← C2×C42×D5⋊AGL(1,𝔽5) #72269253
Order 6400.
17460 conjugacy classes of subgroups.
The subgroup lattice has 465 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C42×#1044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C42×D52 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C4×#87830 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C42×D5⋊AGL(1,𝔽5) | C2 | 1 | 16 | yes | maximal, direct product factor |
| 5 | C22×C4×D5⋊AGL(1,𝔽5) | C2 | 1 | 6 | yes | maximal |
| 6 | C2×C42×#1043 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C23×D5⋊AGL(1,𝔽5) | C22 | 1 | 4 | yes | — |
| 8 | C22×C4×D52 | C22 | 1 | 3 | yes | — |
| 9 | C22×C4×#1044 | C22 | 1 | 6 | yes | — |
| 10 | C22×C4×#1043 | C22 | 1 | 6 | yes | — |
| 11 | C22×#87830 | C22 | 1 | 12 | yes | — |
| 12 | C2×C4×D5⋊AGL(1,𝔽5) | C4 | 1 | 96 | yes | direct product factor |
| 13 | C2×C4×D5⋊AGL(1,𝔽5) | C22 | 1 | 48 | yes | — |
| 14 | C2×C42×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C42×C5×D5 | C4 | 1 | 2 | yes | complemented |
| 16 | C2×C4×#6036 | C22 | 1 | 3 | yes | — |
| 17 | C2×C4×D5×Dic5 | C4 | 1 | 6 | yes | complemented |
| 18 | C42×D52 | C4 | 1 | 8 | yes | complemented |
| 19 | C42×D52 | C22 | 1 | 8 | yes | — |
| 20 | C42×#1044 | C22 | 1 | 8 | yes | complemented |
| 21 | C42×#1043 | C22 | 1 | 8 | yes | complemented |
| 22 | C4×#87830 | C22 | 1 | 48 | yes | complemented |
| 23 | C22×C42×AGL(1,𝔽5) | — | 5 | 2 | no | maximal |
| 24 | C23×D52 | C23 | 1 | 1 | yes | characteristic |
| 25 | C23×#1044 | C23 | 1 | 4 | yes | — |
| 26 | C23×#1043 | C23 | 1 | 4 | yes | — |
| 27 | C22×D5⋊AGL(1,𝔽5) | C2×C4 | 1 | 96 | yes | — |
| 28 | C22×D5⋊AGL(1,𝔽5) | C23 | 1 | 16 | yes | — |
| 29 | C22×C4×C5⋊D5 | C23 | 1 | 3 | yes | — |
| 30 | C22×C4×C5×D5 | C2×C4 | 1 | 6 | yes | — |
| 31 | C22×#6036 | C23 | 1 | 3 | yes | — |
| 32 | C22×D5×Dic5 | C2×C4 | 1 | 6 | yes | — |
| 33 | C2×C4×D52 | C2×C4 | 1 | 12 | yes | — |
| 34 | C2×C4×D52 | C2×C4 | 1 | 48 | yes | — |
| 35 | C2×C4×D52 | C23 | 1 | 12 | yes | — |
| 36 | C2×C4×#1044 | C2×C4 | 1 | 48 | yes | complemented |
| 37 | C2×C4×#1044 | C23 | 1 | 24 | yes | — |
| 38 | C2×C4×#1043 | C2×C4 | 1 | 48 | yes | complemented |
| 39 | C2×C4×#1043 | C23 | 1 | 24 | yes | — |
| 40 | C2×#87830 | C2×C4 | 1 | 96 | yes | complemented |
| 41 | C2×#87830 | C23 | 1 | 48 | yes | — |
| 42 | C4×D5⋊AGL(1,𝔽5) | C2×C4 | 1 | 384 | yes | direct product factor |
| 43 | C2×C42×C52 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 44 | C2×C4×#1039 | C2×C4 | 1 | 3 | yes | complemented |
| 45 | C42×C5⋊D5 | C2×C4 | 1 | 4 | yes | complemented |
| 46 | C42×C5⋊D5 | C23 | 1 | 4 | yes | — |
| 47 | C2×C4×C5×Dic5 | C2×C4 | 1 | 6 | yes | complemented |
| 48 | C42×C5×D5 | C2×C4 | 1 | 16 | yes | complemented |
| 49 | C2×Dic52 | C2×C4 | 1 | 6 | yes | complemented |
| 50 | C4×#6036 | C2×C4 | 1 | 12 | yes | complemented |
| 51 | C4×#6036 | C23 | 1 | 12 | yes | — |
| 52 | C4×D5×Dic5 | C2×C4 | 1 | 48 | yes | complemented |
| 53 | C23×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 54 | C22×C42×D5 | — | 5 | 2 | no | — |
| 55 | C2×C42×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 56 | C2×C42×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 57 | C2×C42×AGL(1,𝔽5) | — | 5 | 32 | no | — |
| 58 | C2×C42×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 59 | C2×C42×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 60 | C23×C5⋊D5 | C24 | 1 | 1 | yes | characteristic |
| 61 | C23×C5×D5 | C22×C4 | 1 | 2 | yes | — |
| 62 | C22×D52 | C22×C4 | 1 | 2 | yes | — |
| 63 | C22×D52 | C22×C4 | 1 | 24 | yes | — |
| 64 | C22×D52 | C24 | 1 | 2 | yes | — |
| 65 | C22×#1044 | C22×C4 | 1 | 48 | yes | — |
| 66 | C22×#1044 | C24 | 1 | 8 | yes | — |
| 67 | C22×#1043 | C22×C4 | 1 | 48 | yes | — |
| 68 | C22×#1043 | C24 | 1 | 8 | yes | — |
| 69 | C2×D5⋊AGL(1,𝔽5) | C42 | 1 | 256 | yes | direct product factor |
| 70 | C2×D5⋊AGL(1,𝔽5) | C22×C4 | 1 | 192 | yes | — |
| 71 | C22×C4×C52 | C22×C4 | 1 | 3 | yes | — |
| 72 | C22×#1039 | C22×C4 | 1 | 3 | yes | — |
| 73 | C2×C4×C5⋊D5 | C22×C4 | 1 | 6 | yes | — |
| 74 | C2×C4×C5⋊D5 | C22×C4 | 1 | 24 | yes | — |
| 75 | C2×C4×C5⋊D5 | C24 | 1 | 6 | yes | — |
| 76 | C22×C5×Dic5 | C22×C4 | 1 | 6 | yes | — |
| 77 | C2×C4×C5×D5 | C42 | 1 | 48 | yes | complemented |
| 78 | C2×C4×C5×D5 | C22×C4 | 1 | 24 | yes | — |
| 79 | C2×#6036 | C22×C4 | 1 | 6 | yes | — |
| 80 | C2×#6036 | C22×C4 | 1 | 24 | yes | — |
| 81 | C2×#6036 | C24 | 1 | 6 | yes | — |
| 82 | C2×D5×Dic5 | C42 | 1 | 48 | yes | complemented |
| 83 | C2×D5×Dic5 | C22×C4 | 1 | 24 | yes | — |
| 84 | C4×D52 | C42 | 1 | 96 | yes | complemented |
| 85 | C4×D52 | C22×C4 | 1 | 96 | yes | — |
| 86 | C4×#1044 | C22×C4 | 1 | 96 | yes | complemented |
| 87 | C4×#1043 | C22×C4 | 1 | 96 | yes | complemented |
| 88 | #87830 | C22×C4 | 1 | 192 | yes | complemented |
| 89 | C42×C52 | C22×C4 | 1 | 4 | yes | complemented |
| 90 | C4×#1039 | C22×C4 | 1 | 12 | yes | complemented |
| 91 | C4×C5×Dic5 | C22×C4 | 1 | 24 | yes | complemented |
| 92 | Dic52 | C22×C4 | 1 | 24 | yes | complemented |
| 93 | C24×AGL(1,𝔽5) | — | 5 | 8 | no | — |
| 94 | C23×C4×D5 | — | 5 | 6 | no | — |
| 95 | C22×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 96 | C22×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 97 | C22×C4×AGL(1,𝔽5) | — | 5 | 192 | no | — |
| 98 | C22×C4×AGL(1,𝔽5) | — | 5 | 96 | no | — |
| 99 | C22×C4×AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 100 | C22×C4×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 101 | C22×C42×C5 | — | 5 | 2 | no | — |
| 102 | C22×C4×Dic5 | — | 5 | 6 | no | — |
| 103 | C2×C42×D5 | — | 5 | 6 | no | — |
| 104 | C2×C42×D5 | — | 5 | 16 | no | — |
| 105 | C2×C42×D5 | — | 5 | 16 | no | — |
| 106 | C2×C42×D5 | — | 5 | 6 | no | — |
| 107 | C2×C42×D5 | — | 5 | 2 | no | — |
| 108 | C2×C42×D5 | — | 10 | 2 | no | — |
| 109 | C2×C42×D5 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 110 | C42×AGL(1,𝔽5) | — | 5 | 16 | no | — |
| 111 | C42×AGL(1,𝔽5) | — | 5 | 96 | no | — |
| 112 | C42×AGL(1,𝔽5) | — | 5 | 16 | no | — |
| 113 | C42×AGL(1,𝔽5) | — | 10 | 16 | no | — |
| 114 | C22×C43 | — | 25 | 1 | no | Sylow |
| 115 | C23×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 116 | C22×C5⋊D5 | C23×C4 | 1 | 12 | yes | — |
| 117 | C22×C5⋊D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 118 | C22×C5⋊D5 | C25 | 1 | 1 | yes | characteristic |
| 119 | C22×C5×D5 | C2×C42 | 1 | 24 | yes | — |
| 120 | C22×C5×D5 | C23×C4 | 1 | 4 | yes | — |
| 121 | C2×D52 | C2×C42 | 1 | 24 | yes | — |
| 122 | C2×D52 | C2×C42 | 1 | 64 | yes | — |
| 123 | C2×D52 | C23×C4 | 1 | 24 | yes | — |
| 124 | C2×#1044 | C2×C42 | 1 | 64 | yes | complemented |
| 125 | C2×#1044 | C23×C4 | 1 | 48 | yes | — |
| 126 | C2×#1043 | C2×C42 | 1 | 64 | yes | complemented |
| 127 | C2×#1043 | C23×C4 | 1 | 48 | yes | — |
| 128 | D5⋊AGL(1,𝔽5) | C2×C42 | 1 | 256 | yes | direct product factor |
| 129 | C2×C4×C52 | C2×C42 | 1 | 12 | yes | complemented |
| 130 | C2×C4×C52 | C23×C4 | 1 | 6 | yes | — |
| 131 | C2×#1039 | C2×C42 | 1 | 12 | yes | complemented |
| 132 | C2×#1039 | C23×C4 | 1 | 6 | yes | — |
| 133 | C4×C5⋊D5 | C2×C42 | 1 | 24 | yes | complemented |
| 134 | C4×C5⋊D5 | C23×C4 | 1 | 24 | yes | — |
| 135 | C2×C5×Dic5 | C2×C42 | 1 | 24 | yes | complemented |
| 136 | C2×C5×Dic5 | C23×C4 | 1 | 12 | yes | — |
| 137 | C4×C5×D5 | C2×C42 | 1 | 96 | yes | complemented |
| 138 | #6036 | C2×C42 | 1 | 24 | yes | complemented |
| 139 | #6036 | C23×C4 | 1 | 24 | yes | — |
| 140 | D5×Dic5 | C2×C42 | 1 | 96 | yes | complemented |
| 141 | C24×D5 | — | 5 | 2 | no | — |
| 142 | C23×AGL(1,𝔽5) | — | 5 | 192 | no | — |
| 143 | C23×AGL(1,𝔽5) | — | 5 | 32 | no | — |
| 144 | C23×AGL(1,𝔽5) | — | 5 | 8 | no | — |
| 145 | C23×AGL(1,𝔽5) | — | 5 | 8 | no | — |
| 146 | C23×AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 147 | C23×C4×C5 | — | 5 | 6 | no | — |
| 148 | C23×Dic5 | — | 5 | 6 | no | — |
| 149 | C22×C4×D5 | — | 5 | 6 | no | — |
| 150 | C22×C4×D5 | — | 5 | 6 | no | — |
| 151 | C22×C4×D5 | — | 5 | 6 | no | — |
| 152 | C22×C4×D5 | — | 5 | 96 | no | — |
| 153 | C22×C4×D5 | — | 5 | 24 | no | — |
| 154 | C22×C4×D5 | — | 5 | 24 | no | — |
| 155 | C22×C4×D5 | — | 10 | 6 | no | — |
| 156 | C22×C4×D5 | C2×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 157 | C2×C4×AGL(1,𝔽5) | — | 5 | 96 | no | — |
| 158 | C2×C4×AGL(1,𝔽5) | — | 5 | 48 | no | — |
| 159 | C2×C4×AGL(1,𝔽5) | — | 5 | 96 | no | — |
| 160 | C2×C4×AGL(1,𝔽5) | — | 5 | 48 | no | — |
| 161 | C2×C4×AGL(1,𝔽5) | — | 5 | 96 | no | — |
| 162 | C2×C4×AGL(1,𝔽5) | — | 5 | 768 | no | — |
| 163 | C2×C4×AGL(1,𝔽5) | — | 5 | 192 | no | — |
| 164 | C2×C4×AGL(1,𝔽5) | — | 10 | 96 | no | — |
| 165 | C2×C4×AGL(1,𝔽5) | — | 10 | 48 | no | — |
| 166 | C2×C42×C5 | — | 2 | 2 | no | — |
| 167 | C2×C42×C5 | — | 5 | 6 | no | — |
| 168 | C2×C42×C5 | — | 5 | 16 | no | — |
| 169 | C2×C42×C5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 170 | C2×C4×Dic5 | — | 5 | 6 | no | — |
| 171 | C2×C4×Dic5 | — | 5 | 12 | no | — |
| 172 | C2×C4×Dic5 | — | 5 | 48 | no | — |
| 173 | C2×C4×Dic5 | — | 10 | 6 | no | — |
| 174 | C2×C4×Dic5 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 175 | C42×D5 | — | 5 | 48 | no | — |
| 176 | C42×D5 | — | 5 | 8 | no | — |
| 177 | C42×D5 | — | 5 | 8 | no | — |
| 178 | C42×D5 | — | 5 | 24 | no | — |
| 179 | C42×D5 | — | 5 | 24 | no | — |
| 180 | C42×D5 | — | 10 | 8 | no | — |
| 181 | C42×D5 | — | 10 | 8 | no | — |
| 182 | C42×D5 | C2×AGL(1,𝔽5) | 1 | 16 | yes | complemented |
| 183 | C23×C42 | — | 25 | 1 | no | — |
| 184 | C23×C42 | — | 25 | 6 | no | — |
| 185 | C2×C43 | — | 25 | 16 | no | — |
| 186 | C2×C43 | — | 25 | 6 | no | — |
| 187 | C2×C43 | — | 25 | 1 | no | — |
| 188 | C2×C43 | — | 25 | 1 | no | — |
| 189 | C22×C52 | C22×C42 | 1 | 6 | yes | — |
| 190 | C22×C52 | C24×C4 | 1 | 1 | yes | characteristic |
| 191 | C2×C5⋊D5 | C22×C42 | 1 | 16 | yes | — |
| 192 | C2×C5⋊D5 | C22×C42 | 1 | 6 | yes | — |
| 193 | C2×C5⋊D5 | C24×C4 | 1 | 6 | yes | — |
| 194 | C2×C5×D5 | C43 | 1 | 32 | yes | complemented |
| 195 | C2×C5×D5 | C22×C42 | 1 | 24 | yes | — |
| 196 | D52 | C43 | 1 | 32 | yes | complemented |
| 197 | D52 | C22×C42 | 1 | 32 | yes | — |
| 198 | #1044 | C22×C42 | 1 | 32 | yes | complemented |
| 199 | #1043 | C22×C42 | 1 | 32 | yes | complemented |
| 200 | C4×C52 | C22×C42 | 1 | 12 | yes | complemented |
| 201 | #1039 | C22×C42 | 1 | 12 | yes | complemented |
| 202 | C5×Dic5 | C22×C42 | 1 | 24 | yes | complemented |
| 203 | C24×C5 | — | 5 | 2 | no | — |
| 204 | C23×D5 | — | 5 | 2 | no | — |
| 205 | C23×D5 | — | 5 | 48 | no | — |
| 206 | C23×D5 | — | 5 | 4 | no | — |
| 207 | C23×D5 | — | 5 | 4 | no | — |
| 208 | C23×D5 | — | 10 | 2 | no | — |
| 209 | C23×D5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 210 | C22×AGL(1,𝔽5) | — | 5 | 16 | no | — |
| 211 | C22×AGL(1,𝔽5) | — | 5 | 16 | no | — |
| 212 | C22×AGL(1,𝔽5) | — | 5 | 384 | no | — |
| 213 | C22×AGL(1,𝔽5) | — | 5 | 96 | no | — |
| 214 | C22×AGL(1,𝔽5) | — | 5 | 96 | no | — |
| 215 | C22×AGL(1,𝔽5) | — | 5 | 512 | no | — |
| 216 | C22×AGL(1,𝔽5) | — | 10 | 16 | no | — |
| 217 | C22×AGL(1,𝔽5) | — | 10 | 96 | no | — |
| 218 | C22×C4×C5 | — | 2 | 6 | no | — |
| 219 | C22×C4×C5 | — | 5 | 6 | no | — |
| 220 | C22×C4×C5 | — | 5 | 48 | no | — |
| 221 | C22×C4×C5 | — | 5 | 24 | no | — |
| 222 | C22×C4×C5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 223 | C22×Dic5 | — | 5 | 6 | no | — |
| 224 | C22×Dic5 | — | 5 | 48 | no | — |
| 225 | C22×Dic5 | — | 5 | 24 | no | — |
| 226 | C22×Dic5 | — | 10 | 6 | no | — |
| 227 | C22×Dic5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 228 | C2×C4×D5 | — | 5 | 48 | no | — |
| 229 | C2×C4×D5 | — | 5 | 24 | no | — |
| 230 | C2×C4×D5 | — | 5 | 48 | no | — |
| 231 | C2×C4×D5 | — | 5 | 12 | no | — |
| 232 | C2×C4×D5 | — | 5 | 12 | no | — |
| 233 | C2×C4×D5 | — | 5 | 48 | no | — |
| 234 | C2×C4×D5 | — | 5 | 12 | no | — |
| 235 | C2×C4×D5 | — | 5 | 12 | no | — |
| 236 | C2×C4×D5 | — | 5 | 192 | no | — |
| 237 | C2×C4×D5 | — | 5 | 192 | no | — |
| 238 | C2×C4×D5 | — | 10 | 12 | no | — |
| 239 | C2×C4×D5 | — | 10 | 48 | no | — |
| 240 | C2×C4×D5 | — | 10 | 12 | no | — |
| 241 | C2×C4×D5 | C4×AGL(1,𝔽5) | 1 | 48 | yes | complemented |
| 242 | C2×C4×D5 | C22×AGL(1,𝔽5) | 1 | 24 | yes | — |
| 243 | C4×AGL(1,𝔽5) | — | 5 | 384 | no | — |
| 244 | C4×AGL(1,𝔽5) | — | 5 | 192 | no | — |
| 245 | C4×AGL(1,𝔽5) | — | 5 | 192 | no | — |
| 246 | C4×AGL(1,𝔽5) | — | 10 | 192 | no | — |
| 247 | C42×C5 | — | 2 | 8 | no | — |
| 248 | C42×C5 | — | 5 | 24 | no | — |
| 249 | C42×C5 | C22×AGL(1,𝔽5) | 1 | 8 | yes | complemented |
| 250 | C4×Dic5 | — | 5 | 24 | no | — |
| 251 | C4×Dic5 | — | 5 | 48 | no | — |
| 252 | C4×Dic5 | — | 10 | 24 | no | — |
| 253 | C4×Dic5 | C22×AGL(1,𝔽5) | 1 | 24 | yes | complemented |
| 254 | C24×C4 | — | 25 | 3 | no | — |
| 255 | C24×C4 | — | 25 | 4 | no | — |
| 256 | C22×C42 | — | 5 | 2 | no | — |
| 257 | C22×C42 | — | 25 | 8 | no | — |
| 258 | C22×C42 | — | 25 | 3 | no | — |
| 259 | C22×C42 | — | 25 | 8 | no | — |
| 260 | C22×C42 | — | 25 | 6 | no | — |
| 261 | C22×C42 | — | 25 | 96 | no | — |
| 262 | C22×C42 | — | 25 | 6 | no | — |
| 263 | C22×C42 | — | 25 | 48 | no | — |
| 264 | C22×C42 | — | 25 | 12 | no | — |
| 265 | C22×C42 | — | 25 | 6 | no | — |
| 266 | C22×C42 | — | 25 | 1 | no | — |
| 267 | C43 | — | 25 | 8 | no | — |
| 268 | C43 | — | 25 | 48 | no | — |
| 269 | C43 | — | 25 | 8 | no | — |
| 270 | C2×C52 | C2×C43 | 1 | 4 | yes | complemented |
| 271 | C2×C52 | C23×C42 | 1 | 3 | yes | — |
| 272 | C5⋊D5 | C2×C43 | 1 | 4 | yes | complemented |
| 273 | C5⋊D5 | C23×C42 | 1 | 4 | yes | — |
| 274 | C5×D5 | C2×C43 | 1 | 16 | yes | complemented |
| 275 | C23×C5 | — | 2 | 2 | no | — |
| 276 | C23×C5 | — | 5 | 24 | no | — |
| 277 | C23×C5 | — | 5 | 4 | no | — |
| 278 | C23×C5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 279 | C22×D5 | — | 5 | 24 | no | — |
| 280 | C22×D5 | — | 5 | 2 | no | — |
| 281 | C22×D5 | — | 5 | 2 | no | — |
| 282 | C22×D5 | — | 5 | 128 | no | — |
| 283 | C22×D5 | — | 5 | 48 | no | — |
| 284 | C22×D5 | — | 5 | 48 | no | — |
| 285 | C22×D5 | — | 10 | 2 | no | — |
| 286 | C22×D5 | — | 10 | 24 | no | — |
| 287 | C22×D5 | — | 10 | 2 | no | — |
| 288 | C22×D5 | C2×C4×AGL(1,𝔽5) | 1 | 24 | yes | — |
| 289 | C22×D5 | C23×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 290 | C2×AGL(1,𝔽5) | — | 5 | 512 | no | — |
| 291 | C2×AGL(1,𝔽5) | — | 5 | 128 | no | — |
| 292 | C2×AGL(1,𝔽5) | — | 5 | 96 | no | — |
| 293 | C2×AGL(1,𝔽5) | — | 5 | 128 | no | — |
| 294 | C2×AGL(1,𝔽5) | — | 5 | 96 | no | — |
| 295 | C2×AGL(1,𝔽5) | — | 10 | 128 | no | — |
| 296 | C2×AGL(1,𝔽5) | — | 10 | 96 | no | — |
| 297 | C2×C4×C5 | — | 2 | 12 | no | — |
| 298 | C2×C4×C5 | — | 2 | 24 | no | — |
| 299 | C2×C4×C5 | — | 5 | 24 | no | — |
| 300 | C2×C4×C5 | — | 5 | 12 | no | — |
| 301 | C2×C4×C5 | — | 5 | 96 | no | — |
| 302 | C2×C4×C5 | C2×C4×AGL(1,𝔽5) | 1 | 24 | yes | complemented |
| 303 | C2×C4×C5 | C23×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 304 | C2×Dic5 | — | 5 | 24 | no | — |
| 305 | C2×Dic5 | — | 5 | 12 | no | — |
| 306 | C2×Dic5 | — | 5 | 96 | no | — |
| 307 | C2×Dic5 | — | 10 | 24 | no | — |
| 308 | C2×Dic5 | — | 10 | 12 | no | — |
| 309 | C2×Dic5 | C2×C4×AGL(1,𝔽5) | 1 | 24 | yes | complemented |
| 310 | C2×Dic5 | C23×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 311 | C4×D5 | — | 5 | 96 | no | — |
| 312 | C4×D5 | — | 5 | 48 | no | — |
| 313 | C4×D5 | — | 5 | 48 | no | — |
| 314 | C4×D5 | — | 5 | 48 | no | — |
| 315 | C4×D5 | — | 5 | 48 | no | — |
| 316 | C4×D5 | — | 10 | 48 | no | — |
| 317 | C4×D5 | — | 10 | 48 | no | — |
| 318 | C4×D5 | C2×C4×AGL(1,𝔽5) | 1 | 96 | yes | complemented |
| 319 | C25 | — | 25 | 1 | no | — |
| 320 | C23×C4 | — | 5 | 6 | no | — |
| 321 | C23×C4 | — | 25 | 12 | no | — |
| 322 | C23×C4 | — | 25 | 48 | no | — |
| 323 | C23×C4 | — | 25 | 3 | no | — |
| 324 | C23×C4 | — | 25 | 12 | no | — |
| 325 | C23×C4 | — | 25 | 6 | no | — |
| 326 | C23×C4 | — | 25 | 4 | no | — |
| 327 | C23×C4 | — | 25 | 96 | no | — |
| 328 | C23×C4 | — | 25 | 4 | no | — |
| 329 | C23×C4 | — | 25 | 16 | no | — |
| 330 | C23×C4 | — | 25 | 3 | no | — |
| 331 | C2×C42 | — | 5 | 6 | no | — |
| 332 | C2×C42 | — | 5 | 16 | no | — |
| 333 | C2×C42 | — | 25 | 12 | no | — |
| 334 | C2×C42 | — | 25 | 12 | no | — |
| 335 | C2×C42 | — | 25 | 48 | no | — |
| 336 | C2×C42 | — | 25 | 6 | no | — |
| 337 | C2×C42 | — | 25 | 24 | no | — |
| 338 | C2×C42 | — | 25 | 48 | no | — |
| 339 | C2×C42 | — | 25 | 48 | no | — |
| 340 | C2×C42 | — | 25 | 24 | no | — |
| 341 | C2×C42 | — | 25 | 96 | no | — |
| 342 | C2×C42 | — | 25 | 48 | no | — |
| 343 | C2×C42 | — | 25 | 384 | no | — |
| 344 | C2×C42 | — | 25 | 3 | no | — |
| 345 | C2×C42 | — | 25 | 4 | no | — |
| 346 | C2×C42 | — | 25 | 4 | no | — |
| 347 | C2×C42 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 348 | C52 | C22×C43 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 349 | C22×C5 | — | 2 | 12 | no | — |
| 350 | C22×C5 | — | 2 | 2 | no | — |
| 351 | C22×C5 | — | 5 | 24 | no | — |
| 352 | C22×C5 | — | 5 | 32 | no | — |
| 353 | C22×C5 | C22×C4×AGL(1,𝔽5) | 1 | 12 | yes | — |
| 354 | C22×C5 | C24×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 355 | C2×D5 | — | 5 | 12 | no | — |
| 356 | C2×D5 | — | 5 | 12 | no | — |
| 357 | C2×D5 | — | 5 | 32 | no | — |
| 358 | C2×D5 | — | 5 | 64 | no | — |
| 359 | C2×D5 | — | 5 | 64 | no | — |
| 360 | C2×D5 | — | 10 | 12 | no | — |
| 361 | C2×D5 | — | 10 | 12 | no | — |
| 362 | C2×D5 | — | 10 | 32 | no | — |
| 363 | C2×D5 | C42×AGL(1,𝔽5) | 1 | 32 | yes | complemented |
| 364 | C2×D5 | C22×C4×AGL(1,𝔽5) | 1 | 24 | yes | — |
| 365 | AGL(1,𝔽5) | — | 5 | 64 | no | — |
| 366 | AGL(1,𝔽5) | — | 5 | 64 | no | — |
| 367 | AGL(1,𝔽5) | — | 10 | 64 | no | — |
| 368 | C4×C5 | — | 2 | 24 | no | — |
| 369 | C4×C5 | — | 5 | 24 | no | — |
| 370 | C4×C5 | C22×C4×AGL(1,𝔽5) | 1 | 24 | yes | complemented |
| 371 | Dic5 | — | 5 | 24 | no | — |
| 372 | Dic5 | — | 10 | 24 | no | — |
| 373 | Dic5 | C22×C4×AGL(1,𝔽5) | 1 | 24 | yes | complemented |
| 374 | C24 | — | 5 | 2 | no | — |
| 375 | C24 | — | 25 | 2 | no | — |
| 376 | C24 | — | 25 | 24 | no | — |
| 377 | C24 | — | 25 | 2 | no | — |
| 378 | C24 | — | 25 | 1 | no | — |
| 379 | C22×C4 | — | 5 | 6 | no | — |
| 380 | C22×C4 | — | 5 | 24 | no | — |
| 381 | C22×C4 | — | 5 | 48 | no | — |
| 382 | C22×C4 | — | 25 | 6 | no | — |
| 383 | C22×C4 | — | 25 | 24 | no | — |
| 384 | C22×C4 | — | 25 | 6 | no | — |
| 385 | C22×C4 | — | 25 | 96 | no | — |
| 386 | C22×C4 | — | 25 | 96 | no | — |
| 387 | C22×C4 | — | 25 | 24 | no | — |
| 388 | C22×C4 | — | 25 | 48 | no | — |
| 389 | C22×C4 | — | 25 | 8 | no | — |
| 390 | C22×C4 | — | 25 | 8 | no | — |
| 391 | C22×C4 | — | 25 | 48 | no | — |
| 392 | C22×C4 | — | 25 | 192 | no | — |
| 393 | C22×C4 | — | 25 | 48 | no | — |
| 394 | C22×C4 | — | 25 | 256 | no | — |
| 395 | C22×C4 | — | 25 | 3 | no | — |
| 396 | C22×C4 | — | 25 | 6 | no | — |
| 397 | C22×C4 | — | 25 | 6 | no | — |
| 398 | C22×C4 | — | 25 | 24 | no | — |
| 399 | C22×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 400 | C42 | — | 5 | 24 | no | — |
| 401 | C42 | — | 25 | 24 | no | — |
| 402 | C42 | — | 25 | 192 | no | — |
| 403 | C42 | — | 25 | 96 | no | — |
| 404 | C42 | — | 25 | 96 | no | — |
| 405 | C42 | — | 25 | 12 | no | — |
| 406 | C42 | C2×D5⋊AGL(1,𝔽5) | 1 | 4 | yes | direct product factor |
| 407 | C2×C5 | — | 2 | 8 | no | — |
| 408 | C2×C5 | — | 2 | 6 | no | — |
| 409 | C2×C5 | — | 5 | 16 | no | — |
| 410 | C2×C5 | C2×C42×AGL(1,𝔽5) | 1 | 8 | yes | complemented |
| 411 | C2×C5 | C23×C4×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 412 | D5 | — | 5 | 8 | no | — |
| 413 | D5 | — | 5 | 8 | no | — |
| 414 | D5 | — | 10 | 8 | no | — |
| 415 | D5 | — | 10 | 8 | no | — |
| 416 | D5 | C2×C42×AGL(1,𝔽5) | 1 | 16 | yes | complemented |
| 417 | C23 | — | 5 | 24 | no | — |
| 418 | C23 | — | 5 | 4 | no | — |
| 419 | C23 | — | 25 | 24 | no | — |
| 420 | C23 | — | 25 | 64 | no | — |
| 421 | C23 | — | 25 | 24 | no | — |
| 422 | C23 | — | 25 | 12 | no | — |
| 423 | C23 | — | 25 | 1 | no | — |
| 424 | C23 | — | 25 | 1 | no | — |
| 425 | C23 | C22×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 426 | C2×C4 | — | 5 | 24 | no | — |
| 427 | C2×C4 | — | 5 | 12 | no | — |
| 428 | C2×C4 | — | 5 | 96 | no | — |
| 429 | C2×C4 | — | 25 | 24 | no | — |
| 430 | C2×C4 | — | 25 | 24 | no | — |
| 431 | C2×C4 | — | 25 | 96 | no | — |
| 432 | C2×C4 | — | 25 | 48 | no | — |
| 433 | C2×C4 | — | 25 | 48 | no | — |
| 434 | C2×C4 | — | 25 | 64 | no | — |
| 435 | C2×C4 | — | 25 | 256 | no | — |
| 436 | C2×C4 | — | 25 | 64 | no | — |
| 437 | C2×C4 | — | 25 | 12 | no | — |
| 438 | C2×C4 | — | 25 | 6 | no | — |
| 439 | C2×C4 | — | 25 | 24 | no | — |
| 440 | C2×C4 | — | 25 | 24 | no | — |
| 441 | C2×C4 | C4×D5⋊AGL(1,𝔽5) | 1 | 12 | yes | direct product factor |
| 442 | C2×C4 | C22×D5⋊AGL(1,𝔽5) | 1 | 6 | yes | — |
| 443 | C5 | — | 2 | 2 | no | — |
| 444 | C5 | C22×C42×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 445 | C22 | — | 5 | 32 | no | — |
| 446 | C22 | — | 5 | 24 | no | — |
| 447 | C22 | — | 25 | 32 | no | — |
| 448 | C22 | — | 25 | 32 | no | — |
| 449 | C22 | — | 25 | 16 | no | — |
| 450 | C22 | — | 25 | 6 | no | — |
| 451 | C22 | — | 25 | 6 | no | — |
| 452 | C22 | C2×C4×D5⋊AGL(1,𝔽5) | 1 | 6 | yes | — |
| 453 | C22 | C23×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 454 | C4 | — | 5 | 24 | no | — |
| 455 | C4 | — | 25 | 32 | no | — |
| 456 | C4 | — | 25 | 32 | no | — |
| 457 | C4 | — | 25 | 12 | no | — |
| 458 | C4 | C2×C4×D5⋊AGL(1,𝔽5) | 1 | 12 | yes | direct product factor |
| 459 | C2 | — | 5 | 16 | no | — |
| 460 | C2 | — | 25 | 4 | no | — |
| 461 | C2 | — | 25 | 4 | no | — |
| 462 | C2 | C22×C4×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 463 | C2 | C42×D5⋊AGL(1,𝔽5) | 1 | 4 | yes | direct product factor |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C2×C42×#1044 | C2 | semidirect |
| 3. C2×C4×#87830 | C2 | semidirect |
| 4. C42×D5⋊AGL(1,𝔽5) | C2 | direct (N × H) |
| 6. C2×C42×#1043 | C2 | semidirect |
| 12. C2×C4×D5⋊AGL(1,𝔽5) | C4 | direct (N × H) |
| 15. C2×C42×C5×D5 | C4 | semidirect |
| 17. C2×C4×D5×Dic5 | C4 | semidirect |
| 18. C42×D52 | C4 | semidirect |
| 20. C42×#1044 | C22 | semidirect |
| 21. C42×#1043 | C22 | semidirect |
| 22. C4×#87830 | C22 | semidirect |
| 36. C2×C4×#1044 | C2×C4 | semidirect |
| 38. C2×C4×#1043 | C2×C4 | semidirect |
| 40. C2×#87830 | C2×C4 | semidirect |
| 42. C4×D5⋊AGL(1,𝔽5) | C2×C4 | direct (N × H) |
| 43. C2×C42×C52 | C2×C4 | semidirect |
| 44. C2×C4×#1039 | C2×C4 | semidirect |
| 45. C42×C5⋊D5 | C2×C4 | semidirect |
| 47. C2×C4×C5×Dic5 | C2×C4 | semidirect |
| 48. C42×C5×D5 | C2×C4 | semidirect |
| 49. C2×Dic52 | C2×C4 | semidirect |
| 50. C4×#6036 | C2×C4 | semidirect |
| 52. C4×D5×Dic5 | C2×C4 | semidirect |
| 69. C2×D5⋊AGL(1,𝔽5) | C42 | direct (N × H) |
| 77. C2×C4×C5×D5 | C42 | semidirect |
| 82. C2×D5×Dic5 | C42 | semidirect |
| 84. C4×D52 | C42 | semidirect |
| 86. C4×#1044 | C22×C4 | semidirect |
| 87. C4×#1043 | C22×C4 | semidirect |
| 88. #87830 | C22×C4 | semidirect |
| 89. C42×C52 | C22×C4 | semidirect |
| 90. C4×#1039 | C22×C4 | semidirect |
| 91. C4×C5×Dic5 | C22×C4 | semidirect |
| 92. Dic52 | C22×C4 | semidirect |
| 109. C2×C42×D5 | AGL(1,𝔽5) | semidirect |
| 124. C2×#1044 | C2×C42 | semidirect |
| 126. C2×#1043 | C2×C42 | semidirect |
| 128. D5⋊AGL(1,𝔽5) | C2×C42 | direct (N × H) |
| 129. C2×C4×C52 | C2×C42 | semidirect |
| 131. C2×#1039 | C2×C42 | semidirect |
| 133. C4×C5⋊D5 | C2×C42 | semidirect |
| 135. C2×C5×Dic5 | C2×C42 | semidirect |
| 137. C4×C5×D5 | C2×C42 | semidirect |
| 138. #6036 | C2×C42 | semidirect |
| 140. D5×Dic5 | C2×C42 | semidirect |
| 169. C2×C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 174. C2×C4×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 182. C42×D5 | C2×AGL(1,𝔽5) | semidirect |
| 194. C2×C5×D5 | C43 | semidirect |
| 196. D52 | C43 | semidirect |
| 198. #1044 | C22×C42 | semidirect |
| 199. #1043 | C22×C42 | semidirect |
| 200. C4×C52 | C22×C42 | semidirect |
| 201. #1039 | C22×C42 | semidirect |
| 202. C5×Dic5 | C22×C42 | semidirect |
| 241. C2×C4×D5 | C4×AGL(1,𝔽5) | semidirect |
| 249. C42×C5 | C22×AGL(1,𝔽5) | semidirect |
| 253. C4×Dic5 | C22×AGL(1,𝔽5) | semidirect |
| 270. C2×C52 | C2×C43 | semidirect |
| 272. C5⋊D5 | C2×C43 | semidirect |
| 274. C5×D5 | C2×C43 | semidirect |
| 302. C2×C4×C5 | C2×C4×AGL(1,𝔽5) | semidirect |
| 309. C2×Dic5 | C2×C4×AGL(1,𝔽5) | semidirect |
| 318. C4×D5 | C2×C4×AGL(1,𝔽5) | semidirect |
| 347. C2×C42 | D5⋊AGL(1,𝔽5) | direct (N × H) |
| 348. C52 | C22×C43 | semidirect |
| 363. C2×D5 | C42×AGL(1,𝔽5) | semidirect |
| 370. C4×C5 | C22×C4×AGL(1,𝔽5) | semidirect |
| 373. Dic5 | C22×C4×AGL(1,𝔽5) | semidirect |
| 406. C42 | C2×D5⋊AGL(1,𝔽5) | direct (N × H) |
| 410. C2×C5 | C2×C42×AGL(1,𝔽5) | semidirect |
| 416. D5 | C2×C42×AGL(1,𝔽5) | semidirect |
| 441. C2×C4 | C4×D5⋊AGL(1,𝔽5) | direct (N × H) |
| 444. C5 | C22×C42×AGL(1,𝔽5) | semidirect |
| 458. C4 | C2×C4×D5⋊AGL(1,𝔽5) | direct (N × H) |
| 463. C2 | C42×D5⋊AGL(1,𝔽5) | 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