Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1176 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#92019 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11752404 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#65761 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11751723 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11751707 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10605012 | — | 3 | 1 | no | maximal, Hall |
| 7 | C22×D60 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C2×C5×#235 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×C3×#709 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#6790 | — | 2 | 1 | no | — |
| 11 | C2×#6790 | — | 2 | 1 | no | — |
| 12 | #92019 | — | 2 | 4 | no | — |
| 13 | #92019 | — | 2 | 4 | no | — |
| 14 | C2×D3×D20 | — | 2 | 1 | no | — |
| 15 | C2×D5×D12 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×D5×D12 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#6773 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#6773 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#6769 | — | 2 | 1 | no | — |
| 20 | #91989 | C22 | 1 | 2 | yes | complemented |
| 21 | C3×D5⋊M16 | C22 | 1 | 2 | yes | complemented |
| 22 | #91240 | — | 2 | 1 | no | — |
| 23 | #91228 | — | 2 | 1 | no | — |
| 24 | C3×#4013 | — | 2 | 1 | no | — |
| 25 | C3×#4005 | — | 2 | 1 | no | — |
| 26 | #91157 | — | 2 | 4 | no | — |
| 27 | #91152 | — | 2 | 4 | no | — |
| 28 | #70139 | — | 5 | 1 | no | maximal, Hall |
| 29 | C2×#4149 | — | 3 | 1 | no | — |
| 30 | #65784 | — | 3 | 2 | no | — |
| 31 | #65767 | — | 3 | 2 | no | — |
| 32 | #65761 | D3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #65745 | — | 3 | 1 | no | — |
| 34 | C23×D15 | — | 2 | 1 | no | — |
| 35 | C22×D3×D5 | — | 2 | 1 | no | — |
| 36 | C22×D3×D5 | — | 2 | 1 | no | — |
| 37 | C22×C3×C4×C5 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×D60 | — | 2 | 1 | no | — |
| 39 | C2×D60 | — | 2 | 2 | no | — |
| 40 | C2×D60 | — | 2 | 2 | no | — |
| 41 | C2×D60 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C2×D60 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C2×C5×#67 | — | 2 | 1 | no | — |
| 44 | C5×#235 | — | 2 | 2 | no | — |
| 45 | C5×#235 | — | 2 | 2 | no | — |
| 46 | C2×C5×D12 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C2×C4×C5×D3 | — | 2 | 1 | no | — |
| 48 | C2×C5×Dic6 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×C3×C22⋊D5 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×C3×C22⋊D5 | D4 | 1 | 1 | yes | characteristic |
| 51 | C3×#709 | — | 2 | 2 | no | — |
| 52 | C3×#709 | — | 2 | 2 | no | — |
| 53 | C2×C3×D20 | D4 | 1 | 1 | yes | characteristic |
| 54 | C2×C3×C4×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×C3×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×C3×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 57 | #6790 | — | 2 | 8 | no | — |
| 58 | #6790 | — | 2 | 8 | no | — |
| 59 | C2×#1203 | — | 2 | 1 | no | — |
| 60 | C2×#1203 | — | 2 | 1 | no | — |
| 61 | C2×#1202 | — | 2 | 1 | no | — |
| 62 | C2×#1202 | — | 2 | 1 | no | — |
| 63 | C2×#1200 | — | 2 | 1 | no | — |
| 64 | C2×#1200 | — | 2 | 1 | no | — |
| 65 | D3×D20 | — | 2 | 8 | no | — |
| 66 | D5×D12 | — | 2 | 2 | no | — |
| 67 | D5×D12 | — | 2 | 2 | no | — |
| 68 | D5×D12 | — | 2 | 2 | no | — |
| 69 | D5×D12 | D4 | 1 | 4 | yes | — |
| 70 | #6773 | — | 2 | 2 | no | — |
| 71 | #6773 | — | 2 | 2 | no | — |
| 72 | #6773 | — | 2 | 2 | no | — |
| 73 | #6773 | D4 | 1 | 4 | yes | — |
| 74 | #6769 | — | 2 | 8 | no | — |
| 75 | #6763 | — | 2 | 2 | no | — |
| 76 | C4⋊ΓL(1,𝔽16) | — | 2 | 2 | no | — |
| 77 | C4×ΓL(1,𝔽16) | — | 2 | 2 | no | — |
| 78 | C3×#704 | — | 2 | 2 | no | — |
| 79 | C3×#700 | — | 2 | 2 | no | — |
| 80 | C3×D5⋊C8 | — | 2 | 2 | no | — |
| 81 | C2×#1009 | — | 5 | 1 | no | — |
| 82 | C3×#413 | — | 5 | 1 | no | — |
| 83 | #5240 | — | 5 | 1 | no | — |
| 84 | #5139 | — | 5 | 2 | no | — |
| 85 | #5131 | — | 5 | 2 | no | — |
| 86 | C2×C5×#41 | — | 3 | 1 | no | — |
| 87 | #4149 | — | 6 | 4 | no | — |
| 88 | #4149 | — | 6 | 4 | no | — |
| 89 | C2×#713 | — | 3 | 1 | no | — |
| 90 | C2×#713 | — | 3 | 1 | no | — |
| 91 | C2×D4×D5 | — | 3 | 1 | no | — |
| 92 | C2×D4×D5 | — | 3 | 1 | no | — |
| 93 | C2×D4×D5 | — | 6 | 1 | no | — |
| 94 | C2×D4×D5 | — | 6 | 1 | no | — |
| 95 | C2×#709 | — | 6 | 1 | no | — |
| 96 | C2×#709 | C2×D3 | 1 | 1 | yes | characteristic |
| 97 | C22×D20 | — | 3 | 1 | no | — |
| 98 | C22×D20 | — | 6 | 1 | no | — |
| 99 | #4130 | — | 3 | 2 | no | — |
| 100 | D5⋊M16 | C2×D3 | 1 | 2 | yes | complemented |
| 101 | #4013 | — | 2 | 1 | no | — |
| 102 | #4011 | — | 6 | 1 | no | — |
| 103 | #4010 | — | 6 | 4 | no | — |
| 104 | #4007 | — | 6 | 4 | no | — |
| 105 | #4005 | — | 2 | 1 | no | — |
| 106 | #3999 | — | 6 | 1 | no | — |
| 107 | #1795 | — | 15 | 1 | no | Sylow |
| 108 | C23×C3×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 109 | C22×D15 | — | 2 | 1 | no | — |
| 110 | C22×D15 | — | 2 | 1 | no | — |
| 111 | C22×D15 | — | 2 | 4 | no | — |
| 112 | C22×D15 | — | 8 | 2 | no | — |
| 113 | C22×C5×D3 | — | 2 | 1 | no | — |
| 114 | C22×C3×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C22×C3×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×D3×D5 | — | 2 | 4 | no | — |
| 117 | C2×D3×D5 | — | 2 | 4 | no | — |
| 118 | C2×D3×D5 | — | 8 | 2 | no | — |
| 119 | C2×D3×D5 | — | 8 | 2 | no | — |
| 120 | C2×ΓL(1,𝔽16) | — | 4 | 2 | no | — |
| 121 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 122 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 123 | C2×C3×C4×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 124 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 125 | D60 | — | 2 | 4 | no | — |
| 126 | D60 | — | 2 | 1 | no | — |
| 127 | D60 | — | 2 | 1 | no | — |
| 128 | D60 | C22⋊C4 | 1 | 2 | yes | — |
| 129 | D60 | C22⋊C4 | 1 | 2 | yes | — |
| 130 | C5×#67 | — | 2 | 4 | no | — |
| 131 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 132 | C5×D12 | — | 2 | 1 | no | — |
| 133 | C5×D12 | C22⋊C4 | 1 | 2 | yes | — |
| 134 | C4×C5×D3 | — | 2 | 4 | no | — |
| 135 | C5×Dic6 | — | 2 | 1 | no | — |
| 136 | C5×Dic6 | C22⋊C4 | 1 | 2 | yes | — |
| 137 | C3×C22⋊D5 | — | 2 | 2 | no | — |
| 138 | C3×C22⋊D5 | — | 2 | 2 | no | — |
| 139 | C2×C3×Dic5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C3×D20 | — | 2 | 2 | no | — |
| 142 | C3×C4×D5 | — | 2 | 1 | no | — |
| 143 | C3×C4×D5 | — | 2 | 1 | no | — |
| 144 | C3×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 145 | C3×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 146 | C3×Dic10 | — | 2 | 2 | no | — |
| 147 | #1203 | — | 2 | 4 | no | — |
| 148 | #1203 | — | 2 | 4 | no | — |
| 149 | #1202 | — | 2 | 4 | no | — |
| 150 | #1202 | — | 2 | 4 | no | — |
| 151 | #1200 | — | 2 | 4 | no | — |
| 152 | #1200 | — | 2 | 4 | no | — |
| 153 | C3×#170 | — | 4 | 2 | no | — |
| 154 | C2×C3×#41 | — | 5 | 1 | no | — |
| 155 | #1009 | — | 10 | 4 | no | — |
| 156 | #1009 | — | 10 | 4 | no | — |
| 157 | C2×#239 | — | 10 | 1 | no | — |
| 158 | C2×D3×D4 | — | 10 | 1 | no | — |
| 159 | C2×D3×D4 | — | 10 | 1 | no | — |
| 160 | C2×D3×D4 | — | 10 | 1 | no | — |
| 161 | C2×#235 | — | 5 | 1 | no | — |
| 162 | C2×#235 | — | 5 | 1 | no | — |
| 163 | C2×#235 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 164 | C22×D12 | — | 5 | 1 | no | — |
| 165 | C22×D12 | — | 5 | 1 | no | — |
| 166 | C22×D12 | — | 5 | 1 | no | — |
| 167 | C2×C3×M16 | — | 5 | 2 | no | — |
| 168 | #926 | — | 5 | 2 | no | — |
| 169 | C3×#101 | — | 10 | 1 | no | — |
| 170 | C3×#100 | — | 10 | 1 | no | — |
| 171 | #834 | — | 10 | 1 | no | — |
| 172 | #834 | — | 10 | 1 | no | — |
| 173 | #825 | — | 10 | 4 | no | — |
| 174 | #821 | — | 10 | 4 | no | — |
| 175 | C23×D5 | — | 6 | 1 | no | — |
| 176 | C23×D5 | — | 6 | 1 | no | — |
| 177 | C23×D5 | — | 6 | 1 | no | — |
| 178 | C5×#41 | — | 6 | 2 | no | — |
| 179 | C5×#41 | — | 6 | 2 | no | — |
| 180 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 181 | C2×C5×D4 | — | 3 | 1 | no | — |
| 182 | C2×C5×D4 | — | 6 | 1 | no | — |
| 183 | C22×C4×C5 | — | 6 | 1 | no | — |
| 184 | C22×C4×C5 | C4×D3 | 1 | 1 | yes | characteristic |
| 185 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 186 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 187 | C2×C22⋊D5 | D12 | 1 | 1 | yes | characteristic |
| 188 | C2×C22⋊D5 | #67 | 1 | 1 | yes | characteristic |
| 189 | #713 | — | 3 | 4 | no | — |
| 190 | #713 | — | 6 | 2 | no | — |
| 191 | #713 | — | 6 | 2 | no | — |
| 192 | #713 | — | 6 | 2 | no | — |
| 193 | D4×D5 | — | 3 | 4 | no | — |
| 194 | D4×D5 | — | 6 | 2 | no | — |
| 195 | D4×D5 | — | 6 | 2 | no | — |
| 196 | D4×D5 | — | 6 | 8 | no | — |
| 197 | D4×D5 | — | 6 | 8 | no | — |
| 198 | D4×D5 | — | 6 | 2 | no | — |
| 199 | #709 | — | 2 | 2 | no | — |
| 200 | #709 | — | 2 | 2 | no | — |
| 201 | #709 | — | 6 | 8 | no | — |
| 202 | C2×D20 | — | 3 | 1 | no | — |
| 203 | C2×D20 | — | 3 | 1 | no | — |
| 204 | C2×D20 | — | 6 | 8 | no | — |
| 205 | C2×D20 | — | 6 | 2 | no | — |
| 206 | C2×D20 | — | 6 | 2 | no | — |
| 207 | C2×D20 | — | 6 | 1 | no | — |
| 208 | C2×D20 | — | 6 | 1 | no | — |
| 209 | C2×D20 | — | 6 | 1 | no | — |
| 210 | C2×D20 | D12 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×D5 | — | 6 | 1 | no | — |
| 212 | C2×C4×D5 | — | 6 | 1 | no | — |
| 213 | C2×C4×D5 | C4×D3 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 215 | C2×Dic10 | #67 | 1 | 1 | yes | characteristic |
| 216 | C22⋊AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 217 | #704 | — | 2 | 2 | no | — |
| 218 | C4⋊AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 219 | C4×AGL(1,𝔽5) | — | 6 | 2 | no | — |
| 220 | #700 | — | 2 | 2 | no | — |
| 221 | D5⋊C8 | — | 2 | 2 | no | — |
| 222 | C2×H(5,𝔽2) | — | 15 | 1 | no | — |
| 223 | #421 | — | 15 | 2 | no | — |
| 224 | #418 | — | 15 | 2 | no | — |
| 225 | #413 | — | 5 | 1 | no | — |
| 226 | #410 | — | 15 | 1 | no | — |
| 227 | C22×C3×C5 | — | 2 | 1 | no | — |
| 228 | C22×C3×C5 | — | 4 | 1 | no | — |
| 229 | C22×C3×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 230 | C2×D15 | — | 2 | 2 | no | — |
| 231 | C2×D15 | — | 2 | 2 | no | — |
| 232 | C2×D15 | — | 4 | 2 | no | — |
| 233 | C2×D15 | — | 4 | 2 | no | — |
| 234 | C2×D15 | — | 8 | 4 | no | — |
| 235 | C2×C5×D3 | — | 2 | 2 | no | — |
| 236 | C2×C5×D3 | — | 4 | 2 | no | — |
| 237 | C2×C3×D5 | — | 2 | 1 | no | — |
| 238 | C2×C3×D5 | — | 4 | 1 | no | — |
| 239 | C2×C3×D5 | — | 4 | 1 | no | — |
| 240 | C2×C3×D5 | #120 | 1 | 2 | yes | — |
| 241 | D3×D5 | — | 8 | 4 | no | — |
| 242 | D3×D5 | — | 8 | 4 | no | — |
| 243 | ΓL(1,𝔽16) | — | 8 | 2 | no | — |
| 244 | C3×C4×C5 | — | 2 | 1 | no | — |
| 245 | C3×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 246 | C3×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 247 | C3×Dic5 | — | 2 | 1 | no | — |
| 248 | C3×Dic5 | #120 | 1 | 2 | yes | — |
| 249 | C5×Dic3 | — | 2 | 2 | no | — |
| 250 | C23×D3 | — | 10 | 1 | no | — |
| 251 | C23×D3 | — | 10 | 1 | no | — |
| 252 | C23×D3 | — | 10 | 1 | no | — |
| 253 | C3×#41 | — | 10 | 2 | no | — |
| 254 | C3×#41 | — | 10 | 2 | no | — |
| 255 | C2×C3×Q8 | — | 5 | 1 | no | — |
| 256 | C2×C3×D4 | — | 5 | 1 | no | — |
| 257 | C2×C3×D4 | — | 5 | 1 | no | — |
| 258 | C2×C3×D4 | — | 5 | 1 | no | — |
| 259 | C22×C3×C4 | — | 5 | 1 | no | — |
| 260 | C22×C3×C4 | — | 5 | 1 | no | — |
| 261 | C22×C3×C4 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 262 | C2×#67 | — | 2 | 1 | no | — |
| 263 | C2×#67 | — | 10 | 1 | no | — |
| 264 | C2×#67 | — | 10 | 1 | no | — |
| 265 | #239 | — | 10 | 8 | no | — |
| 266 | D3×D4 | — | 10 | 8 | no | — |
| 267 | D3×D4 | — | 10 | 8 | no | — |
| 268 | D3×D4 | — | 10 | 8 | no | — |
| 269 | #235 | — | 2 | 2 | no | — |
| 270 | #235 | — | 2 | 2 | no | — |
| 271 | #235 | — | 5 | 4 | no | — |
| 272 | #235 | — | 10 | 2 | no | — |
| 273 | #235 | — | 10 | 2 | no | — |
| 274 | #235 | — | 10 | 2 | no | — |
| 275 | C2×D12 | — | 5 | 1 | no | — |
| 276 | C2×D12 | — | 5 | 1 | no | — |
| 277 | C2×D12 | — | 5 | 4 | no | — |
| 278 | C2×D12 | — | 10 | 2 | no | — |
| 279 | C2×D12 | — | 10 | 2 | no | — |
| 280 | C2×D12 | — | 10 | 2 | no | — |
| 281 | C2×D12 | — | 10 | 2 | no | — |
| 282 | C2×D12 | — | 10 | 1 | no | — |
| 283 | C2×D12 | — | 10 | 1 | no | — |
| 284 | C2×D12 | — | 10 | 1 | no | — |
| 285 | C2×D12 | — | 10 | 2 | no | — |
| 286 | C2×D12 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 287 | C2×C4×D3 | — | 2 | 1 | no | — |
| 288 | C2×C4×D3 | — | 10 | 1 | no | — |
| 289 | C2×C4×D3 | — | 10 | 1 | no | — |
| 290 | C2×Dic6 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 291 | C3×M16 | — | 10 | 2 | no | — |
| 292 | C3×M16 | — | 10 | 2 | no | — |
| 293 | C2×C3×C8 | — | 10 | 2 | no | — |
| 294 | #217 | — | 10 | 2 | no | — |
| 295 | C4⋊Dic3 | — | 10 | 2 | no | — |
| 296 | C4×Dic3 | — | 10 | 2 | no | — |
| 297 | C23×C5 | — | 6 | 1 | no | — |
| 298 | C23×C5 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 299 | C22×D5 | — | 6 | 4 | no | — |
| 300 | C22×D5 | — | 6 | 1 | no | — |
| 301 | C22×D5 | — | 6 | 1 | no | — |
| 302 | C22×D5 | — | 6 | 4 | no | — |
| 303 | C22×D5 | — | 6 | 4 | no | — |
| 304 | C22×D5 | — | 24 | 2 | no | — |
| 305 | C22×D5 | — | 24 | 2 | no | — |
| 306 | C22×D5 | — | 24 | 2 | no | — |
| 307 | C22×D5 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 308 | C22×D5 | C2×D12 | 1 | 1 | yes | characteristic |
| 309 | C2×AGL(1,𝔽5) | — | 12 | 2 | no | — |
| 310 | C5×Q8 | — | 3 | 2 | no | — |
| 311 | C5×Q8 | — | 6 | 1 | no | — |
| 312 | C5×D4 | — | 3 | 2 | no | — |
| 313 | C5×D4 | — | 6 | 4 | no | — |
| 314 | C5×D4 | — | 6 | 1 | no | — |
| 315 | C2×C4×C5 | — | 2 | 1 | no | — |
| 316 | C2×C4×C5 | — | 2 | 1 | no | — |
| 317 | C2×C4×C5 | — | 6 | 4 | no | — |
| 318 | C2×C4×C5 | — | 6 | 1 | no | — |
| 319 | C2×C4×C5 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 320 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 321 | C22⋊D5 | — | 2 | 2 | no | — |
| 322 | C22⋊D5 | — | 2 | 2 | no | — |
| 323 | C22⋊D5 | — | 6 | 4 | no | — |
| 324 | C22⋊D5 | — | 6 | 4 | no | — |
| 325 | C2×Dic5 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 326 | C2×Dic5 | C2×#67 | 1 | 1 | yes | characteristic |
| 327 | D20 | — | 2 | 2 | no | — |
| 328 | D20 | — | 3 | 2 | no | — |
| 329 | D20 | — | 3 | 2 | no | — |
| 330 | D20 | — | 6 | 4 | no | — |
| 331 | D20 | — | 6 | 4 | no | — |
| 332 | D20 | — | 6 | 4 | no | — |
| 333 | D20 | — | 6 | 1 | no | — |
| 334 | D20 | — | 6 | 1 | no | — |
| 335 | C4×D5 | — | 2 | 1 | no | — |
| 336 | C4×D5 | — | 2 | 1 | no | — |
| 337 | C4×D5 | — | 6 | 4 | no | — |
| 338 | C4×D5 | — | 6 | 4 | no | — |
| 339 | C4×D5 | D3×D4 | 1 | 2 | yes | — |
| 340 | C4×D5 | D3×D4 | 1 | 2 | yes | — |
| 341 | Dic10 | — | 2 | 2 | no | — |
| 342 | #170 | — | 4 | 2 | no | — |
| 343 | H(5,𝔽2) | — | 30 | 4 | no | — |
| 344 | H(5,𝔽2) | — | 30 | 4 | no | — |
| 345 | C2×#41 | — | 3 | 1 | no | — |
| 346 | C2×#41 | — | 5 | 1 | no | — |
| 347 | C2×#41 | — | 15 | 1 | no | — |
| 348 | C2×#41 | — | 15 | 1 | no | — |
| 349 | C2×#41 | — | 30 | 1 | no | — |
| 350 | C22×D4 | — | 15 | 1 | no | — |
| 351 | C22×D4 | — | 15 | 1 | no | — |
| 352 | C22×D4 | — | 15 | 1 | no | — |
| 353 | C22×D4 | — | 30 | 1 | no | — |
| 354 | C22×D4 | — | 30 | 1 | no | — |
| 355 | C22×D4 | — | 30 | 1 | no | — |
| 356 | C2×M16 | — | 5 | 2 | no | — |
| 357 | #117 | — | 15 | 2 | no | — |
| 358 | #104 | — | 30 | 4 | no | — |
| 359 | #102 | — | 30 | 4 | no | — |
| 360 | #101 | — | 10 | 1 | no | — |
| 361 | #100 | — | 10 | 1 | no | — |
| 362 | #99 | — | 30 | 1 | no | — |
| 363 | #99 | — | 30 | 1 | no | — |
| 364 | C2×C3×C5 | — | 2 | 1 | no | — |
| 365 | C2×C3×C5 | — | 4 | 1 | no | — |
| 366 | C2×C3×C5 | #379 | 1 | 1 | yes | characteristic |
| 367 | D15 | — | 4 | 2 | no | — |
| 368 | D15 | — | 4 | 2 | no | — |
| 369 | C3×D5 | — | 2 | 2 | no | — |
| 370 | C3×D5 | — | 4 | 1 | no | — |
| 371 | C5×D3 | — | 4 | 2 | no | — |
| 372 | C23×C3 | — | 5 | 1 | no | — |
| 373 | C23×C3 | — | 5 | 1 | no | — |
| 374 | C23×C3 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 375 | C22×D3 | — | 2 | 1 | no | — |
| 376 | C22×D3 | — | 10 | 4 | no | — |
| 377 | C22×D3 | — | 10 | 4 | no | — |
| 378 | C22×D3 | — | 10 | 1 | no | — |
| 379 | C22×D3 | — | 10 | 1 | no | — |
| 380 | C22×D3 | — | 10 | 4 | no | — |
| 381 | C22×D3 | — | 40 | 2 | no | — |
| 382 | C22×D3 | — | 40 | 2 | no | — |
| 383 | C22×D3 | — | 40 | 2 | no | — |
| 384 | C3×Q8 | — | 10 | 2 | no | — |
| 385 | C3×D4 | — | 10 | 2 | no | — |
| 386 | C3×D4 | — | 10 | 2 | no | — |
| 387 | C3×D4 | — | 10 | 2 | no | — |
| 388 | C2×C3×C4 | — | 2 | 1 | no | — |
| 389 | C2×C3×C4 | — | 2 | 1 | no | — |
| 390 | C2×C3×C4 | — | 5 | 1 | no | — |
| 391 | C2×C3×C4 | — | 5 | 2 | no | — |
| 392 | C2×C3×C4 | — | 5 | 2 | no | — |
| 393 | C2×C3×C4 | — | 5 | 1 | no | — |
| 394 | C2×C3×C4 | — | 10 | 1 | no | — |
| 395 | C2×C3×C4 | — | 10 | 1 | no | — |
| 396 | C2×C3×C4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 397 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 398 | #67 | — | 2 | 4 | no | — |
| 399 | #67 | — | 10 | 4 | no | — |
| 400 | #67 | — | 10 | 4 | no | — |
| 401 | C2×Dic3 | — | 2 | 1 | no | — |
| 402 | C2×Dic3 | — | 20 | 2 | no | — |
| 403 | D12 | — | 2 | 1 | no | — |
| 404 | D12 | — | 5 | 2 | no | — |
| 405 | D12 | — | 5 | 2 | no | — |
| 406 | D12 | — | 10 | 4 | no | — |
| 407 | D12 | — | 10 | 4 | no | — |
| 408 | D12 | — | 10 | 4 | no | — |
| 409 | D12 | — | 10 | 1 | no | — |
| 410 | D12 | — | 10 | 1 | no | — |
| 411 | D12 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 412 | C4×D3 | — | 2 | 4 | no | — |
| 413 | C4×D3 | — | 10 | 4 | no | — |
| 414 | C4×D3 | — | 10 | 4 | no | — |
| 415 | Dic6 | — | 2 | 1 | no | — |
| 416 | Dic6 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 417 | C3×C8 | — | 20 | 2 | no | — |
| 418 | C22×C5 | — | 2 | 1 | no | — |
| 419 | C22×C5 | — | 4 | 1 | no | — |
| 420 | C22×C5 | — | 6 | 2 | no | — |
| 421 | C22×C5 | — | 12 | 2 | no | — |
| 422 | C22×C5 | C2×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 423 | C2×D5 | — | 2 | 1 | no | — |
| 424 | C2×D5 | — | 4 | 1 | no | — |
| 425 | C2×D5 | — | 4 | 1 | no | — |
| 426 | C2×D5 | — | 6 | 2 | no | — |
| 427 | C2×D5 | — | 6 | 2 | no | — |
| 428 | C2×D5 | — | 12 | 2 | no | — |
| 429 | C2×D5 | — | 12 | 2 | no | — |
| 430 | C2×D5 | — | 24 | 4 | no | — |
| 431 | C2×D5 | — | 24 | 4 | no | — |
| 432 | C2×D5 | — | 24 | 4 | no | — |
| 433 | C2×D5 | #882 | 1 | 2 | yes | — |
| 434 | AGL(1,𝔽5) | — | 24 | 2 | no | — |
| 435 | C4×C5 | — | 2 | 1 | no | — |
| 436 | C4×C5 | — | 6 | 2 | no | — |
| 437 | C4×C5 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 438 | C4×C5 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 439 | Dic5 | — | 2 | 1 | no | — |
| 440 | Dic5 | #937 | 1 | 2 | yes | — |
| 441 | C24 | — | 30 | 1 | no | — |
| 442 | C24 | — | 30 | 1 | no | — |
| 443 | C24 | — | 30 | 1 | no | — |
| 444 | #41 | — | 6 | 2 | no | — |
| 445 | #41 | — | 6 | 2 | no | — |
| 446 | #41 | — | 10 | 2 | no | — |
| 447 | #41 | — | 10 | 2 | no | — |
| 448 | #41 | — | 15 | 4 | no | — |
| 449 | #41 | — | 30 | 2 | no | — |
| 450 | #41 | — | 30 | 8 | no | — |
| 451 | #41 | — | 30 | 2 | no | — |
| 452 | #41 | — | 30 | 2 | no | — |
| 453 | C2×Q8 | — | 3 | 1 | no | — |
| 454 | C2×Q8 | — | 5 | 1 | no | — |
| 455 | C2×D4 | — | 3 | 1 | no | — |
| 456 | C2×D4 | — | 5 | 1 | no | — |
| 457 | C2×D4 | — | 5 | 1 | no | — |
| 458 | C2×D4 | — | 5 | 1 | no | — |
| 459 | C2×D4 | — | 6 | 1 | no | — |
| 460 | C2×D4 | — | 15 | 4 | no | — |
| 461 | C2×D4 | — | 15 | 1 | no | — |
| 462 | C2×D4 | — | 15 | 1 | no | — |
| 463 | C2×D4 | — | 30 | 2 | no | — |
| 464 | C2×D4 | — | 30 | 2 | no | — |
| 465 | C2×D4 | — | 30 | 2 | no | — |
| 466 | C2×D4 | — | 30 | 1 | no | — |
| 467 | C2×D4 | — | 30 | 1 | no | — |
| 468 | C2×D4 | — | 30 | 8 | no | — |
| 469 | C2×D4 | — | 30 | 1 | no | — |
| 470 | C2×D4 | — | 30 | 1 | no | — |
| 471 | C2×D4 | — | 30 | 2 | no | — |
| 472 | C2×D4 | — | 30 | 2 | no | — |
| 473 | C2×D4 | — | 30 | 8 | no | — |
| 474 | C2×D4 | — | 30 | 8 | no | — |
| 475 | C2×D4 | — | 30 | 1 | no | — |
| 476 | C22×C4 | — | 5 | 1 | no | — |
| 477 | C22×C4 | — | 5 | 1 | no | — |
| 478 | C22×C4 | — | 6 | 1 | no | — |
| 479 | C22×C4 | — | 30 | 1 | no | — |
| 480 | C22×C4 | — | 30 | 1 | no | — |
| 481 | C22×C4 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 482 | M16 | — | 10 | 2 | no | — |
| 483 | M16 | — | 10 | 2 | no | — |
| 484 | C2×C8 | — | 10 | 2 | no | — |
| 485 | C4⋊C4 | — | 30 | 2 | no | — |
| 486 | C22⋊C4 | — | 30 | 2 | no | — |
| 487 | C42 | — | 30 | 2 | no | — |
| 488 | C3×C5 | #1795 | 1 | 1 | yes | characteristic, complemented, Hall |
| 489 | C22×C3 | — | 2 | 1 | no | — |
| 490 | C22×C3 | — | 4 | 1 | no | — |
| 491 | C22×C3 | — | 5 | 2 | no | — |
| 492 | C22×C3 | — | 10 | 1 | no | — |
| 493 | C22×C3 | — | 20 | 1 | no | — |
| 494 | C22×C3 | — | 20 | 1 | no | — |
| 495 | C22×C3 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 496 | C2×D3 | — | 2 | 2 | no | — |
| 497 | C2×D3 | — | 4 | 2 | no | — |
| 498 | C2×D3 | — | 10 | 2 | no | — |
| 499 | C2×D3 | — | 10 | 2 | no | — |
| 500 | C2×D3 | — | 20 | 2 | no | — |
| 501 | C2×D3 | — | 20 | 2 | no | — |
| 502 | C2×D3 | — | 40 | 4 | no | — |
| 503 | C2×D3 | — | 40 | 4 | no | — |
| 504 | C2×D3 | — | 40 | 4 | no | — |
| 505 | C3×C4 | — | 2 | 1 | no | — |
| 506 | C3×C4 | — | 5 | 2 | no | — |
| 507 | C3×C4 | — | 10 | 1 | no | — |
| 508 | C3×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 509 | C3×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 510 | Dic3 | — | 2 | 2 | no | — |
| 511 | Dic3 | — | 40 | 2 | no | — |
| 512 | C2×C5 | — | 2 | 1 | no | — |
| 513 | C2×C5 | — | 4 | 1 | no | — |
| 514 | C2×C5 | — | 12 | 2 | no | — |
| 515 | C2×C5 | #4955 | 1 | 1 | yes | characteristic |
| 516 | D5 | — | 2 | 2 | no | — |
| 517 | D5 | — | 4 | 1 | no | — |
| 518 | D5 | — | 12 | 2 | no | — |
| 519 | D5 | — | 12 | 2 | no | — |
| 520 | C23 | — | 5 | 1 | no | — |
| 521 | C23 | — | 5 | 1 | no | — |
| 522 | C23 | — | 6 | 1 | no | — |
| 523 | C23 | — | 30 | 4 | no | — |
| 524 | C23 | — | 30 | 4 | no | — |
| 525 | C23 | — | 30 | 4 | no | — |
| 526 | C23 | — | 30 | 1 | no | — |
| 527 | C23 | — | 30 | 1 | no | — |
| 528 | C23 | — | 120 | 2 | no | — |
| 529 | C23 | — | 120 | 2 | no | — |
| 530 | C23 | — | 120 | 2 | no | — |
| 531 | C23 | (C2×D3)⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 532 | Q8 | — | 3 | 2 | no | — |
| 533 | Q8 | — | 6 | 1 | no | — |
| 534 | Q8 | — | 10 | 2 | no | — |
| 535 | D4 | — | 3 | 2 | no | — |
| 536 | D4 | — | 6 | 4 | no | — |
| 537 | D4 | — | 6 | 1 | no | — |
| 538 | D4 | — | 10 | 2 | no | — |
| 539 | D4 | — | 10 | 2 | no | — |
| 540 | D4 | — | 10 | 2 | no | — |
| 541 | D4 | — | 15 | 2 | no | — |
| 542 | D4 | — | 15 | 2 | no | — |
| 543 | D4 | — | 30 | 4 | no | — |
| 544 | D4 | — | 30 | 4 | no | — |
| 545 | D4 | — | 30 | 4 | no | — |
| 546 | D4 | — | 30 | 4 | no | — |
| 547 | D4 | — | 30 | 4 | no | — |
| 548 | D4 | — | 30 | 1 | no | — |
| 549 | D4 | — | 30 | 1 | no | — |
| 550 | C2×C4 | — | 2 | 1 | no | — |
| 551 | C2×C4 | — | 2 | 1 | no | — |
| 552 | C2×C4 | — | 5 | 1 | no | — |
| 553 | C2×C4 | — | 5 | 2 | no | — |
| 554 | C2×C4 | — | 5 | 2 | no | — |
| 555 | C2×C4 | — | 5 | 1 | no | — |
| 556 | C2×C4 | — | 6 | 4 | no | — |
| 557 | C2×C4 | — | 6 | 1 | no | — |
| 558 | C2×C4 | — | 10 | 1 | no | — |
| 559 | C2×C4 | — | 10 | 1 | no | — |
| 560 | C2×C4 | — | 30 | 4 | no | — |
| 561 | C2×C4 | — | 30 | 4 | no | — |
| 562 | C2×C4 | — | 60 | 2 | no | — |
| 563 | C2×C4 | (C2×D3)⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 564 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 565 | C8 | — | 20 | 2 | no | — |
| 566 | C2×C3 | — | 2 | 1 | no | — |
| 567 | C2×C3 | — | 4 | 1 | no | — |
| 568 | C2×C3 | — | 10 | 2 | no | — |
| 569 | C2×C3 | — | 20 | 1 | no | — |
| 570 | C2×C3 | #65800 | 1 | 1 | yes | characteristic |
| 571 | D3 | — | 4 | 2 | no | — |
| 572 | D3 | — | 20 | 2 | no | — |
| 573 | D3 | — | 20 | 2 | no | — |
| 574 | C5 | #70139 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 575 | C22 | — | 2 | 1 | no | — |
| 576 | C22 | — | 4 | 1 | no | — |
| 577 | C22 | — | 5 | 2 | no | — |
| 578 | C22 | — | 6 | 2 | no | — |
| 579 | C22 | — | 10 | 1 | no | — |
| 580 | C22 | — | 12 | 2 | no | — |
| 581 | C22 | — | 20 | 1 | no | — |
| 582 | C22 | — | 20 | 1 | no | — |
| 583 | C22 | — | 30 | 2 | no | — |
| 584 | C22 | — | 30 | 2 | no | — |
| 585 | C22 | — | 60 | 2 | no | — |
| 586 | C22 | — | 60 | 2 | no | — |
| 587 | C22 | — | 120 | 4 | no | — |
| 588 | C22 | — | 120 | 4 | no | — |
| 589 | C22 | — | 120 | 4 | no | — |
| 590 | C22 | C2×(C2×D3)⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 591 | C4 | — | 2 | 1 | no | — |
| 592 | C4 | — | 5 | 2 | no | — |
| 593 | C4 | — | 6 | 2 | no | — |
| 594 | C4 | — | 10 | 1 | no | — |
| 595 | C4 | — | 120 | 2 | no | — |
| 596 | C4 | D3×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 597 | C4 | D3×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 598 | C3 | #10605012 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 599 | C2 | — | 2 | 1 | no | — |
| 600 | C2 | — | 4 | 1 | no | — |
| 601 | C2 | — | 10 | 2 | no | — |
| 602 | C2 | — | 12 | 2 | no | — |
| 603 | C2 | — | 20 | 1 | no | — |
| 604 | C2 | — | 60 | 2 | no | — |
| 605 | C2 | — | 60 | 2 | no | — |
| 606 | C2 | #11752025 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11752404 | C2 | semidirect |
| 3. C3×#65761 | C2 | semidirect |
| 4. #11751723 | C2 | semidirect |
| 5. #11751707 | C2 | semidirect |
| 7. C22×D60 | C4 | semidirect |
| 8. C2×C5×#235 | C4 | semidirect |
| 15. C2×D5×D12 | C4 | semidirect |
| 17. C2×#6773 | C4 | semidirect |
| 20. #91989 | C22 | semidirect |
| 21. C3×D5⋊M16 | C22 | semidirect |
| 32. #65761 | D3 | semidirect |
| 100. D5⋊M16 | C2×D3 | semidirect |
| 163. C2×#235 | AGL(1,𝔽5) | semidirect |
| 488. C3×C5 | #1795 | semidirect |
| 574. C5 | #70139 | semidirect |
| 598. C3 | #10605012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92019 | 2 |
| #11752404 | 2 |
| C3×#65761 | 2 |
| #11751723 | 2 |
| #11751707 | 2 |
| #10605012 | 3 |
| #70139 | 5 |