← AGL(1,𝔽5)×#948 #14411503
Order 1920.
1144 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D5⋊#948 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#41×AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | D5×#948 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11751697 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11751695 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | AGL(1,𝔽5)×#208 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×AGL(1,𝔽5)×C3⋊C8 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | AGL(1,𝔽5)×#131 | — | 3 | 1 | no | maximal, Hall |
| 9 | C3×D5×#41 | C22 | 1 | 1 | yes | characteristic |
| 10 | #91992 | C4 | 1 | 2 | yes | complemented |
| 11 | #91990 | C4 | 1 | 6 | yes | complemented |
| 12 | D5⋊#208 | C22 | 1 | 3 | yes | — |
| 13 | C2×D5⋊(C3⋊C8) | C22 | 1 | 3 | yes | — |
| 14 | C3×Q8×AGL(1,𝔽5) | C4 | 1 | 2 | yes | — |
| 15 | C3×D4×AGL(1,𝔽5) | C4 | 1 | 6 | yes | — |
| 16 | C3×#4130 | C22 | 1 | 3 | yes | — |
| 17 | C2×C3×C4×AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 18 | #91837 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | C5×#948 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #91284 | C4 | 1 | 3 | yes | complemented |
| 21 | #91283 | C4 | 1 | 3 | yes | complemented |
| 22 | D5×#208 | C22 | 1 | 3 | yes | — |
| 23 | C2×D5×C3⋊C8 | C22 | 1 | 3 | yes | — |
| 24 | #91149 | C22 | 1 | 6 | yes | — |
| 25 | AGL(1,𝔽5)×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 26 | AGL(1,𝔽5)×C3⋊C8 | C22 | 1 | 3 | yes | — |
| 27 | AGL(1,𝔽5)×C3⋊C8 | C22 | 1 | 3 | yes | — |
| 28 | AGL(1,𝔽5)×C3⋊C8 | C22 | 1 | 3 | yes | — |
| 29 | C4×#948 | — | 5 | 1 | no | maximal, Hall |
| 30 | #41×AGL(1,𝔽5) | D3 | 1 | 1 | yes | characteristic |
| 31 | D5⋊#131 | — | 3 | 1 | no | — |
| 32 | D5×#131 | — | 3 | 1 | no | — |
| 33 | #65728 | — | 3 | 3 | no | — |
| 34 | M16×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 35 | #65718 | — | 3 | 3 | no | — |
| 36 | C2×C8×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 37 | C22×C3×AGL(1,𝔽5) | C2×C4 | 1 | 6 | yes | — |
| 38 | C3×C5×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C3×#713 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C3×Q8×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C3×#711 | C2×C4 | 1 | 3 | yes | — |
| 42 | C3×D4×D5 | C2×C4 | 1 | 3 | yes | — |
| 43 | C3×#709 | C2×C4 | 1 | 3 | yes | — |
| 44 | C2×C3×C4×D5 | C23 | 1 | 3 | yes | — |
| 45 | #6762 | C2×C4 | 1 | 6 | yes | complemented |
| 46 | C2×C3⋊#170 | C2×C4 | 1 | 6 | yes | complemented |
| 47 | #6758 | C2×C4 | 1 | 6 | yes | complemented |
| 48 | D5⋊(C3⋊C8) | C2×C4 | 1 | 6 | yes | complemented |
| 49 | D5⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 50 | D5⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 51 | C3×C22⋊AGL(1,𝔽5) | C2×C4 | 1 | 6 | yes | — |
| 52 | C3×C4⋊AGL(1,𝔽5) | C2×C4 | 1 | 6 | yes | — |
| 53 | C3×C4×AGL(1,𝔽5) | C2×C4 | 1 | 6 | yes | — |
| 54 | C3×C4×AGL(1,𝔽5) | C23 | 1 | 1 | yes | characteristic |
| 55 | C3×C4×AGL(1,𝔽5) | C23 | 1 | 3 | yes | — |
| 56 | #6710 | C2×C4 | 1 | 3 | yes | complemented |
| 57 | C2×C3⋊#168 | C2×C4 | 1 | 3 | yes | complemented |
| 58 | C5×#208 | C2×C4 | 1 | 3 | yes | complemented |
| 59 | C2×C5×C3⋊C8 | C2×C4 | 1 | 3 | yes | complemented |
| 60 | #6649 | C2×C4 | 1 | 6 | yes | complemented |
| 61 | D5×C3⋊C8 | C2×C4 | 1 | 3 | yes | complemented |
| 62 | D5×C3⋊C8 | C2×C4 | 1 | 3 | yes | complemented |
| 63 | D5×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 64 | D5×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 65 | C3×C4×#41 | — | 5 | 1 | no | — |
| 66 | C2×#948 | — | 5 | 1 | no | — |
| 67 | C2×#948 | — | 5 | 1 | no | — |
| 68 | #4997 | — | 5 | 3 | no | — |
| 69 | #4997 | — | 5 | 3 | no | — |
| 70 | C4×#208 | — | 5 | 3 | no | — |
| 71 | C2×C4×C3⋊C8 | — | 5 | 3 | no | — |
| 72 | D5×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 73 | Q8×AGL(1,𝔽5) | Dic3 | 1 | 2 | yes | — |
| 74 | #4133 | — | 3 | 2 | no | — |
| 75 | D4×AGL(1,𝔽5) | Dic3 | 1 | 6 | yes | — |
| 76 | #4131 | — | 3 | 6 | no | — |
| 77 | #4130 | C2×D3 | 1 | 3 | yes | — |
| 78 | C2×C4×AGL(1,𝔽5) | C2×D3 | 1 | 3 | yes | — |
| 79 | D5⋊M16 | — | 3 | 3 | no | — |
| 80 | C2×D5⋊C8 | — | 3 | 3 | no | — |
| 81 | C5×#131 | — | 3 | 1 | no | — |
| 82 | #4094 | — | 3 | 1 | no | — |
| 83 | #4053 | — | 3 | 3 | no | — |
| 84 | D5×M16 | — | 3 | 3 | no | — |
| 85 | #4047 | — | 3 | 3 | no | — |
| 86 | C2×C8×D5 | — | 3 | 3 | no | — |
| 87 | #3992 | — | 3 | 6 | no | — |
| 88 | C8×AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 89 | C8×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 90 | C8×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 91 | C8×AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 92 | C4×#131 | — | 15 | 1 | no | Sylow |
| 93 | C22×C3×D5 | C22×C4 | 1 | 3 | yes | — |
| 94 | C2×C3×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 95 | C2×C3×AGL(1,𝔽5) | C22×C4 | 1 | 6 | yes | — |
| 96 | C2×C3×AGL(1,𝔽5) | C22×C4 | 1 | 2 | yes | — |
| 97 | C3×C5×Q8 | C42 | 1 | 1 | yes | characteristic |
| 98 | C3×C5×D4 | C42 | 1 | 3 | yes | — |
| 99 | C2×C3×C4×C5 | C22×C4 | 1 | 3 | yes | — |
| 100 | C3×C22⋊D5 | C42 | 1 | 6 | yes | — |
| 101 | C2×C3×Dic5 | C22×C4 | 1 | 3 | yes | — |
| 102 | C3×D20 | C42 | 1 | 3 | yes | — |
| 103 | C3×C4×D5 | C22×C4 | 1 | 3 | yes | — |
| 104 | C3×C4×D5 | C22×C4 | 1 | 3 | yes | — |
| 105 | C3×C4×D5 | C22×C4 | 1 | 3 | yes | — |
| 106 | C3×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 107 | C3×Dic10 | C42 | 1 | 3 | yes | — |
| 108 | C3⋊#170 | C22×C4 | 1 | 2 | yes | — |
| 109 | C3⋊#170 | C22×C4 | 1 | 6 | yes | — |
| 110 | C3⋊#168 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | C3⋊#168 | C22×C4 | 1 | 3 | yes | — |
| 112 | C5×C3⋊C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 113 | C5×C3⋊C8 | C22×C4 | 1 | 3 | yes | — |
| 114 | C2×C3×#41 | — | 5 | 1 | no | — |
| 115 | C3×C4×Q8 | — | 5 | 2 | no | — |
| 116 | C3×C4×D4 | — | 5 | 6 | no | — |
| 117 | C3×#117 | — | 5 | 3 | no | — |
| 118 | C2×C3×C42 | — | 5 | 3 | no | — |
| 119 | #948 | — | 5 | 6 | no | — |
| 120 | #948 | — | 5 | 2 | no | — |
| 121 | #948 | — | 5 | 1 | no | — |
| 122 | #948 | — | 5 | 3 | no | — |
| 123 | #948 | — | 5 | 3 | no | — |
| 124 | #948 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 125 | C2×#208 | — | 5 | 3 | no | — |
| 126 | C2×#208 | — | 5 | 3 | no | — |
| 127 | C22×C3⋊C8 | — | 5 | 3 | no | — |
| 128 | C22×C3⋊C8 | — | 5 | 3 | no | — |
| 129 | #803 | — | 5 | 6 | no | — |
| 130 | C4×C3⋊C8 | — | 5 | 1 | no | — |
| 131 | C4×C3⋊C8 | — | 5 | 3 | no | — |
| 132 | C4×C3⋊C8 | — | 5 | 3 | no | — |
| 133 | C4×C3⋊C8 | — | 5 | 3 | no | — |
| 134 | C22×AGL(1,𝔽5) | C2×Dic3 | 1 | 6 | yes | — |
| 135 | C5×#41 | C4×D3 | 1 | 1 | yes | characteristic |
| 136 | #713 | C4×D3 | 1 | 1 | yes | characteristic |
| 137 | Q8×D5 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 138 | #711 | C4×D3 | 1 | 3 | yes | — |
| 139 | D4×D5 | C2×Dic3 | 1 | 3 | yes | — |
| 140 | #709 | C4×D3 | 1 | 3 | yes | — |
| 141 | C2×C4×D5 | C22×D3 | 1 | 3 | yes | — |
| 142 | C22⋊AGL(1,𝔽5) | C2×Dic3 | 1 | 6 | yes | — |
| 143 | #704 | — | 3 | 6 | no | — |
| 144 | C2×#170 | — | 3 | 6 | no | — |
| 145 | C4⋊AGL(1,𝔽5) | C2×Dic3 | 1 | 6 | yes | — |
| 146 | C4×AGL(1,𝔽5) | C2×Dic3 | 1 | 6 | yes | — |
| 147 | C4×AGL(1,𝔽5) | C22×D3 | 1 | 1 | yes | characteristic |
| 148 | C4×AGL(1,𝔽5) | C22×D3 | 1 | 3 | yes | — |
| 149 | #700 | — | 3 | 6 | no | — |
| 150 | D5⋊C8 | — | 3 | 6 | no | — |
| 151 | D5⋊C8 | — | 3 | 1 | no | — |
| 152 | D5⋊C8 | — | 3 | 3 | no | — |
| 153 | C5×M16 | — | 3 | 3 | no | — |
| 154 | C2×C5×C8 | — | 3 | 3 | no | — |
| 155 | #681 | — | 3 | 3 | no | — |
| 156 | C2×#168 | — | 3 | 3 | no | — |
| 157 | #676 | — | 3 | 6 | no | — |
| 158 | C8×D5 | — | 3 | 3 | no | — |
| 159 | C8×D5 | — | 3 | 3 | no | — |
| 160 | C8×D5 | — | 3 | 1 | no | — |
| 161 | C8×D5 | — | 3 | 3 | no | — |
| 162 | C2×#131 | — | 15 | 1 | no | — |
| 163 | C2×#131 | — | 15 | 1 | no | — |
| 164 | C4×#41 | — | 5 | 1 | no | — |
| 165 | #405 | — | 15 | 3 | no | — |
| 166 | #405 | — | 15 | 3 | no | — |
| 167 | C4×M16 | — | 15 | 3 | no | — |
| 168 | C2×C4×C8 | — | 15 | 3 | no | — |
| 169 | C22×C3×C5 | C2×C42 | 1 | 3 | yes | — |
| 170 | C2×C3×D5 | — | 2 | 6 | no | — |
| 171 | C2×C3×D5 | C2×C42 | 1 | 3 | yes | — |
| 172 | C2×C3×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 173 | C3×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 174 | C3×AGL(1,𝔽5) | #131 | 1 | 4 | yes | complemented |
| 175 | C3×C4×C5 | C2×C42 | 1 | 3 | yes | — |
| 176 | C3×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 177 | C3×Dic5 | C2×C42 | 1 | 3 | yes | — |
| 178 | C3×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 179 | C3×#41 | — | 5 | 1 | no | — |
| 180 | C3×#41 | — | 5 | 3 | no | — |
| 181 | C3×#41 | — | 5 | 3 | no | — |
| 182 | C3×#41 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 183 | C2×C3×Q8 | — | 5 | 1 | no | — |
| 184 | C2×C3×D4 | — | 5 | 3 | no | — |
| 185 | C22×C3×C4 | — | 5 | 3 | no | — |
| 186 | C22×C3×C4 | — | 5 | 6 | no | — |
| 187 | C3×C4⋊C4 | — | 5 | 6 | no | — |
| 188 | C3×C22⋊C4 | — | 5 | 6 | no | — |
| 189 | C3×C42 | — | 5 | 1 | no | — |
| 190 | C3×C42 | — | 5 | 3 | no | — |
| 191 | C3×C42 | — | 5 | 6 | no | — |
| 192 | #208 | — | 5 | 6 | no | — |
| 193 | #208 | — | 5 | 6 | no | — |
| 194 | #208 | — | 5 | 3 | no | — |
| 195 | #208 | — | 5 | 6 | no | — |
| 196 | #208 | C2×AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 197 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 198 | C2×C3⋊C8 | — | 5 | 3 | no | — |
| 199 | C2×C3⋊C8 | — | 5 | 6 | no | — |
| 200 | C2×C3⋊C8 | — | 5 | 6 | no | — |
| 201 | C2×C3⋊C8 | — | 5 | 3 | no | — |
| 202 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 203 | C2×C3⋊C8 | — | 5 | 3 | no | — |
| 204 | C2×C3⋊C8 | — | 5 | 3 | no | — |
| 205 | C2×C3⋊C8 | — | 5 | 3 | no | — |
| 206 | C2×C3⋊C8 | C2×AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 207 | C22×D5 | C22×Dic3 | 1 | 3 | yes | — |
| 208 | C2×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 209 | C2×AGL(1,𝔽5) | C22×Dic3 | 1 | 6 | yes | — |
| 210 | C2×AGL(1,𝔽5) | C22×Dic3 | 1 | 2 | yes | — |
| 211 | C5×Q8 | C4×Dic3 | 1 | 1 | yes | characteristic |
| 212 | C5×D4 | C4×Dic3 | 1 | 3 | yes | — |
| 213 | C2×C4×C5 | C2×C4×D3 | 1 | 3 | yes | — |
| 214 | C22⋊D5 | C4×Dic3 | 1 | 6 | yes | — |
| 215 | C2×Dic5 | C2×C4×D3 | 1 | 3 | yes | — |
| 216 | D20 | C4×Dic3 | 1 | 3 | yes | — |
| 217 | C4×D5 | C2×C4×D3 | 1 | 3 | yes | — |
| 218 | C4×D5 | C2×C4×D3 | 1 | 3 | yes | — |
| 219 | C4×D5 | C22×Dic3 | 1 | 3 | yes | — |
| 220 | C4×D5 | C23×D3 | 1 | 1 | yes | characteristic |
| 221 | Dic10 | C4×Dic3 | 1 | 3 | yes | — |
| 222 | #170 | — | 3 | 2 | no | — |
| 223 | #170 | — | 3 | 6 | no | — |
| 224 | C5×C8 | — | 3 | 1 | no | — |
| 225 | C5×C8 | — | 3 | 3 | no | — |
| 226 | #168 | — | 3 | 1 | no | — |
| 227 | #168 | — | 3 | 3 | no | — |
| 228 | C2×#41 | — | 5 | 1 | no | — |
| 229 | #131 | — | 3 | 1 | no | — |
| 230 | #131 | — | 15 | 3 | no | — |
| 231 | #131 | — | 15 | 3 | no | — |
| 232 | #131 | — | 15 | 6 | no | — |
| 233 | #131 | — | 15 | 2 | no | — |
| 234 | #131 | — | 15 | 1 | no | — |
| 235 | C2×M16 | — | 15 | 3 | no | — |
| 236 | C2×M16 | — | 15 | 3 | no | — |
| 237 | C22×C8 | — | 15 | 3 | no | — |
| 238 | C22×C8 | — | 15 | 3 | no | — |
| 239 | C4×Q8 | — | 5 | 2 | no | — |
| 240 | C4×D4 | — | 5 | 6 | no | — |
| 241 | #117 | — | 5 | 3 | no | — |
| 242 | C2×C42 | — | 5 | 3 | no | — |
| 243 | #97 | — | 15 | 6 | no | — |
| 244 | C4×C8 | — | 15 | 1 | no | — |
| 245 | C4×C8 | — | 15 | 3 | no | — |
| 246 | C4×C8 | — | 15 | 3 | no | — |
| 247 | C4×C8 | — | 15 | 3 | no | — |
| 248 | C2×C3×C5 | — | 2 | 3 | no | — |
| 249 | C2×C3×C5 | C22×C42 | 1 | 1 | yes | characteristic |
| 250 | C3×D5 | — | 2 | 3 | no | — |
| 251 | C3×D5 | C2×#131 | 1 | 2 | yes | — |
| 252 | C23×C3 | — | 5 | 3 | no | — |
| 253 | C3×Q8 | — | 5 | 3 | no | — |
| 254 | C3×Q8 | C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 255 | C3×D4 | — | 5 | 6 | no | — |
| 256 | C3×D4 | — | 5 | 3 | no | — |
| 257 | C3×D4 | C4×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 258 | C2×C3×C4 | — | 5 | 2 | no | — |
| 259 | C2×C3×C4 | — | 5 | 3 | no | — |
| 260 | C2×C3×C4 | — | 5 | 3 | no | — |
| 261 | C2×C3×C4 | — | 5 | 3 | no | — |
| 262 | C2×C3×C4 | — | 5 | 3 | no | — |
| 263 | C2×C3×C4 | — | 5 | 1 | no | — |
| 264 | C2×C3×C4 | — | 5 | 6 | no | — |
| 265 | C2×C3×C4 | — | 10 | 12 | no | — |
| 266 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 267 | C3⋊C8 | — | 5 | 2 | no | — |
| 268 | C3⋊C8 | — | 5 | 6 | no | — |
| 269 | C3⋊C8 | — | 5 | 1 | no | — |
| 270 | C3⋊C8 | — | 5 | 3 | no | — |
| 271 | C3⋊C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 272 | C3⋊C8 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 273 | C22×C5 | C2×C4×Dic3 | 1 | 3 | yes | — |
| 274 | C2×D5 | — | 2 | 6 | no | — |
| 275 | C2×D5 | C2×C4×Dic3 | 1 | 3 | yes | — |
| 276 | C2×D5 | C23×Dic3 | 1 | 1 | yes | characteristic |
| 277 | AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 278 | AGL(1,𝔽5) | #948 | 1 | 4 | yes | direct product factor |
| 279 | C4×C5 | C2×C4×Dic3 | 1 | 3 | yes | — |
| 280 | C4×C5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 281 | Dic5 | C2×C4×Dic3 | 1 | 3 | yes | — |
| 282 | Dic5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 283 | #41 | — | 5 | 1 | no | — |
| 284 | #41 | — | 5 | 3 | no | — |
| 285 | #41 | — | 5 | 3 | no | — |
| 286 | #41 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 287 | C2×Q8 | — | 5 | 1 | no | — |
| 288 | C2×D4 | — | 5 | 3 | no | — |
| 289 | C22×C4 | — | 5 | 3 | no | — |
| 290 | C22×C4 | — | 5 | 6 | no | — |
| 291 | M16 | — | 3 | 3 | no | — |
| 292 | M16 | — | 15 | 6 | no | — |
| 293 | M16 | — | 15 | 6 | no | — |
| 294 | M16 | — | 15 | 6 | no | — |
| 295 | M16 | — | 15 | 3 | no | — |
| 296 | C2×C8 | — | 3 | 3 | no | — |
| 297 | C2×C8 | — | 15 | 1 | no | — |
| 298 | C2×C8 | — | 15 | 3 | no | — |
| 299 | C2×C8 | — | 15 | 3 | no | — |
| 300 | C2×C8 | — | 15 | 3 | no | — |
| 301 | C2×C8 | — | 15 | 1 | no | — |
| 302 | C2×C8 | — | 15 | 3 | no | — |
| 303 | C2×C8 | — | 15 | 6 | no | — |
| 304 | C2×C8 | — | 15 | 6 | no | — |
| 305 | C2×C8 | — | 15 | 3 | no | — |
| 306 | C4⋊C4 | — | 5 | 6 | no | — |
| 307 | C22⋊C4 | — | 5 | 6 | no | — |
| 308 | C42 | — | 5 | 1 | no | — |
| 309 | C42 | — | 5 | 3 | no | — |
| 310 | C42 | — | 5 | 6 | no | — |
| 311 | C3×C5 | C4×#131 | 1 | 1 | yes | characteristic, complemented, Hall |
| 312 | C22×C3 | — | 5 | 1 | no | — |
| 313 | C22×C3 | — | 5 | 3 | no | — |
| 314 | C22×C3 | — | 10 | 6 | no | — |
| 315 | C22×C3 | C2×C4×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 316 | C3×C4 | — | 5 | 4 | no | — |
| 317 | C3×C4 | — | 5 | 3 | no | — |
| 318 | C3×C4 | — | 5 | 1 | no | — |
| 319 | C3×C4 | — | 10 | 6 | no | — |
| 320 | C3×C4 | C2×C4×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 321 | C3×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 322 | C2×C5 | — | 2 | 3 | no | — |
| 323 | C2×C5 | C22×C4×Dic3 | 1 | 1 | yes | characteristic |
| 324 | D5 | — | 2 | 3 | no | — |
| 325 | D5 | C2×#948 | 1 | 2 | yes | — |
| 326 | C23 | — | 5 | 3 | no | — |
| 327 | Q8 | — | 5 | 3 | no | — |
| 328 | Q8 | Dic3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 329 | D4 | — | 5 | 6 | no | — |
| 330 | D4 | — | 5 | 3 | no | — |
| 331 | D4 | Dic3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 332 | C2×C4 | — | 5 | 2 | no | — |
| 333 | C2×C4 | — | 5 | 3 | no | — |
| 334 | C2×C4 | — | 5 | 3 | no | — |
| 335 | C2×C4 | — | 5 | 3 | no | — |
| 336 | C2×C4 | — | 5 | 1 | no | — |
| 337 | C2×C4 | — | 5 | 3 | no | — |
| 338 | C2×C4 | — | 5 | 6 | no | — |
| 339 | C2×C4 | — | 10 | 12 | no | — |
| 340 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 341 | C8 | — | 3 | 1 | no | — |
| 342 | C8 | — | 3 | 3 | no | — |
| 343 | C8 | — | 15 | 2 | no | — |
| 344 | C8 | — | 15 | 6 | no | — |
| 345 | C8 | — | 15 | 1 | no | — |
| 346 | C8 | — | 15 | 3 | no | — |
| 347 | C2×C3 | — | 2 | 3 | no | — |
| 348 | C2×C3 | — | 5 | 2 | no | — |
| 349 | C2×C3 | — | 10 | 3 | no | — |
| 350 | C2×C3 | C22×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 351 | C5 | C4×#948 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 352 | C22 | — | 5 | 1 | no | — |
| 353 | C22 | — | 5 | 3 | no | — |
| 354 | C22 | — | 10 | 6 | no | — |
| 355 | C22 | C2×Dic3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 356 | C4 | — | 5 | 4 | no | — |
| 357 | C4 | — | 5 | 1 | no | — |
| 358 | C4 | — | 5 | 3 | no | — |
| 359 | C4 | — | 10 | 6 | no | — |
| 360 | C4 | C2×Dic3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 361 | C4 | C22×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 362 | C3 | AGL(1,𝔽5)×#131 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 363 | C2 | — | 2 | 3 | no | — |
| 364 | C2 | — | 5 | 2 | no | — |
| 365 | C2 | — | 10 | 3 | no | — |
| 366 | C2 | C22×Dic3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta