Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1600 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 1600 conjugacy classes of subgroups — too many to draw. Only its 204 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, complemented |
| 2 | #11754936 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #11751345 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#5243 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11749181 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11749176 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | D5×#834 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10612042 | — | 3 | 1 | no | maximal, Hall |
| 9 | C3×C5×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#4149 | — | 2 | 3 | no | — |
| 11 | C3×D5×#41 | — | 2 | 3 | no | — |
| 12 | C3×#4144 | — | 2 | 3 | no | — |
| 13 | C3×#4144 | C22 | 1 | 3 | yes | — |
| 14 | C2×C3×D4×D5 | — | 2 | 3 | no | — |
| 15 | C2×C3×D4×D5 | C22 | 1 | 3 | yes | — |
| 16 | C22×#1202 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #91826 | C22 | 1 | 3 | yes | complemented |
| 18 | C5×#935 | C22 | 1 | 3 | yes | complemented |
| 19 | #91572 | C22 | 1 | 3 | yes | complemented |
| 20 | #91564 | — | 2 | 3 | no | — |
| 21 | #91550 | — | 2 | 3 | no | — |
| 22 | D5×#217 | C22 | 1 | 3 | yes | complemented |
| 23 | #91536 | C22 | 1 | 3 | yes | complemented |
| 24 | #91409 | — | 2 | 3 | no | — |
| 25 | #91348 | — | 2 | 3 | no | — |
| 26 | #91118 | C22 | 1 | 3 | yes | complemented |
| 27 | C5×#834 | C22 | 1 | 3 | yes | complemented |
| 28 | #90995 | C22 | 1 | 6 | yes | complemented |
| 29 | #84110 | — | 5 | 1 | no | maximal, Hall |
| 30 | D5×H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | #65987 | — | 3 | 3 | no | — |
| 32 | C5×#458 | — | 3 | 1 | no | — |
| 33 | #65533 | — | 3 | 1 | no | — |
| 34 | #65342 | — | 3 | 3 | no | — |
| 35 | D5×#99 | — | 3 | 3 | no | — |
| 36 | #65030 | — | 3 | 3 | no | — |
| 37 | C23×D15 | C23 | 1 | 1 | yes | characteristic, complemented |
| 38 | C23×C3×D5 | — | 2 | 1 | no | — |
| 39 | C23×C3×D5 | D4 | 1 | 3 | yes | complemented |
| 40 | C23×C3×D5 | C23 | 1 | 1 | yes | characteristic |
| 41 | C3×C5×#41 | — | 2 | 3 | no | — |
| 42 | C2×C3×C5×D4 | — | 2 | 3 | no | — |
| 43 | C2×C3×C5×D4 | C23 | 1 | 3 | yes | — |
| 44 | C2×#1220 | — | 2 | 3 | no | — |
| 45 | C22×C5×Dic3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×C3×C22⋊D5 | — | 2 | 3 | no | — |
| 47 | C2×C3×C22⋊D5 | — | 2 | 3 | no | — |
| 48 | C2×C3×C22⋊D5 | D4 | 1 | 3 | yes | complemented |
| 49 | C2×C3×C22⋊D5 | C23 | 1 | 3 | yes | — |
| 50 | C3×#713 | — | 2 | 3 | no | — |
| 51 | C3×Q8×D5 | — | 2 | 1 | no | — |
| 52 | C3×#711 | — | 2 | 3 | no | — |
| 53 | C3×#711 | — | 2 | 6 | no | — |
| 54 | C3×D4×D5 | — | 2 | 3 | no | — |
| 55 | C3×D4×D5 | — | 2 | 6 | no | — |
| 56 | C3×D4×D5 | — | 2 | 6 | no | — |
| 57 | C3×D4×D5 | — | 2 | 6 | no | — |
| 58 | C3×D4×D5 | — | 2 | 6 | no | — |
| 59 | C3×#709 | — | 2 | 6 | no | — |
| 60 | C3×#709 | — | 2 | 3 | no | — |
| 61 | C2×C3×D20 | — | 2 | 3 | no | — |
| 62 | C2×C3×D20 | D4 | 1 | 3 | yes | complemented |
| 63 | C2×C3×C4×D5 | — | 2 | 3 | no | — |
| 64 | C2×C3×C4×D5 | D4 | 1 | 3 | yes | complemented |
| 65 | C2×#1202 | — | 2 | 3 | no | — |
| 66 | C2×#1202 | — | 2 | 3 | no | — |
| 67 | C2×#1202 | — | 2 | 3 | no | — |
| 68 | C2×D5×Dic3 | — | 2 | 3 | no | — |
| 69 | #6719 | C23 | 1 | 3 | yes | complemented |
| 70 | #6714 | — | 2 | 3 | no | — |
| 71 | C5×#217 | — | 2 | 3 | no | — |
| 72 | C5×#217 | C23 | 1 | 3 | yes | complemented |
| 73 | C5×Dic3⋊C4 | — | 2 | 3 | no | — |
| 74 | #6669 | — | 2 | 3 | no | — |
| 75 | #6667 | — | 2 | 3 | no | — |
| 76 | #6665 | — | 2 | 3 | no | — |
| 77 | #6665 | — | 2 | 3 | no | — |
| 78 | C2×C3×H(5,𝔽2) | — | 5 | 1 | no | — |
| 79 | #5804 | — | 5 | 3 | no | — |
| 80 | #5244 | — | 5 | 1 | no | — |
| 81 | #5244 | — | 5 | 3 | no | — |
| 82 | #5243 | — | 5 | 3 | no | — |
| 83 | #5243 | D5 | 1 | 1 | yes | characteristic, complemented |
| 84 | C2×#834 | — | 5 | 3 | no | — |
| 85 | C5×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 86 | #4149 | — | 2 | 3 | no | — |
| 87 | D5×#41 | — | 2 | 3 | no | — |
| 88 | #4144 | — | 2 | 3 | no | — |
| 89 | #4144 | C2×D3 | 1 | 3 | yes | — |
| 90 | C2×D4×D5 | — | 2 | 3 | no | — |
| 91 | C2×D4×D5 | C2×D3 | 1 | 3 | yes | — |
| 92 | C22×D20 | — | 3 | 1 | no | — |
| 93 | C5×#123 | — | 3 | 3 | no | — |
| 94 | #4083 | — | 3 | 3 | no | — |
| 95 | #4075 | — | 3 | 3 | no | — |
| 96 | #4041 | — | 6 | 3 | no | — |
| 97 | #4040 | — | 6 | 3 | no | — |
| 98 | #4030 | — | 6 | 3 | no | — |
| 99 | #4028 | — | 3 | 3 | no | — |
| 100 | #4028 | — | 6 | 3 | no | — |
| 101 | D5×C22⋊C4 | — | 3 | 3 | no | — |
| 102 | C5×#99 | — | 3 | 3 | no | — |
| 103 | #3966 | — | 3 | 3 | no | — |
| 104 | #3938 | — | 3 | 6 | no | — |
| 105 | #3026 | — | 15 | 1 | no | Sylow |
| 106 | C23×C3×C5 | — | 2 | 1 | no | — |
| 107 | C23×C3×C5 | C2×D4 | 1 | 3 | yes | — |
| 108 | C23×C3×C5 | C24 | 1 | 1 | yes | characteristic |
| 109 | C22×D15 | — | 2 | 3 | no | — |
| 110 | C22×D15 | — | 8 | 1 | no | — |
| 111 | C22×C3×D5 | — | 2 | 3 | no | — |
| 112 | C22×C3×D5 | — | 2 | 3 | no | — |
| 113 | C22×C3×D5 | — | 2 | 3 | no | — |
| 114 | C22×C3×D5 | — | 8 | 1 | no | — |
| 115 | C22×C3×D5 | — | 8 | 3 | no | — |
| 116 | C22×C3×D5 | — | 8 | 2 | no | — |
| 117 | C22×C3×D5 | C2×D4 | 1 | 3 | yes | — |
| 118 | C22×C3×D5 | C2×D4 | 1 | 3 | yes | — |
| 119 | C22×C3×D5 | C2×D4 | 1 | 3 | yes | — |
| 120 | C3×C5×Q8 | — | 2 | 1 | no | — |
| 121 | C3×C5×D4 | — | 2 | 3 | no | — |
| 122 | C3×C5×D4 | — | 2 | 6 | no | — |
| 123 | C2×C3×C4×C5 | — | 2 | 3 | no | — |
| 124 | C2×C3×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 125 | #1220 | — | 8 | 3 | no | — |
| 126 | C2×Dic15 | — | 2 | 3 | no | — |
| 127 | C2×C5×Dic3 | — | 2 | 3 | no | — |
| 128 | C2×C5×Dic3 | — | 2 | 3 | no | — |
| 129 | C3×C22⋊D5 | — | 2 | 6 | no | — |
| 130 | C3×C22⋊D5 | — | 2 | 6 | no | — |
| 131 | C3×C22⋊D5 | — | 2 | 6 | no | — |
| 132 | C2×C3×Dic5 | — | 2 | 3 | no | — |
| 133 | C2×C3×Dic5 | C2×D4 | 1 | 3 | yes | — |
| 134 | C3×D20 | — | 2 | 3 | no | — |
| 135 | C3×D20 | — | 2 | 6 | no | — |
| 136 | C3×C4×D5 | — | 2 | 6 | no | — |
| 137 | C3×C4×D5 | — | 2 | 3 | no | — |
| 138 | C3×C4×D5 | — | 2 | 3 | no | — |
| 139 | C3×Dic10 | — | 2 | 3 | no | — |
| 140 | #1202 | — | 4 | 1 | no | — |
| 141 | #1202 | — | 4 | 3 | no | — |
| 142 | #1202 | — | 8 | 3 | no | — |
| 143 | D5×Dic3 | — | 8 | 3 | no | — |
| 144 | C3×H(5,𝔽2) | — | 5 | 3 | no | — |
| 145 | C3×H(5,𝔽2) | — | 10 | 3 | no | — |
| 146 | C3×H(5,𝔽2) | — | 10 | 3 | no | — |
| 147 | C3×H(5,𝔽2) | C2×D5 | 1 | 1 | yes | characteristic |
| 148 | C2×C3×#41 | — | 10 | 3 | no | — |
| 149 | C22×C3×D4 | — | 5 | 3 | no | — |
| 150 | C22×C3×D4 | — | 10 | 3 | no | — |
| 151 | C22×#67 | — | 5 | 1 | no | — |
| 152 | #953 | — | 10 | 3 | no | — |
| 153 | C2×#217 | — | 5 | 3 | no | — |
| 154 | #939 | — | 10 | 3 | no | — |
| 155 | #939 | — | 10 | 3 | no | — |
| 156 | #937 | — | 5 | 3 | no | — |
| 157 | #937 | — | 5 | 3 | no | — |
| 158 | #935 | — | 5 | 3 | no | — |
| 159 | #935 | C2×D5 | 1 | 3 | yes | complemented |
| 160 | #929 | — | 10 | 3 | no | — |
| 161 | #834 | — | 5 | 3 | no | — |
| 162 | #834 | — | 5 | 6 | no | — |
| 163 | #834 | C2×D5 | 1 | 3 | yes | complemented |
| 164 | C23×D5 | — | 2 | 1 | no | — |
| 165 | C23×D5 | — | 3 | 1 | no | — |
| 166 | C23×D5 | #67 | 1 | 3 | yes | complemented |
| 167 | C23×D5 | C22×D3 | 1 | 1 | yes | characteristic |
| 168 | C5×#41 | — | 2 | 3 | no | — |
| 169 | C2×C5×D4 | — | 2 | 3 | no | — |
| 170 | C2×C5×D4 | C22×D3 | 1 | 3 | yes | — |
| 171 | C22×C4×C5 | — | 3 | 1 | no | — |
| 172 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 173 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 174 | C2×C22⋊D5 | — | 6 | 3 | no | — |
| 175 | C2×C22⋊D5 | #67 | 1 | 3 | yes | complemented |
| 176 | C2×C22⋊D5 | C22×D3 | 1 | 3 | yes | — |
| 177 | #713 | — | 2 | 3 | no | — |
| 178 | Q8×D5 | — | 2 | 1 | no | — |
| 179 | #711 | — | 2 | 3 | no | — |
| 180 | #711 | — | 2 | 6 | no | — |
| 181 | D4×D5 | — | 2 | 3 | no | — |
| 182 | D4×D5 | — | 2 | 6 | no | — |
| 183 | D4×D5 | — | 2 | 6 | no | — |
| 184 | D4×D5 | — | 2 | 6 | no | — |
| 185 | D4×D5 | — | 2 | 6 | no | — |
| 186 | #709 | — | 2 | 6 | no | — |
| 187 | #709 | — | 2 | 3 | no | — |
| 188 | C2×D20 | — | 2 | 3 | no | — |
| 189 | C2×D20 | — | 6 | 3 | no | — |
| 190 | C2×D20 | — | 6 | 3 | no | — |
| 191 | C2×D20 | — | 6 | 3 | no | — |
| 192 | C2×D20 | #67 | 1 | 3 | yes | complemented |
| 193 | C2×C4×D5 | — | 2 | 3 | no | — |
| 194 | C2×C4×D5 | — | 6 | 3 | no | — |
| 195 | C2×C4×D5 | #67 | 1 | 3 | yes | complemented |
| 196 | C5×C4⋊C4 | — | 6 | 3 | no | — |
| 197 | C5×C22⋊C4 | — | 3 | 3 | no | — |
| 198 | C5×C22⋊C4 | — | 6 | 3 | no | — |
| 199 | C22⋊Dic5 | — | 3 | 3 | no | — |
| 200 | #685 | — | 6 | 3 | no | — |
| 201 | #685 | — | 6 | 3 | no | — |
| 202 | #685 | — | 6 | 3 | no | — |
| 203 | #685 | — | 6 | 3 | no | — |
| 204 | #683 | — | 6 | 3 | no | — |
| 205 | C2×H(5,𝔽2) | — | 5 | 1 | no | — |
| 206 | #534 | — | 15 | 3 | no | — |
| 207 | #458 | — | 3 | 1 | no | — |
| 208 | #458 | — | 15 | 3 | no | — |
| 209 | B(4,𝔽2) | — | 15 | 3 | no | — |
| 210 | B(4,𝔽2) | — | 15 | 1 | no | — |
| 211 | C2×#99 | — | 15 | 3 | no | — |
| 212 | C22×C3×C5 | — | 2 | 3 | no | — |
| 213 | C22×C3×C5 | — | 4 | 1 | no | — |
| 214 | C22×C3×C5 | — | 4 | 3 | no | — |
| 215 | C22×C3×C5 | — | 8 | 1 | no | — |
| 216 | C22×C3×C5 | C22×D4 | 1 | 3 | yes | — |
| 217 | C2×D15 | — | 4 | 3 | no | — |
| 218 | C2×D15 | — | 4 | 3 | no | — |
| 219 | C2×D15 | — | 4 | 1 | no | — |
| 220 | C2×C3×D5 | — | 2 | 3 | no | — |
| 221 | C2×C3×D5 | — | 4 | 3 | no | — |
| 222 | C2×C3×D5 | — | 4 | 3 | no | — |
| 223 | C2×C3×D5 | — | 4 | 6 | no | — |
| 224 | C2×C3×D5 | — | 4 | 3 | no | — |
| 225 | C2×C3×D5 | — | 8 | 3 | no | — |
| 226 | C2×C3×D5 | — | 8 | 3 | no | — |
| 227 | C2×C3×D5 | #120 | 1 | 1 | yes | characteristic |
| 228 | C2×C3×D5 | #120 | 1 | 3 | yes | — |
| 229 | C3×C4×C5 | — | 2 | 3 | no | — |
| 230 | Dic15 | — | 4 | 3 | no | — |
| 231 | C3×Dic5 | — | 2 | 3 | no | — |
| 232 | C5×Dic3 | — | 4 | 3 | no | — |
| 233 | C5×Dic3 | — | 4 | 1 | no | — |
| 234 | C24×C3 | — | 5 | 1 | no | — |
| 235 | C24×C3 | — | 5 | 3 | no | — |
| 236 | C24×C3 | — | 10 | 1 | no | — |
| 237 | C23×D3 | — | 5 | 1 | no | — |
| 238 | C3×#41 | — | 2 | 3 | no | — |
| 239 | C3×#41 | — | 10 | 6 | no | — |
| 240 | C3×#41 | — | 10 | 6 | no | — |
| 241 | C3×#41 | — | 10 | 3 | no | — |
| 242 | C3×#41 | — | 10 | 3 | no | — |
| 243 | C3×#41 | — | 10 | 3 | no | — |
| 244 | C2×C3×Q8 | — | 10 | 1 | no | — |
| 245 | C2×C3×D4 | — | 2 | 3 | no | — |
| 246 | C2×C3×D4 | — | 5 | 3 | no | — |
| 247 | C2×C3×D4 | — | 5 | 3 | no | — |
| 248 | C2×C3×D4 | — | 5 | 3 | no | — |
| 249 | C2×C3×D4 | — | 10 | 3 | no | — |
| 250 | C2×C3×D4 | — | 10 | 6 | no | — |
| 251 | C2×C3×D4 | — | 10 | 6 | no | — |
| 252 | C2×C3×D4 | — | 10 | 6 | no | — |
| 253 | C2×C3×D4 | — | 10 | 3 | no | — |
| 254 | C2×C3×D4 | — | 10 | 6 | no | — |
| 255 | C2×C3×D4 | — | 10 | 3 | no | — |
| 256 | C2×C3×D4 | — | 10 | 3 | no | — |
| 257 | C2×C3×D4 | C22×D5 | 1 | 3 | yes | — |
| 258 | C22×C3×C4 | — | 5 | 3 | no | — |
| 259 | C22×C3×C4 | — | 10 | 3 | no | — |
| 260 | C2×#67 | — | 10 | 3 | no | — |
| 261 | C2×#67 | — | 10 | 3 | no | — |
| 262 | C2×#67 | — | 10 | 3 | no | — |
| 263 | C2×#67 | — | 10 | 3 | no | — |
| 264 | C22×Dic3 | — | 10 | 3 | no | — |
| 265 | C22×Dic3 | C22×D5 | 1 | 1 | yes | characteristic, complemented |
| 266 | #217 | — | 2 | 3 | no | — |
| 267 | #217 | — | 5 | 3 | no | — |
| 268 | #217 | — | 10 | 3 | no | — |
| 269 | #217 | — | 10 | 3 | no | — |
| 270 | #217 | C22×D5 | 1 | 3 | yes | complemented |
| 271 | (C2×D3)⋊C4 | — | 10 | 3 | no | — |
| 272 | (C2×D3)⋊C4 | — | 10 | 3 | no | — |
| 273 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 274 | Dic3⋊C4 | — | 10 | 3 | no | — |
| 275 | C23×C5 | — | 2 | 1 | no | — |
| 276 | C23×C5 | C2×#67 | 1 | 3 | yes | — |
| 277 | C23×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 278 | C22×D5 | — | 2 | 3 | no | — |
| 279 | C22×D5 | — | 2 | 3 | no | — |
| 280 | C22×D5 | — | 2 | 3 | no | — |
| 281 | C22×D5 | — | 6 | 3 | no | — |
| 282 | C22×D5 | — | 8 | 1 | no | — |
| 283 | C22×D5 | — | 8 | 3 | no | — |
| 284 | C22×D5 | — | 8 | 2 | no | — |
| 285 | C22×D5 | — | 24 | 1 | no | — |
| 286 | C22×D5 | C2×#67 | 1 | 3 | yes | — |
| 287 | C22×D5 | C2×#67 | 1 | 3 | yes | — |
| 288 | C22×D5 | C2×#67 | 1 | 3 | yes | — |
| 289 | C5×Q8 | — | 2 | 1 | no | — |
| 290 | C5×D4 | — | 2 | 3 | no | — |
| 291 | C5×D4 | — | 2 | 6 | no | — |
| 292 | C2×C4×C5 | — | 2 | 3 | no | — |
| 293 | C2×C4×C5 | — | 6 | 3 | no | — |
| 294 | C2×C4×C5 | — | 6 | 3 | no | — |
| 295 | C2×C4×C5 | C2×#67 | 1 | 3 | yes | — |
| 296 | C22⋊D5 | — | 2 | 6 | no | — |
| 297 | C22⋊D5 | — | 2 | 6 | no | — |
| 298 | C22⋊D5 | — | 2 | 6 | no | — |
| 299 | C22⋊D5 | — | 24 | 3 | no | — |
| 300 | C2×Dic5 | — | 2 | 3 | no | — |
| 301 | C2×Dic5 | — | 6 | 3 | no | — |
| 302 | C2×Dic5 | C2×#67 | 1 | 3 | yes | — |
| 303 | D20 | — | 2 | 3 | no | — |
| 304 | D20 | — | 2 | 6 | no | — |
| 305 | D20 | — | 12 | 1 | no | — |
| 306 | D20 | — | 12 | 3 | no | — |
| 307 | D20 | — | 24 | 3 | no | — |
| 308 | C4×D5 | — | 2 | 6 | no | — |
| 309 | C4×D5 | — | 2 | 3 | no | — |
| 310 | C4×D5 | — | 2 | 3 | no | — |
| 311 | C4×D5 | — | 24 | 3 | no | — |
| 312 | Dic10 | — | 2 | 3 | no | — |
| 313 | H(5,𝔽2) | — | 5 | 3 | no | — |
| 314 | H(5,𝔽2) | — | 10 | 3 | no | — |
| 315 | H(5,𝔽2) | — | 10 | 3 | no | — |
| 316 | H(5,𝔽2) | D3×D5 | 1 | 1 | yes | characteristic |
| 317 | C2×#41 | — | 10 | 3 | no | — |
| 318 | C22×D4 | — | 5 | 3 | no | — |
| 319 | C22×D4 | — | 10 | 3 | no | — |
| 320 | C22×D4 | — | 15 | 1 | no | — |
| 321 | #123 | — | 3 | 3 | no | — |
| 322 | #123 | — | 15 | 3 | no | — |
| 323 | #123 | — | 30 | 3 | no | — |
| 324 | #121 | — | 30 | 3 | no | — |
| 325 | #121 | — | 30 | 3 | no | — |
| 326 | #120 | — | 15 | 3 | no | — |
| 327 | #120 | — | 15 | 3 | no | — |
| 328 | #120 | — | 30 | 3 | no | — |
| 329 | C2×C22⋊C4 | — | 15 | 3 | no | — |
| 330 | #99 | — | 3 | 3 | no | — |
| 331 | #99 | — | 15 | 6 | no | — |
| 332 | #99 | — | 15 | 3 | no | — |
| 333 | C2×C3×C5 | — | 2 | 3 | no | — |
| 334 | C2×C3×C5 | — | 4 | 3 | no | — |
| 335 | C2×C3×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 336 | D15 | — | 8 | 1 | no | — |
| 337 | C3×D5 | — | 2 | 1 | no | — |
| 338 | C3×D5 | — | 2 | 3 | no | — |
| 339 | C3×D5 | — | 4 | 3 | no | — |
| 340 | C23×C3 | — | 2 | 1 | no | — |
| 341 | C23×C3 | — | 5 | 3 | no | — |
| 342 | C23×C3 | — | 5 | 3 | no | — |
| 343 | C23×C3 | — | 5 | 3 | no | — |
| 344 | C23×C3 | — | 10 | 3 | no | — |
| 345 | C23×C3 | — | 10 | 3 | no | — |
| 346 | C23×C3 | — | 10 | 3 | no | — |
| 347 | C23×C3 | — | 40 | 1 | no | — |
| 348 | C23×C3 | — | 40 | 3 | no | — |
| 349 | C23×C3 | — | 40 | 2 | no | — |
| 350 | C23×C3 | D4×D5 | 1 | 3 | yes | — |
| 351 | C23×C3 | C23×D5 | 1 | 1 | yes | characteristic |
| 352 | C22×D3 | — | 10 | 3 | no | — |
| 353 | C22×D3 | — | 40 | 1 | no | — |
| 354 | C3×Q8 | — | 2 | 1 | no | — |
| 355 | C3×Q8 | — | 10 | 3 | no | — |
| 356 | C3×D4 | — | 2 | 3 | no | — |
| 357 | C3×D4 | — | 2 | 6 | no | — |
| 358 | C3×D4 | — | 10 | 6 | no | — |
| 359 | C3×D4 | — | 10 | 3 | no | — |
| 360 | C3×D4 | — | 10 | 6 | no | — |
| 361 | C3×D4 | — | 10 | 6 | no | — |
| 362 | C3×D4 | — | 10 | 6 | no | — |
| 363 | C2×C3×C4 | — | 2 | 3 | no | — |
| 364 | C2×C3×C4 | — | 5 | 3 | no | — |
| 365 | C2×C3×C4 | — | 10 | 3 | no | — |
| 366 | C2×C3×C4 | — | 10 | 3 | no | — |
| 367 | C2×C3×C4 | — | 10 | 6 | no | — |
| 368 | C2×C3×C4 | — | 10 | 3 | no | — |
| 369 | C2×C3×C4 | D4×D5 | 1 | 3 | yes | — |
| 370 | #67 | — | 20 | 1 | no | — |
| 371 | #67 | — | 20 | 3 | no | — |
| 372 | #67 | — | 40 | 3 | no | — |
| 373 | #67 | — | 40 | 3 | no | — |
| 374 | C2×Dic3 | — | 2 | 3 | no | — |
| 375 | C2×Dic3 | — | 2 | 3 | no | — |
| 376 | C2×Dic3 | — | 10 | 3 | no | — |
| 377 | C2×Dic3 | — | 40 | 3 | no | — |
| 378 | C22×C5 | — | 2 | 3 | no | — |
| 379 | C22×C5 | — | 4 | 1 | no | — |
| 380 | C22×C5 | — | 4 | 3 | no | — |
| 381 | C22×C5 | — | 8 | 1 | no | — |
| 382 | C22×C5 | C22×#67 | 1 | 3 | yes | — |
| 383 | C2×D5 | — | 2 | 3 | no | — |
| 384 | C2×D5 | — | 4 | 3 | no | — |
| 385 | C2×D5 | — | 4 | 3 | no | — |
| 386 | C2×D5 | — | 4 | 6 | no | — |
| 387 | C2×D5 | — | 4 | 3 | no | — |
| 388 | C2×D5 | — | 8 | 3 | no | — |
| 389 | C2×D5 | — | 8 | 3 | no | — |
| 390 | C2×D5 | — | 12 | 3 | no | — |
| 391 | C2×D5 | — | 12 | 3 | no | — |
| 392 | C2×D5 | — | 12 | 1 | no | — |
| 393 | C2×D5 | #953 | 1 | 1 | yes | characteristic |
| 394 | C2×D5 | #953 | 1 | 3 | yes | — |
| 395 | C4×C5 | — | 2 | 3 | no | — |
| 396 | C4×C5 | — | 12 | 3 | no | — |
| 397 | C4×C5 | — | 12 | 1 | no | — |
| 398 | Dic5 | — | 2 | 3 | no | — |
| 399 | Dic5 | — | 12 | 3 | no | — |
| 400 | C24 | — | 5 | 1 | no | — |
| 401 | C24 | — | 5 | 3 | no | — |
| 402 | C24 | — | 10 | 1 | no | — |
| 403 | C24 | — | 15 | 1 | no | — |
| 404 | #41 | — | 2 | 3 | no | — |
| 405 | #41 | — | 10 | 6 | no | — |
| 406 | #41 | — | 10 | 6 | no | — |
| 407 | #41 | — | 10 | 3 | no | — |
| 408 | #41 | — | 10 | 3 | no | — |
| 409 | #41 | — | 10 | 3 | no | — |
| 410 | C2×Q8 | — | 10 | 1 | no | — |
| 411 | C2×D4 | — | 2 | 3 | no | — |
| 412 | C2×D4 | — | 5 | 3 | no | — |
| 413 | C2×D4 | — | 5 | 3 | no | — |
| 414 | C2×D4 | — | 5 | 3 | no | — |
| 415 | C2×D4 | — | 10 | 3 | no | — |
| 416 | C2×D4 | — | 10 | 6 | no | — |
| 417 | C2×D4 | — | 10 | 6 | no | — |
| 418 | C2×D4 | — | 10 | 6 | no | — |
| 419 | C2×D4 | — | 10 | 3 | no | — |
| 420 | C2×D4 | — | 10 | 6 | no | — |
| 421 | C2×D4 | — | 10 | 3 | no | — |
| 422 | C2×D4 | — | 10 | 3 | no | — |
| 423 | C2×D4 | — | 30 | 3 | no | — |
| 424 | C2×D4 | — | 30 | 3 | no | — |
| 425 | C2×D4 | — | 30 | 3 | no | — |
| 426 | C2×D4 | — | 30 | 3 | no | — |
| 427 | C2×D4 | C2×D3×D5 | 1 | 3 | yes | — |
| 428 | C22×C4 | — | 3 | 1 | no | — |
| 429 | C22×C4 | — | 5 | 3 | no | — |
| 430 | C22×C4 | — | 10 | 3 | no | — |
| 431 | C22×C4 | — | 30 | 3 | no | — |
| 432 | C4⋊C4 | — | 6 | 3 | no | — |
| 433 | C4⋊C4 | — | 30 | 3 | no | — |
| 434 | C22⋊C4 | — | 3 | 3 | no | — |
| 435 | C22⋊C4 | — | 6 | 3 | no | — |
| 436 | C22⋊C4 | — | 15 | 3 | no | — |
| 437 | C22⋊C4 | — | 30 | 3 | no | — |
| 438 | C22⋊C4 | — | 30 | 3 | no | — |
| 439 | C22⋊C4 | — | 30 | 3 | no | — |
| 440 | C22⋊C4 | — | 30 | 3 | no | — |
| 441 | C3×C5 | #3026 | 1 | 1 | yes | characteristic, complemented, Hall |
| 442 | C22×C3 | — | 2 | 3 | no | — |
| 443 | C22×C3 | — | 4 | 1 | no | — |
| 444 | C22×C3 | — | 4 | 3 | no | — |
| 445 | C22×C3 | — | 5 | 1 | no | — |
| 446 | C22×C3 | — | 5 | 3 | no | — |
| 447 | C22×C3 | — | 8 | 1 | no | — |
| 448 | C22×C3 | — | 10 | 3 | no | — |
| 449 | C22×C3 | — | 20 | 3 | no | — |
| 450 | C22×C3 | — | 20 | 3 | no | — |
| 451 | C22×C3 | — | 20 | 3 | no | — |
| 452 | C22×C3 | — | 20 | 6 | no | — |
| 453 | C22×C3 | — | 40 | 3 | no | — |
| 454 | C22×C3 | — | 40 | 3 | no | — |
| 455 | C22×C3 | C2×D4×D5 | 1 | 3 | yes | — |
| 456 | C2×D3 | — | 20 | 3 | no | — |
| 457 | C2×D3 | — | 20 | 3 | no | — |
| 458 | C2×D3 | — | 20 | 1 | no | — |
| 459 | C3×C4 | — | 2 | 3 | no | — |
| 460 | C3×C4 | — | 10 | 3 | no | — |
| 461 | Dic3 | — | 4 | 3 | no | — |
| 462 | Dic3 | — | 4 | 1 | no | — |
| 463 | Dic3 | — | 20 | 3 | no | — |
| 464 | C2×C5 | — | 2 | 3 | no | — |
| 465 | C2×C5 | — | 4 | 3 | no | — |
| 466 | C2×C5 | C2×#953 | 1 | 1 | yes | characteristic |
| 467 | D5 | — | 2 | 1 | no | — |
| 468 | D5 | — | 2 | 3 | no | — |
| 469 | D5 | — | 4 | 3 | no | — |
| 470 | D5 | — | 24 | 1 | no | — |
| 471 | C23 | — | 2 | 1 | no | — |
| 472 | C23 | — | 5 | 3 | no | — |
| 473 | C23 | — | 5 | 3 | no | — |
| 474 | C23 | — | 5 | 3 | no | — |
| 475 | C23 | — | 10 | 3 | no | — |
| 476 | C23 | — | 10 | 3 | no | — |
| 477 | C23 | — | 10 | 3 | no | — |
| 478 | C23 | — | 30 | 3 | no | — |
| 479 | C23 | — | 40 | 1 | no | — |
| 480 | C23 | — | 40 | 3 | no | — |
| 481 | C23 | — | 40 | 2 | no | — |
| 482 | C23 | — | 120 | 1 | no | — |
| 483 | C23 | D5×#67 | 1 | 3 | yes | — |
| 484 | C23 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 485 | Q8 | — | 2 | 1 | no | — |
| 486 | Q8 | — | 10 | 3 | no | — |
| 487 | D4 | — | 2 | 3 | no | — |
| 488 | D4 | — | 2 | 6 | no | — |
| 489 | D4 | — | 10 | 6 | no | — |
| 490 | D4 | — | 10 | 3 | no | — |
| 491 | D4 | — | 10 | 6 | no | — |
| 492 | D4 | — | 10 | 6 | no | — |
| 493 | D4 | — | 10 | 6 | no | — |
| 494 | D4 | — | 60 | 1 | no | — |
| 495 | D4 | — | 60 | 3 | no | — |
| 496 | D4 | — | 120 | 3 | no | — |
| 497 | D4 | — | 120 | 3 | no | — |
| 498 | C2×C4 | — | 2 | 3 | no | — |
| 499 | C2×C4 | — | 5 | 3 | no | — |
| 500 | C2×C4 | — | 6 | 3 | no | — |
| 501 | C2×C4 | — | 6 | 3 | no | — |
| 502 | C2×C4 | — | 10 | 3 | no | — |
| 503 | C2×C4 | — | 10 | 3 | no | — |
| 504 | C2×C4 | — | 10 | 6 | no | — |
| 505 | C2×C4 | — | 10 | 3 | no | — |
| 506 | C2×C4 | — | 30 | 3 | no | — |
| 507 | C2×C4 | — | 120 | 3 | no | — |
| 508 | C2×C4 | D5×#67 | 1 | 3 | yes | — |
| 509 | C2×C3 | — | 2 | 3 | no | — |
| 510 | C2×C3 | — | 4 | 3 | no | — |
| 511 | C2×C3 | — | 10 | 1 | no | — |
| 512 | C2×C3 | — | 10 | 3 | no | — |
| 513 | C2×C3 | — | 20 | 3 | no | — |
| 514 | C2×C3 | D5×#120 | 1 | 1 | yes | characteristic |
| 515 | D3 | — | 40 | 1 | no | — |
| 516 | C5 | #84110 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 517 | C22 | — | 2 | 3 | no | — |
| 518 | C22 | — | 4 | 1 | no | — |
| 519 | C22 | — | 4 | 3 | no | — |
| 520 | C22 | — | 5 | 1 | no | — |
| 521 | C22 | — | 5 | 3 | no | — |
| 522 | C22 | — | 8 | 1 | no | — |
| 523 | C22 | — | 10 | 3 | no | — |
| 524 | C22 | — | 20 | 3 | no | — |
| 525 | C22 | — | 20 | 3 | no | — |
| 526 | C22 | — | 20 | 3 | no | — |
| 527 | C22 | — | 20 | 6 | no | — |
| 528 | C22 | — | 40 | 3 | no | — |
| 529 | C22 | — | 40 | 3 | no | — |
| 530 | C22 | — | 60 | 3 | no | — |
| 531 | C22 | — | 60 | 3 | no | — |
| 532 | C22 | — | 60 | 1 | no | — |
| 533 | C22 | C2×D5×#67 | 1 | 3 | yes | — |
| 534 | C4 | — | 2 | 3 | no | — |
| 535 | C4 | — | 10 | 3 | no | — |
| 536 | C4 | — | 12 | 3 | no | — |
| 537 | C4 | — | 12 | 1 | no | — |
| 538 | C4 | — | 60 | 3 | no | — |
| 539 | C3 | #10612042 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 540 | C2 | — | 2 | 3 | no | — |
| 541 | C2 | — | 4 | 3 | no | — |
| 542 | C2 | — | 10 | 1 | no | — |
| 543 | C2 | — | 10 | 3 | no | — |
| 544 | C2 | — | 20 | 3 | no | — |
| 545 | C2 | — | 120 | 1 | no | — |
| 546 | C2 | D5×#953 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×D5×H(5,𝔽2) | C2 | semidirect |
| 2. #11754936 | C2 | semidirect |
| 3. #11751345 | C2 | semidirect |
| 4. C5×#5243 | C2 | semidirect |
| 5. #11749181 | C2 | semidirect |
| 6. #11749176 | C2 | semidirect |
| 7. D5×#834 | C2 | semidirect |
| 16. C22×#1202 | C22 | semidirect |
| 17. #91826 | C22 | semidirect |
| 18. C5×#935 | C22 | semidirect |
| 19. #91572 | C22 | semidirect |
| 22. D5×#217 | C22 | semidirect |
| 23. #91536 | C22 | semidirect |
| 26. #91118 | C22 | semidirect |
| 27. C5×#834 | C22 | semidirect |
| 28. #90995 | C22 | semidirect |
| 30. D5×H(5,𝔽2) | D3 | semidirect |
| 37. C23×D15 | C23 | semidirect |
| 39. C23×C3×D5 | D4 | semidirect |
| 45. C22×C5×Dic3 | C23 | semidirect |
| 48. C2×C3×C22⋊D5 | D4 | semidirect |
| 62. C2×C3×D20 | D4 | semidirect |
| 64. C2×C3×C4×D5 | D4 | semidirect |
| 69. #6719 | C23 | semidirect |
| 72. C5×#217 | C23 | semidirect |
| 83. #5243 | D5 | semidirect |
| 159. #935 | C2×D5 | semidirect |
| 163. #834 | C2×D5 | semidirect |
| 166. C23×D5 | #67 | semidirect |
| 175. C2×C22⋊D5 | #67 | semidirect |
| 192. C2×D20 | #67 | semidirect |
| 195. C2×C4×D5 | #67 | semidirect |
| 265. C22×Dic3 | C22×D5 | semidirect |
| 270. #217 | C22×D5 | semidirect |
| 441. C3×C5 | #3026 | semidirect |
| 516. C5 | #84110 | semidirect |
| 539. C3 | #10612042 | 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 |
| #11754936 | 2 |
| #11751345 | 2 |
| C5×#5243 | 2 |
| #11749181 | 2 |
| #11749176 | 2 |
| D5×#834 | 2 |
| #10612042 | 3 |
| #84110 | 5 |