186 | C2×#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 187 | #676 | C42 | 1 | 8 | yes | complemented |
| 188 | C8×D5 | C42 | 1 | 4 | yes | complemented |
| 189 | C8×D5 | C42 | 1 | 4 | yes | complemented |
| 190 | C8×D5 | C22×C4 | 1 | 2 | yes | — |
| 191 | C8×D5 | C22×C4 | 1 | 2 | yes | — |
| 192 | C8×D5 | C22×C4 | 1 | 4 | yes | — |
| 193 | C8×D5 | C22×C4 | 1 | 2 | yes | — |
| 194 | C8×D5 | C22×C4 | 1 | 4 | yes | — |
| 195 | C8×D5 | C22×C4 | 1 | 2 | yes | — |
| 196 | C22×M16 | — | 5 | 1 | no | — |
| 197 | C22×M16 | — | 5 | 1 | no | — |
| 198 | C23×C8 | — | 5 | 1 | no | — |
| 199 | C23×C8 | — | 5 | 1 | no | — |
| 200 | C2×#117 | — | 5 | 1 | no | — |
| 201 | C2×#117 | — | 5 | 1 | no | — |
| 202 | C22×C42 | — | 5 | 1 | no | — |
| 203 | #405 | — | 5 | 4 | no | — |
| 204 | #405 | — | 5 | 4 | no | — |
| 205 | #405 | — | 5 | 8 | no | — |
| 206 | #405 | — | 5 | 8 | no | — |
| 207 | #405 | — | 5 | 1 | no | — |
| 208 | #405 | — | 5 | 1 | no | — |
| 209 | #405 | — | 5 | 1 | no | — |
| 210 | #405 | — | 5 | 2 | no | — |
| 211 | #405 | — | 5 | 2 | no | — |
| 212 | #405 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 213 | C4×M16 | — | 5 | 8 | no | — |
| 214 | C2×#97 | — | 5 | 2 | no | — |
| 215 | C2×#97 | — | 5 | 2 | no | — |
| 216 | C2×#97 | — | 5 | 2 | no | — |
| 217 | C2×#97 | — | 5 | 2 | no | — |
| 218 | C2×#97 | — | 5 | 2 | no | — |
| 219 | C2×C4×C8 | — | 5 | 8 | no | — |
| 220 | C2×C4×C8 | — | 5 | 1 | no | — |
| 221 | C2×C4×C8 | — | 5 | 1 | no | — |
| 222 | C2×C4×C8 | — | 5 | 1 | no | — |
| 223 | C2×C4×C8 | — | 5 | 1 | no | — |
| 224 | C2×C4×C8 | — | 5 | 2 | no | — |
| 225 | C2×C4×C8 | — | 5 | 2 | no | — |
| 226 | C2×C4×C8 | — | 5 | 2 | no | — |
| 227 | C2×C4×C8 | — | 5 | 2 | no | — |
| 228 | C2×C4×C8 | — | 5 | 2 | no | — |
| 229 | C4×C4⋊C4 | — | 5 | 4 | no | — |
| 230 | C4×C22⋊C4 | — | 5 | 4 | no | — |
| 231 | #376 | — | 5 | 2 | no | — |
| 232 | C43 | — | 5 | 2 | no | — |
| 233 | C23×C5 | C2×C42 | 1 | 1 | yes | characteristic |
| 234 | C22×D5 | — | 2 | 4 | no | — |
| 235 | C22×D5 | C2×C42 | 1 | 1 | yes | characteristic |
| 236 | C22×D5 | C2×C42 | 1 | 2 | yes | — |
| 237 | C22×D5 | C2×C42 | 1 | 2 | yes | — |
| 238 | C22×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 239 | C2×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 240 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 241 | C2×AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 242 | C2×AGL(1,𝔽5) | C2×C42 | 1 | 4 | yes | — |
| 243 | C2×AGL(1,𝔽5) | C2×C42 | 1 | 8 | yes | — |
| 244 | C2×AGL(1,𝔽5) | C2×C42 | 1 | 4 | yes | — |
| 245 | C2×AGL(1,𝔽5) | #131 | 1 | 8 | yes | — |
| 246 | C2×C4×C5 | C2×C42 | 1 | 4 | yes | — |
| 247 | C2×C4×C5 | C2×C42 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×C5 | C2×C42 | 1 | 2 | yes | — |
| 249 | C2×C4×C5 | C2×C42 | 1 | 2 | yes | — |
| 250 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 251 | C2×Dic5 | C2×C42 | 1 | 4 | yes | — |
| 252 | C2×Dic5 | C2×C42 | 1 | 1 | yes | characteristic |
| 253 | C2×Dic5 | C2×C42 | 1 | 2 | yes | — |
| 254 | C2×Dic5 | C2×C42 | 1 | 2 | yes | — |
| 255 | C2×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 256 | C4×D5 | — | 2 | 8 | no | — |
| 257 | C4×D5 | C2×C42 | 1 | 2 | yes | — |
| 258 | C4×D5 | C2×C42 | 1 | 2 | yes | — |
| 259 | C4×D5 | C2×C42 | 1 | 2 | yes | — |
| 260 | C4×D5 | C2×C42 | 1 | 2 | yes | — |
| 261 | C4×D5 | C2×C42 | 1 | 2 | yes | — |
| 262 | C4×D5 | C2×C42 | 1 | 2 | yes | — |
| 263 | C4×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 264 | C4×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 265 | C4×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 266 | C4×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 267 | #170 | C2×C42 | 1 | 4 | yes | — |
| 268 | #170 | C2×C42 | 1 | 4 | yes | — |
| 269 | #170 | C2×C42 | 1 | 8 | yes | — |
| 270 | C5×C8 | C2×C42 | 1 | 2 | yes | — |
| 271 | C5×C8 | C2×C42 | 1 | 2 | yes | — |
| 272 | C5×C8 | C2×C42 | 1 | 4 | yes | — |
| 273 | #168 | C2×C42 | 1 | 2 | yes | — |
| 274 | #168 | C2×C42 | 1 | 2 | yes | — |
| 275 | #168 | C2×C42 | 1 | 4 | yes | — |
| 276 | C23×C4 | — | 5 | 1 | no | — |
| 277 | C23×C4 | — | 5 | 2 | no | — |
| 278 | C2×M16 | — | 5 | 2 | no | — |
| 279 | C2×M16 | — | 5 | 4 | no | — |
| 280 | C2×M16 | — | 5 | 4 | no | — |
| 281 | C2×M16 | — | 5 | 2 | no | — |
| 282 | C2×M16 | — | 5 | 1 | no | — |
| 283 | C2×M16 | — | 5 | 4 | no | — |
| 284 | C2×M16 | — | 5 | 4 | no | — |
| 285 | C2×M16 | — | 5 | 2 | no | — |
| 286 | C2×M16 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 287 | C22×C8 | — | 5 | 4 | no | — |
| 288 | C22×C8 | — | 5 | 4 | no | — |
| 289 | C22×C8 | — | 5 | 2 | no | — |
| 290 | C22×C8 | — | 5 | 1 | no | — |
| 291 | C22×C8 | — | 5 | 1 | no | — |
| 292 | C22×C8 | — | 5 | 2 | no | — |
| 293 | C22×C8 | — | 5 | 2 | no | — |
| 294 | C22×C8 | — | 5 | 1 | no | — |
| 295 | C22×C8 | — | 5 | 4 | no | — |
| 296 | C22×C8 | — | 5 | 4 | no | — |
| 297 | C22×C8 | — | 5 | 1 | no | — |
| 298 | C22×C8 | — | 5 | 1 | no | — |
| 299 | C22×C8 | — | 5 | 2 | no | — |
| 300 | C22×C8 | — | 5 | 1 | no | — |
| 301 | C22×C8 | — | 5 | 1 | no | — |
| 302 | C22×C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 303 | #117 | — | 5 | 4 | no | — |
| 304 | #117 | — | 5 | 4 | no | — |
| 305 | #117 | — | 5 | 1 | no | — |
| 306 | #117 | — | 5 | 2 | no | — |
| 307 | #117 | — | 5 | 2 | no | — |
| 308 | #117 | — | 5 | 2 | no | — |
| 309 | #117 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 310 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 311 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 312 | C2×C22⋊C4 | — | 5 | 2 | no | — |
| 313 | C2×C22⋊C4 | — | 5 | 2 | no | — |
| 314 | C2×C42 | — | 5 | 2 | no | — |
| 315 | C2×C42 | — | 5 | 2 | no | — |
| 316 | C2×C42 | — | 5 | 4 | no | — |
| 317 | C2×C42 | — | 5 | 4 | no | — |
| 318 | C2×C42 | — | 5 | 1 | no | — |
| 319 | C2×C42 | — | 5 | 1 | no | — |
| 320 | C2×C42 | — | 5 | 2 | no | — |
| 321 | C2×C42 | — | 5 | 8 | no | — |
| 322 | #97 | — | 5 | 8 | no | — |
| 323 | #97 | — | 5 | 8 | no | — |
| 324 | #97 | — | 5 | 8 | no | — |
| 325 | #97 | — | 5 | 8 | no | — |
| 326 | #97 | — | 5 | 2 | no | — |
| 327 | #97 | — | 5 | 2 | no | — |
| 328 | #97 | — | 5 | 2 | no | — |
| 329 | #97 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 330 | C4×C8 | — | 5 | 4 | no | — |
| 331 | C4×C8 | — | 5 | 4 | no | — |
| 332 | C4×C8 | — | 5 | 4 | no | — |
| 333 | C4×C8 | — | 5 | 4 | no | — |
| 334 | C4×C8 | — | 5 | 8 | no | — |
| 335 | C4×C8 | — | 5 | 8 | no | — |
| 336 | C4×C8 | — | 5 | 8 | no | — |
| 337 | C4×C8 | — | 5 | 8 | no | — |
| 338 | C4×C8 | — | 5 | 2 | no | — |
| 339 | C4×C8 | — | 5 | 2 | no | — |
| 340 | C4×C8 | — | 5 | 2 | no | — |
| 341 | C4×C8 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 342 | #95 | — | 5 | 8 | no | — |
| 343 | C22×C5 | — | 2 | 2 | no | — |
| 344 | C22×C5 | C43 | 1 | 2 | yes | — |
| 345 | C22×C5 | C22×C42 | 1 | 1 | yes | characteristic |
| 346 | C2×D5 | — | 2 | 2 | no | — |
| 347 | C2×D5 | — | 2 | 4 | no | — |
| 348 | C2×D5 | — | 2 | 4 | no | — |
| 349 | C2×D5 | C43 | 1 | 2 | yes | — |
| 350 | C2×D5 | C22×C42 | 1 | 1 | yes | characteristic |
| 351 | C2×D5 | C22×C42 | 1 | 1 | yes | characteristic |
| 352 | C2×D5 | C2×#131 | 1 | 4 | yes | — |
| 353 | AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 354 | AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 355 | AGL(1,𝔽5) | #405 | 1 | 8 | yes | direct product factor |
| 356 | C4×C5 | — | 2 | 4 | no | — |
| 357 | C4×C5 | C43 | 1 | 2 | yes | — |
| 358 | C4×C5 | C22×C42 | 1 | 1 | yes | characteristic |
| 359 | C4×C5 | C22×C42 | 1 | 1 | yes | characteristic |
| 360 | Dic5 | — | 2 | 4 | no | — |
| 361 | Dic5 | C43 | 1 | 2 | yes | — |
| 362 | Dic5 | C22×C42 | 1 | 1 | yes | characteristic |
| 363 | Dic5 | C22×C42 | 1 | 1 | yes | characteristic |
| 364 | C24 | — | 5 | 1 | no | — |
| 365 | C22×C4 | — | 5 | 2 | no | — |
| 366 | C22×C4 | — | 5 | 1 | no | — |
| 367 | C22×C4 | — | 5 | 1 | no | — |
| 368 | C22×C4 | — | 5 | 2 | no | — |
| 369 | C22×C4 | — | 5 | 2 | no | — |
| 370 | C22×C4 | — | 5 | 2 | no | — |
| 371 | C22×C4 | — | 5 | 2 | no | — |
| 372 | C22×C4 | — | 5 | 1 | no | — |
| 373 | C22×C4 | — | 5 | 1 | no | — |
| 374 | C22×C4 | — | 5 | 1 | no | — |
| 375 | C22×C4 | — | 5 | 2 | no | — |
| 376 | C22×C4 | — | 5 | 4 | no | — |
| 377 | C22×C4 | — | 5 | 8 | no | — |
| 378 | C22×C4 | — | 5 | 4 | no | — |
| 379 | C22×C4 | — | 10 | 8 | no | — |
| 380 | C22×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 381 | M16 | — | 5 | 8 | no | — |
| 382 | M16 | — | 5 | 8 | no | — |
| 383 | M16 | — | 5 | 4 | no | — |
| 384 | M16 | — | 5 | 8 | no | — |
| 385 | M16 | C4×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 386 | C2×C8 | — | 5 | 2 | no | — |
| 387 | C2×C8 | — | 5 | 2 | no | — |
| 388 | C2×C8 | — | 5 | 2 | no | — |
| 389 | C2×C8 | — | 5 | 2 | no | — |
| 390 | C2×C8 | — | 5 | 4 | no | — |
| 391 | C2×C8 | — | 5 | 4 | no | — |
| 392 | C2×C8 | — | 5 | 4 | no | — |
| 393 | C2×C8 | — | 5 | 2 | no | — |
| 394 | C2×C8 | — | 5 | 2 | no | — |
| 395 | C2×C8 | — | 5 | 8 | no | — |
| 396 | C2×C8 | — | 5 | 8 | no | — |
| 397 | C2×C8 | — | 5 | 4 | no | — |
| 398 | C2×C8 | — | 5 | 1 | no | — |
| 399 | C2×C8 | — | 5 | 2 | no | — |
| 400 | C2×C8 | — | 5 | 1 | no | — |
| 401 | C2×C8 | — | 5 | 2 | no | — |
| 402 | C2×C8 | — | 5 | 2 | no | — |
| 403 | C2×C8 | — | 5 | 2 | no | — |
| 404 | C2×C8 | — | 5 | 4 | no | — |
| 405 | C2×C8 | — | 5 | 4 | no | — |
| 406 | C2×C8 | — | 5 | 2 | no | — |
| 407 | C2×C8 | — | 5 | 4 | no | — |
| 408 | C2×C8 | — | 5 | 4 | no | — |
| 409 | C2×C8 | C4×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 410 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 411 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 412 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 413 | C4⋊C4 | — | 5 | 8 | no | — |
| 414 | C4⋊C4 | — | 5 | 4 | no | — |
| 415 | C4⋊C4 | — | 5 | 2 | no | — |
| 416 | C4⋊C4 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 417 | C22⋊C4 | — | 5 | 8 | no | — |
| 418 | C22⋊C4 | — | 5 | 2 | no | — |
| 419 | C22⋊C4 | — | 5 | 4 | no | — |
| 420 | C22⋊C4 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 421 | C42 | — | 5 | 2 | no | — |
| 422 | C42 | — | 5 | 2 | no | — |
| 423 | C42 | — | 5 | 2 | no | — |
| 424 | C42 | — | 5 | 4 | no | — |
| 425 | C42 | — | 5 | 4 | no | — |
| 426 | C42 | — | 5 | 2 | no | — |
| 427 | C42 | — | 5 | 8 | no | — |
| 428 | C42 | — | 5 | 4 | no | — |
| 429 | C42 | — | 5 | 2 | no | — |
| 430 | C42 | — | 10 | 16 | no | — |
| 431 | C42 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 432 | C2×C5 | — | 2 | 2 | no | — |
| 433 | C2×C5 | C2×C43 | 1 | 1 | yes | characteristic |
| 434 | C2×C5 | C4×#131 | 1 | 2 | yes | — |
| 435 | D5 | — | 2 | 2 | no | — |
| 436 | D5 | C2×#405 | 1 | 2 | yes | — |
| 437 | D5 | C4×#131 | 1 | 2 | yes | — |
| 438 | C23 | — | 5 | 1 | no | — |
| 439 | C23 | — | 5 | 2 | no | — |
| 440 | C23 | — | 5 | 2 | no | — |
| 441 | C23 | — | 5 | 1 | no | — |
| 442 | C23 | — | 10 | 4 | no | — |
| 443 | C23 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 444 | C2×C4 | — | 5 | 4 | no | — |
| 445 | C2×C4 | — | 5 | 8 | no | — |
| 446 | C2×C4 | — | 5 | 2 | no | — |
| 447 | C2×C4 | — | 5 | 2 | no | — |
| 448 | C2×C4 | — | 5 | 1 | no | — |
| 449 | C2×C4 | — | 5 | 1 | no | — |
| 450 | C2×C4 | — | 5 | 2 | no | — |
| 451 | C2×C4 | — | 5 | 2 | no | — |
| 452 | C2×C4 | — | 5 | 2 | no | — |
| 453 | C2×C4 | — | 5 | 2 | no | — |
| 454 | C2×C4 | — | 5 | 1 | no | — |
| 455 | C2×C4 | — | 5 | 1 | no | — |
| 456 | C2×C4 | — | 5 | 1 | no | — |
| 457 | C2×C4 | — | 5 | 1 | no | — |
| 458 | C2×C4 | — | 5 | 2 | no | — |
| 459 | C2×C4 | — | 5 | 2 | no | — |
| 460 | C2×C4 | — | 5 | 4 | no | — |
| 461 | C2×C4 | — | 5 | 8 | no | — |
| 462 | C2×C4 | — | 5 | 4 | no | — |
| 463 | C2×C4 | — | 10 | 8 | no | — |
| 464 | C2×C4 | — | 10 | 16 | no | — |
| 465 | C2×C4 | — | 10 | 8 | no | — |
| 466 | C2×C4 | — | 10 | 4 | no | — |
| 467 | C2×C4 | C2×C4×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 468 | C2×C4 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 469 | C2×C4 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 470 | C2×C4 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 471 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 472 | C8 | — | 5 | 4 | no | — |
| 473 | C8 | — | 5 | 4 | no | — |
| 474 | C8 | — | 5 | 8 | no | — |
| 475 | C8 | — | 5 | 2 | no | — |
| 476 | C8 | — | 5 | 2 | no | — |
| 477 | C8 | — | 5 | 4 | no | — |
| 478 | C8 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 479 | C8 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 480 | C8 | C2×C4×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 481 | C5 | C4×#405 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 482 | C22 | — | 2 | 2 | no | — |
| 483 | C22 | — | 5 | 4 | no | — |
| 484 | C22 | — | 5 | 1 | no | — |
| 485 | C22 | — | 5 | 1 | no | — |
| 486 | C22 | — | 5 | 2 | no | — |
| 487 | C22 | — | 10 | 4 | no | — |
| 488 | C22 | — | 10 | 4 | no | — |
| 489 | C22 | — | 10 | 2 | no | — |
| 490 | C22 | C42×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 491 | C22 | C22×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 492 | C4 | — | 2 | 4 | no | — |
| 493 | C4 | — | 5 | 8 | no | — |
| 494 | C4 | — | 5 | 1 | no | — |
| 495 | C4 | — | 5 | 1 | no | — |
| 496 | C4 | — | 5 | 2 | no | — |
| 497 | C4 | — | 10 | 4 | no | — |
| 498 | C4 | — | 10 | 8 | no | — |
| 499 | C4 | — | 10 | 4 | no | — |
| 500 | C4 | C42×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 501 | C4 | C22×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 502 | C4 | C22×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 503 | C2 | — | 2 | 2 | no | — |
| 504 | C2 | — | 5 | 2 | no | — |
| 505 | C2 | — | 5 | 2 | no | — |
| 506 | C2 | — | 10 | 2 | no | — |
| 507 | C2 | C2×C42×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 508 | C2 | AGL(1,𝔽5)×#131 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 8. #10603877 | C2 | semidirect |
| 9. AGL(1,𝔽5)×#97 | C2 | semidirect |
| 10. #10603838 | C2 | semidirect |
| 11. C4×C8×AGL(1,𝔽5) | C2 | semidirect |
| 19. #65728 | C4 | semidirect |
| 20. M16×AGL(1,𝔽5) | C4 | semidirect |
| 21. #65718 | C4 | semidirect |
| 25. C2×C8×AGL(1,𝔽5) | C4 | semidirect |
| 34. #65701 | C4 | semidirect |
| 36. #65691 | C4 | semidirect |
| 41. C5×#405 | C4 | semidirect |
| 42. #65411 | C4 | semidirect |
| 43. #65390 | C4 | semidirect |
| 44. #65286 | C4 | semidirect |
| 45. #64997 | C4 | semidirect |
| 47. #64978 | C4 | semidirect |
| 97. #4002 | C2×C4 | semidirect |
| 98. C4×#170 | C2×C4 | semidirect |
| 100. #3992 | C2×C4 | semidirect |
| 101. #3992 | C2×C4 | semidirect |
| 107. C8×AGL(1,𝔽5) | C2×C4 | semidirect |
| 108. C8×AGL(1,𝔽5) | C2×C4 | semidirect |
| 109. C5×#97 | C2×C4 | semidirect |
| 110. C4×C5×C8 | C2×C4 | semidirect |
| 111. #3947 | C2×C4 | semidirect |
| 112. #3947 | C2×C4 | semidirect |
| 113. C8×Dic5 | C2×C4 | semidirect |
| 114. C8×Dic5 | C2×C4 | semidirect |
| 115. #3935 | C2×C4 | semidirect |
| 116. C4×#168 | C2×C4 | semidirect |
| 146. #704 | C42 | semidirect |
| 147. C2×#170 | C42 | semidirect |
| 160. #700 | C42 | semidirect |
| 161. D5⋊C8 | C42 | semidirect |
| 168. C5×M16 | C42 | semidirect |
| 169. C2×C5×C8 | C42 | semidirect |
| 182. #681 | C42 | semidirect |
| 183. C2×#168 | C42 | semidirect |
| 187. #676 | C42 | semidirect |
| 188. C8×D5 | C42 | semidirect |
| 189. C8×D5 | C42 | semidirect |
| 212. #405 | AGL(1,𝔽5) | direct (N × H) |
| 329. #97 | C2×AGL(1,𝔽5) | semidirect |
| 341. C4×C8 | C2×AGL(1,𝔽5) | semidirect |
| 355. AGL(1,𝔽5) | #405 | direct (N × H) |
| 385. M16 | C4×AGL(1,𝔽5) | semidirect |
| 409. C2×C8 | C4×AGL(1,𝔽5) | semidirect |
| 481. C5 | C4×#405 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta