Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1432 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1432 conjugacy classes of subgroups — too many to draw. Only its 187 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 | #11757148 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11756407 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×C5×#458 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11751344 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11751154 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11750843 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11750841 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10612040 | — | 3 | 1 | no | maximal, Hall |
| 9 | C3×C5×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 10 | #92101 | — | 2 | 3 | no | — |
| 11 | #41×D15 | — | 2 | 3 | no | — |
| 12 | #92095 | — | 2 | 3 | no | — |
| 13 | #92095 | C22 | 1 | 3 | yes | — |
| 14 | C2×#6819 | — | 2 | 3 | no | — |
| 15 | C2×#6819 | C22 | 1 | 3 | yes | — |
| 16 | C22×Dic30 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C3×C5×#123 | C22 | 1 | 3 | yes | complemented |
| 18 | #91824 | C22 | 1 | 3 | yes | complemented |
| 19 | #91818 | C22 | 1 | 3 | yes | complemented |
| 20 | #91785 | — | 2 | 3 | no | — |
| 21 | #91777 | — | 2 | 3 | no | — |
| 22 | #91775 | C22 | 1 | 3 | yes | complemented |
| 23 | #91774 | — | 2 | 3 | no | — |
| 24 | #91767 | — | 2 | 3 | no | — |
| 25 | #91766 | C22 | 1 | 3 | yes | complemented |
| 26 | C3×C5×#99 | C22 | 1 | 3 | yes | complemented |
| 27 | #91118 | C22 | 1 | 3 | yes | complemented |
| 28 | #91090 | C22 | 1 | 6 | yes | complemented |
| 29 | #80309 | — | 5 | 1 | no | maximal, Hall |
| 30 | #66285 | — | 3 | 1 | no | — |
| 31 | #65982 | — | 3 | 3 | no | — |
| 32 | C5×#458 | D3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #65532 | — | 3 | 1 | no | — |
| 34 | #65342 | — | 3 | 3 | no | — |
| 35 | #65031 | — | 3 | 3 | no | — |
| 36 | #65029 | — | 3 | 3 | no | — |
| 37 | C3×C5×#41 | — | 2 | 3 | no | — |
| 38 | C2×C3×C5×D4 | — | 2 | 3 | no | — |
| 39 | C2×C3×C5×D4 | C23 | 1 | 3 | yes | — |
| 40 | C22×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 41 | C2×#1220 | — | 2 | 3 | no | — |
| 42 | C2×#1220 | — | 2 | 3 | no | — |
| 43 | C2×#1220 | D4 | 1 | 3 | yes | — |
| 44 | C2×#1220 | C23 | 1 | 3 | yes | — |
| 45 | C22×Dic15 | — | 2 | 1 | no | — |
| 46 | C22×Dic15 | D4 | 1 | 3 | yes | — |
| 47 | C22×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 48 | C22×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 49 | #6821 | — | 2 | 1 | no | — |
| 50 | Q8×D15 | — | 2 | 3 | no | — |
| 51 | #6819 | — | 2 | 3 | no | — |
| 52 | #6819 | — | 2 | 6 | no | — |
| 53 | #6819 | — | 2 | 6 | no | — |
| 54 | #6819 | — | 2 | 6 | no | — |
| 55 | #6819 | — | 2 | 6 | no | — |
| 56 | D4×D15 | — | 2 | 3 | no | — |
| 57 | D4×D15 | — | 2 | 6 | no | — |
| 58 | #6817 | — | 2 | 6 | no | — |
| 59 | #6817 | — | 2 | 3 | no | — |
| 60 | C2×C4×D15 | — | 2 | 3 | no | — |
| 61 | C2×C4×D15 | D4 | 1 | 3 | yes | — |
| 62 | C2×Dic30 | — | 2 | 3 | no | — |
| 63 | C2×Dic30 | — | 2 | 3 | no | — |
| 64 | C2×Dic30 | — | 2 | 3 | no | — |
| 65 | C2×Dic30 | D4 | 1 | 3 | yes | — |
| 66 | C3×C5×C4⋊C4 | — | 2 | 3 | no | — |
| 67 | C3×C5×C22⋊C4 | — | 2 | 3 | no | — |
| 68 | C3×C5×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 69 | #6719 | — | 2 | 3 | no | — |
| 70 | #6719 | C23 | 1 | 3 | yes | — |
| 71 | #6714 | — | 2 | 3 | no | — |
| 72 | #6714 | — | 2 | 3 | no | — |
| 73 | C4⋊Dic15 | — | 2 | 3 | no | — |
| 74 | #6712 | — | 2 | 3 | no | — |
| 75 | #6712 | — | 2 | 3 | no | — |
| 76 | #6712 | — | 2 | 3 | no | — |
| 77 | C4×Dic15 | — | 2 | 3 | no | — |
| 78 | #5966 | — | 5 | 1 | no | — |
| 79 | #5648 | — | 5 | 3 | no | — |
| 80 | C3×#458 | D5 | 1 | 1 | yes | characteristic, complemented |
| 81 | #5243 | — | 5 | 1 | no | — |
| 82 | #5053 | — | 5 | 3 | no | — |
| 83 | #4742 | — | 5 | 3 | no | — |
| 84 | #4740 | — | 5 | 3 | no | — |
| 85 | C5×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 86 | #4150 | — | 6 | 3 | no | — |
| 87 | D5×#41 | — | 6 | 3 | no | — |
| 88 | #4144 | — | 3 | 3 | no | — |
| 89 | #4144 | — | 6 | 3 | no | — |
| 90 | C2×#711 | — | 3 | 3 | no | — |
| 91 | C2×#711 | — | 6 | 3 | no | — |
| 92 | C22×Dic10 | — | 3 | 1 | no | — |
| 93 | C5×#123 | C2×D3 | 1 | 3 | yes | complemented |
| 94 | #4081 | — | 3 | 3 | no | — |
| 95 | #4075 | — | 3 | 3 | no | — |
| 96 | #4042 | — | 6 | 3 | no | — |
| 97 | #4034 | — | 6 | 3 | no | — |
| 98 | #4032 | — | 3 | 3 | no | — |
| 99 | #4031 | — | 6 | 3 | no | — |
| 100 | #4024 | — | 6 | 3 | no | — |
| 101 | #4023 | — | 3 | 3 | no | — |
| 102 | C5×#99 | C2×D3 | 1 | 3 | yes | complemented |
| 103 | #3966 | — | 3 | 3 | no | — |
| 104 | #3938 | — | 3 | 6 | no | — |
| 105 | #3028 | — | 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 | C2×D4 | 1 | 3 | yes | — |
| 111 | C3×C5×Q8 | — | 2 | 1 | no | — |
| 112 | C3×C5×D4 | — | 2 | 3 | no | — |
| 113 | C3×C5×D4 | — | 2 | 6 | no | — |
| 114 | C2×C3×C4×C5 | — | 2 | 3 | no | — |
| 115 | C2×C3×C4×C5 | — | 2 | 3 | no | — |
| 116 | C2×C3×C4×C5 | — | 2 | 3 | no | — |
| 117 | C2×C3×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 118 | #1220 | — | 2 | 6 | no | — |
| 119 | #1220 | — | 2 | 6 | no | — |
| 120 | #1220 | — | 2 | 6 | no | — |
| 121 | C2×Dic15 | — | 2 | 3 | no | — |
| 122 | C2×Dic15 | — | 2 | 3 | no | — |
| 123 | C2×Dic15 | — | 2 | 3 | no | — |
| 124 | C2×Dic15 | — | 2 | 3 | no | — |
| 125 | C2×Dic15 | — | 2 | 3 | no | — |
| 126 | C2×Dic15 | C2×D4 | 1 | 3 | yes | — |
| 127 | C2×Dic15 | C2×D4 | 1 | 3 | yes | — |
| 128 | C2×Dic15 | C2×D4 | 1 | 3 | yes | — |
| 129 | D60 | — | 2 | 3 | no | — |
| 130 | C4×D15 | — | 2 | 6 | no | — |
| 131 | C4×D15 | — | 2 | 3 | no | — |
| 132 | C4×D15 | — | 2 | 3 | no | — |
| 133 | Dic30 | — | 2 | 3 | no | — |
| 134 | Dic30 | — | 2 | 6 | no | — |
| 135 | Dic30 | — | 4 | 3 | no | — |
| 136 | Dic30 | — | 4 | 1 | no | — |
| 137 | C3×H(5,𝔽2) | C2×D5 | 1 | 1 | yes | characteristic |
| 138 | #1010 | — | 10 | 3 | no | — |
| 139 | D3×#41 | — | 10 | 3 | no | — |
| 140 | #1004 | — | 5 | 3 | no | — |
| 141 | #1004 | — | 10 | 3 | no | — |
| 142 | C2×#237 | — | 5 | 3 | no | — |
| 143 | C2×#237 | — | 10 | 3 | no | — |
| 144 | C22×Dic6 | — | 5 | 1 | no | — |
| 145 | C3×#123 | C2×D5 | 1 | 3 | yes | complemented |
| 146 | #935 | — | 5 | 3 | no | — |
| 147 | #929 | — | 5 | 3 | no | — |
| 148 | #896 | — | 10 | 3 | no | — |
| 149 | #888 | — | 10 | 3 | no | — |
| 150 | #886 | — | 5 | 3 | no | — |
| 151 | #885 | — | 10 | 3 | no | — |
| 152 | #878 | — | 10 | 3 | no | — |
| 153 | #877 | — | 5 | 3 | no | — |
| 154 | C3×#99 | C2×D5 | 1 | 3 | yes | complemented |
| 155 | #834 | — | 5 | 3 | no | — |
| 156 | #806 | — | 5 | 6 | no | — |
| 157 | C5×#41 | — | 2 | 3 | no | — |
| 158 | C2×C5×D4 | — | 2 | 3 | no | — |
| 159 | C2×C5×D4 | C22×D3 | 1 | 3 | yes | — |
| 160 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 161 | C2×C22⋊D5 | — | 3 | 3 | no | — |
| 162 | C2×C22⋊D5 | — | 3 | 3 | no | — |
| 163 | C2×C22⋊D5 | — | 6 | 3 | no | — |
| 164 | C2×C22⋊D5 | — | 6 | 3 | no | — |
| 165 | C22×Dic5 | — | 3 | 1 | no | — |
| 166 | C22×Dic5 | — | 3 | 3 | no | — |
| 167 | C22×Dic5 | — | 3 | 1 | no | — |
| 168 | C22×Dic5 | — | 6 | 1 | no | — |
| 169 | #713 | — | 6 | 1 | no | — |
| 170 | Q8×D5 | — | 6 | 3 | no | — |
| 171 | #711 | — | 6 | 6 | no | — |
| 172 | #711 | — | 6 | 6 | no | — |
| 173 | #711 | — | 6 | 6 | no | — |
| 174 | #711 | — | 6 | 3 | no | — |
| 175 | #711 | — | 6 | 6 | no | — |
| 176 | D4×D5 | — | 6 | 6 | no | — |
| 177 | D4×D5 | — | 6 | 3 | no | — |
| 178 | #709 | — | 6 | 6 | no | — |
| 179 | #709 | — | 6 | 3 | no | — |
| 180 | C2×C4×D5 | — | 3 | 3 | no | — |
| 181 | C2×C4×D5 | — | 6 | 3 | no | — |
| 182 | C2×Dic10 | — | 3 | 3 | no | — |
| 183 | C2×Dic10 | — | 6 | 3 | no | — |
| 184 | C2×Dic10 | — | 6 | 3 | no | — |
| 185 | C2×Dic10 | — | 6 | 3 | no | — |
| 186 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 187 | C5×C22⋊C4 | — | 2 | 3 | no | — |
| 188 | C5×C22⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 189 | C22⋊Dic5 | — | 3 | 3 | no | — |
| 190 | C22⋊Dic5 | — | 6 | 3 | no | — |
| 191 | #685 | — | 6 | 3 | no | — |
| 192 | #685 | — | 6 | 3 | no | — |
| 193 | C4⋊Dic5 | — | 6 | 3 | no | — |
| 194 | #683 | — | 6 | 3 | no | — |
| 195 | #683 | — | 6 | 3 | no | — |
| 196 | #683 | — | 6 | 3 | no | — |
| 197 | C4×Dic5 | — | 6 | 3 | no | — |
| 198 | #585 | — | 15 | 1 | no | — |
| 199 | #536 | — | 15 | 3 | no | — |
| 200 | #458 | — | 15 | 1 | no | — |
| 201 | #458 | — | 15 | 3 | no | — |
| 202 | #458 | — | 15 | 3 | no | — |
| 203 | #458 | D15 | 1 | 1 | yes | characteristic, complemented |
| 204 | #410 | — | 15 | 3 | no | — |
| 205 | C22×C3×C5 | — | 2 | 3 | no | — |
| 206 | C22×C3×C5 | — | 4 | 1 | no | — |
| 207 | C22×C3×C5 | — | 4 | 3 | no | — |
| 208 | C22×C3×C5 | — | 8 | 1 | no | — |
| 209 | C22×C3×C5 | C22×D4 | 1 | 3 | yes | — |
| 210 | C2×D15 | — | 2 | 3 | no | — |
| 211 | C2×D15 | — | 4 | 3 | no | — |
| 212 | C2×D15 | — | 8 | 3 | no | — |
| 213 | C3×C4×C5 | — | 2 | 3 | no | — |
| 214 | C3×C4×C5 | — | 4 | 3 | no | — |
| 215 | C3×C4×C5 | — | 4 | 1 | no | — |
| 216 | Dic15 | — | 2 | 3 | no | — |
| 217 | Dic15 | — | 4 | 3 | no | — |
| 218 | Dic15 | — | 4 | 1 | no | — |
| 219 | Dic15 | #120 | 1 | 3 | yes | — |
| 220 | Dic15 | #120 | 1 | 1 | yes | characteristic |
| 221 | C3×#41 | — | 2 | 3 | no | — |
| 222 | C2×C3×D4 | — | 2 | 3 | no | — |
| 223 | C2×C3×D4 | C22×D5 | 1 | 3 | yes | — |
| 224 | C22×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 225 | C2×#67 | — | 5 | 3 | no | — |
| 226 | C2×#67 | — | 5 | 3 | no | — |
| 227 | C2×#67 | — | 10 | 3 | no | — |
| 228 | C2×#67 | — | 10 | 3 | no | — |
| 229 | C22×Dic3 | — | 5 | 1 | no | — |
| 230 | C22×Dic3 | — | 5 | 3 | no | — |
| 231 | C22×Dic3 | — | 5 | 1 | no | — |
| 232 | C22×Dic3 | — | 10 | 1 | no | — |
| 233 | #239 | — | 10 | 1 | no | — |
| 234 | D3×Q8 | — | 10 | 3 | no | — |
| 235 | #237 | — | 10 | 6 | no | — |
| 236 | #237 | — | 10 | 6 | no | — |
| 237 | #237 | — | 10 | 6 | no | — |
| 238 | #237 | — | 10 | 3 | no | — |
| 239 | #237 | — | 10 | 6 | no | — |
| 240 | D3×D4 | — | 10 | 6 | no | — |
| 241 | D3×D4 | — | 10 | 3 | no | — |
| 242 | #235 | — | 10 | 6 | no | — |
| 243 | #235 | — | 10 | 3 | no | — |
| 244 | C2×C4×D3 | — | 5 | 3 | no | — |
| 245 | C2×C4×D3 | — | 10 | 3 | no | — |
| 246 | C2×Dic6 | — | 5 | 3 | no | — |
| 247 | C2×Dic6 | — | 10 | 3 | no | — |
| 248 | C2×Dic6 | — | 10 | 3 | no | — |
| 249 | C2×Dic6 | — | 10 | 3 | no | — |
| 250 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 251 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 252 | C3×C22⋊C4 | C22×D5 | 1 | 3 | yes | — |
| 253 | #217 | — | 5 | 3 | no | — |
| 254 | #217 | — | 10 | 3 | no | — |
| 255 | (C2×D3)⋊C4 | — | 10 | 3 | no | — |
| 256 | (C2×D3)⋊C4 | — | 10 | 3 | no | — |
| 257 | C4⋊Dic3 | — | 10 | 3 | no | — |
| 258 | Dic3⋊C4 | — | 10 | 3 | no | — |
| 259 | Dic3⋊C4 | — | 10 | 3 | no | — |
| 260 | Dic3⋊C4 | — | 10 | 3 | no | — |
| 261 | C4×Dic3 | — | 10 | 3 | no | — |
| 262 | C23×C5 | — | 2 | 1 | no | — |
| 263 | C23×C5 | D3×D4 | 1 | 3 | yes | — |
| 264 | C23×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 265 | C22×D5 | — | 3 | 3 | no | — |
| 266 | C22×D5 | — | 6 | 3 | no | — |
| 267 | C5×Q8 | — | 2 | 1 | no | — |
| 268 | C5×D4 | — | 2 | 3 | no | — |
| 269 | C5×D4 | — | 2 | 6 | no | — |
| 270 | C2×C4×C5 | — | 2 | 3 | no | — |
| 271 | C2×C4×C5 | — | 2 | 3 | no | — |
| 272 | C2×C4×C5 | — | 2 | 3 | no | — |
| 273 | C2×C4×C5 | D3×D4 | 1 | 3 | yes | — |
| 274 | C22⋊D5 | — | 6 | 6 | no | — |
| 275 | C22⋊D5 | — | 6 | 6 | no | — |
| 276 | C22⋊D5 | — | 6 | 6 | no | — |
| 277 | C2×Dic5 | — | 3 | 3 | no | — |
| 278 | C2×Dic5 | — | 3 | 3 | no | — |
| 279 | C2×Dic5 | — | 3 | 3 | no | — |
| 280 | C2×Dic5 | — | 6 | 3 | no | — |
| 281 | C2×Dic5 | — | 6 | 3 | no | — |
| 282 | C2×Dic5 | — | 6 | 3 | no | — |
| 283 | C2×Dic5 | — | 6 | 3 | no | — |
| 284 | C2×Dic5 | — | 6 | 3 | no | — |
| 285 | D20 | — | 6 | 3 | no | — |
| 286 | C4×D5 | — | 6 | 3 | no | — |
| 287 | C4×D5 | — | 6 | 3 | no | — |
| 288 | C4×D5 | — | 6 | 6 | no | — |
| 289 | Dic10 | — | 6 | 6 | no | — |
| 290 | Dic10 | — | 6 | 3 | no | — |
| 291 | Dic10 | — | 12 | 3 | no | — |
| 292 | Dic10 | — | 12 | 1 | no | — |
| 293 | 2−1+4 | — | 30 | 3 | no | — |
| 294 | H(5,𝔽2) | — | 15 | 3 | no | — |
| 295 | H(5,𝔽2) | — | 30 | 3 | no | — |
| 296 | H(5,𝔽2) | C2×D15 | 1 | 1 | yes | characteristic |
| 297 | C2×#41 | — | 15 | 3 | no | — |
| 298 | C2×#41 | — | 30 | 3 | no | — |
| 299 | C2×#41 | — | 30 | 3 | no | — |
| 300 | C22×Q8 | — | 15 | 1 | no | — |
| 301 | C4⋊Q8 | — | 30 | 3 | no | — |
| 302 | #124 | — | 30 | 3 | no | — |
| 303 | #123 | — | 15 | 3 | no | — |
| 304 | #123 | — | 15 | 3 | no | — |
| 305 | #123 | — | 15 | 3 | no | — |
| 306 | #123 | C2×D15 | 1 | 3 | yes | complemented |
| 307 | C22⋊Q8 | — | 30 | 3 | no | — |
| 308 | C22⋊Q8 | — | 30 | 3 | no | — |
| 309 | #117 | — | 15 | 3 | no | — |
| 310 | #99 | — | 15 | 3 | no | — |
| 311 | #99 | — | 15 | 6 | no | — |
| 312 | #99 | C2×D15 | 1 | 3 | yes | complemented |
| 313 | C2×C3×C5 | — | 2 | 3 | no | — |
| 314 | C2×C3×C5 | — | 4 | 3 | no | — |
| 315 | C2×C3×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 316 | D15 | — | 4 | 3 | no | — |
| 317 | C23×C3 | — | 2 | 1 | no | — |
| 318 | C23×C3 | D4×D5 | 1 | 3 | yes | — |
| 319 | C23×C3 | C23×D5 | 1 | 1 | yes | characteristic |
| 320 | C22×D3 | — | 5 | 3 | no | — |
| 321 | C22×D3 | — | 10 | 3 | no | — |
| 322 | C3×Q8 | — | 2 | 1 | no | — |
| 323 | C3×D4 | — | 2 | 3 | no | — |
| 324 | C3×D4 | — | 2 | 6 | no | — |
| 325 | C2×C3×C4 | — | 2 | 3 | no | — |
| 326 | C2×C3×C4 | — | 2 | 3 | no | — |
| 327 | C2×C3×C4 | — | 2 | 3 | no | — |
| 328 | C2×C3×C4 | D4×D5 | 1 | 3 | yes | — |
| 329 | #67 | — | 10 | 6 | no | — |
| 330 | #67 | — | 10 | 6 | no | — |
| 331 | #67 | — | 10 | 6 | no | — |
| 332 | C2×Dic3 | — | 5 | 3 | no | — |
| 333 | C2×Dic3 | — | 5 | 3 | no | — |
| 334 | C2×Dic3 | — | 5 | 3 | no | — |
| 335 | C2×Dic3 | — | 10 | 3 | no | — |
| 336 | C2×Dic3 | — | 10 | 3 | no | — |
| 337 | C2×Dic3 | — | 10 | 3 | no | — |
| 338 | C2×Dic3 | — | 10 | 3 | no | — |
| 339 | C2×Dic3 | — | 10 | 3 | no | — |
| 340 | D12 | — | 10 | 3 | no | — |
| 341 | C4×D3 | — | 10 | 3 | no | — |
| 342 | C4×D3 | — | 10 | 3 | no | — |
| 343 | C4×D3 | — | 10 | 6 | no | — |
| 344 | Dic6 | — | 10 | 6 | no | — |
| 345 | Dic6 | — | 10 | 3 | no | — |
| 346 | Dic6 | — | 20 | 3 | no | — |
| 347 | Dic6 | — | 20 | 1 | no | — |
| 348 | C22×C5 | — | 2 | 3 | no | — |
| 349 | C22×C5 | — | 4 | 1 | no | — |
| 350 | C22×C5 | — | 4 | 3 | no | — |
| 351 | C22×C5 | — | 8 | 1 | no | — |
| 352 | C22×C5 | C2×D3×D4 | 1 | 3 | yes | — |
| 353 | C2×D5 | — | 6 | 3 | no | — |
| 354 | C2×D5 | — | 12 | 3 | no | — |
| 355 | C2×D5 | — | 24 | 3 | no | — |
| 356 | C4×C5 | — | 2 | 3 | no | — |
| 357 | C4×C5 | — | 4 | 3 | no | — |
| 358 | C4×C5 | — | 4 | 1 | no | — |
| 359 | Dic5 | — | 3 | 3 | no | — |
| 360 | Dic5 | — | 3 | 1 | no | — |
| 361 | Dic5 | — | 6 | 3 | no | — |
| 362 | Dic5 | — | 12 | 3 | no | — |
| 363 | Dic5 | — | 12 | 1 | no | — |
| 364 | #41 | — | 2 | 3 | no | — |
| 365 | #41 | — | 30 | 6 | no | — |
| 366 | #41 | — | 30 | 6 | no | — |
| 367 | #41 | — | 30 | 6 | no | — |
| 368 | #41 | — | 30 | 6 | no | — |
| 369 | #41 | — | 30 | 3 | no | — |
| 370 | #41 | — | 30 | 6 | no | — |
| 371 | #41 | — | 30 | 1 | no | — |
| 372 | #41 | — | 30 | 3 | no | — |
| 373 | C2×Q8 | — | 15 | 3 | no | — |
| 374 | C2×Q8 | — | 30 | 3 | no | — |
| 375 | C2×Q8 | — | 30 | 3 | no | — |
| 376 | C2×Q8 | — | 30 | 3 | no | — |
| 377 | C2×Q8 | — | 30 | 3 | no | — |
| 378 | C2×D4 | — | 2 | 3 | no | — |
| 379 | C2×D4 | — | 15 | 3 | no | — |
| 380 | C2×D4 | — | 15 | 3 | no | — |
| 381 | C2×D4 | — | 30 | 6 | no | — |
| 382 | C2×D4 | — | 30 | 3 | no | — |
| 383 | C2×D4 | — | 30 | 3 | no | — |
| 384 | C2×D4 | — | 30 | 3 | no | — |
| 385 | C2×D4 | C22×D15 | 1 | 3 | yes | — |
| 386 | C22×C4 | — | 15 | 1 | no | — |
| 387 | C22×C4 | — | 15 | 3 | no | — |
| 388 | C22×C4 | — | 15 | 3 | no | — |
| 389 | C22×C4 | — | 15 | 1 | no | — |
| 390 | C22×C4 | — | 30 | 3 | no | — |
| 391 | C22×C4 | — | 30 | 1 | no | — |
| 392 | C22×C4 | C22×D15 | 1 | 1 | yes | characteristic |
| 393 | C4⋊C4 | — | 2 | 3 | no | — |
| 394 | C4⋊C4 | — | 30 | 3 | no | — |
| 395 | C4⋊C4 | — | 30 | 3 | no | — |
| 396 | C4⋊C4 | — | 30 | 3 | no | — |
| 397 | C4⋊C4 | — | 30 | 3 | no | — |
| 398 | C22⋊C4 | — | 2 | 3 | no | — |
| 399 | C22⋊C4 | — | 15 | 3 | no | — |
| 400 | C22⋊C4 | — | 30 | 3 | no | — |
| 401 | C22⋊C4 | — | 30 | 3 | no | — |
| 402 | C22⋊C4 | — | 30 | 3 | no | — |
| 403 | C22⋊C4 | C22×D15 | 1 | 3 | yes | — |
| 404 | C42 | — | 30 | 3 | no | — |
| 405 | C3×C5 | #3028 | 1 | 1 | yes | characteristic, complemented, Hall |
| 406 | C22×C3 | — | 2 | 3 | no | — |
| 407 | C22×C3 | — | 4 | 1 | no | — |
| 408 | C22×C3 | — | 4 | 3 | no | — |
| 409 | C22×C3 | — | 8 | 1 | no | — |
| 410 | C22×C3 | C2×D4×D5 | 1 | 3 | yes | — |
| 411 | C2×D3 | — | 10 | 3 | no | — |
| 412 | C2×D3 | — | 20 | 3 | no | — |
| 413 | C2×D3 | — | 40 | 3 | no | — |
| 414 | C3×C4 | — | 2 | 3 | no | — |
| 415 | C3×C4 | — | 4 | 3 | no | — |
| 416 | C3×C4 | — | 4 | 1 | no | — |
| 417 | Dic3 | — | 5 | 3 | no | — |
| 418 | Dic3 | — | 5 | 1 | no | — |
| 419 | Dic3 | — | 10 | 3 | no | — |
| 420 | Dic3 | — | 20 | 3 | no | — |
| 421 | Dic3 | — | 20 | 1 | no | — |
| 422 | C2×C5 | — | 2 | 3 | no | — |
| 423 | C2×C5 | — | 4 | 3 | no | — |
| 424 | C2×C5 | D3×#120 | 1 | 1 | yes | characteristic |
| 425 | D5 | — | 12 | 3 | no | — |
| 426 | C23 | — | 2 | 1 | no | — |
| 427 | C23 | — | 15 | 3 | no | — |
| 428 | C23 | — | 30 | 3 | no | — |
| 429 | C23 | D4×D15 | 1 | 3 | yes | — |
| 430 | C23 | C23×D15 | 1 | 1 | yes | characteristic |
| 431 | Q8 | — | 2 | 1 | no | — |
| 432 | Q8 | — | 30 | 6 | no | — |
| 433 | Q8 | — | 30 | 3 | no | — |
| 434 | Q8 | — | 60 | 1 | no | — |
| 435 | Q8 | — | 60 | 3 | no | — |
| 436 | D4 | — | 2 | 3 | no | — |
| 437 | D4 | — | 2 | 6 | no | — |
| 438 | D4 | — | 30 | 3 | no | — |
| 439 | D4 | — | 30 | 6 | no | — |
| 440 | D4 | — | 30 | 6 | no | — |
| 441 | D4 | — | 30 | 6 | no | — |
| 442 | C2×C4 | — | 2 | 3 | no | — |
| 443 | C2×C4 | — | 2 | 3 | no | — |
| 444 | C2×C4 | — | 2 | 3 | no | — |
| 445 | C2×C4 | — | 15 | 3 | no | — |
| 446 | C2×C4 | — | 15 | 3 | no | — |
| 447 | C2×C4 | — | 15 | 3 | no | — |
| 448 | C2×C4 | — | 30 | 3 | no | — |
| 449 | C2×C4 | — | 30 | 3 | no | — |
| 450 | C2×C4 | — | 30 | 6 | no | — |
| 451 | C2×C4 | — | 30 | 3 | no | — |
| 452 | C2×C4 | — | 30 | 3 | no | — |
| 453 | C2×C4 | — | 30 | 3 | no | — |
| 454 | C2×C4 | — | 30 | 3 | no | — |
| 455 | C2×C4 | — | 30 | 3 | no | — |
| 456 | C2×C4 | D4×D15 | 1 | 3 | yes | — |
| 457 | C2×C3 | — | 2 | 3 | no | — |
| 458 | C2×C3 | — | 4 | 3 | no | — |
| 459 | C2×C3 | D5×#120 | 1 | 1 | yes | characteristic |
| 460 | D3 | — | 20 | 3 | no | — |
| 461 | C5 | #80309 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 462 | C22 | — | 2 | 3 | no | — |
| 463 | C22 | — | 4 | 1 | no | — |
| 464 | C22 | — | 4 | 3 | no | — |
| 465 | C22 | — | 8 | 1 | no | — |
| 466 | C22 | — | 30 | 3 | no | — |
| 467 | C22 | — | 60 | 3 | no | — |
| 468 | C22 | — | 120 | 3 | no | — |
| 469 | C22 | C2×D4×D15 | 1 | 3 | yes | — |
| 470 | C4 | — | 2 | 3 | no | — |
| 471 | C4 | — | 4 | 3 | no | — |
| 472 | C4 | — | 4 | 1 | no | — |
| 473 | C4 | — | 15 | 1 | no | — |
| 474 | C4 | — | 15 | 3 | no | — |
| 475 | C4 | — | 30 | 3 | no | — |
| 476 | C4 | — | 60 | 3 | no | — |
| 477 | C4 | — | 60 | 1 | no | — |
| 478 | C3 | #10612040 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 479 | C2 | — | 2 | 3 | no | — |
| 480 | C2 | — | 4 | 3 | no | — |
| 481 | C2 | — | 60 | 3 | no | — |
| 482 | C2 | D15×#120 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11756407 | C2 | semidirect |
| 3. C3×C5×#458 | C2 | semidirect |
| 4. #11751344 | C2 | semidirect |
| 5. #11751154 | C2 | semidirect |
| 6. #11750843 | C2 | semidirect |
| 7. #11750841 | C2 | semidirect |
| 16. C22×Dic30 | C22 | semidirect |
| 17. C3×C5×#123 | C22 | semidirect |
| 18. #91824 | C22 | semidirect |
| 19. #91818 | C22 | semidirect |
| 22. #91775 | C22 | semidirect |
| 25. #91766 | C22 | semidirect |
| 26. C3×C5×#99 | C22 | semidirect |
| 27. #91118 | C22 | semidirect |
| 28. #91090 | C22 | semidirect |
| 32. C5×#458 | D3 | semidirect |
| 80. C3×#458 | D5 | semidirect |
| 93. C5×#123 | C2×D3 | semidirect |
| 102. C5×#99 | C2×D3 | semidirect |
| 145. C3×#123 | C2×D5 | semidirect |
| 154. C3×#99 | C2×D5 | semidirect |
| 203. #458 | D15 | semidirect |
| 306. #123 | C2×D15 | semidirect |
| 312. #99 | C2×D15 | semidirect |
| 405. C3×C5 | #3028 | semidirect |
| 461. C5 | #80309 | semidirect |
| 478. C3 | #10612040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757148 | 2 |
| #11756407 | 2 |
| C3×C5×#458 | 2 |
| #11751344 | 2 |
| #11751154 | 2 |
| #11750843 | 2 |
| #11750841 | 2 |
| #10612040 | 3 |
| #80309 | 5 |