Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1340 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 1340 conjugacy classes of subgroups — too many to draw. Only its 157 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 | C3×D5×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11752438 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | D5⋊#834 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #10605017 | — | 3 | 1 | no | maximal, Hall |
| 5 | C23×ΓL(1,𝔽16) | C22 | 1 | 1 | yes | characteristic, complemented |
| 6 | C3×C5×H(5,𝔽2) | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | C3×#4149 | — | 2 | 3 | no | — |
| 8 | C3×D5×#41 | — | 2 | 3 | no | — |
| 9 | C3×#4144 | — | 2 | 3 | no | — |
| 10 | C3×#4144 | C4 | 1 | 3 | yes | complemented |
| 11 | C2×C3×D4×D5 | — | 2 | 3 | no | — |
| 12 | C2×C3×D4×D5 | C22 | 1 | 3 | yes | — |
| 13 | C2×#6763 | — | 2 | 3 | no | — |
| 14 | C2×#6763 | C22 | 1 | 3 | yes | complemented |
| 15 | #91240 | — | 2 | 3 | no | — |
| 16 | #91235 | — | 2 | 3 | no | — |
| 17 | #91228 | — | 2 | 3 | no | — |
| 18 | #72142 | — | 5 | 1 | no | maximal, Hall |
| 19 | D5×H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic |
| 20 | #65779 | — | 3 | 3 | no | — |
| 21 | D5⋊#99 | — | 3 | 3 | no | — |
| 22 | C23×C3×D5 | — | 2 | 1 | no | — |
| 23 | C23×C3×D5 | D4 | 1 | 3 | yes | — |
| 24 | C23×C3×D5 | C23 | 1 | 1 | yes | characteristic |
| 25 | C22×ΓL(1,𝔽16) | — | 2 | 3 | no | — |
| 26 | C22×ΓL(1,𝔽16) | — | 2 | 3 | no | — |
| 27 | C22×ΓL(1,𝔽16) | — | 4 | 2 | no | — |
| 28 | C3×C5×#41 | — | 2 | 3 | no | — |
| 29 | C2×C3×C5×D4 | — | 2 | 3 | no | — |
| 30 | C2×C3×C5×D4 | C2×C4 | 1 | 3 | yes | — |
| 31 | C2×C3×C22⋊D5 | — | 2 | 3 | no | — |
| 32 | C2×C3×C22⋊D5 | — | 2 | 3 | no | — |
| 33 | C2×C3×C22⋊D5 | C2×C4 | 1 | 3 | yes | — |
| 34 | C2×C3×C22⋊D5 | D4 | 1 | 3 | yes | — |
| 35 | C3×#713 | — | 2 | 3 | no | — |
| 36 | C3×Q8×D5 | — | 2 | 1 | no | — |
| 37 | C3×#711 | — | 2 | 3 | no | — |
| 38 | C3×#711 | — | 2 | 6 | no | — |
| 39 | C3×D4×D5 | — | 2 | 3 | no | — |
| 40 | C3×D4×D5 | — | 2 | 6 | no | — |
| 41 | C3×D4×D5 | — | 2 | 6 | no | — |
| 42 | C3×D4×D5 | — | 2 | 6 | no | — |
| 43 | C3×D4×D5 | — | 2 | 6 | no | — |
| 44 | C3×#709 | — | 2 | 6 | no | — |
| 45 | C3×#709 | — | 2 | 3 | no | — |
| 46 | C2×C3×D20 | — | 2 | 3 | no | — |
| 47 | C2×C3×D20 | D4 | 1 | 3 | yes | — |
| 48 | C2×C3×C4×D5 | — | 2 | 3 | no | — |
| 49 | C2×C3×C4×D5 | D4 | 1 | 3 | yes | — |
| 50 | #6763 | — | 2 | 6 | no | — |
| 51 | #6763 | — | 4 | 6 | no | — |
| 52 | C2×C3×H(5,𝔽2) | — | 5 | 1 | no | — |
| 53 | #5220 | — | 5 | 3 | no | — |
| 54 | C2×#834 | — | 5 | 3 | no | — |
| 55 | C23×AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 56 | C5×H(5,𝔽2) | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 57 | #4149 | — | 2 | 3 | no | — |
| 58 | D5×#41 | — | 2 | 3 | no | — |
| 59 | #4144 | — | 2 | 3 | no | — |
| 60 | #4144 | Dic3 | 1 | 3 | yes | complemented |
| 61 | C2×D4×D5 | — | 2 | 3 | no | — |
| 62 | C2×D4×D5 | C2×D3 | 1 | 3 | yes | — |
| 63 | C2×C22⋊AGL(1,𝔽5) | — | 3 | 3 | no | — |
| 64 | C2×C22⋊AGL(1,𝔽5) | — | 6 | 3 | no | — |
| 65 | #4011 | — | 6 | 3 | no | — |
| 66 | (C2×AGL(1,𝔽5))⋊C4 | — | 6 | 3 | no | — |
| 67 | #3999 | — | 6 | 3 | no | — |
| 68 | #1790 | — | 15 | 1 | no | Sylow |
| 69 | C23×C3×C5 | — | 2 | 1 | no | — |
| 70 | C23×C3×C5 | C22⋊C4 | 1 | 3 | yes | complemented |
| 71 | C23×C3×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 72 | C22×C3×D5 | — | 2 | 3 | no | — |
| 73 | C22×C3×D5 | — | 2 | 3 | no | — |
| 74 | C22×C3×D5 | — | 2 | 3 | no | — |
| 75 | C22×C3×D5 | — | 4 | 1 | no | — |
| 76 | C22×C3×D5 | — | 4 | 1 | no | — |
| 77 | C22×C3×D5 | — | 4 | 3 | no | — |
| 78 | C22×C3×D5 | — | 4 | 3 | no | — |
| 79 | C22×C3×D5 | — | 8 | 1 | no | — |
| 80 | C22×C3×D5 | — | 8 | 1 | no | — |
| 81 | C22×C3×D5 | C22⋊C4 | 1 | 3 | yes | complemented |
| 82 | C22×C3×D5 | C2×D4 | 1 | 3 | yes | — |
| 83 | C22×C3×D5 | C2×D4 | 1 | 3 | yes | — |
| 84 | C2×ΓL(1,𝔽16) | — | 2 | 6 | no | — |
| 85 | C2×ΓL(1,𝔽16) | — | 4 | 3 | no | — |
| 86 | C2×ΓL(1,𝔽16) | — | 4 | 1 | no | — |
| 87 | C2×ΓL(1,𝔽16) | — | 4 | 3 | no | — |
| 88 | C2×ΓL(1,𝔽16) | — | 4 | 3 | no | — |
| 89 | C2×ΓL(1,𝔽16) | — | 4 | 3 | no | — |
| 90 | C3×C5×Q8 | — | 2 | 1 | no | — |
| 91 | C3×C5×D4 | — | 2 | 3 | no | — |
| 92 | C3×C5×D4 | — | 2 | 6 | no | — |
| 93 | C2×C3×C4×C5 | — | 2 | 3 | no | — |
| 94 | C2×C3×C4×C5 | C22⋊C4 | 1 | 3 | yes | complemented |
| 95 | C3×C22⋊D5 | — | 2 | 6 | no | — |
| 96 | C3×C22⋊D5 | — | 2 | 6 | no | — |
| 97 | C3×C22⋊D5 | — | 2 | 6 | no | — |
| 98 | C2×C3×Dic5 | — | 2 | 3 | no | — |
| 99 | C2×C3×Dic5 | C22⋊C4 | 1 | 3 | yes | complemented |
| 100 | C3×D20 | — | 2 | 3 | no | — |
| 101 | C3×D20 | — | 2 | 6 | no | — |
| 102 | C3×C4×D5 | — | 2 | 6 | no | — |
| 103 | C3×C4×D5 | — | 2 | 3 | no | — |
| 104 | C3×C4×D5 | — | 2 | 3 | no | — |
| 105 | C3×Dic10 | — | 2 | 3 | no | — |
| 106 | C3×H(5,𝔽2) | — | 5 | 3 | no | — |
| 107 | C3×H(5,𝔽2) | — | 10 | 3 | no | — |
| 108 | C3×H(5,𝔽2) | — | 10 | 3 | no | — |
| 109 | C3×H(5,𝔽2) | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 110 | C2×C3×#41 | — | 10 | 3 | no | — |
| 111 | C22×C3×D4 | — | 5 | 3 | no | — |
| 112 | C22×C3×D4 | — | 10 | 3 | no | — |
| 113 | C23×Dic3 | — | 5 | 1 | no | — |
| 114 | C2×#217 | — | 5 | 3 | no | — |
| 115 | C2×#217 | — | 10 | 3 | no | — |
| 116 | #834 | — | 10 | 3 | no | — |
| 117 | #834 | — | 10 | 3 | no | — |
| 118 | C3⋊#95 | — | 10 | 3 | no | — |
| 119 | C23×D5 | — | 2 | 1 | no | — |
| 120 | C23×D5 | #67 | 1 | 3 | yes | — |
| 121 | C23×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 122 | C22×AGL(1,𝔽5) | — | 6 | 3 | no | — |
| 123 | C22×AGL(1,𝔽5) | — | 6 | 3 | no | — |
| 124 | C22×AGL(1,𝔽5) | — | 12 | 2 | no | — |
| 125 | C5×#41 | — | 2 | 3 | no | — |
| 126 | C2×C5×D4 | — | 2 | 3 | no | — |
| 127 | C2×C5×D4 | C2×Dic3 | 1 | 3 | yes | — |
| 128 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 129 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 130 | C2×C22⋊D5 | C2×Dic3 | 1 | 3 | yes | — |
| 131 | C2×C22⋊D5 | #67 | 1 | 3 | yes | — |
| 132 | #713 | — | 2 | 3 | no | — |
| 133 | Q8×D5 | — | 2 | 1 | no | — |
| 134 | #711 | — | 2 | 3 | no | — |
| 135 | #711 | — | 2 | 6 | no | — |
| 136 | D4×D5 | — | 2 | 3 | no | — |
| 137 | D4×D5 | — | 2 | 6 | no | — |
| 138 | D4×D5 | — | 2 | 6 | no | — |
| 139 | D4×D5 | — | 2 | 6 | no | — |
| 140 | D4×D5 | — | 2 | 6 | no | — |
| 141 | #709 | — | 2 | 6 | no | — |
| 142 | #709 | — | 2 | 3 | no | — |
| 143 | C2×D20 | — | 2 | 3 | no | — |
| 144 | C2×D20 | #67 | 1 | 3 | yes | — |
| 145 | C2×C4×D5 | — | 2 | 3 | no | — |
| 146 | C2×C4×D5 | #67 | 1 | 3 | yes | — |
| 147 | C22⋊AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 148 | C22⋊AGL(1,𝔽5) | — | 12 | 6 | no | — |
| 149 | C2×H(5,𝔽2) | — | 5 | 1 | no | — |
| 150 | C2×#99 | — | 15 | 3 | no | — |
| 151 | #386 | — | 15 | 3 | no | — |
| 152 | C22×C3×C5 | — | 2 | 3 | no | — |
| 153 | C22×C3×C5 | — | 4 | 1 | no | — |
| 154 | C22×C3×C5 | — | 4 | 3 | no | — |
| 155 | C22×C3×C5 | — | 8 | 1 | no | — |
| 156 | C22×C3×C5 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 157 | C2×C3×D5 | — | 2 | 3 | no | — |
| 158 | C2×C3×D5 | — | 2 | 3 | no | — |
| 159 | C2×C3×D5 | — | 2 | 3 | no | — |
| 160 | C2×C3×D5 | — | 4 | 3 | no | — |
| 161 | C2×C3×D5 | — | 4 | 3 | no | — |
| 162 | C2×C3×D5 | — | 4 | 3 | no | — |
| 163 | C2×C3×D5 | — | 4 | 3 | no | — |
| 164 | C2×C3×D5 | — | 8 | 3 | no | — |
| 165 | C2×C3×D5 | — | 8 | 3 | no | — |
| 166 | C2×C3×D5 | #120 | 1 | 3 | yes | — |
| 167 | C2×C3×D5 | #120 | 1 | 1 | yes | characteristic |
| 168 | ΓL(1,𝔽16) | — | 4 | 2 | no | — |
| 169 | ΓL(1,𝔽16) | — | 8 | 3 | no | — |
| 170 | C3×C4×C5 | — | 2 | 3 | no | — |
| 171 | C3×Dic5 | — | 2 | 3 | no | — |
| 172 | C24×C3 | — | 5 | 1 | no | — |
| 173 | C24×C3 | — | 5 | 3 | no | — |
| 174 | C24×C3 | — | 10 | 1 | no | — |
| 175 | C3×#41 | — | 2 | 3 | no | — |
| 176 | C3×#41 | — | 10 | 6 | no | — |
| 177 | C3×#41 | — | 10 | 6 | no | — |
| 178 | C3×#41 | — | 10 | 3 | no | — |
| 179 | C3×#41 | — | 10 | 3 | no | — |
| 180 | C3×#41 | — | 10 | 3 | no | — |
| 181 | C2×C3×Q8 | — | 10 | 1 | no | — |
| 182 | C2×C3×D4 | — | 2 | 3 | no | — |
| 183 | C2×C3×D4 | — | 5 | 3 | no | — |
| 184 | C2×C3×D4 | — | 5 | 3 | no | — |
| 185 | C2×C3×D4 | — | 5 | 3 | no | — |
| 186 | C2×C3×D4 | — | 10 | 3 | no | — |
| 187 | C2×C3×D4 | — | 10 | 6 | no | — |
| 188 | C2×C3×D4 | — | 10 | 6 | no | — |
| 189 | C2×C3×D4 | — | 10 | 6 | no | — |
| 190 | C2×C3×D4 | — | 10 | 3 | no | — |
| 191 | C2×C3×D4 | — | 10 | 6 | no | — |
| 192 | C2×C3×D4 | — | 10 | 3 | no | — |
| 193 | C2×C3×D4 | — | 10 | 3 | no | — |
| 194 | C2×C3×D4 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 195 | C22×C3×C4 | — | 5 | 3 | no | — |
| 196 | C22×C3×C4 | — | 10 | 3 | no | — |
| 197 | C22×Dic3 | — | 10 | 3 | no | — |
| 198 | C22×Dic3 | — | 10 | 3 | no | — |
| 199 | C22×Dic3 | — | 20 | 2 | no | — |
| 200 | #217 | — | 10 | 6 | no | — |
| 201 | #217 | — | 20 | 6 | no | — |
| 202 | C23×C5 | — | 2 | 1 | no | — |
| 203 | C23×C5 | #217 | 1 | 3 | yes | complemented |
| 204 | C23×C5 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 205 | C22×D5 | — | 2 | 3 | no | — |
| 206 | C22×D5 | — | 2 | 3 | no | — |
| 207 | C22×D5 | — | 2 | 3 | no | — |
| 208 | C22×D5 | — | 4 | 1 | no | — |
| 209 | C22×D5 | — | 4 | 1 | no | — |
| 210 | C22×D5 | — | 4 | 3 | no | — |
| 211 | C22×D5 | — | 4 | 3 | no | — |
| 212 | C22×D5 | — | 8 | 1 | no | — |
| 213 | C22×D5 | — | 8 | 1 | no | — |
| 214 | C22×D5 | #217 | 1 | 3 | yes | complemented |
| 215 | C22×D5 | C2×#67 | 1 | 3 | yes | — |
| 216 | C22×D5 | C2×#67 | 1 | 3 | yes | — |
| 217 | C2×AGL(1,𝔽5) | — | 6 | 6 | no | — |
| 218 | C2×AGL(1,𝔽5) | — | 12 | 3 | no | — |
| 219 | C2×AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 220 | C2×AGL(1,𝔽5) | — | 12 | 3 | no | — |
| 221 | C2×AGL(1,𝔽5) | — | 12 | 3 | no | — |
| 222 | C2×AGL(1,𝔽5) | — | 12 | 3 | no | — |
| 223 | C5×Q8 | — | 2 | 1 | no | — |
| 224 | C5×D4 | — | 2 | 3 | no | — |
| 225 | C5×D4 | — | 2 | 6 | no | — |
| 226 | C2×C4×C5 | — | 2 | 3 | no | — |
| 227 | C2×C4×C5 | #217 | 1 | 3 | yes | complemented |
| 228 | C22⋊D5 | — | 2 | 6 | no | — |
| 229 | C22⋊D5 | — | 2 | 6 | no | — |
| 230 | C22⋊D5 | — | 2 | 6 | no | — |
| 231 | C2×Dic5 | — | 2 | 3 | no | — |
| 232 | C2×Dic5 | #217 | 1 | 3 | yes | complemented |
| 233 | D20 | — | 2 | 3 | no | — |
| 234 | D20 | — | 2 | 6 | no | — |
| 235 | C4×D5 | — | 2 | 6 | no | — |
| 236 | C4×D5 | — | 2 | 3 | no | — |
| 237 | C4×D5 | — | 2 | 3 | no | — |
| 238 | Dic10 | — | 2 | 3 | no | — |
| 239 | H(5,𝔽2) | — | 5 | 3 | no | — |
| 240 | H(5,𝔽2) | — | 10 | 3 | no | — |
| 241 | H(5,𝔽2) | — | 10 | 3 | no | — |
| 242 | H(5,𝔽2) | ΓL(1,𝔽16) | 1 | 1 | yes | characteristic, complemented |
| 243 | C2×#41 | — | 10 | 3 | no | — |
| 244 | C22×D4 | — | 5 | 3 | no | — |
| 245 | C22×D4 | — | 10 | 3 | no | — |
| 246 | C23×C4 | — | 15 | 1 | no | — |
| 247 | C2×C22⋊C4 | — | 15 | 3 | no | — |
| 248 | C2×C22⋊C4 | — | 30 | 3 | no | — |
| 249 | #99 | — | 30 | 3 | no | — |
| 250 | #99 | — | 30 | 3 | no | — |
| 251 | #95 | — | 30 | 3 | no | — |
| 252 | C2×C3×C5 | — | 2 | 3 | no | — |
| 253 | C2×C3×C5 | — | 4 | 3 | no | — |
| 254 | C2×C3×C5 | #379 | 1 | 1 | yes | characteristic |
| 255 | C3×D5 | — | 2 | 3 | no | — |
| 256 | C3×D5 | — | 4 | 3 | no | — |
| 257 | C3×D5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 258 | C3×D5 | #458 | 1 | 1 | yes | characteristic |
| 259 | C23×C3 | — | 2 | 1 | no | — |
| 260 | C23×C3 | — | 5 | 3 | no | — |
| 261 | C23×C3 | — | 5 | 3 | no | — |
| 262 | C23×C3 | — | 5 | 3 | no | — |
| 263 | C23×C3 | — | 10 | 3 | no | — |
| 264 | C23×C3 | — | 10 | 3 | no | — |
| 265 | C23×C3 | — | 10 | 3 | no | — |
| 266 | C23×C3 | — | 20 | 1 | no | — |
| 267 | C23×C3 | — | 20 | 1 | no | — |
| 268 | C23×C3 | — | 20 | 3 | no | — |
| 269 | C23×C3 | — | 20 | 3 | no | — |
| 270 | C23×C3 | — | 40 | 1 | no | — |
| 271 | C23×C3 | — | 40 | 1 | no | — |
| 272 | C23×C3 | C22⋊AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 273 | C23×C3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 274 | C3×Q8 | — | 2 | 1 | no | — |
| 275 | C3×Q8 | — | 10 | 3 | no | — |
| 276 | C3×D4 | — | 2 | 3 | no | — |
| 277 | C3×D4 | — | 2 | 6 | no | — |
| 278 | C3×D4 | — | 10 | 6 | no | — |
| 279 | C3×D4 | — | 10 | 3 | no | — |
| 280 | C3×D4 | — | 10 | 6 | no | — |
| 281 | C3×D4 | — | 10 | 6 | no | — |
| 282 | C3×D4 | — | 10 | 6 | no | — |
| 283 | C2×C3×C4 | — | 2 | 3 | no | — |
| 284 | C2×C3×C4 | — | 5 | 3 | no | — |
| 285 | C2×C3×C4 | — | 10 | 3 | no | — |
| 286 | C2×C3×C4 | — | 10 | 3 | no | — |
| 287 | C2×C3×C4 | — | 10 | 6 | no | — |
| 288 | C2×C3×C4 | — | 10 | 3 | no | — |
| 289 | C2×C3×C4 | C22⋊AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 290 | C2×Dic3 | — | 10 | 6 | no | — |
| 291 | C2×Dic3 | — | 20 | 1 | no | — |
| 292 | C2×Dic3 | — | 20 | 3 | no | — |
| 293 | C2×Dic3 | — | 20 | 3 | no | — |
| 294 | C2×Dic3 | — | 20 | 3 | no | — |
| 295 | C2×Dic3 | — | 20 | 3 | no | — |
| 296 | C22×C5 | — | 2 | 3 | no | — |
| 297 | C22×C5 | — | 4 | 1 | no | — |
| 298 | C22×C5 | — | 4 | 3 | no | — |
| 299 | C22×C5 | — | 8 | 1 | no | — |
| 300 | C22×C5 | C2×#217 | 1 | 3 | yes | — |
| 301 | C2×D5 | — | 2 | 3 | no | — |
| 302 | C2×D5 | — | 2 | 3 | no | — |
| 303 | C2×D5 | — | 2 | 3 | no | — |
| 304 | C2×D5 | — | 4 | 3 | no | — |
| 305 | C2×D5 | — | 4 | 3 | no | — |
| 306 | C2×D5 | — | 4 | 3 | no | — |
| 307 | C2×D5 | — | 4 | 3 | no | — |
| 308 | C2×D5 | — | 8 | 3 | no | — |
| 309 | C2×D5 | — | 8 | 3 | no | — |
| 310 | C2×D5 | #953 | 1 | 3 | yes | — |
| 311 | C2×D5 | #953 | 1 | 1 | yes | characteristic |
| 312 | AGL(1,𝔽5) | — | 12 | 2 | no | — |
| 313 | AGL(1,𝔽5) | — | 24 | 3 | no | — |
| 314 | C4×C5 | — | 2 | 3 | no | — |
| 315 | Dic5 | — | 2 | 3 | no | — |
| 316 | C24 | — | 5 | 1 | no | — |
| 317 | C24 | — | 5 | 3 | no | — |
| 318 | C24 | — | 10 | 1 | no | — |
| 319 | #41 | — | 2 | 3 | no | — |
| 320 | #41 | — | 10 | 6 | no | — |
| 321 | #41 | — | 10 | 6 | no | — |
| 322 | #41 | — | 10 | 3 | no | — |
| 323 | #41 | — | 10 | 3 | no | — |
| 324 | #41 | — | 10 | 3 | no | — |
| 325 | C2×Q8 | — | 10 | 1 | no | — |
| 326 | C2×D4 | — | 2 | 3 | no | — |
| 327 | C2×D4 | — | 5 | 3 | no | — |
| 328 | C2×D4 | — | 5 | 3 | no | — |
| 329 | C2×D4 | — | 5 | 3 | no | — |
| 330 | C2×D4 | — | 10 | 3 | no | — |
| 331 | C2×D4 | — | 10 | 6 | no | — |
| 332 | C2×D4 | — | 10 | 6 | no | — |
| 333 | C2×D4 | — | 10 | 6 | no | — |
| 334 | C2×D4 | — | 10 | 3 | no | — |
| 335 | C2×D4 | — | 10 | 6 | no | — |
| 336 | C2×D4 | — | 10 | 3 | no | — |
| 337 | C2×D4 | — | 10 | 3 | no | — |
| 338 | C2×D4 | C2×ΓL(1,𝔽16) | 1 | 3 | yes | — |
| 339 | C22×C4 | — | 5 | 3 | no | — |
| 340 | C22×C4 | — | 10 | 3 | no | — |
| 341 | C22×C4 | — | 30 | 3 | no | — |
| 342 | C22×C4 | — | 30 | 3 | no | — |
| 343 | C22×C4 | — | 60 | 2 | no | — |
| 344 | C22⋊C4 | — | 30 | 6 | no | — |
| 345 | C22⋊C4 | — | 60 | 6 | no | — |
| 346 | C3×C5 | #1790 | 1 | 1 | yes | characteristic, complemented, Hall |
| 347 | C22×C3 | — | 2 | 3 | no | — |
| 348 | C22×C3 | — | 4 | 1 | no | — |
| 349 | C22×C3 | — | 4 | 3 | no | — |
| 350 | C22×C3 | — | 5 | 1 | no | — |
| 351 | C22×C3 | — | 5 | 3 | no | — |
| 352 | C22×C3 | — | 8 | 1 | no | — |
| 353 | C22×C3 | — | 10 | 3 | no | — |
| 354 | C22×C3 | — | 10 | 3 | no | — |
| 355 | C22×C3 | — | 10 | 3 | no | — |
| 356 | C22×C3 | — | 20 | 3 | no | — |
| 357 | C22×C3 | — | 20 | 3 | no | — |
| 358 | C22×C3 | — | 20 | 3 | no | — |
| 359 | C22×C3 | — | 20 | 3 | no | — |
| 360 | C22×C3 | — | 40 | 3 | no | — |
| 361 | C22×C3 | — | 40 | 3 | no | — |
| 362 | C22×C3 | C2×C22⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 363 | C3×C4 | — | 2 | 3 | no | — |
| 364 | C3×C4 | — | 10 | 3 | no | — |
| 365 | Dic3 | — | 20 | 2 | no | — |
| 366 | Dic3 | — | 40 | 3 | no | — |
| 367 | C2×C5 | — | 2 | 3 | no | — |
| 368 | C2×C5 | — | 4 | 3 | no | — |
| 369 | C2×C5 | #5247 | 1 | 1 | yes | characteristic |
| 370 | D5 | — | 2 | 3 | no | — |
| 371 | D5 | — | 4 | 3 | no | — |
| 372 | D5 | #5243 | 1 | 1 | yes | characteristic |
| 373 | D5 | #5244 | 1 | 1 | yes | characteristic |
| 374 | C23 | — | 2 | 1 | no | — |
| 375 | C23 | — | 5 | 3 | no | — |
| 376 | C23 | — | 5 | 3 | no | — |
| 377 | C23 | — | 5 | 3 | no | — |
| 378 | C23 | — | 10 | 3 | no | — |
| 379 | C23 | — | 10 | 3 | no | — |
| 380 | C23 | — | 10 | 3 | no | — |
| 381 | C23 | — | 20 | 1 | no | — |
| 382 | C23 | — | 20 | 1 | no | — |
| 383 | C23 | — | 20 | 3 | no | — |
| 384 | C23 | — | 20 | 3 | no | — |
| 385 | C23 | — | 40 | 1 | no | — |
| 386 | C23 | — | 40 | 1 | no | — |
| 387 | C23 | #6763 | 1 | 3 | yes | complemented |
| 388 | C23 | C22×ΓL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 389 | Q8 | — | 2 | 1 | no | — |
| 390 | Q8 | — | 10 | 3 | no | — |
| 391 | D4 | — | 2 | 3 | no | — |
| 392 | D4 | — | 2 | 6 | no | — |
| 393 | D4 | — | 10 | 6 | no | — |
| 394 | D4 | — | 10 | 3 | no | — |
| 395 | D4 | — | 10 | 6 | no | — |
| 396 | D4 | — | 10 | 6 | no | — |
| 397 | D4 | — | 10 | 6 | no | — |
| 398 | C2×C4 | — | 2 | 3 | no | — |
| 399 | C2×C4 | — | 5 | 3 | no | — |
| 400 | C2×C4 | — | 10 | 3 | no | — |
| 401 | C2×C4 | — | 10 | 3 | no | — |
| 402 | C2×C4 | — | 10 | 6 | no | — |
| 403 | C2×C4 | — | 10 | 3 | no | — |
| 404 | C2×C4 | — | 30 | 6 | no | — |
| 405 | C2×C4 | — | 60 | 1 | no | — |
| 406 | C2×C4 | — | 60 | 3 | no | — |
| 407 | C2×C4 | — | 60 | 3 | no | — |
| 408 | C2×C4 | — | 60 | 3 | no | — |
| 409 | C2×C4 | — | 60 | 3 | no | — |
| 410 | C2×C4 | #6763 | 1 | 3 | yes | complemented |
| 411 | C2×C3 | — | 2 | 3 | no | — |
| 412 | C2×C3 | — | 4 | 3 | no | — |
| 413 | C2×C3 | — | 5 | 1 | no | — |
| 414 | C2×C3 | — | 5 | 1 | no | — |
| 415 | C2×C3 | — | 10 | 3 | no | — |
| 416 | C2×C3 | — | 20 | 3 | no | — |
| 417 | C2×C3 | #65800 | 1 | 1 | yes | characteristic |
| 418 | C5 | #72142 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 419 | C22 | — | 2 | 3 | no | — |
| 420 | C22 | — | 4 | 1 | no | — |
| 421 | C22 | — | 4 | 3 | no | — |
| 422 | C22 | — | 5 | 1 | no | — |
| 423 | C22 | — | 5 | 3 | no | — |
| 424 | C22 | — | 8 | 1 | no | — |
| 425 | C22 | — | 10 | 3 | no | — |
| 426 | C22 | — | 10 | 3 | no | — |
| 427 | C22 | — | 10 | 3 | no | — |
| 428 | C22 | — | 20 | 3 | no | — |
| 429 | C22 | — | 20 | 3 | no | — |
| 430 | C22 | — | 20 | 3 | no | — |
| 431 | C22 | — | 20 | 3 | no | — |
| 432 | C22 | — | 40 | 3 | no | — |
| 433 | C22 | — | 40 | 3 | no | — |
| 434 | C22 | C2×#6763 | 1 | 3 | yes | — |
| 435 | C4 | — | 2 | 3 | no | — |
| 436 | C4 | — | 10 | 3 | no | — |
| 437 | C4 | — | 60 | 2 | no | — |
| 438 | C4 | — | 120 | 3 | no | — |
| 439 | C3 | #10605017 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 440 | C2 | — | 2 | 3 | no | — |
| 441 | C2 | — | 4 | 3 | no | — |
| 442 | C2 | — | 5 | 1 | no | — |
| 443 | C2 | — | 5 | 1 | no | — |
| 444 | C2 | — | 10 | 3 | no | — |
| 445 | C2 | — | 20 | 3 | no | — |
| 446 | C2 | #11752459 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11752438 | C2 | semidirect |
| 3. D5⋊#834 | C2 | semidirect |
| 5. C23×ΓL(1,𝔽16) | C22 | semidirect |
| 6. C3×C5×H(5,𝔽2) | C4 | semidirect |
| 10. C3×#4144 | C4 | semidirect |
| 14. C2×#6763 | C22 | semidirect |
| 56. C5×H(5,𝔽2) | Dic3 | semidirect |
| 60. #4144 | Dic3 | semidirect |
| 70. C23×C3×C5 | C22⋊C4 | semidirect |
| 81. C22×C3×D5 | C22⋊C4 | semidirect |
| 94. C2×C3×C4×C5 | C22⋊C4 | semidirect |
| 99. C2×C3×Dic5 | C22⋊C4 | semidirect |
| 109. C3×H(5,𝔽2) | AGL(1,𝔽5) | semidirect |
| 203. C23×C5 | #217 | semidirect |
| 214. C22×D5 | #217 | semidirect |
| 227. C2×C4×C5 | #217 | semidirect |
| 232. C2×Dic5 | #217 | semidirect |
| 242. H(5,𝔽2) | ΓL(1,𝔽16) | semidirect |
| 272. C23×C3 | C22⋊AGL(1,𝔽5) | semidirect |
| 289. C2×C3×C4 | C22⋊AGL(1,𝔽5) | semidirect |
| 346. C3×C5 | #1790 | semidirect |
| 387. C23 | #6763 | semidirect |
| 410. C2×C4 | #6763 | semidirect |
| 418. C5 | #72142 | semidirect |
| 439. C3 | #10605017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×H(5,𝔽2) | 2 |
| #11752438 | 2 |
| D5⋊#834 | 2 |
| #10605017 | 3 |
| #72142 | 5 |