Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2816 conjugacy classes of subgroups.
The subgroup lattice has 656 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D15×2−1+4 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×C5×#578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11756597 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11756538 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | D15×#137 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #11756530 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | D15×#135 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #11756525 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×Q16×D15 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11756512 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D15×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | D5×#578 | — | 3 | 1 | no | maximal, Hall |
| 13 | C3×C5×2−1+4 | C22 | 1 | 2 | yes | complemented |
| 14 | #92101 | — | 2 | 6 | no | — |
| 15 | #92101 | C22 | 1 | 6 | yes | complemented |
| 16 | #92101 | C22 | 1 | 2 | yes | complemented |
| 17 | #41×D15 | — | 2 | 6 | no | — |
| 18 | #41×D15 | C22 | 1 | 6 | yes | — |
| 19 | #41×D15 | C22 | 1 | 1 | yes | characteristic |
| 20 | #92098 | — | 2 | 2 | no | — |
| 21 | #92098 | C22 | 1 | 6 | yes | complemented |
| 22 | C2×Q8×D15 | — | 2 | 2 | no | — |
| 23 | C2×Q8×D15 | C22 | 1 | 6 | yes | — |
| 24 | C3×C5×#137 | C22 | 1 | 6 | yes | complemented |
| 25 | C3×C5×#135 | C22 | 1 | 3 | yes | complemented |
| 26 | C2×C3×C5×Q16 | C22 | 1 | 3 | yes | complemented |
| 27 | C3×C5×#131 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #91840 | C22 | 1 | 6 | yes | complemented |
| 29 | #91839 | C22 | 1 | 6 | yes | complemented |
| 30 | #91837 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C2×#6718 | C22 | 1 | 6 | yes | complemented |
| 32 | #91831 | C22 | 1 | 6 | yes | complemented |
| 33 | #91808 | C22 | 1 | 3 | yes | complemented |
| 34 | #91807 | C22 | 1 | 12 | yes | complemented |
| 35 | Q16×D15 | C22 | 1 | 3 | yes | — |
| 36 | Q16×D15 | C22 | 1 | 6 | yes | — |
| 37 | Q16×D15 | C22 | 1 | 6 | yes | complemented |
| 38 | Q16×D15 | C22 | 1 | 6 | yes | complemented |
| 39 | #91805 | C22 | 1 | 6 | yes | complemented |
| 40 | #91804 | C22 | 1 | 12 | yes | complemented |
| 41 | SD16×D15 | C22 | 1 | 6 | yes | — |
| 42 | #91801 | C22 | 1 | 3 | yes | complemented |
| 43 | D8×D15 | C22 | 1 | 1 | yes | characteristic |
| 44 | #91798 | C22 | 1 | 6 | yes | complemented |
| 45 | #91796 | C22 | 1 | 3 | yes | complemented |
| 46 | M16×D15 | C22 | 1 | 3 | yes | — |
| 47 | C2×Dic60 | C22 | 1 | 3 | yes | complemented |
| 48 | #91793 | C22 | 1 | 3 | yes | complemented |
| 49 | #91790 | C22 | 1 | 3 | yes | complemented |
| 50 | C2×C8×D15 | C22 | 1 | 3 | yes | — |
| 51 | D3×#578 | — | 5 | 1 | no | maximal, Hall |
| 52 | D5×2−1+4 | — | 3 | 2 | no | — |
| 53 | C5×#578 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #66172 | — | 3 | 2 | no | — |
| 55 | #66113 | — | 3 | 6 | no | — |
| 56 | D5×#137 | — | 3 | 6 | no | — |
| 57 | #66105 | — | 3 | 3 | no | — |
| 58 | D5×#135 | — | 3 | 3 | no | — |
| 59 | #66100 | — | 3 | 3 | no | — |
| 60 | C2×D5×Q16 | — | 3 | 3 | no | — |
| 61 | #66087 | — | 3 | 1 | no | — |
| 62 | D5×#131 | — | 3 | 1 | no | — |
| 63 | C3×C5×#41 | — | 2 | 6 | no | — |
| 64 | C3×C5×#41 | C23 | 1 | 6 | yes | — |
| 65 | C3×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C3×C5×Q8 | — | 2 | 2 | no | — |
| 67 | C2×C3×C5×Q8 | C23 | 1 | 6 | yes | — |
| 68 | #6821 | — | 2 | 6 | no | — |
| 69 | #6821 | D4 | 1 | 1 | yes | characteristic |
| 70 | #6821 | C23 | 1 | 6 | yes | — |
| 71 | Q8×D15 | — | 2 | 2 | no | — |
| 72 | Q8×D15 | — | 2 | 6 | no | — |
| 73 | Q8×D15 | — | 2 | 6 | no | — |
| 74 | Q8×D15 | — | 2 | 6 | no | — |
| 75 | Q8×D15 | D4 | 1 | 1 | yes | characteristic |
| 76 | Q8×D15 | C23 | 1 | 6 | yes | — |
| 77 | Q8×D15 | C23 | 1 | 12 | yes | — |
| 78 | #6819 | — | 2 | 6 | no | — |
| 79 | #6819 | — | 2 | 12 | no | — |
| 80 | #6819 | — | 2 | 6 | no | — |
| 81 | #6819 | D4 | 1 | 3 | yes | — |
| 82 | #6819 | C23 | 1 | 6 | yes | — |
| 83 | D4×D15 | — | 2 | 6 | no | — |
| 84 | D4×D15 | D4 | 1 | 3 | yes | — |
| 85 | D4×D15 | C23 | 1 | 2 | yes | — |
| 86 | #6817 | — | 2 | 12 | no | — |
| 87 | #6817 | — | 2 | 6 | no | — |
| 88 | #6817 | — | 2 | 6 | no | — |
| 89 | #6817 | C23 | 1 | 3 | yes | — |
| 90 | #6817 | C23 | 1 | 6 | yes | — |
| 91 | C2×C4×D15 | — | 2 | 6 | no | — |
| 92 | C2×C4×D15 | — | 2 | 6 | no | — |
| 93 | C2×C4×D15 | C23 | 1 | 3 | yes | — |
| 94 | C2×Dic30 | — | 2 | 6 | no | — |
| 95 | C2×Dic30 | — | 2 | 6 | no | — |
| 96 | C2×Dic30 | C23 | 1 | 6 | yes | — |
| 97 | C3×C5×Q16 | C23 | 1 | 3 | yes | — |
| 98 | C3×C5×Q16 | C23 | 1 | 6 | yes | — |
| 99 | C3×C5×SD16 | C23 | 1 | 6 | yes | — |
| 100 | C3×C5×D8 | C23 | 1 | 1 | yes | characteristic |
| 101 | C3×C5×M16 | C23 | 1 | 3 | yes | — |
| 102 | C2×C3×C5×C8 | C23 | 1 | 3 | yes | — |
| 103 | #6718 | C23 | 1 | 12 | yes | — |
| 104 | #6718 | C23 | 1 | 6 | yes | — |
| 105 | #6717 | C23 | 1 | 6 | yes | — |
| 106 | #6716 | C23 | 1 | 6 | yes | — |
| 107 | #6715 | C23 | 1 | 2 | yes | — |
| 108 | #6710 | C23 | 1 | 3 | yes | — |
| 109 | C2×C3⋊#168 | C23 | 1 | 3 | yes | — |
| 110 | Dic60 | C23 | 1 | 3 | yes | — |
| 111 | Dic60 | C23 | 1 | 6 | yes | — |
| 112 | D120 | C23 | 1 | 1 | yes | characteristic |
| 113 | #6706 | C23 | 1 | 6 | yes | — |
| 114 | #6705 | C23 | 1 | 6 | yes | — |
| 115 | C8×D15 | C23 | 1 | 1 | yes | characteristic |
| 116 | C8×D15 | C23 | 1 | 3 | yes | — |
| 117 | C8×D15 | C23 | 1 | 3 | yes | — |
| 118 | C8×D15 | C23 | 1 | 3 | yes | — |
| 119 | D3×2−1+4 | — | 5 | 2 | no | — |
| 120 | C3×#578 | D5 | 1 | 1 | yes | characteristic, complemented |
| 121 | #5838 | — | 5 | 2 | no | — |
| 122 | #5779 | — | 5 | 6 | no | — |
| 123 | D3×#137 | — | 5 | 6 | no | — |
| 124 | #5771 | — | 5 | 3 | no | — |
| 125 | D3×#135 | — | 5 | 3 | no | — |
| 126 | #5766 | — | 5 | 3 | no | — |
| 127 | C2×D3×Q16 | — | 5 | 3 | no | — |
| 128 | #5753 | — | 5 | 1 | no | — |
| 129 | D3×#131 | — | 5 | 1 | no | — |
| 130 | C5×2−1+4 | C2×D3 | 1 | 2 | yes | complemented |
| 131 | #4150 | — | 3 | 2 | no | — |
| 132 | #4150 | — | 3 | 6 | no | — |
| 133 | #4150 | — | 6 | 6 | no | — |
| 134 | D5×#41 | — | 3 | 1 | no | — |
| 135 | D5×#41 | — | 3 | 6 | no | — |
| 136 | D5×#41 | — | 6 | 6 | no | — |
| 137 | #4147 | — | 3 | 6 | no | — |
| 138 | #4147 | — | 6 | 2 | no | — |
| 139 | C2×Q8×D5 | — | 3 | 6 | no | — |
| 140 | C2×Q8×D5 | — | 6 | 2 | no | — |
| 141 | C5×#137 | C2×D3 | 1 | 6 | yes | complemented |
| 142 | C5×#135 | C2×D3 | 1 | 3 | yes | complemented |
| 143 | C2×C5×Q16 | C2×D3 | 1 | 3 | yes | complemented |
| 144 | C5×#131 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 145 | #4097 | — | 3 | 6 | no | — |
| 146 | #4096 | — | 3 | 6 | no | — |
| 147 | #4094 | — | 3 | 1 | no | — |
| 148 | C2×#689 | — | 3 | 6 | no | — |
| 149 | #4088 | — | 3 | 6 | no | — |
| 150 | #4065 | — | 3 | 3 | no | — |
| 151 | #4064 | — | 3 | 12 | no | — |
| 152 | D5×Q16 | — | 3 | 3 | no | — |
| 153 | D5×Q16 | — | 3 | 6 | no | — |
| 154 | D5×Q16 | — | 3 | 6 | no | — |
| 155 | D5×Q16 | — | 3 | 6 | no | — |
| 156 | #4062 | — | 3 | 6 | no | — |
| 157 | #4061 | — | 3 | 12 | no | — |
| 158 | D5×SD16 | — | 3 | 6 | no | — |
| 159 | #4058 | — | 3 | 3 | no | — |
| 160 | D5×D8 | — | 3 | 1 | no | — |
| 161 | #4055 | — | 3 | 6 | no | — |
| 162 | #4053 | — | 3 | 3 | no | — |
| 163 | D5×M16 | — | 3 | 3 | no | — |
| 164 | C2×Dic20 | — | 3 | 3 | no | — |
| 165 | #4050 | — | 3 | 3 | no | — |
| 166 | #4047 | — | 3 | 3 | no | — |
| 167 | C2×C8×D5 | — | 3 | 3 | no | — |
| 168 | C2×#578 | — | 15 | 1 | no | Sylow |
| 169 | C22×D15 | — | 2 | 2 | no | — |
| 170 | C22×D15 | C2×D4 | 1 | 3 | yes | — |
| 171 | C3×C5×Q8 | — | 2 | 6 | no | — |
| 172 | C3×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C3×C5×Q8 | C24 | 1 | 6 | yes | — |
| 174 | C3×C5×D4 | — | 2 | 6 | no | — |
| 175 | C3×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 176 | C3×C5×D4 | C24 | 1 | 2 | yes | — |
| 177 | C2×C3×C4×C5 | — | 2 | 6 | no | — |
| 178 | C2×C3×C4×C5 | — | 2 | 6 | no | — |
| 179 | C2×C3×C4×C5 | C24 | 1 | 3 | yes | — |
| 180 | #1220 | — | 2 | 6 | no | — |
| 181 | #1220 | — | 2 | 6 | no | — |
| 182 | #1220 | — | 2 | 2 | no | — |
| 183 | #1220 | C2×D4 | 1 | 6 | yes | — |
| 184 | C2×Dic15 | — | 2 | 6 | no | — |
| 185 | C2×Dic15 | — | 2 | 6 | no | — |
| 186 | C2×Dic15 | C2×D4 | 1 | 3 | yes | — |
| 187 | D60 | — | 2 | 6 | no | — |
| 188 | D60 | C2×D4 | 1 | 3 | yes | — |
| 189 | D60 | C24 | 1 | 2 | yes | — |
| 190 | C4×D15 | — | 2 | 6 | no | — |
| 191 | C4×D15 | — | 2 | 12 | no | — |
| 192 | C4×D15 | — | 2 | 6 | no | — |
| 193 | C4×D15 | — | 2 | 6 | no | — |
| 194 | C4×D15 | C2×D4 | 1 | 3 | yes | — |
| 195 | C4×D15 | C2×D4 | 1 | 3 | yes | — |
| 196 | C4×D15 | C24 | 1 | 1 | yes | characteristic |
| 197 | C4×D15 | C24 | 1 | 3 | yes | — |
| 198 | Dic30 | — | 2 | 6 | no | — |
| 199 | Dic30 | — | 2 | 6 | no | — |
| 200 | Dic30 | — | 2 | 12 | no | — |
| 201 | Dic30 | C2×D4 | 1 | 3 | yes | — |
| 202 | Dic30 | C24 | 1 | 6 | yes | — |
| 203 | C3×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 204 | C3×C5×C8 | C24 | 1 | 3 | yes | — |
| 205 | C3⋊#168 | C24 | 1 | 1 | yes | characteristic |
| 206 | C3⋊#168 | C24 | 1 | 3 | yes | — |
| 207 | C3×2−1+4 | C2×D5 | 1 | 2 | yes | complemented |
| 208 | #1010 | — | 5 | 2 | no | — |
| 209 | #1010 | — | 5 | 6 | no | — |
| 210 | #1010 | — | 10 | 6 | no | — |
| 211 | D3×#41 | — | 5 | 1 | no | — |
| 212 | D3×#41 | — | 5 | 6 | no | — |
| 213 | D3×#41 | — | 10 | 6 | no | — |
| 214 | #1007 | — | 5 | 6 | no | — |
| 215 | #1007 | — | 10 | 2 | no | — |
| 216 | C2×D3×Q8 | — | 5 | 6 | no | — |
| 217 | C2×D3×Q8 | — | 10 | 2 | no | — |
| 218 | C3×#137 | C2×D5 | 1 | 6 | yes | complemented |
| 219 | C3×#135 | C2×D5 | 1 | 3 | yes | complemented |
| 220 | C2×C3×Q16 | C2×D5 | 1 | 3 | yes | complemented |
| 221 | C3×#131 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 222 | #951 | — | 5 | 6 | no | — |
| 223 | #950 | — | 5 | 6 | no | — |
| 224 | #948 | — | 5 | 1 | no | — |
| 225 | C2×#216 | — | 5 | 6 | no | — |
| 226 | #942 | — | 5 | 6 | no | — |
| 227 | #919 | — | 5 | 3 | no | — |
| 228 | #918 | — | 5 | 12 | no | — |
| 229 | D3×Q16 | — | 5 | 3 | no | — |
| 230 | D3×Q16 | — | 5 | 6 | no | — |
| 231 | D3×Q16 | — | 5 | 6 | no | — |
| 232 | D3×Q16 | — | 5 | 6 | no | — |
| 233 | #916 | — | 5 | 6 | no | — |
| 234 | #915 | — | 5 | 12 | no | — |
| 235 | D3×SD16 | — | 5 | 6 | no | — |
| 236 | #912 | — | 5 | 3 | no | — |
| 237 | D3×D8 | — | 5 | 1 | no | — |
| 238 | #909 | — | 5 | 6 | no | — |
| 239 | #907 | — | 5 | 3 | no | — |
| 240 | D3×M16 | — | 5 | 3 | no | — |
| 241 | C2×Dic12 | — | 5 | 3 | no | — |
| 242 | #904 | — | 5 | 3 | no | — |
| 243 | #901 | — | 5 | 3 | no | — |
| 244 | C2×D3×C8 | — | 5 | 3 | no | — |
| 245 | C5×#41 | — | 2 | 6 | no | — |
| 246 | C5×#41 | C22×D3 | 1 | 6 | yes | — |
| 247 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 248 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 249 | C2×C5×Q8 | C22×D3 | 1 | 6 | yes | — |
| 250 | #713 | — | 3 | 1 | no | — |
| 251 | #713 | — | 3 | 6 | no | — |
| 252 | #713 | — | 6 | 6 | no | — |
| 253 | Q8×D5 | — | 3 | 1 | no | — |
| 254 | Q8×D5 | — | 3 | 6 | no | — |
| 255 | Q8×D5 | — | 3 | 12 | no | — |
| 256 | Q8×D5 | — | 6 | 6 | no | — |
| 257 | Q8×D5 | — | 6 | 6 | no | — |
| 258 | Q8×D5 | — | 6 | 6 | no | — |
| 259 | Q8×D5 | — | 6 | 2 | no | — |
| 260 | #711 | — | 3 | 3 | no | — |
| 261 | #711 | — | 3 | 6 | no | — |
| 262 | #711 | — | 6 | 6 | no | — |
| 263 | #711 | — | 6 | 12 | no | — |
| 264 | #711 | — | 6 | 6 | no | — |
| 265 | D4×D5 | — | 3 | 3 | no | — |
| 266 | D4×D5 | — | 3 | 2 | no | — |
| 267 | D4×D5 | — | 6 | 6 | no | — |
| 268 | #709 | — | 3 | 3 | no | — |
| 269 | #709 | — | 3 | 6 | no | — |
| 270 | #709 | — | 6 | 6 | no | — |
| 271 | #709 | — | 6 | 6 | no | — |
| 272 | #709 | — | 6 | 12 | no | — |
| 273 | C2×C4×D5 | — | 3 | 3 | no | — |
| 274 | C2×C4×D5 | — | 6 | 6 | no | — |
| 275 | C2×C4×D5 | — | 6 | 6 | no | — |
| 276 | C2×Dic10 | — | 3 | 6 | no | — |
| 277 | C2×Dic10 | — | 6 | 6 | no | — |
| 278 | C2×Dic10 | — | 6 | 6 | no | — |
| 279 | C5×Q16 | C22×D3 | 1 | 3 | yes | — |
| 280 | C5×Q16 | C22×D3 | 1 | 6 | yes | — |
| 281 | C5×SD16 | C22×D3 | 1 | 6 | yes | — |
| 282 | C5×D8 | C22×D3 | 1 | 1 | yes | characteristic |
| 283 | C5×M16 | C22×D3 | 1 | 3 | yes | — |
| 284 | C2×C5×C8 | C22×D3 | 1 | 3 | yes | — |
| 285 | #689 | — | 3 | 6 | no | — |
| 286 | #689 | — | 3 | 12 | no | — |
| 287 | #688 | — | 3 | 6 | no | — |
| 288 | #687 | — | 3 | 6 | no | — |
| 289 | #686 | — | 3 | 2 | no | — |
| 290 | #681 | — | 3 | 3 | no | — |
| 291 | C2×#168 | — | 3 | 3 | no | — |
| 292 | Dic20 | — | 3 | 3 | no | — |
| 293 | Dic20 | — | 3 | 6 | no | — |
| 294 | D40 | — | 3 | 1 | no | — |
| 295 | #677 | — | 3 | 6 | no | — |
| 296 | #676 | — | 3 | 6 | no | — |
| 297 | C8×D5 | — | 3 | 1 | no | — |
| 298 | C8×D5 | — | 3 | 3 | no | — |
| 299 | C8×D5 | — | 3 | 3 | no | — |
| 300 | C8×D5 | — | 3 | 3 | no | — |
| 301 | C2×2−1+4 | — | 15 | 2 | no | — |
| 302 | #578 | — | 15 | 2 | no | — |
| 303 | #578 | — | 15 | 6 | no | — |
| 304 | #578 | — | 15 | 3 | no | — |
| 305 | #578 | — | 15 | 3 | no | — |
| 306 | #578 | — | 15 | 1 | no | — |
| 307 | #578 | D15 | 1 | 1 | yes | characteristic, direct product factor |
| 308 | C2×#137 | — | 15 | 6 | no | — |
| 309 | C2×#135 | — | 15 | 3 | no | — |
| 310 | C22×Q16 | — | 15 | 3 | no | — |
| 311 | C2×#131 | — | 15 | 1 | no | — |
| 312 | C22×C3×C5 | — | 2 | 2 | no | — |
| 313 | C22×C3×C5 | C22×D4 | 1 | 3 | yes | — |
| 314 | C2×D15 | — | 2 | 6 | no | — |
| 315 | C2×D15 | — | 2 | 2 | no | — |
| 316 | C2×D15 | — | 4 | 4 | no | — |
| 317 | C2×D15 | C22×D4 | 1 | 3 | yes | — |
| 318 | C2×D15 | C22×D4 | 1 | 1 | yes | characteristic |
| 319 | C3×C4×C5 | — | 2 | 6 | no | — |
| 320 | C3×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 321 | C3×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 322 | Dic15 | — | 2 | 6 | no | — |
| 323 | Dic15 | C22×D4 | 1 | 1 | yes | characteristic |
| 324 | Dic15 | C22×D4 | 1 | 3 | yes | — |
| 325 | C3×#41 | — | 2 | 6 | no | — |
| 326 | C3×#41 | C22×D5 | 1 | 6 | yes | — |
| 327 | C3×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 328 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 329 | C2×C3×Q8 | C22×D5 | 1 | 6 | yes | — |
| 330 | #239 | — | 5 | 1 | no | — |
| 331 | #239 | — | 5 | 6 | no | — |
| 332 | #239 | — | 10 | 6 | no | — |
| 333 | D3×Q8 | — | 5 | 1 | no | — |
| 334 | D3×Q8 | — | 5 | 6 | no | — |
| 335 | D3×Q8 | — | 5 | 12 | no | — |
| 336 | D3×Q8 | — | 10 | 6 | no | — |
| 337 | D3×Q8 | — | 10 | 6 | no | — |
| 338 | D3×Q8 | — | 10 | 6 | no | — |
| 339 | D3×Q8 | — | 10 | 2 | no | — |
| 340 | #237 | — | 5 | 3 | no | — |
| 341 | #237 | — | 5 | 6 | no | — |
| 342 | #237 | — | 10 | 6 | no | — |
| 343 | #237 | — | 10 | 12 | no | — |
| 344 | #237 | — | 10 | 6 | no | — |
| 345 | D3×D4 | — | 5 | 3 | no | — |
| 346 | D3×D4 | — | 5 | 2 | no | — |
| 347 | D3×D4 | — | 10 | 6 | no | — |
| 348 | #235 | — | 5 | 3 | no | — |
| 349 | #235 | — | 5 | 6 | no | — |
| 350 | #235 | — | 10 | 6 | no | — |
| 351 | #235 | — | 10 | 6 | no | — |
| 352 | #235 | — | 10 | 12 | no | — |
| 353 | C2×C4×D3 | — | 5 | 3 | no | — |
| 354 | C2×C4×D3 | — | 10 | 6 | no | — |
| 355 | C2×C4×D3 | — | 10 | 6 | no | — |
| 356 | C2×Dic6 | — | 5 | 6 | no | — |
| 357 | C2×Dic6 | — | 10 | 6 | no | — |
| 358 | C2×Dic6 | — | 10 | 6 | no | — |
| 359 | C3×Q16 | C22×D5 | 1 | 3 | yes | — |
| 360 | C3×Q16 | C22×D5 | 1 | 6 | yes | — |
| 361 | C3×SD16 | C22×D5 | 1 | 6 | yes | — |
| 362 | C3×D8 | C22×D5 | 1 | 1 | yes | characteristic |
| 363 | C3×M16 | C22×D5 | 1 | 3 | yes | — |
| 364 | C2×C3×C8 | C22×D5 | 1 | 3 | yes | — |
| 365 | #216 | — | 5 | 12 | no | — |
| 366 | #216 | — | 5 | 6 | no | — |
| 367 | #215 | — | 5 | 6 | no | — |
| 368 | #214 | — | 5 | 6 | no | — |
| 369 | #213 | — | 5 | 2 | no | — |
| 370 | #208 | — | 5 | 3 | no | — |
| 371 | C2×C3⋊C8 | — | 5 | 3 | no | — |
| 372 | Dic12 | — | 5 | 3 | no | — |
| 373 | Dic12 | — | 5 | 6 | no | — |
| 374 | D24 | — | 5 | 1 | no | — |
| 375 | #204 | — | 5 | 6 | no | — |
| 376 | ΓL(1,𝔽25) | — | 5 | 6 | no | — |
| 377 | D3×C8 | — | 5 | 1 | no | — |
| 378 | D3×C8 | — | 5 | 3 | no | — |
| 379 | D3×C8 | — | 5 | 3 | no | — |
| 380 | D3×C8 | — | 5 | 3 | no | — |
| 381 | C22×D5 | — | 3 | 3 | no | — |
| 382 | C22×D5 | — | 6 | 2 | no | — |
| 383 | C5×Q8 | — | 2 | 6 | no | — |
| 384 | C5×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 385 | C5×Q8 | C23×D3 | 1 | 6 | yes | — |
| 386 | C5×D4 | — | 2 | 6 | no | — |
| 387 | C5×D4 | D3×D4 | 1 | 3 | yes | — |
| 388 | C5×D4 | C23×D3 | 1 | 2 | yes | — |
| 389 | C2×C4×C5 | — | 2 | 6 | no | — |
| 390 | C2×C4×C5 | — | 2 | 6 | no | — |
| 391 | C2×C4×C5 | C23×D3 | 1 | 3 | yes | — |
| 392 | C22⋊D5 | — | 3 | 6 | no | — |
| 393 | C22⋊D5 | — | 6 | 2 | no | — |
| 394 | C22⋊D5 | — | 6 | 6 | no | — |
| 395 | C22⋊D5 | — | 6 | 6 | no | — |
| 396 | C2×Dic5 | — | 3 | 3 | no | — |
| 397 | C2×Dic5 | — | 6 | 6 | no | — |
| 398 | C2×Dic5 | — | 6 | 6 | no | — |
| 399 | D20 | — | 3 | 3 | no | — |
| 400 | D20 | — | 3 | 2 | no | — |
| 401 | D20 | — | 6 | 6 | no | — |
| 402 | C4×D5 | — | 3 | 3 | no | — |
| 403 | C4×D5 | — | 3 | 3 | no | — |
| 404 | C4×D5 | — | 3 | 1 | no | — |
| 405 | C4×D5 | — | 3 | 3 | no | — |
| 406 | C4×D5 | — | 6 | 6 | no | — |
| 407 | C4×D5 | — | 6 | 6 | no | — |
| 408 | C4×D5 | — | 6 | 12 | no | — |
| 409 | C4×D5 | — | 6 | 6 | no | — |
| 410 | Dic10 | — | 3 | 3 | no | — |
| 411 | Dic10 | — | 3 | 6 | no | — |
| 412 | Dic10 | — | 6 | 12 | no | — |
| 413 | Dic10 | — | 6 | 6 | no | — |
| 414 | Dic10 | — | 6 | 6 | no | — |
| 415 | C5×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 416 | C5×C8 | C23×D3 | 1 | 3 | yes | — |
| 417 | #168 | — | 3 | 1 | no | — |
| 418 | #168 | — | 3 | 3 | no | — |
| 419 | 2−1+4 | — | 15 | 6 | no | — |
| 420 | 2−1+4 | — | 15 | 2 | no | — |
| 421 | 2−1+4 | — | 15 | 6 | no | — |
| 422 | 2−1+4 | — | 30 | 2 | no | — |
| 423 | 2−1+4 | — | 30 | 6 | no | — |
| 424 | 2−1+4 | C2×D15 | 1 | 2 | yes | complemented |
| 425 | C2×#41 | — | 15 | 1 | no | — |
| 426 | C2×#41 | — | 15 | 6 | no | — |
| 427 | C2×#41 | — | 30 | 6 | no | — |
| 428 | C22×Q8 | — | 15 | 6 | no | — |
| 429 | C22×Q8 | — | 30 | 2 | no | — |
| 430 | #137 | — | 15 | 6 | no | — |
| 431 | #137 | — | 15 | 6 | no | — |
| 432 | #137 | — | 15 | 12 | no | — |
| 433 | #137 | — | 15 | 12 | no | — |
| 434 | #137 | — | 15 | 6 | no | — |
| 435 | #137 | C2×D15 | 1 | 6 | yes | complemented |
| 436 | #135 | — | 15 | 6 | no | — |
| 437 | #135 | — | 15 | 3 | no | — |
| 438 | #135 | — | 15 | 6 | no | — |
| 439 | #135 | — | 15 | 3 | no | — |
| 440 | #135 | — | 15 | 3 | no | — |
| 441 | #135 | C2×D15 | 1 | 3 | yes | complemented |
| 442 | C2×Q16 | — | 15 | 6 | no | — |
| 443 | C2×Q16 | — | 15 | 3 | no | — |
| 444 | C2×Q16 | — | 15 | 6 | no | — |
| 445 | C2×Q16 | — | 15 | 6 | no | — |
| 446 | C2×Q16 | — | 15 | 6 | no | — |
| 447 | C2×Q16 | — | 15 | 3 | no | — |
| 448 | C2×Q16 | C2×D15 | 1 | 3 | yes | complemented |
| 449 | C2×SD16 | — | 15 | 6 | no | — |
| 450 | C2×D8 | — | 15 | 1 | no | — |
| 451 | #131 | — | 15 | 1 | no | — |
| 452 | #131 | — | 15 | 3 | no | — |
| 453 | #131 | — | 15 | 3 | no | — |
| 454 | #131 | C2×D15 | 1 | 1 | yes | characteristic, complemented |
| 455 | C2×M16 | — | 15 | 3 | no | — |
| 456 | C22×C8 | — | 15 | 3 | no | — |
| 457 | C2×C3×C5 | — | 2 | 3 | no | — |
| 458 | C2×C3×C5 | — | 4 | 2 | no | — |
| 459 | C2×C3×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 460 | D15 | — | 2 | 3 | no | — |
| 461 | D15 | — | 4 | 2 | no | — |
| 462 | D15 | #578 | 1 | 2 | yes | direct product factor |
| 463 | C22×D3 | — | 5 | 3 | no | — |
| 464 | C22×D3 | — | 10 | 2 | no | — |
| 465 | C3×Q8 | — | 2 | 6 | no | — |
| 466 | C3×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 467 | C3×Q8 | C23×D5 | 1 | 6 | yes | — |
| 468 | C3×D4 | — | 2 | 6 | no | — |
| 469 | C3×D4 | D4×D5 | 1 | 3 | yes | — |
| 470 | C3×D4 | C23×D5 | 1 | 2 | yes | — |
| 471 | C2×C3×C4 | — | 2 | 6 | no | — |
| 472 | C2×C3×C4 | — | 2 | 6 | no | — |
| 473 | C2×C3×C4 | C23×D5 | 1 | 3 | yes | — |
| 474 | #67 | — | 5 | 6 | no | — |
| 475 | #67 | — | 10 | 2 | no | — |
| 476 | #67 | — | 10 | 6 | no | — |
| 477 | #67 | — | 10 | 6 | no | — |
| 478 | C2×Dic3 | — | 5 | 3 | no | — |
| 479 | C2×Dic3 | — | 10 | 6 | no | — |
| 480 | C2×Dic3 | — | 10 | 6 | no | — |
| 481 | D12 | — | 5 | 3 | no | — |
| 482 | D12 | — | 5 | 2 | no | — |
| 483 | D12 | — | 10 | 6 | no | — |
| 484 | C4×D3 | — | 5 | 3 | no | — |
| 485 | C4×D3 | — | 5 | 3 | no | — |
| 486 | C4×D3 | — | 5 | 1 | no | — |
| 487 | C4×D3 | — | 5 | 3 | no | — |
| 488 | C4×D3 | — | 10 | 6 | no | — |
| 489 | C4×D3 | — | 10 | 6 | no | — |
| 490 | C4×D3 | — | 10 | 12 | no | — |
| 491 | C4×D3 | — | 10 | 6 | no | — |
| 492 | Dic6 | — | 5 | 3 | no | — |
| 493 | Dic6 | — | 5 | 6 | no | — |
| 494 | Dic6 | — | 10 | 12 | no | — |
| 495 | Dic6 | — | 10 | 6 | no | — |
| 496 | Dic6 | — | 10 | 6 | no | — |
| 497 | C3×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 498 | C3×C8 | C23×D5 | 1 | 3 | yes | — |
| 499 | C3⋊C8 | — | 5 | 1 | no | — |
| 500 | C3⋊C8 | — | 5 | 3 | no | — |
| 501 | C22×C5 | — | 2 | 2 | no | — |
| 502 | C22×C5 | C2×D3×D4 | 1 | 3 | yes | — |
| 503 | C2×D5 | — | 3 | 1 | no | — |
| 504 | C2×D5 | — | 3 | 3 | no | — |
| 505 | C2×D5 | — | 6 | 6 | no | — |
| 506 | C2×D5 | — | 6 | 2 | no | — |
| 507 | C2×D5 | — | 12 | 4 | no | — |
| 508 | C4×C5 | — | 2 | 6 | no | — |
| 509 | C4×C5 | C2×D3×D4 | 1 | 3 | yes | — |
| 510 | C4×C5 | C24×D3 | 1 | 1 | yes | characteristic |
| 511 | Dic5 | — | 3 | 3 | no | — |
| 512 | Dic5 | — | 3 | 1 | no | — |
| 513 | Dic5 | — | 6 | 6 | no | — |
| 514 | #41 | — | 2 | 6 | no | — |
| 515 | #41 | — | 15 | 1 | no | — |
| 516 | #41 | — | 15 | 3 | no | — |
| 517 | #41 | — | 15 | 3 | no | — |
| 518 | #41 | — | 15 | 6 | no | — |
| 519 | #41 | — | 15 | 6 | no | — |
| 520 | #41 | — | 15 | 6 | no | — |
| 521 | #41 | — | 30 | 6 | no | — |
| 522 | #41 | — | 30 | 12 | no | — |
| 523 | #41 | — | 30 | 6 | no | — |
| 524 | #41 | — | 30 | 6 | no | — |
| 525 | #41 | — | 30 | 12 | no | — |
| 526 | #41 | — | 30 | 6 | no | — |
| 527 | #41 | — | 30 | 6 | no | — |
| 528 | #41 | C22×D15 | 1 | 6 | yes | — |
| 529 | #41 | C22×D15 | 1 | 1 | yes | characteristic |
| 530 | C2×Q8 | — | 2 | 2 | no | — |
| 531 | C2×Q8 | — | 15 | 1 | no | — |
| 532 | C2×Q8 | — | 15 | 6 | no | — |
| 533 | C2×Q8 | — | 15 | 12 | no | — |
| 534 | C2×Q8 | — | 15 | 6 | no | — |
| 535 | C2×Q8 | — | 30 | 6 | no | — |
| 536 | C2×Q8 | — | 30 | 6 | no | — |
| 537 | C2×Q8 | — | 30 | 6 | no | — |
| 538 | C2×Q8 | — | 30 | 6 | no | — |
| 539 | C2×Q8 | — | 30 | 6 | no | — |
| 540 | C2×Q8 | — | 30 | 2 | no | — |
| 541 | C2×Q8 | C22×D15 | 1 | 6 | yes | — |
| 542 | C2×D4 | — | 15 | 3 | no | — |
| 543 | C2×D4 | — | 15 | 2 | no | — |
| 544 | C2×D4 | — | 30 | 6 | no | — |
| 545 | C22×C4 | — | 15 | 3 | no | — |
| 546 | C22×C4 | — | 30 | 6 | no | — |
| 547 | C22×C4 | — | 30 | 6 | no | — |
| 548 | Q16 | — | 15 | 6 | no | — |
| 549 | Q16 | — | 15 | 12 | no | — |
| 550 | Q16 | — | 15 | 3 | no | — |
| 551 | Q16 | — | 15 | 6 | no | — |
| 552 | Q16 | C22×D15 | 1 | 3 | yes | — |
| 553 | Q16 | C22×D15 | 1 | 6 | yes | — |
| 554 | SD16 | — | 15 | 6 | no | — |
| 555 | SD16 | — | 15 | 6 | no | — |
| 556 | SD16 | — | 15 | 6 | no | — |
| 557 | SD16 | C22×D15 | 1 | 6 | yes | — |
| 558 | D8 | — | 15 | 2 | no | — |
| 559 | D8 | — | 15 | 1 | no | — |
| 560 | D8 | C22×D15 | 1 | 1 | yes | characteristic |
| 561 | M16 | — | 15 | 3 | no | — |
| 562 | M16 | — | 15 | 6 | no | — |
| 563 | M16 | C22×D15 | 1 | 3 | yes | — |
| 564 | C2×C8 | — | 15 | 3 | no | — |
| 565 | C2×C8 | — | 15 | 1 | no | — |
| 566 | C2×C8 | — | 15 | 3 | no | — |
| 567 | C2×C8 | — | 15 | 3 | no | — |
| 568 | C2×C8 | — | 15 | 3 | no | — |
| 569 | C2×C8 | C22×D15 | 1 | 3 | yes | — |
| 570 | C3×C5 | C2×#578 | 1 | 1 | yes | characteristic, complemented, Hall |
| 571 | C22×C3 | — | 2 | 2 | no | — |
| 572 | C22×C3 | C2×D4×D5 | 1 | 3 | yes | — |
| 573 | C2×D3 | — | 5 | 1 | no | — |
| 574 | C2×D3 | — | 5 | 3 | no | — |
| 575 | C2×D3 | — | 10 | 6 | no | — |
| 576 | C2×D3 | — | 10 | 2 | no | — |
| 577 | C2×D3 | — | 20 | 4 | no | — |
| 578 | C3×C4 | — | 2 | 6 | no | — |
| 579 | C3×C4 | C2×D4×D5 | 1 | 3 | yes | — |
| 580 | C3×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 581 | Dic3 | — | 5 | 3 | no | — |
| 582 | Dic3 | — | 5 | 1 | no | — |
| 583 | Dic3 | — | 10 | 6 | no | — |
| 584 | C2×C5 | — | 2 | 3 | no | — |
| 585 | C2×C5 | — | 4 | 2 | no | — |
| 586 | C2×C5 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 587 | D5 | — | 3 | 2 | no | — |
| 588 | D5 | — | 6 | 3 | no | — |
| 589 | D5 | — | 12 | 2 | no | — |
| 590 | C23 | — | 15 | 3 | no | — |
| 591 | C23 | — | 30 | 2 | no | — |
| 592 | Q8 | — | 2 | 6 | no | — |
| 593 | Q8 | — | 15 | 3 | no | — |
| 594 | Q8 | — | 15 | 6 | no | — |
| 595 | Q8 | — | 30 | 6 | no | — |
| 596 | Q8 | — | 30 | 12 | no | — |
| 597 | Q8 | — | 30 | 6 | no | — |
| 598 | Q8 | D4×D15 | 1 | 1 | yes | characteristic |
| 599 | Q8 | C23×D15 | 1 | 6 | yes | — |
| 600 | D4 | — | 2 | 6 | no | — |
| 601 | D4 | — | 15 | 6 | no | — |
| 602 | D4 | — | 15 | 3 | no | — |
| 603 | D4 | — | 15 | 2 | no | — |
| 604 | D4 | — | 30 | 6 | no | — |
| 605 | D4 | — | 30 | 2 | no | — |
| 606 | D4 | — | 30 | 6 | no | — |
| 607 | D4 | — | 30 | 6 | no | — |
| 608 | D4 | D4×D15 | 1 | 3 | yes | — |
| 609 | D4 | C23×D15 | 1 | 2 | yes | — |
| 610 | C2×C4 | — | 2 | 6 | no | — |
| 611 | C2×C4 | — | 2 | 6 | no | — |
| 612 | C2×C4 | — | 15 | 3 | no | — |
| 613 | C2×C4 | — | 15 | 3 | no | — |
| 614 | C2×C4 | — | 15 | 3 | no | — |
| 615 | C2×C4 | — | 15 | 1 | no | — |
| 616 | C2×C4 | — | 15 | 3 | no | — |
| 617 | C2×C4 | — | 30 | 6 | no | — |
| 618 | C2×C4 | — | 30 | 6 | no | — |
| 619 | C2×C4 | — | 30 | 12 | no | — |
| 620 | C2×C4 | — | 30 | 6 | no | — |
| 621 | C2×C4 | — | 30 | 6 | no | — |
| 622 | C2×C4 | — | 30 | 6 | no | — |
| 623 | C2×C4 | C23×D15 | 1 | 3 | yes | — |
| 624 | C8 | — | 15 | 1 | no | — |
| 625 | C8 | — | 15 | 3 | no | — |
| 626 | C8 | C23×D15 | 1 | 1 | yes | characteristic |
| 627 | C8 | C23×D15 | 1 | 3 | yes | — |
| 628 | C2×C3 | — | 2 | 3 | no | — |
| 629 | C2×C3 | — | 4 | 2 | no | — |
| 630 | C2×C3 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 631 | D3 | — | 5 | 2 | no | — |
| 632 | D3 | — | 10 | 3 | no | — |
| 633 | D3 | — | 20 | 2 | no | — |
| 634 | C5 | D3×#578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 635 | C22 | — | 2 | 2 | no | — |
| 636 | C22 | — | 15 | 1 | no | — |
| 637 | C22 | — | 15 | 3 | no | — |
| 638 | C22 | — | 30 | 6 | no | — |
| 639 | C22 | — | 30 | 2 | no | — |
| 640 | C22 | — | 60 | 4 | no | — |
| 641 | C22 | C2×D4×D15 | 1 | 3 | yes | — |
| 642 | C4 | — | 2 | 6 | no | — |
| 643 | C4 | — | 15 | 1 | no | — |
| 644 | C4 | — | 15 | 3 | no | — |
| 645 | C4 | — | 30 | 6 | no | — |
| 646 | C4 | C2×D4×D15 | 1 | 3 | yes | — |
| 647 | C4 | C24×D15 | 1 | 1 | yes | characteristic |
| 648 | C3 | D5×#578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 649 | C2 | — | 2 | 3 | no | — |
| 650 | C2 | — | 4 | 2 | no | — |
| 651 | C2 | — | 15 | 2 | no | — |
| 652 | C2 | — | 30 | 3 | no | — |
| 653 | C2 | — | 60 | 2 | no | — |
| 654 | C2 | C22×D4×D15 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D15×2−1+4 | C2 | semidirect |
| 2. C3×C5×#578 | C2 | semidirect |
| 3. #11756597 | C2 | semidirect |
| 4. #11756538 | C2 | semidirect |
| 5. D15×#137 | C2 | semidirect |
| 6. #11756530 | C2 | semidirect |
| 7. D15×#135 | C2 | semidirect |
| 8. #11756525 | C2 | semidirect |
| 9. C2×Q16×D15 | C2 | semidirect |
| 10. #11756512 | C2 | semidirect |
| 11. D15×#131 | C2 | semidirect |
| 13. C3×C5×2−1+4 | C22 | semidirect |
| 15. #92101 | C22 | semidirect |
| 16. #92101 | C22 | semidirect |
| 21. #92098 | C22 | semidirect |
| 24. C3×C5×#137 | C22 | semidirect |
| 25. C3×C5×#135 | C22 | semidirect |
| 26. C2×C3×C5×Q16 | C22 | semidirect |
| 27. C3×C5×#131 | C22 | semidirect |
| 28. #91840 | C22 | semidirect |
| 29. #91839 | C22 | semidirect |
| 30. #91837 | C22 | semidirect |
| 31. C2×#6718 | C22 | semidirect |
| 32. #91831 | C22 | semidirect |
| 33. #91808 | C22 | semidirect |
| 34. #91807 | C22 | semidirect |
| 37. Q16×D15 | C22 | semidirect |
| 38. Q16×D15 | C22 | semidirect |
| 39. #91805 | C22 | semidirect |
| 40. #91804 | C22 | semidirect |
| 42. #91801 | C22 | semidirect |
| 44. #91798 | C22 | semidirect |
| 45. #91796 | C22 | semidirect |
| 47. C2×Dic60 | C22 | semidirect |
| 48. #91793 | C22 | semidirect |
| 49. #91790 | C22 | semidirect |
| 53. C5×#578 | D3 | semidirect |
| 120. C3×#578 | D5 | semidirect |
| 130. C5×2−1+4 | C2×D3 | semidirect |
| 141. C5×#137 | C2×D3 | semidirect |
| 142. C5×#135 | C2×D3 | semidirect |
| 143. C2×C5×Q16 | C2×D3 | semidirect |
| 144. C5×#131 | C2×D3 | semidirect |
| 207. C3×2−1+4 | C2×D5 | semidirect |
| 218. C3×#137 | C2×D5 | semidirect |
| 219. C3×#135 | C2×D5 | semidirect |
| 220. C2×C3×Q16 | C2×D5 | semidirect |
| 221. C3×#131 | C2×D5 | semidirect |
| 307. #578 | D15 | direct (N × H) |
| 424. 2−1+4 | C2×D15 | semidirect |
| 435. #137 | C2×D15 | semidirect |
| 441. #135 | C2×D15 | semidirect |
| 448. C2×Q16 | C2×D15 | semidirect |
| 454. #131 | C2×D15 | semidirect |
| 462. D15 | #578 | direct (N × H) |
| 570. C3×C5 | C2×#578 | semidirect |
| 634. C5 | D3×#578 | semidirect |
| 648. C3 | D5×#578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D15×2−1+4 | 2 |
| C3×C5×#578 | 2 |
| #11756597 | 2 |
| #11756538 | 2 |
| D15×#137 | 2 |
| #11756530 | 2 |
| D15×#135 | 2 |
| #11756525 | 2 |
| C2×Q16×D15 | 2 |
| #11756512 | 2 |
| D15×#131 | 2 |
| D5×#578 | 3 |
| D3×#578 | 5 |