Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
622 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 622 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 | #10624208 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C5×#3805 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#67141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#6782 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10624053 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10624050 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10624038 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | D3×#1204 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #92020 | — | 3 | 2 | no | maximal |
| 11 | C2×C3⋊Dic15 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C5×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#1220 | C22 | 1 | 2 | yes | — |
| 14 | C3×C5×#67 | C22 | 1 | 2 | yes | — |
| 15 | C2×C32×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 16 | #67158 | C22 | 1 | 1 | yes | characteristic |
| 17 | #67157 | C22 | 1 | 1 | yes | characteristic |
| 18 | #67154 | C22 | 1 | 2 | yes | — |
| 19 | #67153 | C22 | 1 | 2 | yes | — |
| 20 | #67150 | C22 | 1 | 2 | yes | — |
| 21 | D3×Dic15 | C22 | 1 | 2 | yes | — |
| 22 | Dic3×D15 | C22 | 1 | 2 | yes | — |
| 23 | C5×#627 | C22 | 1 | 1 | yes | characteristic |
| 24 | C5×#625 | C22 | 1 | 1 | yes | characteristic |
| 25 | C5×D3×Dic3 | C22 | 1 | 2 | yes | — |
| 26 | #67141 | C22 | 1 | 2 | yes | — |
| 27 | #67141 | C22 | 1 | 2 | yes | — |
| 28 | C3×#1204 | C22 | 1 | 2 | yes | — |
| 29 | C3×#1203 | C22 | 1 | 2 | yes | — |
| 30 | C3×#1200 | C22 | 1 | 2 | yes | — |
| 31 | C3×D3×Dic5 | C22 | 1 | 2 | yes | — |
| 32 | #64298 | — | 5 | 1 | no | maximal, Hall |
| 33 | #6819 | — | 3 | 2 | no | — |
| 34 | C5×#237 | — | 3 | 2 | no | — |
| 35 | C3×#711 | — | 3 | 2 | no | — |
| 36 | C2×#1204 | — | 3 | 2 | no | — |
| 37 | C2×#1204 | — | 3 | 2 | no | — |
| 38 | C2×#1204 | — | 6 | 1 | no | — |
| 39 | #6782 | — | 3 | 2 | no | — |
| 40 | #6782 | D3 | 1 | 2 | yes | complemented |
| 41 | #6780 | — | 3 | 2 | no | — |
| 42 | #6780 | — | 3 | 2 | no | — |
| 43 | #6779 | — | 3 | 2 | no | — |
| 44 | #6779 | — | 3 | 2 | no | — |
| 45 | #6771 | — | 3 | 2 | no | — |
| 46 | D15⋊Q8 | — | 3 | 2 | no | — |
| 47 | D3×Dic10 | — | 3 | 2 | no | — |
| 48 | D5×Dic6 | — | 3 | 2 | no | — |
| 49 | C22×C32×C5 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C3×D15 | C23 | 1 | 2 | yes | — |
| 51 | C2×C3×C5×D3 | C23 | 1 | 2 | yes | — |
| 52 | C3⋊Dic15 | C23 | 1 | 2 | yes | — |
| 53 | C5×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 54 | C5×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 55 | C3×Dic15 | C23 | 1 | 2 | yes | — |
| 56 | C3×C5×Dic3 | C23 | 1 | 2 | yes | — |
| 57 | C32×Dic5 | C23 | 1 | 2 | yes | — |
| 58 | #4150 | — | 9 | 1 | no | Hall |
| 59 | C2×#634 | — | 5 | 1 | no | — |
| 60 | C3×#235 | — | 5 | 2 | no | — |
| 61 | #3805 | — | 5 | 1 | no | — |
| 62 | #3805 | — | 5 | 2 | no | — |
| 63 | #3805 | D5 | 1 | 1 | yes | characteristic, complemented |
| 64 | #3795 | — | 5 | 2 | no | — |
| 65 | #3795 | — | 5 | 2 | no | — |
| 66 | D3×Dic6 | — | 5 | 2 | no | — |
| 67 | D3×Dic6 | — | 5 | 2 | no | — |
| 68 | C3×C5×D4 | — | 3 | 2 | no | — |
| 69 | #1220 | — | 3 | 2 | no | — |
| 70 | #1220 | C2×D3 | 1 | 2 | yes | — |
| 71 | C2×Dic15 | — | 3 | 2 | no | — |
| 72 | C2×Dic15 | — | 3 | 2 | no | — |
| 73 | C2×Dic15 | — | 6 | 1 | no | — |
| 74 | C4×D15 | — | 3 | 2 | no | — |
| 75 | Dic30 | — | 3 | 2 | no | — |
| 76 | C5×#67 | — | 3 | 2 | no | — |
| 77 | C5×#67 | C2×D3 | 1 | 2 | yes | — |
| 78 | C2×C5×Dic3 | — | 3 | 2 | no | — |
| 79 | C2×C5×Dic3 | — | 3 | 2 | no | — |
| 80 | C2×C5×Dic3 | — | 6 | 1 | no | — |
| 81 | C4×C5×D3 | — | 3 | 2 | no | — |
| 82 | C5×Dic6 | — | 3 | 2 | no | — |
| 83 | C3×C22⋊D5 | — | 3 | 2 | no | — |
| 84 | C3×C22⋊D5 | — | 3 | 2 | no | — |
| 85 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 86 | C2×C3×Dic5 | — | 3 | 2 | no | — |
| 87 | C2×C3×Dic5 | C2×D3 | 1 | 2 | yes | — |
| 88 | C3×C4×D5 | — | 3 | 2 | no | — |
| 89 | C3×Dic10 | — | 3 | 2 | no | — |
| 90 | #1204 | — | 3 | 2 | no | — |
| 91 | #1204 | — | 3 | 2 | no | — |
| 92 | #1204 | — | 3 | 2 | no | — |
| 93 | #1204 | — | 3 | 2 | no | — |
| 94 | #1204 | — | 3 | 2 | no | — |
| 95 | #1204 | — | 3 | 2 | no | — |
| 96 | #1204 | — | 6 | 2 | no | — |
| 97 | #1204 | — | 6 | 2 | no | — |
| 98 | #1204 | C2×D3 | 1 | 2 | yes | — |
| 99 | #1203 | C2×D3 | 1 | 2 | yes | — |
| 100 | #1202 | — | 3 | 2 | no | — |
| 101 | #1201 | — | 3 | 2 | no | — |
| 102 | #1200 | — | 3 | 2 | no | — |
| 103 | #1200 | C2×D3 | 1 | 2 | yes | — |
| 104 | D3×Dic5 | — | 3 | 2 | no | — |
| 105 | D3×Dic5 | C2×D3 | 1 | 2 | yes | — |
| 106 | D5×Dic3 | — | 3 | 2 | no | — |
| 107 | D5×Dic3 | — | 3 | 2 | no | — |
| 108 | #1010 | — | 15 | 2 | no | — |
| 109 | C2×C32×C5 | — | 2 | 1 | no | — |
| 110 | C2×C32×C5 | C24 | 1 | 1 | yes | characteristic |
| 111 | C3×D15 | — | 2 | 2 | no | — |
| 112 | C3×C5×D3 | — | 2 | 2 | no | — |
| 113 | C5×#41 | — | 9 | 1 | no | — |
| 114 | Q8×D5 | — | 9 | 2 | no | — |
| 115 | #711 | — | 3 | 2 | no | — |
| 116 | #711 | — | 9 | 2 | no | — |
| 117 | #711 | — | 9 | 2 | no | — |
| 118 | #709 | — | 9 | 2 | no | — |
| 119 | #709 | — | 9 | 1 | no | — |
| 120 | C2×Dic10 | — | 9 | 2 | no | — |
| 121 | C2×Dic10 | — | 9 | 1 | no | — |
| 122 | C2×C32×C4 | — | 5 | 1 | no | — |
| 123 | C2×C3⋊Dic3 | — | 5 | 1 | no | — |
| 124 | C2×C3⋊Dic3 | C2×D5 | 1 | 1 | yes | characteristic |
| 125 | #634 | — | 5 | 2 | no | — |
| 126 | #634 | — | 5 | 2 | no | — |
| 127 | C3×#67 | — | 5 | 2 | no | — |
| 128 | C3×#67 | C2×D5 | 1 | 2 | yes | — |
| 129 | C3×D12 | — | 5 | 2 | no | — |
| 130 | C3×C4×D3 | — | 5 | 2 | no | — |
| 131 | C3×C4×D3 | — | 5 | 2 | no | — |
| 132 | C3×Dic6 | — | 5 | 2 | no | — |
| 133 | #627 | — | 5 | 1 | no | — |
| 134 | #627 | — | 5 | 2 | no | — |
| 135 | #627 | C2×D5 | 1 | 1 | yes | characteristic |
| 136 | #625 | — | 5 | 2 | no | — |
| 137 | #625 | — | 5 | 1 | no | — |
| 138 | #625 | C2×D5 | 1 | 1 | yes | characteristic |
| 139 | D3×Dic3 | — | 5 | 2 | no | — |
| 140 | D3×Dic3 | — | 5 | 2 | no | — |
| 141 | D3×Dic3 | — | 5 | 2 | no | — |
| 142 | D3×Dic3 | C2×D5 | 1 | 2 | yes | — |
| 143 | C22×C3×C5 | — | 2 | 1 | no | — |
| 144 | C22×C3×C5 | — | 3 | 2 | no | — |
| 145 | C22×C3×C5 | C22×D3 | 1 | 2 | yes | — |
| 146 | C2×D15 | C22×D3 | 1 | 2 | yes | — |
| 147 | C2×C5×D3 | C22×D3 | 1 | 2 | yes | — |
| 148 | C2×C3×D5 | — | 3 | 2 | no | — |
| 149 | C3×C4×C5 | — | 3 | 2 | no | — |
| 150 | Dic15 | — | 3 | 2 | no | — |
| 151 | Dic15 | — | 3 | 2 | no | — |
| 152 | Dic15 | — | 6 | 2 | no | — |
| 153 | Dic15 | C22×D3 | 1 | 2 | yes | — |
| 154 | C3×Dic5 | — | 2 | 2 | no | — |
| 155 | C3×Dic5 | — | 3 | 2 | no | — |
| 156 | C3×Dic5 | C22×D3 | 1 | 2 | yes | — |
| 157 | C3×Dic5 | C22×D3 | 1 | 2 | yes | — |
| 158 | C5×Dic3 | — | 3 | 2 | no | — |
| 159 | C5×Dic3 | — | 3 | 2 | no | — |
| 160 | C5×Dic3 | — | 6 | 1 | no | — |
| 161 | C5×Dic3 | — | 6 | 1 | no | — |
| 162 | C5×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 163 | C3×#41 | — | 15 | 2 | no | — |
| 164 | D3×Q8 | — | 15 | 2 | no | — |
| 165 | D3×Q8 | — | 15 | 2 | no | — |
| 166 | #237 | — | 3 | 2 | no | — |
| 167 | #237 | — | 15 | 2 | no | — |
| 168 | #237 | — | 15 | 2 | no | — |
| 169 | #237 | — | 15 | 2 | no | — |
| 170 | #237 | — | 15 | 2 | no | — |
| 171 | #237 | — | 15 | 2 | no | — |
| 172 | #235 | — | 5 | 2 | no | — |
| 173 | #235 | — | 15 | 2 | no | — |
| 174 | #235 | — | 15 | 2 | no | — |
| 175 | C2×Dic6 | — | 15 | 2 | no | — |
| 176 | C2×Dic6 | — | 15 | 2 | no | — |
| 177 | C2×Dic6 | — | 15 | 2 | no | — |
| 178 | C2×Dic6 | — | 30 | 1 | no | — |
| 179 | C32×C5 | 2−1+4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 180 | C5×Q8 | — | 9 | 1 | no | — |
| 181 | C5×D4 | — | 3 | 2 | no | — |
| 182 | C5×D4 | — | 9 | 1 | no | — |
| 183 | C2×C4×C5 | — | 9 | 2 | no | — |
| 184 | C2×C4×C5 | — | 9 | 1 | no | — |
| 185 | C22⋊D5 | — | 3 | 2 | no | — |
| 186 | C22⋊D5 | — | 3 | 2 | no | — |
| 187 | C22⋊D5 | — | 9 | 2 | no | — |
| 188 | C2×Dic5 | — | 3 | 2 | no | — |
| 189 | C2×Dic5 | — | 9 | 2 | no | — |
| 190 | C2×Dic5 | — | 9 | 1 | no | — |
| 191 | C2×Dic5 | D32 | 1 | 1 | yes | characteristic |
| 192 | D20 | — | 9 | 1 | no | — |
| 193 | C4×D5 | — | 3 | 2 | no | — |
| 194 | C4×D5 | — | 9 | 2 | no | — |
| 195 | C4×D5 | — | 9 | 2 | no | — |
| 196 | Dic10 | — | 3 | 2 | no | — |
| 197 | Dic10 | — | 9 | 1 | no | — |
| 198 | Dic10 | — | 9 | 2 | no | — |
| 199 | Dic10 | — | 9 | 2 | no | — |
| 200 | Dic10 | — | 9 | 2 | no | — |
| 201 | C22×C32 | C22×D5 | 1 | 1 | yes | characteristic |
| 202 | C2×C3×D3 | — | 5 | 2 | no | — |
| 203 | C2×C3×D3 | C22×D5 | 1 | 2 | yes | — |
| 204 | C32×C4 | — | 5 | 2 | no | — |
| 205 | C3⋊Dic3 | — | 5 | 2 | no | — |
| 206 | C3⋊Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 207 | C3⋊Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 208 | C3×Dic3 | — | 5 | 2 | no | — |
| 209 | C3×Dic3 | C22×D5 | 1 | 2 | yes | — |
| 210 | 2−1+4 | — | 45 | 1 | no | Sylow |
| 211 | C2×C3×C5 | — | 2 | 2 | no | — |
| 212 | C2×C3×C5 | — | 2 | 2 | no | — |
| 213 | C2×C3×C5 | — | 2 | 1 | no | — |
| 214 | C2×C3×C5 | — | 6 | 2 | no | — |
| 215 | C2×C3×C5 | C23×D3 | 1 | 2 | yes | — |
| 216 | D15 | — | 2 | 2 | no | — |
| 217 | C3×D5 | — | 6 | 2 | no | — |
| 218 | C5×D3 | — | 2 | 2 | no | — |
| 219 | C3×Q8 | — | 15 | 2 | no | — |
| 220 | C3×D4 | — | 3 | 2 | no | — |
| 221 | C3×D4 | — | 15 | 2 | no | — |
| 222 | C3×D4 | — | 15 | 2 | no | — |
| 223 | C2×C3×C4 | — | 5 | 2 | no | — |
| 224 | C2×C3×C4 | — | 10 | 1 | no | — |
| 225 | C2×C3×C4 | — | 15 | 2 | no | — |
| 226 | C2×C3×C4 | — | 15 | 2 | no | — |
| 227 | #67 | — | 3 | 2 | no | — |
| 228 | #67 | — | 5 | 2 | no | — |
| 229 | #67 | — | 15 | 2 | no | — |
| 230 | #67 | — | 15 | 2 | no | — |
| 231 | #67 | — | 15 | 2 | no | — |
| 232 | #67 | D3×D5 | 1 | 2 | yes | — |
| 233 | C2×Dic3 | — | 3 | 2 | no | — |
| 234 | C2×Dic3 | — | 3 | 2 | no | — |
| 235 | C2×Dic3 | — | 6 | 1 | no | — |
| 236 | C2×Dic3 | — | 15 | 2 | no | — |
| 237 | C2×Dic3 | — | 15 | 2 | no | — |
| 238 | C2×Dic3 | — | 15 | 2 | no | — |
| 239 | C2×Dic3 | — | 15 | 2 | no | — |
| 240 | C2×Dic3 | — | 30 | 1 | no | — |
| 241 | D12 | — | 5 | 2 | no | — |
| 242 | C4×D3 | — | 3 | 2 | no | — |
| 243 | C4×D3 | — | 5 | 2 | no | — |
| 244 | C4×D3 | — | 5 | 2 | no | — |
| 245 | C4×D3 | — | 15 | 2 | no | — |
| 246 | C4×D3 | — | 15 | 2 | no | — |
| 247 | C4×D3 | — | 15 | 2 | no | — |
| 248 | Dic6 | — | 3 | 2 | no | — |
| 249 | Dic6 | — | 5 | 2 | no | — |
| 250 | Dic6 | — | 15 | 2 | no | — |
| 251 | Dic6 | — | 15 | 2 | no | — |
| 252 | Dic6 | — | 15 | 2 | no | — |
| 253 | Dic6 | — | 15 | 2 | no | — |
| 254 | Dic6 | — | 15 | 2 | no | — |
| 255 | Dic6 | — | 15 | 2 | no | — |
| 256 | Dic6 | — | 15 | 2 | no | — |
| 257 | Dic6 | — | 30 | 2 | no | — |
| 258 | Dic6 | — | 30 | 2 | no | — |
| 259 | C22×C5 | — | 3 | 2 | no | — |
| 260 | C22×C5 | C2×D32 | 1 | 1 | yes | characteristic |
| 261 | C2×D5 | — | 3 | 2 | no | — |
| 262 | C4×C5 | — | 3 | 2 | no | — |
| 263 | C4×C5 | — | 9 | 1 | no | — |
| 264 | C4×C5 | — | 9 | 1 | no | — |
| 265 | Dic5 | — | 3 | 2 | no | — |
| 266 | Dic5 | — | 9 | 2 | no | — |
| 267 | Dic5 | C2×D32 | 1 | 2 | yes | — |
| 268 | C2×C32 | — | 2 | 1 | no | — |
| 269 | C2×C32 | C23×D5 | 1 | 1 | yes | characteristic |
| 270 | C3×D3 | — | 2 | 2 | no | — |
| 271 | C3×D3 | — | 10 | 2 | no | — |
| 272 | #41 | — | 9 | 1 | no | — |
| 273 | #41 | — | 15 | 2 | no | — |
| 274 | #41 | — | 45 | 2 | no | — |
| 275 | #41 | — | 45 | 1 | no | — |
| 276 | #41 | — | 45 | 2 | no | — |
| 277 | #41 | — | 45 | 2 | no | — |
| 278 | C2×Q8 | — | 45 | 1 | no | — |
| 279 | C2×Q8 | — | 45 | 2 | no | — |
| 280 | C2×Q8 | — | 45 | 2 | no | — |
| 281 | C3×C5 | — | 2 | 1 | no | — |
| 282 | C3×C5 | #1010 | 1 | 2 | yes | complemented |
| 283 | C22×C3 | — | 2 | 1 | no | — |
| 284 | C22×C3 | — | 3 | 2 | no | — |
| 285 | C22×C3 | — | 15 | 2 | no | — |
| 286 | C22×C3 | C2×D3×D5 | 1 | 2 | yes | — |
| 287 | C2×D3 | — | 5 | 2 | no | — |
| 288 | C2×D3 | C2×D3×D5 | 1 | 2 | yes | — |
| 289 | C3×C4 | — | 3 | 2 | no | — |
| 290 | C3×C4 | — | 5 | 2 | no | — |
| 291 | C3×C4 | — | 5 | 2 | no | — |
| 292 | C3×C4 | — | 10 | 2 | no | — |
| 293 | C3×C4 | — | 15 | 2 | no | — |
| 294 | Dic3 | — | 3 | 2 | no | — |
| 295 | Dic3 | — | 3 | 2 | no | — |
| 296 | Dic3 | — | 5 | 2 | no | — |
| 297 | Dic3 | — | 6 | 1 | no | — |
| 298 | Dic3 | — | 6 | 1 | no | — |
| 299 | Dic3 | — | 15 | 2 | no | — |
| 300 | Dic3 | — | 15 | 2 | no | — |
| 301 | Dic3 | — | 30 | 2 | no | — |
| 302 | Dic3 | C2×D3×D5 | 1 | 2 | yes | — |
| 303 | C2×C5 | — | 2 | 1 | no | — |
| 304 | C2×C5 | — | 6 | 2 | no | — |
| 305 | C2×C5 | C22×D32 | 1 | 1 | yes | characteristic |
| 306 | D5 | — | 6 | 2 | no | — |
| 307 | C32 | #4150 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 308 | Q8 | — | 9 | 1 | no | — |
| 309 | Q8 | — | 15 | 2 | no | — |
| 310 | Q8 | — | 45 | 2 | no | — |
| 311 | Q8 | — | 45 | 2 | no | — |
| 312 | Q8 | — | 45 | 2 | no | — |
| 313 | Q8 | — | 45 | 1 | no | — |
| 314 | D4 | — | 3 | 2 | no | — |
| 315 | D4 | — | 9 | 1 | no | — |
| 316 | D4 | — | 15 | 2 | no | — |
| 317 | D4 | — | 15 | 2 | no | — |
| 318 | D4 | — | 45 | 1 | no | — |
| 319 | D4 | — | 45 | 2 | no | — |
| 320 | C2×C4 | — | 5 | 1 | no | — |
| 321 | C2×C4 | — | 9 | 2 | no | — |
| 322 | C2×C4 | — | 9 | 1 | no | — |
| 323 | C2×C4 | — | 15 | 2 | no | — |
| 324 | C2×C4 | — | 15 | 2 | no | — |
| 325 | C2×C4 | — | 45 | 2 | no | — |
| 326 | C2×C4 | — | 45 | 2 | no | — |
| 327 | C2×C4 | — | 45 | 2 | no | — |
| 328 | C2×C4 | — | 45 | 1 | no | — |
| 329 | C2×C3 | — | 2 | 2 | no | — |
| 330 | C2×C3 | — | 2 | 2 | no | — |
| 331 | C2×C3 | — | 2 | 1 | no | — |
| 332 | C2×C3 | — | 6 | 2 | no | — |
| 333 | C2×C3 | — | 30 | 2 | no | — |
| 334 | C2×C3 | C22×D3×D5 | 1 | 2 | yes | — |
| 335 | D3 | — | 2 | 2 | no | — |
| 336 | D3 | — | 10 | 2 | no | — |
| 337 | C5 | #64298 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 338 | C22 | — | 3 | 2 | no | — |
| 339 | C22 | — | 15 | 2 | no | — |
| 340 | C22 | D32×D5 | 1 | 1 | yes | characteristic |
| 341 | C4 | — | 3 | 2 | no | — |
| 342 | C4 | — | 5 | 2 | no | — |
| 343 | C4 | — | 9 | 1 | no | — |
| 344 | C4 | — | 9 | 1 | no | — |
| 345 | C4 | — | 15 | 2 | no | — |
| 346 | C4 | — | 45 | 2 | no | — |
| 347 | C3 | — | 2 | 1 | no | — |
| 348 | C3 | #92020 | 1 | 2 | yes | complemented |
| 349 | C2 | — | 2 | 1 | no | — |
| 350 | C2 | — | 6 | 2 | no | — |
| 351 | C2 | — | 30 | 2 | no | — |
| 352 | 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. #10624208 | C2 | semidirect |
| 3. C5×#3805 | C2 | semidirect |
| 4. C2×#67141 | C2 | semidirect |
| 5. C3×#6782 | C2 | semidirect |
| 6. #10624053 | C2 | semidirect |
| 7. #10624050 | C2 | semidirect |
| 8. #10624038 | C2 | semidirect |
| 9. D3×#1204 | C2 | semidirect |
| 40. #6782 | D3 | semidirect |
| 63. #3805 | D5 | semidirect |
| 179. C32×C5 | 2−1+4 | semidirect |
| 282. C3×C5 | #1010 | semidirect |
| 307. C32 | #4150 | semidirect |
| 337. C5 | #64298 | semidirect |
| 348. C3 | #92020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624229 | 2 |
| #10624208 | 2 |
| C5×#3805 | 2 |
| C2×#67141 | 2 |
| C3×#6782 | 2 |
| #10624053 | 2 |
| #10624050 | 2 |
| #10624038 | 2 |
| D3×#1204 | 2 |
| #92020 | 3 |
| #64298 | 5 |