← C2×AGL(1,𝔽5)×#100 #13033360
Order 1280.
1970 conjugacy classes of subgroups.
The subgroup lattice has 590 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×D4×AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×D5⋊#100 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×M16×AGL(1,𝔽5) | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×D5×#100 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C2×#64899 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | AGL(1,𝔽5)×#100 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 7 | C24×AGL(1,𝔽5) | C4 | 1 | 2 | yes | — |
| 8 | C22×D4×D5 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×C22⋊AGL(1,𝔽5) | C4 | 1 | 2 | yes | — |
| 10 | C2×D4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 11 | C2×D4×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 12 | C2×D4×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 13 | C2×D4×AGL(1,𝔽5) | C4 | 1 | 4 | yes | — |
| 14 | C2×D4×AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 15 | C22×C4⋊AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 16 | C22×C4×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×D5⋊M16 | C22 | 1 | 2 | yes | — |
| 18 | C2×D5×M16 | C22 | 1 | 2 | yes | — |
| 19 | C2×#4013 | C4 | 1 | 4 | yes | complemented |
| 20 | D5⋊#100 | C4 | 1 | 4 | yes | complemented |
| 21 | D5⋊#100 | C22 | 1 | 4 | yes | — |
| 22 | M16×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 23 | M16×AGL(1,𝔽5) | C22 | 1 | 8 | yes | complemented |
| 24 | C2×#3992 | — | 2 | 2 | no | — |
| 25 | C2×C8×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 26 | C2×C5×#100 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#3965 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×#3955 | C4 | 1 | 2 | yes | complemented |
| 29 | D5×#100 | C4 | 1 | 4 | yes | complemented |
| 30 | D5×#100 | C22 | 1 | 4 | yes | — |
| 31 | #64899 | C22 | 1 | 8 | yes | complemented |
| 32 | C2×C4×#100 | — | 5 | 1 | no | maximal, Sylow |
| 33 | C24×D5 | C2×C4 | 1 | 2 | yes | — |
| 34 | C23×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 35 | C23×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 36 | C23×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 37 | C23×AGL(1,𝔽5) | — | 4 | 8 | no | — |
| 38 | C23×AGL(1,𝔽5) | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C23×AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 40 | C23×AGL(1,𝔽5) | C2×C4 | 1 | 8 | yes | — |
| 41 | C23×AGL(1,𝔽5) | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C22×C5×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C22×C22⋊D5 | C2×C4 | 1 | 2 | yes | — |
| 44 | C2×D4×D5 | — | 2 | 2 | no | — |
| 45 | C2×D4×D5 | — | 2 | 2 | no | — |
| 46 | C2×D4×D5 | — | 2 | 2 | no | — |
| 47 | C2×D4×D5 | — | 2 | 2 | no | — |
| 48 | C2×D4×D5 | C2×C4 | 1 | 2 | yes | — |
| 49 | C2×D4×D5 | C2×C4 | 1 | 2 | yes | — |
| 50 | C2×D4×D5 | C2×C4 | 1 | 2 | yes | — |
| 51 | C2×D4×D5 | C23 | 1 | 2 | yes | — |
| 52 | C22×D20 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C22×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C22⋊AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 55 | C2×C22⋊AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 56 | C2×C22⋊AGL(1,𝔽5) | C2×C4 | 1 | 8 | yes | — |
| 57 | C2×#704 | C2×C4 | 1 | 4 | yes | complemented |
| 58 | D4×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 59 | D4×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 60 | D4×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 61 | D4×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 62 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 63 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 64 | C2×C4⋊AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 65 | C2×C4⋊AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 66 | C2×C4×AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 67 | C2×C4×AGL(1,𝔽5) | D4 | 1 | 2 | yes | — |
| 68 | C2×C4×AGL(1,𝔽5) | D4 | 1 | 2 | yes | — |
| 69 | C2×C4×AGL(1,𝔽5) | D4 | 1 | 4 | yes | — |
| 70 | C2×C4×AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 71 | D5⋊M16 | — | 2 | 2 | no | — |
| 72 | D5⋊M16 | — | 2 | 2 | no | — |
| 73 | D5⋊M16 | C2×C4 | 1 | 4 | yes | complemented |
| 74 | D5⋊M16 | C23 | 1 | 4 | yes | — |
| 75 | C2×#700 | — | 2 | 2 | no | — |
| 76 | C2×D5⋊C8 | — | 2 | 2 | no | — |
| 77 | C2×C5×M16 | C2×C4 | 1 | 2 | yes | complemented |
| 78 | C2×#681 | C2×C4 | 1 | 2 | yes | complemented |
| 79 | D5×M16 | — | 2 | 2 | no | — |
| 80 | D5×M16 | — | 2 | 2 | no | — |
| 81 | D5×M16 | C2×C4 | 1 | 4 | yes | complemented |
| 82 | D5×M16 | C23 | 1 | 4 | yes | — |
| 83 | C2×#676 | — | 2 | 2 | no | — |
| 84 | C2×C8×D5 | — | 2 | 2 | no | — |
| 85 | #4013 | C2×C4 | 1 | 16 | yes | complemented |
| 86 | #3992 | — | 2 | 8 | no | — |
| 87 | C8×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 88 | C5×#100 | C2×C4 | 1 | 4 | yes | complemented |
| 89 | #3965 | C2×C4 | 1 | 4 | yes | complemented |
| 90 | #3955 | C2×C4 | 1 | 8 | yes | complemented |
| 91 | C22×C4×D4 | — | 5 | 1 | no | — |
| 92 | C22×#100 | — | 5 | 1 | no | — |
| 93 | C22×#100 | — | 5 | 1 | no | — |
| 94 | C2×C4×M16 | — | 5 | 2 | no | — |
| 95 | C4×#100 | — | 5 | 8 | no | — |
| 96 | C2×#343 | — | 5 | 2 | no | — |
| 97 | C24×C5 | C42 | 1 | 2 | yes | — |
| 98 | C23×D5 | — | 2 | 2 | no | — |
| 99 | C23×D5 | — | 2 | 2 | no | — |
| 100 | C23×D5 | — | 2 | 2 | no | — |
| 101 | C23×D5 | — | 2 | 2 | no | — |
| 102 | C23×D5 | — | 4 | 4 | no | — |
| 103 | C23×D5 | — | 4 | 4 | no | — |
| 104 | C23×D5 | C42 | 1 | 2 | yes | — |
| 105 | C23×D5 | C42 | 1 | 4 | yes | — |
| 106 | C23×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 107 | C23×D5 | C22×C4 | 1 | 4 | yes | — |
| 108 | C22×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 109 | C22×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 110 | C22×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 111 | C22×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 112 | C22×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 113 | C22×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 114 | C22×AGL(1,𝔽5) | — | 4 | 8 | no | — |
| 115 | C22×AGL(1,𝔽5) | — | 4 | 16 | no | — |
| 116 | C22×AGL(1,𝔽5) | — | 4 | 16 | no | — |
| 117 | C22×AGL(1,𝔽5) | — | 4 | 8 | no | — |
| 118 | C22×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 119 | C22×AGL(1,𝔽5) | C22⋊C4 | 1 | 2 | yes | — |
| 120 | C22×AGL(1,𝔽5) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 121 | C22×AGL(1,𝔽5) | C22⋊C4 | 1 | 2 | yes | — |
| 122 | C22×AGL(1,𝔽5) | C22⋊C4 | 1 | 2 | yes | — |
| 123 | C22×AGL(1,𝔽5) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 124 | C22×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 125 | C22×AGL(1,𝔽5) | C22×C4 | 1 | 4 | yes | — |
| 126 | C22×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 127 | C2×C5×D4 | — | 2 | 2 | no | — |
| 128 | C2×C5×D4 | — | 2 | 2 | no | — |
| 129 | C2×C5×D4 | C42 | 1 | 2 | yes | — |
| 130 | C2×C5×D4 | C22×C4 | 1 | 2 | yes | — |
| 131 | C22×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 132 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 133 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 134 | C2×C22⋊D5 | C42 | 1 | 4 | yes | — |
| 135 | C2×C22⋊D5 | C22×C4 | 1 | 4 | yes | — |
| 136 | C22×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 137 | D4×D5 | — | 2 | 4 | no | — |
| 138 | D4×D5 | — | 2 | 4 | no | — |
| 139 | D4×D5 | — | 2 | 4 | no | — |
| 140 | D4×D5 | — | 2 | 4 | no | — |
| 141 | D4×D5 | — | 2 | 4 | no | — |
| 142 | D4×D5 | — | 2 | 4 | no | — |
| 143 | D4×D5 | — | 2 | 4 | no | — |
| 144 | D4×D5 | — | 2 | 4 | no | — |
| 145 | C2×D20 | — | 2 | 2 | no | — |
| 146 | C2×D20 | — | 2 | 2 | no | — |
| 147 | C2×D20 | C42 | 1 | 2 | yes | — |
| 148 | C2×D20 | C22×C4 | 1 | 2 | yes | — |
| 149 | C2×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 151 | C2×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 153 | C2×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 154 | C2×C4×D5 | #41 | 1 | 2 | yes | — |
| 155 | C2×C4×D5 | #41 | 1 | 2 | yes | — |
| 156 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 157 | C22⋊AGL(1,𝔽5) | — | 2 | 16 | no | — |
| 158 | #704 | — | 2 | 4 | no | — |
| 159 | #704 | C22×C4 | 1 | 8 | yes | complemented |
| 160 | C2×#170 | — | 2 | 4 | no | — |
| 161 | C4⋊AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 162 | C4⋊AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 163 | C4×AGL(1,𝔽5) | C22⋊C4 | 1 | 4 | yes | — |
| 164 | C4×AGL(1,𝔽5) | C22⋊C4 | 1 | 4 | yes | — |
| 165 | C4×AGL(1,𝔽5) | C2×D4 | 1 | 4 | yes | — |
| 166 | C4×AGL(1,𝔽5) | C2×D4 | 1 | 4 | yes | — |
| 167 | #700 | — | 2 | 4 | no | — |
| 168 | #700 | — | 2 | 4 | no | — |
| 169 | D5⋊C8 | — | 2 | 4 | no | — |
| 170 | D5⋊C8 | — | 2 | 4 | no | — |
| 171 | C5×M16 | — | 2 | 2 | no | — |
| 172 | C5×M16 | C22×C4 | 1 | 4 | yes | complemented |
| 173 | C2×C5×C8 | — | 2 | 2 | no | — |
| 174 | #681 | — | 2 | 2 | no | — |
| 175 | #681 | C22×C4 | 1 | 4 | yes | complemented |
| 176 | C2×#168 | — | 2 | 2 | no | — |
| 177 | #676 | — | 2 | 4 | no | — |
| 178 | #676 | — | 2 | 4 | no | — |
| 179 | C8×D5 | — | 2 | 4 | no | — |
| 180 | C8×D5 | — | 2 | 4 | no | — |
| 181 | C23×D4 | — | 5 | 1 | no | — |
| 182 | C24×C4 | — | 5 | 2 | no | — |
| 183 | C22×M16 | — | 5 | 2 | no | — |
| 184 | C22×M16 | — | 5 | 2 | no | — |
| 185 | C2×C4×D4 | — | 5 | 4 | no | — |
| 186 | C2×C4×D4 | — | 5 | 4 | no | — |
| 187 | C2×C4×D4 | — | 10 | 2 | no | — |
| 188 | C2×C4×D4 | — | 10 | 2 | no | — |
| 189 | C2×C4×D4 | — | 10 | 4 | no | — |
| 190 | C22×C4⋊C4 | — | 5 | 1 | no | — |
| 191 | C22×C22⋊C4 | — | 5 | 2 | no | — |
| 192 | C22×C42 | — | 5 | 1 | no | — |
| 193 | C2×#100 | — | 5 | 4 | no | — |
| 194 | C2×#100 | — | 5 | 4 | no | — |
| 195 | C2×#100 | — | 5 | 4 | no | — |
| 196 | C2×#100 | — | 5 | 1 | no | — |
| 197 | C2×#100 | — | 5 | 2 | no | — |
| 198 | C2×#100 | — | 5 | 4 | no | — |
| 199 | C2×#100 | — | 5 | 4 | no | — |
| 200 | C2×#100 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 201 | C4×M16 | — | 5 | 8 | no | — |
| 202 | C4×M16 | — | 10 | 4 | no | — |
| 203 | C2×#97 | — | 10 | 2 | no | — |
| 204 | C2×C4×C8 | — | 10 | 2 | no | — |
| 205 | #343 | — | 5 | 8 | no | — |
| 206 | C23×C5 | — | 2 | 2 | no | — |
| 207 | C23×C5 | — | 2 | 2 | no | — |
| 208 | C23×C5 | — | 4 | 4 | no | — |
| 209 | C23×C5 | C2×C42 | 1 | 1 | yes | characteristic |
| 210 | C23×C5 | C2×C42 | 1 | 4 | yes | — |
| 211 | C22×D5 | — | 2 | 2 | no | — |
| 212 | C22×D5 | — | 2 | 2 | no | — |
| 213 | C22×D5 | — | 2 | 2 | no | — |
| 214 | C22×D5 | — | 2 | 2 | no | — |
| 215 | C22×D5 | — | 2 | 4 | no | — |
| 216 | C22×D5 | — | 2 | 4 | no | — |
| 217 | C22×D5 | — | 2 | 4 | no | — |
| 218 | C22×D5 | — | 2 | 4 | no | — |
| 219 | C22×D5 | — | 4 | 4 | no | — |
| 220 | C22×D5 | — | 4 | 8 | no | — |
| 221 | C22×D5 | — | 4 | 4 | no | — |
| 222 | C22×D5 | — | 4 | 8 | no | — |
| 223 | C22×D5 | — | 4 | 4 | no | — |
| 224 | C22×D5 | — | 4 | 8 | no | — |
| 225 | C22×D5 | — | 4 | 4 | no | — |
| 226 | C22×D5 | — | 4 | 4 | no | — |
| 227 | C22×D5 | — | 4 | 4 | no | — |
| 228 | C22×D5 | — | 4 | 4 | no | — |
| 229 | C22×D5 | C2×C42 | 1 | 1 | yes | characteristic |
| 230 | C22×D5 | C2×C42 | 1 | 4 | yes | — |
| 231 | C22×D5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 232 | C22×D5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 233 | C22×D5 | #117 | 1 | 1 | yes | characteristic |
| 234 | C22×D5 | #117 | 1 | 1 | yes | characteristic |
| 235 | C22×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 236 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 237 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 238 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 239 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 240 | C2×AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 241 | C2×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 242 | C2×AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 243 | C2×AGL(1,𝔽5) | — | 4 | 16 | no | — |
| 244 | C2×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 245 | C2×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 246 | C2×AGL(1,𝔽5) | — | 4 | 16 | no | — |
| 247 | C2×AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 248 | C2×AGL(1,𝔽5) | #100 | 1 | 4 | yes | direct product factor |
| 249 | C2×AGL(1,𝔽5) | C2×C22⋊C4 | 1 | 4 | yes | — |
| 250 | C2×AGL(1,𝔽5) | C2×C22⋊C4 | 1 | 2 | yes | — |
| 251 | C2×AGL(1,𝔽5) | C2×C22⋊C4 | 1 | 2 | yes | — |
| 252 | C5×D4 | — | 2 | 4 | no | — |
| 253 | C5×D4 | — | 2 | 4 | no | — |
| 254 | C2×C4×C5 | C2×C42 | 1 | 1 | yes | characteristic |
| 255 | C2×C4×C5 | C4×D4 | 1 | 2 | yes | — |
| 256 | C2×C4×C5 | C4×D4 | 1 | 2 | yes | — |
| 257 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 258 | C22⋊D5 | — | 2 | 8 | no | — |
| 259 | C22⋊D5 | — | 2 | 8 | no | — |
| 260 | C2×Dic5 | C2×C42 | 1 | 1 | yes | characteristic |
| 261 | C2×Dic5 | C4×D4 | 1 | 2 | yes | — |
| 262 | C2×Dic5 | C4×D4 | 1 | 2 | yes | — |
| 263 | C2×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 264 | D20 | — | 2 | 4 | no | — |
| 265 | D20 | — | 2 | 4 | no | — |
| 266 | C4×D5 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 267 | C4×D5 | #117 | 1 | 2 | yes | — |
| 268 | C4×D5 | C4×D4 | 1 | 2 | yes | — |
| 269 | C4×D5 | C4×D4 | 1 | 2 | yes | — |
| 270 | C4×D5 | C4×D4 | 1 | 2 | yes | — |
| 271 | C4×D5 | C4×D4 | 1 | 2 | yes | — |
| 272 | C4×D5 | C22×D4 | 1 | 2 | yes | — |
| 273 | C4×D5 | C2×#41 | 1 | 2 | yes | — |
| 274 | #170 | — | 2 | 8 | no | — |
| 275 | C5×C8 | — | 2 | 4 | no | — |
| 276 | #168 | — | 2 | 4 | no | — |
| 277 | C25 | — | 5 | 2 | no | — |
| 278 | C22×D4 | — | 5 | 2 | no | — |
| 279 | C22×D4 | — | 5 | 2 | no | — |
| 280 | C22×D4 | — | 5 | 2 | no | — |
| 281 | C22×D4 | — | 5 | 2 | no | — |
| 282 | C22×D4 | — | 5 | 2 | no | — |
| 283 | C22×D4 | — | 5 | 1 | no | — |
| 284 | C22×D4 | — | 10 | 2 | no | — |
| 285 | C22×D4 | — | 10 | 2 | no | — |
| 286 | C22×D4 | — | 10 | 2 | no | — |
| 287 | C22×D4 | — | 10 | 2 | no | — |
| 288 | C22×D4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 289 | C23×C4 | — | 5 | 1 | no | — |
| 290 | C23×C4 | — | 5 | 1 | no | — |
| 291 | C23×C4 | — | 5 | 1 | no | — |
| 292 | C23×C4 | — | 5 | 2 | no | — |
| 293 | C23×C4 | — | 5 | 8 | no | — |
| 294 | C23×C4 | — | 10 | 2 | no | — |
| 295 | C23×C4 | — | 10 | 4 | no | — |
| 296 | C23×C4 | — | 10 | 2 | no | — |
| 297 | C23×C4 | — | 20 | 8 | no | — |
| 298 | C2×M16 | — | 5 | 4 | no | — |
| 299 | C2×M16 | — | 5 | 4 | no | — |
| 300 | C2×M16 | — | 5 | 4 | no | — |
| 301 | C2×M16 | — | 5 | 2 | no | — |
| 302 | C2×M16 | — | 5 | 4 | no | — |
| 303 | C2×M16 | — | 5 | 4 | no | — |
| 304 | C2×M16 | — | 10 | 2 | no | — |
| 305 | C2×M16 | — | 10 | 2 | no | — |
| 306 | C2×M16 | — | 10 | 2 | no | — |
| 307 | C2×M16 | — | 10 | 2 | no | — |
| 308 | C2×M16 | — | 10 | 2 | no | — |
| 309 | C2×M16 | — | 10 | 2 | no | — |
| 310 | C2×M16 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 311 | C22×C8 | — | 10 | 2 | no | — |
| 312 | C22×C8 | — | 10 | 2 | no | — |
| 313 | C4×D4 | — | 10 | 8 | no | — |
| 314 | C4×D4 | — | 10 | 8 | no | — |
| 315 | C4×D4 | — | 10 | 8 | no | — |
| 316 | C4×D4 | — | 10 | 8 | no | — |
| 317 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 318 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 319 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 320 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 321 | C2×C22⋊C4 | — | 5 | 8 | no | — |
| 322 | C2×C22⋊C4 | — | 10 | 4 | no | — |
| 323 | C2×C22⋊C4 | — | 10 | 4 | no | — |
| 324 | C2×C42 | — | 5 | 2 | no | — |
| 325 | C2×C42 | — | 5 | 2 | no | — |
| 326 | C2×C42 | — | 5 | 2 | no | — |
| 327 | C2×C42 | — | 5 | 2 | no | — |
| 328 | C2×C42 | — | 5 | 4 | no | — |
| 329 | #100 | — | 5 | 16 | no | — |
| 330 | #100 | — | 5 | 4 | no | — |
| 331 | #100 | — | 5 | 8 | no | — |
| 332 | #100 | C2×AGL(1,𝔽5) | 1 | 4 | yes | direct product factor |
| 333 | #97 | — | 10 | 8 | no | — |
| 334 | C4×C8 | — | 10 | 8 | no | — |
| 335 | C22×C5 | — | 2 | 2 | no | — |
| 336 | C22×C5 | — | 2 | 4 | no | — |
| 337 | C22×C5 | — | 4 | 4 | no | — |
| 338 | C22×C5 | — | 4 | 4 | no | — |
| 339 | C22×C5 | — | 4 | 4 | no | — |
| 340 | C22×C5 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 341 | C22×C5 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 342 | C22×C5 | C22×C42 | 1 | 1 | yes | characteristic |
| 343 | C2×D5 | — | 2 | 2 | no | — |
| 344 | C2×D5 | — | 2 | 1 | no | — |
| 345 | C2×D5 | — | 2 | 1 | no | — |
| 346 | C2×D5 | — | 2 | 1 | no | — |
| 347 | C2×D5 | — | 2 | 1 | no | — |
| 348 | C2×D5 | — | 2 | 2 | no | — |
| 349 | C2×D5 | — | 2 | 2 | no | — |
| 350 | C2×D5 | — | 2 | 4 | no | — |
| 351 | C2×D5 | — | 4 | 8 | no | — |
| 352 | C2×D5 | — | 4 | 8 | no | — |
| 353 | C2×D5 | — | 4 | 4 | no | — |
| 354 | C2×D5 | — | 4 | 4 | no | — |
| 355 | C2×D5 | — | 4 | 4 | no | — |
| 356 | C2×D5 | — | 4 | 4 | no | — |
| 357 | C2×D5 | — | 4 | 8 | no | — |
| 358 | C2×D5 | — | 4 | 4 | no | — |
| 359 | C2×D5 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 360 | C2×D5 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 361 | C2×D5 | C2×#100 | 1 | 2 | yes | — |
| 362 | C2×D5 | #413 | 1 | 2 | yes | — |
| 363 | C2×D5 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 364 | C2×D5 | C2×#117 | 1 | 1 | yes | characteristic |
| 365 | AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 366 | AGL(1,𝔽5) | — | 2 | 4 | no | — |
| 367 | AGL(1,𝔽5) | — | 4 | 4 | no | — |
| 368 | AGL(1,𝔽5) | C2×#100 | 1 | 4 | yes | direct product factor |
| 369 | C4×C5 | C4×C22⋊C4 | 1 | 2 | yes | — |
| 370 | C4×C5 | C2×C4×D4 | 1 | 2 | yes | — |
| 371 | Dic5 | C4×C22⋊C4 | 1 | 2 | yes | — |
| 372 | Dic5 | C2×C4×D4 | 1 | 2 | yes | — |
| 373 | C24 | — | 5 | 1 | no | — |
| 374 | C24 | — | 5 | 4 | no | — |
| 375 | C24 | — | 5 | 4 | no | — |
| 376 | C24 | — | 5 | 2 | no | — |
| 377 | C24 | — | 10 | 2 | no | — |
| 378 | C24 | — | 10 | 2 | no | — |
| 379 | C24 | — | 10 | 2 | no | — |
| 380 | C24 | — | 10 | 2 | no | — |
| 381 | C24 | — | 20 | 4 | no | — |
| 382 | C24 | — | 20 | 4 | no | — |
| 383 | C24 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 384 | C2×D4 | — | 2 | 2 | no | — |
| 385 | C2×D4 | — | 2 | 2 | no | — |
| 386 | C2×D4 | — | 5 | 4 | no | — |
| 387 | C2×D4 | — | 5 | 4 | no | — |
| 388 | C2×D4 | — | 5 | 2 | no | — |
| 389 | C2×D4 | — | 5 | 2 | no | — |
| 390 | C2×D4 | — | 10 | 4 | no | — |
| 391 | C2×D4 | — | 10 | 4 | no | — |
| 392 | C2×D4 | — | 10 | 4 | no | — |
| 393 | C2×D4 | — | 10 | 4 | no | — |
| 394 | C2×D4 | — | 10 | 4 | no | — |
| 395 | C2×D4 | — | 10 | 4 | no | — |
| 396 | C2×D4 | — | 10 | 4 | no | — |
| 397 | C2×D4 | — | 10 | 4 | no | — |
| 398 | C2×D4 | — | 10 | 4 | no | — |
| 399 | C2×D4 | — | 10 | 4 | no | — |
| 400 | C2×D4 | — | 10 | 2 | no | — |
| 401 | C2×D4 | — | 10 | 2 | no | — |
| 402 | C2×D4 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 403 | C2×D4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 404 | C22×C4 | — | 5 | 1 | no | — |
| 405 | C22×C4 | — | 5 | 1 | no | — |
| 406 | C22×C4 | — | 5 | 1 | no | — |
| 407 | C22×C4 | — | 5 | 1 | no | — |
| 408 | C22×C4 | — | 5 | 2 | no | — |
| 409 | C22×C4 | — | 5 | 2 | no | — |
| 410 | C22×C4 | — | 5 | 2 | no | — |
| 411 | C22×C4 | — | 5 | 2 | no | — |
| 412 | C22×C4 | — | 5 | 1 | no | — |
| 413 | C22×C4 | — | 5 | 1 | no | — |
| 414 | C22×C4 | — | 5 | 2 | no | — |
| 415 | C22×C4 | — | 5 | 2 | no | — |
| 416 | C22×C4 | — | 5 | 2 | no | — |
| 417 | C22×C4 | — | 5 | 1 | no | — |
| 418 | C22×C4 | — | 5 | 2 | no | — |
| 419 | C22×C4 | — | 5 | 2 | no | — |
| 420 | C22×C4 | — | 5 | 4 | no | — |
| 421 | C22×C4 | — | 10 | 4 | no | — |
| 422 | C22×C4 | — | 10 | 8 | no | — |
| 423 | C22×C4 | — | 10 | 8 | no | — |
| 424 | C22×C4 | — | 10 | 2 | no | — |
| 425 | C22×C4 | — | 10 | 2 | no | — |
| 426 | C22×C4 | — | 20 | 8 | no | — |
| 427 | C22×C4 | — | 20 | 2 | no | — |
| 428 | C22×C4 | — | 20 | 16 | no | — |
| 429 | C22×C4 | — | 20 | 8 | no | — |
| 430 | C22×C4 | — | 20 | 16 | no | — |
| 431 | C22×C4 | — | 20 | 4 | no | — |
| 432 | C22×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 433 | M16 | — | 2 | 2 | no | — |
| 434 | M16 | — | 5 | 8 | no | — |
| 435 | M16 | — | 5 | 4 | no | — |
| 436 | M16 | — | 10 | 4 | no | — |
| 437 | M16 | — | 10 | 4 | no | — |
| 438 | M16 | — | 10 | 4 | no | — |
| 439 | M16 | — | 10 | 4 | no | — |
| 440 | M16 | — | 10 | 4 | no | — |
| 441 | M16 | — | 10 | 2 | no | — |
| 442 | M16 | C22×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 443 | C2×C8 | — | 2 | 2 | no | — |
| 444 | C2×C8 | — | 10 | 4 | no | — |
| 445 | C2×C8 | — | 10 | 4 | no | — |
| 446 | C2×C8 | — | 10 | 4 | no | — |
| 447 | C2×C8 | — | 10 | 4 | no | — |
| 448 | C2×C8 | — | 10 | 4 | no | — |
| 449 | C2×C8 | — | 10 | 2 | no | — |
| 450 | C4⋊C4 | — | 10 | 4 | no | — |
| 451 | C4⋊C4 | — | 10 | 4 | no | — |
| 452 | C22⋊C4 | — | 10 | 16 | no | — |
| 453 | C42 | — | 5 | 4 | no | — |
| 454 | C42 | — | 5 | 4 | no | — |
| 455 | C42 | — | 5 | 4 | no | — |
| 456 | C42 | — | 5 | 4 | no | — |
| 457 | C2×C5 | — | 2 | 1 | no | — |
| 458 | C2×C5 | — | 2 | 1 | no | — |
| 459 | C2×C5 | — | 4 | 4 | no | — |
| 460 | C2×C5 | C4×#100 | 1 | 2 | yes | complemented |
| 461 | C2×C5 | C2×C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 462 | D5 | — | 2 | 1 | no | — |
| 463 | D5 | — | 2 | 1 | no | — |
| 464 | D5 | — | 4 | 4 | no | — |
| 465 | D5 | C4×#100 | 1 | 2 | yes | complemented |
| 466 | D5 | C22×#100 | 1 | 1 | yes | characteristic |
| 467 | D5 | C2×#413 | 1 | 1 | yes | characteristic |
| 468 | C23 | — | 2 | 2 | no | — |
| 469 | C23 | — | 2 | 2 | no | — |
| 470 | C23 | — | 4 | 4 | no | — |
| 471 | C23 | — | 5 | 1 | no | — |
| 472 | C23 | — | 5 | 1 | no | — |
| 473 | C23 | — | 5 | 1 | no | — |
| 474 | C23 | — | 5 | 1 | no | — |
| 475 | C23 | — | 5 | 1 | no | — |
| 476 | C23 | — | 5 | 1 | no | — |
| 477 | C23 | — | 5 | 4 | no | — |
| 478 | C23 | — | 10 | 2 | no | — |
| 479 | C23 | — | 10 | 2 | no | — |
| 480 | C23 | — | 10 | 4 | no | — |
| 481 | C23 | — | 10 | 4 | no | — |
| 482 | C23 | — | 10 | 4 | no | — |
| 483 | C23 | — | 10 | 4 | no | — |
| 484 | C23 | — | 10 | 2 | no | — |
| 485 | C23 | — | 10 | 2 | no | — |
| 486 | C23 | — | 20 | 4 | no | — |
| 487 | C23 | — | 20 | 4 | no | — |
| 488 | C23 | — | 20 | 4 | no | — |
| 489 | C23 | — | 20 | 4 | no | — |
| 490 | C23 | — | 20 | 4 | no | — |
| 491 | C23 | — | 20 | 8 | no | — |
| 492 | C23 | — | 20 | 4 | no | — |
| 493 | C23 | — | 20 | 4 | no | — |
| 494 | C23 | — | 20 | 8 | no | — |
| 495 | C23 | — | 20 | 8 | no | — |
| 496 | C23 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 497 | C23 | C2×C4×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 498 | D4 | — | 2 | 4 | no | — |
| 499 | D4 | — | 2 | 4 | no | — |
| 500 | D4 | — | 10 | 8 | no | — |
| 501 | D4 | — | 10 | 8 | no | — |
| 502 | D4 | — | 10 | 4 | no | — |
| 503 | D4 | — | 10 | 4 | no | — |
| 504 | C2×C4 | — | 5 | 2 | no | — |
| 505 | C2×C4 | — | 5 | 4 | no | — |
| 506 | C2×C4 | — | 5 | 2 | no | — |
| 507 | C2×C4 | — | 5 | 2 | no | — |
| 508 | C2×C4 | — | 5 | 1 | no | — |
| 509 | C2×C4 | — | 5 | 1 | no | — |
| 510 | C2×C4 | — | 5 | 2 | no | — |
| 511 | C2×C4 | — | 5 | 2 | no | — |
| 512 | C2×C4 | — | 5 | 2 | no | — |
| 513 | C2×C4 | — | 5 | 2 | no | — |
| 514 | C2×C4 | — | 5 | 2 | no | — |
| 515 | C2×C4 | — | 5 | 2 | no | — |
| 516 | C2×C4 | — | 5 | 2 | no | — |
| 517 | C2×C4 | — | 5 | 2 | no | — |
| 518 | C2×C4 | — | 5 | 4 | no | — |
| 519 | C2×C4 | — | 5 | 2 | no | — |
| 520 | C2×C4 | — | 10 | 4 | no | — |
| 521 | C2×C4 | — | 10 | 4 | no | — |
| 522 | C2×C4 | — | 10 | 2 | no | — |
| 523 | C2×C4 | — | 10 | 4 | no | — |
| 524 | C2×C4 | — | 10 | 4 | no | — |
| 525 | C2×C4 | — | 20 | 16 | no | — |
| 526 | C2×C4 | — | 20 | 2 | no | — |
| 527 | C2×C4 | — | 20 | 2 | no | — |
| 528 | C2×C4 | — | 20 | 16 | no | — |
| 529 | C2×C4 | — | 20 | 4 | no | — |
| 530 | C2×C4 | — | 20 | 4 | no | — |
| 531 | C2×C4 | — | 20 | 4 | no | — |
| 532 | C2×C4 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 533 | C2×C4 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 534 | C2×C4 | D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 535 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 536 | C8 | — | 2 | 4 | no | — |
| 537 | C8 | — | 10 | 8 | no | — |
| 538 | C8 | — | 10 | 4 | no | — |
| 539 | C5 | C2×C4×#100 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 540 | C22 | — | 2 | 2 | no | — |
| 541 | C22 | — | 2 | 4 | no | — |
| 542 | C22 | — | 4 | 4 | no | — |
| 543 | C22 | — | 4 | 4 | no | — |
| 544 | C22 | — | 4 | 4 | no | — |
| 545 | C22 | — | 5 | 2 | no | — |
| 546 | C22 | — | 5 | 2 | no | — |
| 547 | C22 | — | 5 | 1 | no | — |
| 548 | C22 | — | 5 | 1 | no | — |
| 549 | C22 | — | 5 | 1 | no | — |
| 550 | C22 | — | 5 | 1 | no | — |
| 551 | C22 | — | 10 | 1 | no | — |
| 552 | C22 | — | 10 | 1 | no | — |
| 553 | C22 | — | 10 | 1 | no | — |
| 554 | C22 | — | 10 | 1 | no | — |
| 555 | C22 | — | 10 | 2 | no | — |
| 556 | C22 | — | 10 | 2 | no | — |
| 557 | C22 | — | 10 | 2 | no | — |
| 558 | C22 | — | 10 | 4 | no | — |
| 559 | C22 | — | 20 | 4 | no | — |
| 560 | C22 | — | 20 | 4 | no | — |
| 561 | C22 | — | 20 | 4 | no | — |
| 562 | C22 | — | 20 | 4 | no | — |
| 563 | C22 | — | 20 | 8 | no | — |
| 564 | C22 | — | 20 | 8 | no | — |
| 565 | C22 | — | 20 | 8 | no | — |
| 566 | C22 | — | 20 | 4 | no | — |
| 567 | C22 | C22⋊C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 568 | C22 | C22⋊C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 569 | C22 | C22×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 570 | C4 | — | 5 | 4 | no | — |
| 571 | C4 | — | 5 | 2 | no | — |
| 572 | C4 | — | 5 | 2 | no | — |
| 573 | C4 | — | 10 | 2 | no | — |
| 574 | C4 | — | 10 | 4 | no | — |
| 575 | C4 | — | 20 | 4 | no | — |
| 576 | C4 | C22⋊C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 577 | C4 | C2×D4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 578 | C2 | — | 2 | 1 | no | — |
| 579 | C2 | — | 2 | 1 | no | — |
| 580 | C2 | — | 4 | 4 | no | — |
| 581 | C2 | — | 5 | 1 | no | — |
| 582 | C2 | — | 5 | 1 | no | — |
| 583 | C2 | — | 5 | 2 | no | — |
| 584 | C2 | — | 10 | 1 | no | — |
| 585 | C2 | — | 10 | 1 | no | — |
| 586 | C2 | — | 20 | 4 | no | — |
| 587 | C2 | AGL(1,𝔽5)×#100 | 1 | 2 | yes | direct product factor |
| 588 | C2 | C2×C22⋊C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 3. C2×M16×AGL(1,𝔽5) | C2 | semidirect |
| 5. C2×#64899 | C2 | semidirect |
| 6. AGL(1,𝔽5)×#100 | C2 | direct (N × H) |
| 19. C2×#4013 | C4 | semidirect |
| 20. D5⋊#100 | C4 | semidirect |
| 23. M16×AGL(1,𝔽5) | C22 | semidirect |
| 26. C2×C5×#100 | C4 | semidirect |
| 27. C2×#3965 | C4 | semidirect |
| 28. C2×#3955 | C4 | semidirect |
| 29. D5×#100 | C4 | semidirect |
| 31. #64899 | C22 | semidirect |
| 57. C2×#704 | C2×C4 | semidirect |
| 73. D5⋊M16 | C2×C4 | semidirect |
| 77. C2×C5×M16 | C2×C4 | semidirect |
| 78. C2×#681 | C2×C4 | semidirect |
| 81. D5×M16 | C2×C4 | semidirect |
| 85. #4013 | C2×C4 | semidirect |
| 88. C5×#100 | C2×C4 | semidirect |
| 89. #3965 | C2×C4 | semidirect |
| 90. #3955 | C2×C4 | semidirect |
| 159. #704 | C22×C4 | semidirect |
| 172. C5×M16 | C22×C4 | semidirect |
| 175. #681 | C22×C4 | semidirect |
| 200. C2×#100 | AGL(1,𝔽5) | direct (N × H) |
| 248. C2×AGL(1,𝔽5) | #100 | direct (N × H) |
| 310. C2×M16 | C2×AGL(1,𝔽5) | semidirect |
| 332. #100 | C2×AGL(1,𝔽5) | direct (N × H) |
| 368. AGL(1,𝔽5) | C2×#100 | direct (N × H) |
| 442. M16 | C22×AGL(1,𝔽5) | semidirect |
| 460. C2×C5 | C4×#100 | semidirect |
| 465. D5 | C4×#100 | semidirect |
| 539. C5 | C2×C4×#100 | semidirect |
| 587. C2 | AGL(1,𝔽5)×#100 | 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