← AGL(1,𝔽5)×#815 #14294224
Order 1920.
720 conjugacy classes of subgroups.
The subgroup lattice has 352 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#91221 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3×C8×AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C4×Dic3×AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11751788 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C2×#91150 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C2×AGL(1,𝔽5)×C3⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | D5×#815 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | AGL(1,𝔽5)×#97 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×C4×ΓL(1,𝔽16) | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×D5⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×C4×AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×D5⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×Dic3×AGL(1,𝔽5) | C4 | 1 | 4 | yes | — |
| 14 | C2×C3×C8×D5 | C22 | 1 | 1 | yes | characteristic |
| 15 | C4×D5×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×D5×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 17 | #91221 | C4 | 1 | 4 | yes | complemented |
| 18 | C3×C8×AGL(1,𝔽5) | C4 | 1 | 4 | yes | complemented |
| 19 | #91169 | C4 | 1 | 4 | yes | complemented |
| 20 | #91150 | C4 | 1 | 4 | yes | complemented |
| 21 | AGL(1,𝔽5)×C3⋊C8 | C4 | 1 | 4 | yes | complemented |
| 22 | #91099 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C5×#815 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #90954 | C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | #90953 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | C4×#815 | — | 5 | 1 | no | maximal, Hall |
| 27 | C2×#3992 | — | 3 | 1 | no | — |
| 28 | C2×#3992 | — | 3 | 1 | no | — |
| 29 | C2×C8×AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 30 | C2×C8×AGL(1,𝔽5) | D3 | 1 | 1 | yes | characteristic |
| 31 | C42×AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 32 | #65676 | — | 3 | 1 | no | — |
| 33 | D5×#97 | — | 3 | 1 | no | — |
| 34 | C22×ΓL(1,𝔽16) | C2×C4 | 1 | 2 | yes | — |
| 35 | C22×C3×AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×C3×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 37 | C2×D5×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 38 | C2×C3⋊#170 | C2×C4 | 1 | 2 | yes | — |
| 39 | C4×ΓL(1,𝔽16) | C2×C4 | 1 | 2 | yes | — |
| 40 | C4×ΓL(1,𝔽16) | C2×C4 | 1 | 2 | yes | — |
| 41 | D5⋊(C3⋊C8) | C2×C4 | 1 | 2 | yes | — |
| 42 | D5⋊(C3⋊C8) | C2×C4 | 1 | 2 | yes | — |
| 43 | C2×C3×#170 | C2×C4 | 1 | 2 | yes | — |
| 44 | C3×C4×AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 45 | C3×C4×AGL(1,𝔽5) | C2×C4 | 1 | 2 | yes | — |
| 46 | C3×D5⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 47 | C3×D5⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 48 | Dic3×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 49 | C2×C3×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C4×Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×C3⋊#168 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C4×C5×Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C2×C5×C3⋊C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C2×C3×#168 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C3×C8×D5 | C2×C4 | 1 | 2 | yes | — |
| 56 | C3×C8×D5 | C2×C4 | 1 | 2 | yes | — |
| 57 | Dic3×Dic5 | C2×C4 | 1 | 2 | yes | — |
| 58 | D5×C3⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 59 | D5×C3⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 60 | C2×C3×C4×C8 | — | 5 | 1 | no | — |
| 61 | C2×#815 | — | 5 | 1 | no | — |
| 62 | C2×#815 | — | 5 | 1 | no | — |
| 63 | C2×#815 | — | 5 | 1 | no | — |
| 64 | C2×#815 | — | 5 | 1 | no | — |
| 65 | C42×Dic3 | — | 5 | 1 | no | — |
| 66 | C2×C4×C3⋊C8 | — | 5 | 1 | no | — |
| 67 | C2×C4×AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 68 | C2×C4×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 69 | C2×C4×AGL(1,𝔽5) | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | C2×D5⋊C8 | — | 3 | 1 | no | — |
| 71 | C2×D5⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 72 | C2×C8×D5 | — | 3 | 1 | no | — |
| 73 | C2×C8×D5 | C2×D3 | 1 | 1 | yes | characteristic |
| 74 | C42×D5 | — | 3 | 1 | no | — |
| 75 | #4002 | — | 3 | 4 | no | — |
| 76 | #3992 | — | 3 | 4 | no | — |
| 77 | #3992 | — | 3 | 4 | no | — |
| 78 | C8×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 79 | C8×AGL(1,𝔽5) | Dic3 | 1 | 4 | yes | complemented |
| 80 | C5×#97 | — | 3 | 1 | no | — |
| 81 | #3947 | — | 3 | 1 | no | — |
| 82 | #3947 | — | 3 | 1 | no | — |
| 83 | #3935 | — | 3 | 1 | no | — |
| 84 | C4×#97 | — | 15 | 1 | no | Sylow |
| 85 | C22×C3×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 86 | C2×ΓL(1,𝔽16) | — | 2 | 4 | no | — |
| 87 | C2×ΓL(1,𝔽16) | C42 | 1 | 4 | yes | — |
| 88 | C2×C3×AGL(1,𝔽5) | C42 | 1 | 4 | yes | — |
| 89 | C2×C3×AGL(1,𝔽5) | M16 | 1 | 8 | yes | — |
| 90 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | C2×Dic15 | C42 | 1 | 2 | yes | — |
| 92 | C2×C5×Dic3 | C42 | 1 | 2 | yes | — |
| 93 | C2×C3×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 94 | C3×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C3×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 96 | C3×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 97 | C3×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 98 | D5×Dic3 | — | 2 | 4 | no | — |
| 99 | C3⋊#170 | C42 | 1 | 4 | yes | complemented |
| 100 | C3×#170 | C42 | 1 | 4 | yes | complemented |
| 101 | C3×C5×C8 | C42 | 1 | 2 | yes | complemented |
| 102 | C3⋊#168 | C42 | 1 | 2 | yes | complemented |
| 103 | C3×#168 | C42 | 1 | 2 | yes | complemented |
| 104 | C5×C3⋊C8 | C42 | 1 | 2 | yes | complemented |
| 105 | C22×C3×C8 | — | 5 | 1 | no | — |
| 106 | C22×C3×C8 | — | 5 | 1 | no | — |
| 107 | C2×C3×C42 | — | 5 | 1 | no | — |
| 108 | C2×C4×Dic3 | — | 5 | 1 | no | — |
| 109 | C2×C4×Dic3 | — | 5 | 1 | no | — |
| 110 | C2×C4×Dic3 | — | 5 | 4 | no | — |
| 111 | C22×C3⋊C8 | — | 5 | 1 | no | — |
| 112 | C22×C3⋊C8 | — | 5 | 1 | no | — |
| 113 | C3×C4×C8 | — | 5 | 4 | no | — |
| 114 | #815 | — | 5 | 4 | no | — |
| 115 | #815 | — | 5 | 4 | no | — |
| 116 | #815 | — | 5 | 4 | no | — |
| 117 | #815 | — | 5 | 1 | no | — |
| 118 | #815 | — | 5 | 1 | no | — |
| 119 | #815 | — | 5 | 1 | no | — |
| 120 | #815 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 121 | C4×C3⋊C8 | — | 5 | 4 | no | — |
| 122 | C22×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 123 | C22×AGL(1,𝔽5) | C4×D3 | 1 | 2 | yes | — |
| 124 | C2×C4×D5 | — | 3 | 2 | no | — |
| 125 | C2×C4×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 126 | C2×#170 | — | 3 | 2 | no | — |
| 127 | C2×#170 | C4×D3 | 1 | 2 | yes | — |
| 128 | C4×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 129 | C4×AGL(1,𝔽5) | — | 3 | 2 | no | — |
| 130 | C4×AGL(1,𝔽5) | — | 6 | 8 | no | — |
| 131 | C4×AGL(1,𝔽5) | C4×D3 | 1 | 2 | yes | — |
| 132 | C4×AGL(1,𝔽5) | C2×Dic3 | 1 | 2 | yes | — |
| 133 | D5⋊C8 | — | 3 | 2 | no | — |
| 134 | D5⋊C8 | — | 3 | 2 | no | — |
| 135 | D5⋊C8 | C4×D3 | 1 | 2 | yes | — |
| 136 | D5⋊C8 | C2×Dic3 | 1 | 2 | yes | — |
| 137 | C2×C5×C8 | — | 3 | 1 | no | — |
| 138 | C2×C5×C8 | C4×D3 | 1 | 1 | yes | characteristic |
| 139 | C42×C5 | — | 3 | 1 | no | — |
| 140 | C4×Dic5 | — | 3 | 1 | no | — |
| 141 | C4×Dic5 | — | 3 | 2 | no | — |
| 142 | C2×#168 | — | 3 | 1 | no | — |
| 143 | C2×#168 | C4×D3 | 1 | 1 | yes | characteristic |
| 144 | C8×D5 | — | 3 | 2 | no | — |
| 145 | C8×D5 | — | 3 | 2 | no | — |
| 146 | C8×D5 | C4×D3 | 1 | 2 | yes | — |
| 147 | C8×D5 | C2×Dic3 | 1 | 2 | yes | — |
| 148 | C2×#97 | — | 15 | 1 | no | — |
| 149 | C2×#97 | — | 15 | 1 | no | — |
| 150 | C2×#97 | — | 15 | 1 | no | — |
| 151 | C2×#97 | — | 15 | 1 | no | — |
| 152 | C2×C4×C8 | — | 5 | 1 | no | — |
| 153 | C2×C4×C8 | — | 15 | 1 | no | — |
| 154 | C43 | — | 15 | 1 | no | — |
| 155 | C22×C3×C5 | C2×C42 | 1 | 1 | yes | characteristic |
| 156 | C2×C3×D5 | C2×C42 | 1 | 1 | yes | characteristic |
| 157 | C2×C3×D5 | C2×C42 | 1 | 1 | yes | characteristic |
| 158 | C2×C3×D5 | C2×M16 | 1 | 4 | yes | — |
| 159 | ΓL(1,𝔽16) | — | 2 | 4 | no | — |
| 160 | C3×AGL(1,𝔽5) | #97 | 1 | 8 | yes | complemented |
| 161 | C3×C4×C5 | C2×C42 | 1 | 1 | yes | characteristic |
| 162 | C3×C4×C5 | C2×C42 | 1 | 1 | yes | characteristic |
| 163 | Dic15 | — | 2 | 2 | no | — |
| 164 | C3×Dic5 | C2×C42 | 1 | 1 | yes | characteristic |
| 165 | C3×Dic5 | C2×C42 | 1 | 1 | yes | characteristic |
| 166 | C5×Dic3 | — | 2 | 2 | no | — |
| 167 | C22×C3×C4 | — | 5 | 2 | no | — |
| 168 | C22×C3×C4 | — | 5 | 1 | no | — |
| 169 | C22×Dic3 | — | 5 | 2 | no | — |
| 170 | C22×Dic3 | — | 5 | 2 | no | — |
| 171 | C2×C3×C8 | — | 5 | 2 | no | — |
| 172 | C2×C3×C8 | — | 5 | 2 | no | — |
| 173 | C2×C3×C8 | — | 5 | 2 | no | — |
| 174 | C2×C3×C8 | — | 5 | 1 | no | — |
| 175 | C2×C3×C8 | — | 5 | 2 | no | — |
| 176 | C2×C3×C8 | — | 5 | 2 | no | — |
| 177 | C2×C3×C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 178 | C3×C42 | — | 5 | 2 | no | — |
| 179 | C3×C42 | — | 5 | 2 | no | — |
| 180 | C4×Dic3 | — | 5 | 2 | no | — |
| 181 | C4×Dic3 | — | 5 | 2 | no | — |
| 182 | C4×Dic3 | — | 5 | 1 | no | — |
| 183 | C4×Dic3 | — | 5 | 2 | no | — |
| 184 | C4×Dic3 | — | 10 | 8 | no | — |
| 185 | C4×Dic3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 186 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 187 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 188 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 189 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 190 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 191 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 192 | C2×C3⋊C8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 193 | C22×D5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 194 | C2×AGL(1,𝔽5) | — | 3 | 4 | no | — |
| 195 | C2×AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 196 | C2×AGL(1,𝔽5) | ΓL(1,𝔽25) | 1 | 8 | yes | — |
| 197 | C2×AGL(1,𝔽5) | C4×Dic3 | 1 | 4 | yes | — |
| 198 | C2×C4×C5 | — | 3 | 2 | no | — |
| 199 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 200 | C2×Dic5 | — | 3 | 2 | no | — |
| 201 | C2×Dic5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 202 | C4×D5 | — | 6 | 4 | no | — |
| 203 | C4×D5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 204 | C4×D5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 205 | C4×D5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 206 | C4×D5 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 207 | #170 | — | 3 | 4 | no | — |
| 208 | #170 | C4×Dic3 | 1 | 4 | yes | complemented |
| 209 | C5×C8 | — | 3 | 2 | no | — |
| 210 | C5×C8 | C4×Dic3 | 1 | 2 | yes | complemented |
| 211 | #168 | — | 3 | 2 | no | — |
| 212 | #168 | C4×Dic3 | 1 | 2 | yes | complemented |
| 213 | C22×C8 | — | 5 | 1 | no | — |
| 214 | C22×C8 | — | 5 | 1 | no | — |
| 215 | C22×C8 | — | 15 | 1 | no | — |
| 216 | C22×C8 | — | 15 | 1 | no | — |
| 217 | C2×C42 | — | 5 | 1 | no | — |
| 218 | C2×C42 | — | 15 | 1 | no | — |
| 219 | C2×C42 | — | 15 | 1 | no | — |
| 220 | C2×C42 | — | 15 | 4 | no | — |
| 221 | #97 | — | 3 | 1 | no | — |
| 222 | #97 | — | 15 | 1 | no | — |
| 223 | #97 | — | 15 | 1 | no | — |
| 224 | #97 | — | 15 | 4 | no | — |
| 225 | #97 | — | 15 | 4 | no | — |
| 226 | #97 | — | 15 | 4 | no | — |
| 227 | #97 | — | 15 | 1 | no | — |
| 228 | C4×C8 | — | 5 | 4 | no | — |
| 229 | C4×C8 | — | 15 | 4 | no | — |
| 230 | C2×C3×C5 | C43 | 1 | 1 | yes | characteristic |
| 231 | C2×C3×C5 | C4×M16 | 1 | 2 | yes | — |
| 232 | C3×D5 | C2×#97 | 1 | 2 | yes | — |
| 233 | C3×D5 | C4×M16 | 1 | 2 | yes | — |
| 234 | C23×C3 | — | 5 | 1 | no | — |
| 235 | C2×C3×C4 | — | 5 | 4 | no | — |
| 236 | C2×C3×C4 | — | 5 | 8 | no | — |
| 237 | C2×C3×C4 | — | 5 | 1 | no | — |
| 238 | C2×C3×C4 | — | 5 | 1 | no | — |
| 239 | C2×C3×C4 | — | 5 | 1 | no | — |
| 240 | C2×C3×C4 | — | 5 | 1 | no | — |
| 241 | C2×C3×C4 | — | 5 | 1 | no | — |
| 242 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 243 | C2×Dic3 | — | 5 | 4 | no | — |
| 244 | C2×Dic3 | — | 5 | 2 | no | — |
| 245 | C2×Dic3 | — | 10 | 4 | no | — |
| 246 | C2×Dic3 | — | 10 | 4 | no | — |
| 247 | C2×Dic3 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 248 | C3×C8 | — | 5 | 4 | no | — |
| 249 | C3×C8 | — | 5 | 2 | no | — |
| 250 | C3×C8 | C4×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 251 | C3⋊C8 | — | 5 | 4 | no | — |
| 252 | C3⋊C8 | — | 5 | 2 | no | — |
| 253 | C3⋊C8 | C4×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 254 | C22×C5 | C42×D3 | 1 | 1 | yes | characteristic |
| 255 | C2×D5 | C42×D3 | 1 | 1 | yes | characteristic |
| 256 | C2×D5 | C2×ΓL(1,𝔽25) | 1 | 4 | yes | — |
| 257 | C2×D5 | C2×C4×Dic3 | 1 | 1 | yes | characteristic |
| 258 | AGL(1,𝔽5) | — | 6 | 4 | no | — |
| 259 | AGL(1,𝔽5) | #815 | 1 | 8 | yes | direct product factor |
| 260 | C4×C5 | — | 6 | 2 | no | — |
| 261 | C4×C5 | C42×D3 | 1 | 1 | yes | characteristic |
| 262 | C4×C5 | C2×C4×Dic3 | 1 | 1 | yes | characteristic |
| 263 | Dic5 | — | 6 | 2 | no | — |
| 264 | Dic5 | C42×D3 | 1 | 1 | yes | characteristic |
| 265 | Dic5 | C2×C4×Dic3 | 1 | 1 | yes | characteristic |
| 266 | C22×C4 | — | 5 | 2 | no | — |
| 267 | C22×C4 | — | 5 | 1 | no | — |
| 268 | C22×C4 | — | 15 | 2 | no | — |
| 269 | C22×C4 | — | 15 | 2 | no | — |
| 270 | C2×C8 | — | 3 | 1 | no | — |
| 271 | C2×C8 | — | 5 | 2 | no | — |
| 272 | C2×C8 | — | 5 | 2 | no | — |
| 273 | C2×C8 | — | 5 | 2 | no | — |
| 274 | C2×C8 | — | 5 | 1 | no | — |
| 275 | C2×C8 | — | 5 | 2 | no | — |
| 276 | C2×C8 | — | 5 | 2 | no | — |
| 277 | C2×C8 | — | 15 | 2 | no | — |
| 278 | C2×C8 | — | 15 | 2 | no | — |
| 279 | C2×C8 | — | 15 | 2 | no | — |
| 280 | C2×C8 | — | 15 | 2 | no | — |
| 281 | C2×C8 | — | 15 | 2 | no | — |
| 282 | C2×C8 | — | 15 | 1 | no | — |
| 283 | C2×C8 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 284 | C42 | — | 3 | 1 | no | — |
| 285 | C42 | — | 5 | 2 | no | — |
| 286 | C42 | — | 5 | 2 | no | — |
| 287 | C42 | — | 15 | 2 | no | — |
| 288 | C42 | — | 15 | 2 | no | — |
| 289 | C42 | — | 15 | 2 | no | — |
| 290 | C42 | — | 15 | 1 | no | — |
| 291 | C42 | — | 30 | 8 | no | — |
| 292 | C3×C5 | C4×#97 | 1 | 1 | yes | characteristic, complemented, Hall |
| 293 | C22×C3 | — | 5 | 1 | no | — |
| 294 | C22×C3 | — | 5 | 1 | no | — |
| 295 | C22×C3 | — | 5 | 4 | no | — |
| 296 | C22×C3 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 297 | C3×C4 | — | 5 | 8 | no | — |
| 298 | C3×C4 | — | 5 | 1 | no | — |
| 299 | C3×C4 | — | 5 | 1 | no | — |
| 300 | C3×C4 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 301 | C3×C4 | C2×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 302 | Dic3 | — | 2 | 2 | no | — |
| 303 | Dic3 | — | 10 | 4 | no | — |
| 304 | Dic3 | — | 10 | 2 | no | — |
| 305 | C2×C5 | C4×ΓL(1,𝔽25) | 1 | 2 | yes | — |
| 306 | C2×C5 | C42×Dic3 | 1 | 1 | yes | characteristic |
| 307 | D5 | C4×ΓL(1,𝔽25) | 1 | 2 | yes | — |
| 308 | D5 | C2×#815 | 1 | 2 | yes | — |
| 309 | C23 | — | 5 | 1 | no | — |
| 310 | C2×C4 | — | 3 | 2 | no | — |
| 311 | C2×C4 | — | 5 | 4 | no | — |
| 312 | C2×C4 | — | 5 | 8 | no | — |
| 313 | C2×C4 | — | 5 | 1 | no | — |
| 314 | C2×C4 | — | 5 | 1 | no | — |
| 315 | C2×C4 | — | 5 | 1 | no | — |
| 316 | C2×C4 | — | 5 | 1 | no | — |
| 317 | C2×C4 | — | 5 | 1 | no | — |
| 318 | C2×C4 | — | 15 | 4 | no | — |
| 319 | C2×C4 | — | 15 | 2 | no | — |
| 320 | C2×C4 | — | 30 | 4 | no | — |
| 321 | C2×C4 | — | 30 | 4 | no | — |
| 322 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 323 | C8 | — | 3 | 2 | no | — |
| 324 | C8 | — | 5 | 4 | no | — |
| 325 | C8 | — | 5 | 2 | no | — |
| 326 | C8 | — | 15 | 4 | no | — |
| 327 | C8 | — | 15 | 2 | no | — |
| 328 | C8 | Dic3×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 329 | C2×C3 | — | 5 | 2 | no | — |
| 330 | C2×C3 | — | 5 | 2 | no | — |
| 331 | C2×C3 | C42×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 332 | C2×C3 | M16×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 333 | C5 | C4×#815 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 334 | C22 | — | 5 | 1 | no | — |
| 335 | C22 | — | 5 | 1 | no | — |
| 336 | C22 | — | 5 | 4 | no | — |
| 337 | C22 | C4×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 338 | C4 | — | 5 | 8 | no | — |
| 339 | C4 | — | 5 | 1 | no | — |
| 340 | C4 | — | 5 | 1 | no | — |
| 341 | C4 | — | 6 | 2 | no | — |
| 342 | C4 | — | 30 | 4 | no | — |
| 343 | C4 | — | 30 | 2 | no | — |
| 344 | C4 | C4×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 345 | C4 | C2×Dic3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 346 | C3 | AGL(1,𝔽5)×#97 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 347 | C2 | — | 5 | 2 | no | — |
| 348 | C2 | — | 5 | 2 | no | — |
| 349 | C2 | AGL(1,𝔽5)×ΓL(1,𝔽25) | 1 | 2 | yes | — |
| 350 | C2 | C4×Dic3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 17. #91221 | C4 | semidirect |
| 18. C3×C8×AGL(1,𝔽5) | C4 | semidirect |
| 19. #91169 | C4 | semidirect |
| 20. #91150 | C4 | semidirect |
| 21. AGL(1,𝔽5)×C3⋊C8 | C4 | semidirect |
| 22. #91099 | C4 | semidirect |
| 23. C5×#815 | C4 | semidirect |
| 24. #90954 | C4 | semidirect |
| 25. #90953 | C4 | semidirect |
| 79. C8×AGL(1,𝔽5) | Dic3 | semidirect |
| 99. C3⋊#170 | C42 | semidirect |
| 100. C3×#170 | C42 | semidirect |
| 101. C3×C5×C8 | C42 | semidirect |
| 102. C3⋊#168 | C42 | semidirect |
| 103. C3×#168 | C42 | semidirect |
| 104. C5×C3⋊C8 | C42 | semidirect |
| 120. #815 | AGL(1,𝔽5) | direct (N × H) |
| 160. C3×AGL(1,𝔽5) | #97 | semidirect |
| 208. #170 | C4×Dic3 | semidirect |
| 210. C5×C8 | C4×Dic3 | semidirect |
| 212. #168 | C4×Dic3 | semidirect |
| 250. C3×C8 | C4×AGL(1,𝔽5) | semidirect |
| 253. C3⋊C8 | C4×AGL(1,𝔽5) | semidirect |
| 259. AGL(1,𝔽5) | #815 | direct (N × H) |
| 292. C3×C5 | C4×#97 | semidirect |
| 328. C8 | Dic3×AGL(1,𝔽5) | semidirect |
| 333. C5 | C4×#815 | semidirect |
| 346. C3 | AGL(1,𝔽5)×#97 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta