Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
624 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 140 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 | #10624229 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10624207 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×C5×#627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10624162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#6779 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10624052 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10624047 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10624044 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10624040 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10624038 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | D5×#627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #92000 | — | 3 | 2 | no | maximal |
| 13 | #67184 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C5×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#1220 | C22 | 1 | 2 | yes | — |
| 16 | C2×C3×C5×Dic3 | C22 | 1 | 2 | yes | — |
| 17 | C32×C22⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 18 | #67158 | C22 | 1 | 1 | yes | characteristic |
| 19 | #67157 | C22 | 1 | 1 | yes | characteristic |
| 20 | #67154 | C22 | 1 | 2 | yes | — |
| 21 | #67153 | C22 | 1 | 2 | yes | — |
| 22 | #67151 | C22 | 1 | 2 | yes | — |
| 23 | #67149 | C22 | 1 | 2 | yes | — |
| 24 | Dic3×D15 | C22 | 1 | 2 | yes | — |
| 25 | C5×#627 | C22 | 1 | 1 | yes | characteristic |
| 26 | C5×#627 | C22 | 1 | 2 | yes | — |
| 27 | C5×#627 | C22 | 1 | 1 | yes | characteristic |
| 28 | #67141 | C22 | 1 | 1 | yes | characteristic |
| 29 | #67139 | C22 | 1 | 1 | yes | characteristic |
| 30 | #67137 | C22 | 1 | 1 | yes | characteristic |
| 31 | D5×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 32 | C3×#1204 | C22 | 1 | 2 | yes | — |
| 33 | C3×#1202 | C22 | 1 | 2 | yes | — |
| 34 | C3×#1200 | C22 | 1 | 2 | yes | — |
| 35 | C3×D5×Dic3 | C22 | 1 | 2 | yes | — |
| 36 | #64309 | — | 5 | 1 | no | maximal, Hall |
| 37 | #6817 | — | 3 | 2 | no | — |
| 38 | C2×C5×Dic6 | — | 3 | 2 | no | — |
| 39 | C3×#709 | — | 3 | 2 | no | — |
| 40 | #6779 | — | 3 | 2 | no | — |
| 41 | #6779 | — | 3 | 2 | no | — |
| 42 | #6779 | — | 3 | 2 | no | — |
| 43 | #6779 | — | 6 | 1 | no | — |
| 44 | #6779 | D3 | 1 | 2 | yes | complemented |
| 45 | #6773 | — | 3 | 2 | no | — |
| 46 | #6773 | — | 3 | 2 | no | — |
| 47 | D15⋊Q8 | — | 3 | 2 | no | — |
| 48 | D15⋊Q8 | — | 3 | 2 | no | — |
| 49 | #6766 | — | 3 | 2 | no | — |
| 50 | #6766 | — | 3 | 2 | no | — |
| 51 | D5×Dic6 | — | 3 | 2 | no | — |
| 52 | D5×Dic6 | — | 3 | 2 | no | — |
| 53 | C22×C32×C5 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C3⋊D15 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×C3×D15 | C23 | 1 | 2 | yes | — |
| 56 | C2×C32×D5 | C23 | 1 | 1 | yes | characteristic |
| 57 | C3⋊Dic15 | C23 | 1 | 1 | yes | characteristic |
| 58 | C5×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 59 | C5×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 60 | C3×Dic15 | C23 | 1 | 2 | yes | — |
| 61 | C3×C5×Dic3 | C23 | 1 | 2 | yes | — |
| 62 | C3×C5×Dic3 | C23 | 1 | 2 | yes | — |
| 63 | C32×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 64 | #4147 | — | 9 | 1 | no | Hall |
| 65 | #3830 | — | 5 | 1 | no | — |
| 66 | C3×#237 | — | 5 | 2 | no | — |
| 67 | C2×#627 | — | 5 | 1 | no | — |
| 68 | C2×#627 | D5 | 1 | 1 | yes | characteristic, complemented |
| 69 | #3805 | — | 5 | 1 | no | — |
| 70 | #3805 | — | 5 | 1 | no | — |
| 71 | #3804 | — | 5 | 2 | no | — |
| 72 | #3804 | — | 5 | 2 | no | — |
| 73 | #3798 | — | 5 | 1 | no | — |
| 74 | #3797 | — | 5 | 1 | no | — |
| 75 | D3×Dic6 | — | 5 | 2 | no | — |
| 76 | C2×C3×C4×C5 | — | 3 | 2 | no | — |
| 77 | #1220 | — | 3 | 2 | no | — |
| 78 | #1220 | — | 6 | 1 | no | — |
| 79 | #1220 | C2×D3 | 1 | 2 | yes | — |
| 80 | D60 | — | 3 | 2 | no | — |
| 81 | C4×D15 | — | 3 | 2 | no | — |
| 82 | C4×D15 | — | 3 | 2 | no | — |
| 83 | Dic30 | — | 3 | 2 | no | — |
| 84 | C2×C5×Dic3 | — | 3 | 2 | no | — |
| 85 | C2×C5×Dic3 | — | 6 | 1 | no | — |
| 86 | C2×C5×Dic3 | C2×D3 | 1 | 2 | yes | — |
| 87 | C5×Dic6 | — | 3 | 2 | no | — |
| 88 | C5×Dic6 | — | 3 | 2 | no | — |
| 89 | C5×Dic6 | — | 3 | 2 | no | — |
| 90 | C5×Dic6 | — | 3 | 2 | no | — |
| 91 | C3×C22⋊D5 | — | 2 | 1 | no | — |
| 92 | C3×C22⋊D5 | — | 3 | 2 | no | — |
| 93 | C3×C22⋊D5 | C2×D3 | 1 | 2 | yes | — |
| 94 | C3×D20 | — | 3 | 2 | no | — |
| 95 | C3×C4×D5 | — | 3 | 2 | no | — |
| 96 | C3×C4×D5 | — | 3 | 2 | no | — |
| 97 | C3×Dic10 | — | 3 | 2 | no | — |
| 98 | #1204 | — | 3 | 2 | no | — |
| 99 | #1204 | — | 3 | 2 | no | — |
| 100 | #1204 | — | 3 | 2 | no | — |
| 101 | #1204 | — | 6 | 1 | no | — |
| 102 | #1204 | C2×D3 | 1 | 2 | yes | — |
| 103 | #1202 | — | 3 | 2 | no | — |
| 104 | #1202 | — | 3 | 2 | no | — |
| 105 | #1202 | — | 3 | 2 | no | — |
| 106 | #1202 | — | 6 | 1 | no | — |
| 107 | #1202 | C2×D3 | 1 | 2 | yes | — |
| 108 | #1200 | — | 3 | 2 | no | — |
| 109 | #1200 | — | 3 | 2 | no | — |
| 110 | #1200 | — | 3 | 2 | no | — |
| 111 | #1200 | — | 6 | 1 | no | — |
| 112 | #1200 | C2×D3 | 1 | 2 | yes | — |
| 113 | D5×Dic3 | — | 3 | 2 | no | — |
| 114 | D5×Dic3 | — | 3 | 2 | no | — |
| 115 | D5×Dic3 | — | 3 | 2 | no | — |
| 116 | D5×Dic3 | — | 6 | 1 | no | — |
| 117 | D5×Dic3 | C2×D3 | 1 | 2 | yes | — |
| 118 | #1010 | — | 15 | 2 | no | — |
| 119 | C2×C32×C5 | — | 2 | 1 | no | — |
| 120 | C2×C32×C5 | C24 | 1 | 1 | yes | characteristic |
| 121 | C3⋊D15 | — | 2 | 1 | no | — |
| 122 | C3×D15 | — | 2 | 2 | no | — |
| 123 | C32×D5 | — | 2 | 1 | no | — |
| 124 | C2×C5×Q8 | — | 9 | 1 | no | — |
| 125 | #713 | — | 9 | 1 | no | — |
| 126 | #713 | — | 9 | 2 | no | — |
| 127 | #713 | — | 9 | 1 | no | — |
| 128 | Q8×D5 | — | 9 | 1 | no | — |
| 129 | Q8×D5 | — | 9 | 2 | no | — |
| 130 | Q8×D5 | — | 9 | 1 | no | — |
| 131 | #709 | — | 3 | 2 | no | — |
| 132 | #709 | — | 9 | 1 | no | — |
| 133 | #709 | — | 9 | 2 | no | — |
| 134 | #709 | — | 9 | 1 | no | — |
| 135 | C32×D4 | — | 5 | 1 | no | — |
| 136 | #638 | — | 5 | 1 | no | — |
| 137 | #638 | — | 5 | 1 | no | — |
| 138 | C2×C3⋊Dic3 | — | 5 | 1 | no | — |
| 139 | C2×C3⋊Dic3 | C2×D5 | 1 | 1 | yes | characteristic |
| 140 | C4×C3⋊D3 | — | 5 | 1 | no | — |
| 141 | #634 | — | 5 | 1 | no | — |
| 142 | C3×#67 | — | 5 | 2 | no | — |
| 143 | C3×#67 | — | 5 | 2 | no | — |
| 144 | C2×C3×Dic3 | — | 5 | 2 | no | — |
| 145 | C2×C3×Dic3 | C2×D5 | 1 | 2 | yes | — |
| 146 | C3×C4×D3 | — | 5 | 2 | no | — |
| 147 | C3×Dic6 | — | 5 | 2 | no | — |
| 148 | #627 | — | 5 | 1 | no | — |
| 149 | #627 | — | 5 | 2 | no | — |
| 150 | #627 | C2×D5 | 1 | 2 | yes | — |
| 151 | #627 | C2×D5 | 1 | 1 | yes | characteristic |
| 152 | #627 | C2×D5 | 1 | 1 | yes | characteristic |
| 153 | #626 | — | 5 | 2 | no | — |
| 154 | #625 | — | 5 | 1 | no | — |
| 155 | #624 | — | 5 | 2 | no | — |
| 156 | D3×Dic3 | — | 5 | 2 | no | — |
| 157 | D3×Dic3 | — | 5 | 2 | no | — |
| 158 | C22×C3×C5 | — | 2 | 1 | no | — |
| 159 | C22×C3×C5 | C22×D3 | 1 | 2 | yes | — |
| 160 | C2×D15 | — | 3 | 2 | no | — |
| 161 | C2×D15 | — | 6 | 1 | no | — |
| 162 | C2×D15 | C22×D3 | 1 | 2 | yes | — |
| 163 | C2×C3×D5 | — | 2 | 1 | no | — |
| 164 | C2×C3×D5 | — | 3 | 2 | no | — |
| 165 | C2×C3×D5 | C22×D3 | 1 | 2 | yes | — |
| 166 | C3×C4×C5 | — | 3 | 2 | no | — |
| 167 | C3×C4×C5 | — | 3 | 2 | no | — |
| 168 | Dic15 | — | 3 | 2 | no | — |
| 169 | Dic15 | — | 6 | 1 | no | — |
| 170 | Dic15 | C22×D3 | 1 | 2 | yes | — |
| 171 | C3×Dic5 | — | 2 | 1 | no | — |
| 172 | C3×Dic5 | — | 3 | 2 | no | — |
| 173 | C3×Dic5 | C22×D3 | 1 | 2 | yes | — |
| 174 | C5×Dic3 | — | 3 | 2 | no | — |
| 175 | C5×Dic3 | — | 3 | 2 | no | — |
| 176 | C5×Dic3 | — | 6 | 1 | no | — |
| 177 | C5×Dic3 | — | 6 | 1 | no | — |
| 178 | C5×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 179 | C5×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 180 | C3×#41 | — | 15 | 2 | no | — |
| 181 | D3×Q8 | — | 15 | 2 | no | — |
| 182 | D3×Q8 | — | 15 | 2 | no | — |
| 183 | #237 | — | 5 | 2 | no | — |
| 184 | #237 | — | 15 | 2 | no | — |
| 185 | #237 | — | 15 | 2 | no | — |
| 186 | #237 | — | 15 | 2 | no | — |
| 187 | #237 | — | 15 | 2 | no | — |
| 188 | #237 | — | 15 | 2 | no | — |
| 189 | #237 | — | 30 | 1 | no | — |
| 190 | #235 | — | 15 | 2 | no | — |
| 191 | #235 | — | 15 | 2 | no | — |
| 192 | #235 | — | 15 | 2 | no | — |
| 193 | C2×Dic6 | — | 3 | 2 | no | — |
| 194 | C2×Dic6 | — | 15 | 2 | no | — |
| 195 | C2×Dic6 | — | 15 | 2 | no | — |
| 196 | C32×C5 | 2−1+4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 197 | C5×Q8 | — | 9 | 1 | no | — |
| 198 | C5×Q8 | — | 9 | 2 | no | — |
| 199 | C5×Q8 | — | 9 | 1 | no | — |
| 200 | C2×C4×C5 | — | 3 | 2 | no | — |
| 201 | C2×C4×C5 | — | 9 | 1 | no | — |
| 202 | C22⋊D5 | — | 3 | 2 | no | — |
| 203 | C22⋊D5 | — | 9 | 1 | no | — |
| 204 | C22⋊D5 | D32 | 1 | 1 | yes | characteristic |
| 205 | D20 | — | 3 | 2 | no | — |
| 206 | D20 | — | 9 | 2 | no | — |
| 207 | D20 | — | 9 | 1 | no | — |
| 208 | D20 | — | 9 | 1 | no | — |
| 209 | C4×D5 | — | 3 | 2 | no | — |
| 210 | C4×D5 | — | 3 | 2 | no | — |
| 211 | C4×D5 | — | 9 | 2 | no | — |
| 212 | C4×D5 | — | 9 | 2 | no | — |
| 213 | C4×D5 | — | 9 | 2 | no | — |
| 214 | C4×D5 | — | 9 | 1 | no | — |
| 215 | C4×D5 | — | 9 | 1 | no | — |
| 216 | Dic10 | — | 3 | 2 | no | — |
| 217 | Dic10 | — | 9 | 1 | no | — |
| 218 | Dic10 | — | 9 | 2 | no | — |
| 219 | Dic10 | — | 9 | 1 | no | — |
| 220 | C22×C32 | — | 5 | 1 | no | — |
| 221 | C22×C32 | C22×D5 | 1 | 1 | yes | characteristic |
| 222 | C2×C3⋊D3 | — | 5 | 1 | no | — |
| 223 | C2×C3×D3 | — | 5 | 2 | no | — |
| 224 | C32×C4 | — | 5 | 1 | no | — |
| 225 | C3⋊Dic3 | — | 5 | 1 | no | — |
| 226 | C3⋊Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 227 | C3⋊Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 228 | C3×Dic3 | — | 5 | 2 | no | — |
| 229 | C3×Dic3 | C22×D5 | 1 | 2 | yes | — |
| 230 | C3×Dic3 | C22×D5 | 1 | 2 | yes | — |
| 231 | 2−1+4 | — | 45 | 1 | no | Sylow |
| 232 | C2×C3×C5 | — | 2 | 2 | no | — |
| 233 | C2×C3×C5 | — | 2 | 1 | no | — |
| 234 | C2×C3×C5 | — | 4 | 1 | no | — |
| 235 | C2×C3×C5 | C23×D3 | 1 | 2 | yes | — |
| 236 | D15 | — | 2 | 2 | no | — |
| 237 | D15 | — | 6 | 2 | no | — |
| 238 | D15 | — | 12 | 1 | no | — |
| 239 | C3×D5 | — | 2 | 2 | no | — |
| 240 | C3×D5 | — | 4 | 1 | no | — |
| 241 | C3×D5 | — | 6 | 2 | no | — |
| 242 | C3×Q8 | — | 15 | 2 | no | — |
| 243 | C3×D4 | — | 5 | 2 | no | — |
| 244 | C3×D4 | — | 10 | 1 | no | — |
| 245 | C3×D4 | — | 15 | 2 | no | — |
| 246 | C3×D4 | — | 15 | 2 | no | — |
| 247 | C2×C3×C4 | — | 3 | 2 | no | — |
| 248 | C2×C3×C4 | — | 15 | 2 | no | — |
| 249 | C2×C3×C4 | — | 15 | 2 | no | — |
| 250 | #67 | — | 5 | 2 | no | — |
| 251 | #67 | — | 5 | 2 | no | — |
| 252 | #67 | — | 15 | 2 | no | — |
| 253 | #67 | — | 15 | 2 | no | — |
| 254 | #67 | — | 15 | 2 | no | — |
| 255 | #67 | — | 15 | 2 | no | — |
| 256 | #67 | — | 30 | 1 | no | — |
| 257 | #67 | — | 30 | 1 | no | — |
| 258 | C2×Dic3 | — | 3 | 2 | no | — |
| 259 | C2×Dic3 | — | 5 | 2 | no | — |
| 260 | C2×Dic3 | — | 6 | 1 | no | — |
| 261 | C2×Dic3 | — | 15 | 2 | no | — |
| 262 | C2×Dic3 | — | 15 | 2 | no | — |
| 263 | C2×Dic3 | — | 15 | 2 | no | — |
| 264 | C2×Dic3 | — | 30 | 1 | no | — |
| 265 | C2×Dic3 | D3×D5 | 1 | 2 | yes | — |
| 266 | D12 | — | 15 | 2 | no | — |
| 267 | C4×D3 | — | 5 | 2 | no | — |
| 268 | C4×D3 | — | 15 | 2 | no | — |
| 269 | C4×D3 | — | 15 | 2 | no | — |
| 270 | C4×D3 | — | 15 | 2 | no | — |
| 271 | C4×D3 | — | 15 | 2 | no | — |
| 272 | C4×D3 | — | 15 | 2 | no | — |
| 273 | C4×D3 | — | 30 | 1 | no | — |
| 274 | Dic6 | — | 3 | 2 | no | — |
| 275 | Dic6 | — | 3 | 2 | no | — |
| 276 | Dic6 | — | 3 | 2 | no | — |
| 277 | Dic6 | — | 3 | 2 | no | — |
| 278 | Dic6 | — | 5 | 2 | no | — |
| 279 | Dic6 | — | 15 | 2 | no | — |
| 280 | Dic6 | — | 15 | 2 | no | — |
| 281 | Dic6 | — | 15 | 2 | no | — |
| 282 | Dic6 | — | 15 | 2 | no | — |
| 283 | Dic6 | — | 30 | 1 | no | — |
| 284 | C22×C5 | C2×D32 | 1 | 1 | yes | characteristic |
| 285 | C2×D5 | — | 3 | 2 | no | — |
| 286 | C2×D5 | — | 9 | 1 | no | — |
| 287 | C2×D5 | C2×D32 | 1 | 1 | yes | characteristic |
| 288 | C4×C5 | — | 3 | 2 | no | — |
| 289 | C4×C5 | — | 3 | 2 | no | — |
| 290 | C4×C5 | — | 9 | 1 | no | — |
| 291 | C4×C5 | — | 9 | 1 | no | — |
| 292 | Dic5 | — | 3 | 2 | no | — |
| 293 | Dic5 | — | 9 | 1 | no | — |
| 294 | Dic5 | C2×D32 | 1 | 1 | yes | characteristic |
| 295 | C2×C32 | — | 2 | 1 | no | — |
| 296 | C2×C32 | — | 10 | 1 | no | — |
| 297 | C2×C32 | C23×D5 | 1 | 1 | yes | characteristic |
| 298 | C3⋊D3 | — | 10 | 1 | no | — |
| 299 | C3×D3 | — | 10 | 2 | no | — |
| 300 | #41 | — | 15 | 2 | no | — |
| 301 | #41 | — | 45 | 2 | no | — |
| 302 | #41 | — | 45 | 1 | no | — |
| 303 | #41 | — | 45 | 1 | no | — |
| 304 | #41 | — | 45 | 1 | no | — |
| 305 | #41 | — | 45 | 2 | no | — |
| 306 | #41 | — | 45 | 1 | no | — |
| 307 | C2×Q8 | — | 9 | 1 | no | — |
| 308 | C2×Q8 | — | 45 | 1 | no | — |
| 309 | C2×Q8 | — | 45 | 2 | no | — |
| 310 | C2×Q8 | — | 45 | 1 | no | — |
| 311 | C3×C5 | — | 2 | 1 | no | — |
| 312 | C3×C5 | #1010 | 1 | 2 | yes | complemented |
| 313 | C22×C3 | — | 2 | 1 | no | — |
| 314 | C22×C3 | — | 5 | 2 | no | — |
| 315 | C22×C3 | — | 10 | 1 | no | — |
| 316 | C22×C3 | — | 15 | 2 | no | — |
| 317 | C22×C3 | C2×D3×D5 | 1 | 2 | yes | — |
| 318 | C2×D3 | — | 5 | 2 | no | — |
| 319 | C2×D3 | — | 15 | 2 | no | — |
| 320 | C2×D3 | — | 30 | 1 | no | — |
| 321 | C3×C4 | — | 3 | 2 | no | — |
| 322 | C3×C4 | — | 3 | 2 | no | — |
| 323 | C3×C4 | — | 5 | 2 | no | — |
| 324 | C3×C4 | — | 10 | 1 | no | — |
| 325 | C3×C4 | — | 15 | 2 | no | — |
| 326 | Dic3 | — | 3 | 2 | no | — |
| 327 | Dic3 | — | 3 | 2 | no | — |
| 328 | Dic3 | — | 5 | 2 | no | — |
| 329 | Dic3 | — | 6 | 1 | no | — |
| 330 | Dic3 | — | 6 | 1 | no | — |
| 331 | Dic3 | — | 15 | 2 | no | — |
| 332 | Dic3 | — | 30 | 1 | no | — |
| 333 | Dic3 | C2×D3×D5 | 1 | 2 | yes | — |
| 334 | Dic3 | C2×D3×D5 | 1 | 2 | yes | — |
| 335 | C2×C5 | — | 2 | 1 | no | — |
| 336 | C2×C5 | C22×D32 | 1 | 1 | yes | characteristic |
| 337 | D5 | — | 2 | 1 | no | — |
| 338 | D5 | — | 6 | 2 | no | — |
| 339 | D5 | — | 18 | 1 | no | — |
| 340 | C32 | #4147 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 341 | Q8 | — | 9 | 1 | no | — |
| 342 | Q8 | — | 9 | 2 | no | — |
| 343 | Q8 | — | 9 | 1 | no | — |
| 344 | Q8 | — | 15 | 2 | no | — |
| 345 | Q8 | — | 45 | 2 | no | — |
| 346 | Q8 | — | 45 | 1 | no | — |
| 347 | Q8 | — | 45 | 1 | no | — |
| 348 | D4 | — | 5 | 1 | no | — |
| 349 | D4 | — | 15 | 2 | no | — |
| 350 | D4 | — | 15 | 2 | no | — |
| 351 | D4 | — | 45 | 2 | no | — |
| 352 | D4 | — | 45 | 1 | no | — |
| 353 | D4 | — | 45 | 1 | no | — |
| 354 | D4 | — | 45 | 1 | no | — |
| 355 | C2×C4 | — | 3 | 2 | no | — |
| 356 | C2×C4 | — | 9 | 1 | no | — |
| 357 | C2×C4 | — | 15 | 2 | no | — |
| 358 | C2×C4 | — | 15 | 2 | no | — |
| 359 | C2×C4 | — | 45 | 2 | no | — |
| 360 | C2×C4 | — | 45 | 2 | no | — |
| 361 | C2×C4 | — | 45 | 1 | no | — |
| 362 | C2×C4 | — | 45 | 2 | no | — |
| 363 | C2×C4 | — | 45 | 1 | no | — |
| 364 | C2×C3 | — | 2 | 2 | no | — |
| 365 | C2×C3 | — | 2 | 1 | no | — |
| 366 | C2×C3 | — | 4 | 1 | no | — |
| 367 | C2×C3 | — | 10 | 2 | no | — |
| 368 | C2×C3 | — | 20 | 1 | no | — |
| 369 | C2×C3 | — | 30 | 2 | no | — |
| 370 | C2×C3 | C22×D3×D5 | 1 | 2 | yes | — |
| 371 | D3 | — | 10 | 2 | no | — |
| 372 | D3 | — | 30 | 2 | no | — |
| 373 | D3 | — | 60 | 1 | no | — |
| 374 | C5 | #64309 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 375 | C22 | — | 5 | 1 | no | — |
| 376 | C22 | — | 15 | 2 | no | — |
| 377 | C22 | — | 45 | 1 | no | — |
| 378 | C22 | D32×D5 | 1 | 1 | yes | characteristic |
| 379 | C4 | — | 3 | 2 | no | — |
| 380 | C4 | — | 3 | 2 | no | — |
| 381 | C4 | — | 5 | 1 | no | — |
| 382 | C4 | — | 9 | 1 | no | — |
| 383 | C4 | — | 9 | 1 | no | — |
| 384 | C4 | — | 15 | 2 | no | — |
| 385 | C4 | — | 45 | 1 | no | — |
| 386 | C3 | — | 2 | 1 | no | — |
| 387 | C3 | #92000 | 1 | 2 | yes | complemented |
| 388 | C2 | — | 2 | 1 | no | — |
| 389 | C2 | — | 10 | 1 | no | — |
| 390 | C2 | — | 30 | 2 | no | — |
| 391 | C2 | — | 90 | 1 | no | — |
| 392 | C2 | C2×D32×D5 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×D5 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C22×C32×C5 | C23 |
| hypercenter | C22 | D32×D5 |
| hypocenter | C32×C5 | 2−1+4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624229 | C2 | semidirect |
| 2. #10624207 | C2 | semidirect |
| 3. C2×C5×#627 | C2 | semidirect |
| 4. #10624162 | C2 | semidirect |
| 5. C3×#6779 | C2 | semidirect |
| 6. #10624052 | C2 | semidirect |
| 7. #10624047 | C2 | semidirect |
| 8. #10624044 | C2 | semidirect |
| 9. #10624040 | C2 | semidirect |
| 10. #10624038 | C2 | semidirect |
| 11. D5×#627 | C2 | semidirect |
| 44. #6779 | D3 | semidirect |
| 68. C2×#627 | D5 | semidirect |
| 196. C32×C5 | 2−1+4 | semidirect |
| 312. C3×C5 | #1010 | semidirect |
| 340. C32 | #4147 | semidirect |
| 374. C5 | #64309 | semidirect |
| 387. C3 | #92000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624229 | 2 |
| #10624207 | 2 |
| C2×C5×#627 | 2 |
| #10624162 | 2 |
| C3×#6779 | 2 |
| #10624052 | 2 |
| #10624047 | 2 |
| #10624044 | 2 |
| #10624040 | 2 |
| #10624038 | 2 |
| D5×#627 | 2 |
| #92000 | 3 |
| #64309 | 5 |