Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1544 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1544 conjugacy classes of subgroups — too many to draw. Only its 131 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 | A4×#709 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11756896 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C5×A4⋊Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11756793 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11756754 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11756751 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | D5×A4⋊Q8 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | (C5⋊S4)⋊Q8 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10617886 | — | 3 | 1 | no | maximal, Hall |
| 10 | C2×C4×C5×A4 | C22 | 1 | 1 | yes | characteristic |
| 11 | #92000 | — | 4 | 1 | no | maximal |
| 12 | A4×C22⋊D5 | C22 | 1 | 2 | yes | — |
| 13 | A4×D20 | C22 | 1 | 1 | yes | characteristic |
| 14 | C4×D5×A4 | C22 | 1 | 2 | yes | — |
| 15 | A4×Dic10 | C22 | 1 | 1 | yes | characteristic |
| 16 | #91958 | C22 | 1 | 2 | yes | — |
| 17 | C4⋊(C5⋊S4) | C22 | 1 | 1 | yes | characteristic |
| 18 | C4×C5⋊S4 | C22 | 1 | 2 | yes | — |
| 19 | #91948 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C5×SL(2,ℤ/4) | C22 | 1 | 2 | yes | — |
| 21 | C5×A4⋊Q8 | C22 | 1 | 2 | yes | — |
| 22 | C5×A4⋊Q8 | C22 | 1 | 2 | yes | — |
| 23 | #91905 | C22 | 1 | 4 | yes | — |
| 24 | D5×SL(2,ℤ/4) | C22 | 1 | 4 | yes | — |
| 25 | #91901 | C22 | 1 | 4 | yes | — |
| 26 | #91899 | C22 | 1 | 4 | yes | — |
| 27 | #87490 | — | 5 | 1 | no | maximal, Hall |
| 28 | C2×#4147 | — | 3 | 1 | no | — |
| 29 | C22×#709 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×C5×C22⋊Q8 | — | 3 | 1 | no | — |
| 31 | #66150 | — | 3 | 1 | no | — |
| 32 | #66125 | — | 3 | 1 | no | — |
| 33 | #65967 | — | 3 | 2 | no | — |
| 34 | #65966 | — | 3 | 2 | no | — |
| 35 | #65965 | — | 3 | 2 | no | — |
| 36 | #65964 | — | 3 | 2 | no | — |
| 37 | #65963 | — | 3 | 2 | no | — |
| 38 | #65962 | — | 3 | 2 | no | — |
| 39 | #65961 | — | 3 | 2 | no | — |
| 40 | D5×C22⋊Q8 | — | 3 | 2 | no | — |
| 41 | #65844 | — | 3 | 1 | no | — |
| 42 | #65841 | — | 3 | 4 | no | — |
| 43 | #65838 | — | 3 | 1 | no | — |
| 44 | #65824 | — | 3 | 4 | no | — |
| 45 | C22×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×D5×A4 | C23 | 1 | 2 | yes | — |
| 47 | C2×C5⋊S4 | C23 | 1 | 2 | yes | — |
| 48 | #6817 | — | 4 | 1 | no | — |
| 49 | C2×C5×Dic6 | — | 4 | 1 | no | — |
| 50 | C3×#709 | — | 4 | 1 | no | — |
| 51 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 52 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 53 | #6779 | — | 4 | 4 | no | — |
| 54 | #6773 | — | 4 | 2 | no | — |
| 55 | D15⋊Q8 | — | 4 | 2 | no | — |
| 56 | #6766 | — | 4 | 2 | no | — |
| 57 | D5×Dic6 | — | 4 | 2 | no | — |
| 58 | A4×Dic5 | C23 | 1 | 2 | yes | — |
| 59 | A4⋊Dic5 | C23 | 1 | 2 | yes | — |
| 60 | C5×SL(2,ℤ/4) | C23 | 1 | 4 | yes | — |
| 61 | A4×#41 | — | 5 | 1 | no | — |
| 62 | Q8×S4 | — | 5 | 2 | no | — |
| 63 | #5914 | — | 5 | 4 | no | — |
| 64 | #5914 | — | 5 | 2 | no | — |
| 65 | #5912 | — | 5 | 1 | no | — |
| 66 | #5912 | — | 5 | 2 | no | — |
| 67 | C2×A4⋊Q8 | — | 5 | 2 | no | — |
| 68 | C2×A4⋊Q8 | D5 | 1 | 1 | yes | characteristic, complemented |
| 69 | C22×C5×Q8 | — | 3 | 1 | no | — |
| 70 | C23×C4×C5 | C2×D3 | 1 | 1 | yes | characteristic |
| 71 | C22×C22⋊D5 | C2×D3 | 1 | 2 | yes | — |
| 72 | #4147 | — | 6 | 1 | no | — |
| 73 | #4147 | — | 6 | 2 | no | — |
| 74 | #4147 | — | 6 | 1 | no | — |
| 75 | #4147 | — | 6 | 2 | no | — |
| 76 | #4147 | — | 6 | 1 | no | — |
| 77 | #4147 | — | 6 | 1 | no | — |
| 78 | C2×#713 | — | 3 | 2 | no | — |
| 79 | C2×#713 | — | 3 | 2 | no | — |
| 80 | C2×Q8×D5 | — | 3 | 2 | no | — |
| 81 | C2×Q8×D5 | — | 3 | 2 | no | — |
| 82 | C2×#709 | — | 3 | 1 | no | — |
| 83 | C2×#709 | — | 3 | 2 | no | — |
| 84 | C2×#709 | — | 3 | 1 | no | — |
| 85 | C2×#709 | — | 3 | 2 | no | — |
| 86 | C2×#709 | — | 3 | 1 | no | — |
| 87 | C2×#709 | — | 3 | 1 | no | — |
| 88 | C2×#709 | — | 3 | 4 | no | — |
| 89 | C2×#709 | — | 3 | 1 | no | — |
| 90 | C22×D20 | C2×D3 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×D5 | C2×D3 | 1 | 2 | yes | — |
| 92 | C22×Dic10 | C2×D3 | 1 | 1 | yes | characteristic |
| 93 | C5×C22⋊Q8 | — | 3 | 2 | no | — |
| 94 | C5×C22⋊Q8 | — | 3 | 2 | no | — |
| 95 | C5×C22⋊Q8 | — | 3 | 2 | no | — |
| 96 | C5×C22⋊Q8 | — | 3 | 2 | no | — |
| 97 | C2×C5×C4⋊C4 | — | 3 | 1 | no | — |
| 98 | C2×C5×C4⋊C4 | — | 3 | 2 | no | — |
| 99 | C2×C5×C22⋊C4 | — | 3 | 2 | no | — |
| 100 | #4099 | — | 3 | 2 | no | — |
| 101 | #4093 | — | 3 | 2 | no | — |
| 102 | #4092 | — | 3 | 2 | no | — |
| 103 | #4092 | — | 3 | 2 | no | — |
| 104 | #4090 | — | 3 | 2 | no | — |
| 105 | #4076 | — | 3 | 4 | no | — |
| 106 | #4076 | — | 3 | 1 | no | — |
| 107 | #4076 | — | 3 | 1 | no | — |
| 108 | #4075 | — | 3 | 4 | no | — |
| 109 | #4075 | — | 3 | 2 | no | — |
| 110 | C4×C22⋊D5 | — | 3 | 4 | no | — |
| 111 | C4×C22⋊D5 | — | 3 | 2 | no | — |
| 112 | C4×C22⋊D5 | — | 3 | 2 | no | — |
| 113 | #4072 | — | 3 | 1 | no | — |
| 114 | #4070 | — | 3 | 1 | no | — |
| 115 | #4070 | — | 3 | 1 | no | — |
| 116 | #4043 | — | 3 | 2 | no | — |
| 117 | #4043 | — | 3 | 2 | no | — |
| 118 | #4042 | — | 3 | 4 | no | — |
| 119 | #4042 | — | 3 | 4 | no | — |
| 120 | #4041 | — | 3 | 4 | no | — |
| 121 | #4041 | — | 3 | 2 | no | — |
| 122 | #4041 | — | 3 | 2 | no | — |
| 123 | #4040 | — | 3 | 4 | no | — |
| 124 | #4040 | — | 3 | 4 | no | — |
| 125 | #4039 | — | 3 | 2 | no | — |
| 126 | #4039 | — | 3 | 4 | no | — |
| 127 | #4038 | — | 3 | 2 | no | — |
| 128 | D5×C4⋊C4 | — | 3 | 2 | no | — |
| 129 | D5×C4⋊C4 | — | 3 | 4 | no | — |
| 130 | #4034 | — | 3 | 4 | no | — |
| 131 | #4033 | — | 3 | 2 | no | — |
| 132 | #4031 | — | 3 | 4 | no | — |
| 133 | #4030 | — | 3 | 4 | no | — |
| 134 | #4030 | — | 3 | 4 | no | — |
| 135 | #4029 | — | 3 | 4 | no | — |
| 136 | #4028 | — | 3 | 4 | no | — |
| 137 | #4027 | — | 3 | 4 | no | — |
| 138 | D5×C22⋊C4 | — | 3 | 4 | no | — |
| 139 | #4024 | — | 3 | 4 | no | — |
| 140 | #3489 | — | 15 | 1 | no | Sylow |
| 141 | C2×C5×A4 | — | 2 | 1 | no | — |
| 142 | C2×C5×A4 | C24 | 1 | 1 | yes | characteristic |
| 143 | D5×A4 | — | 2 | 2 | no | — |
| 144 | C5⋊S4 | — | 2 | 2 | no | — |
| 145 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 146 | #1220 | — | 4 | 2 | no | — |
| 147 | D60 | — | 4 | 1 | no | — |
| 148 | C4×D15 | — | 4 | 2 | no | — |
| 149 | Dic30 | — | 4 | 1 | no | — |
| 150 | C2×C5×Dic3 | — | 4 | 2 | no | — |
| 151 | C5×Dic6 | — | 4 | 2 | no | — |
| 152 | C5×Dic6 | — | 4 | 2 | no | — |
| 153 | C3×C22⋊D5 | — | 4 | 2 | no | — |
| 154 | C3×D20 | — | 4 | 1 | no | — |
| 155 | C3×C4×D5 | — | 4 | 2 | no | — |
| 156 | C3×Dic10 | — | 4 | 1 | no | — |
| 157 | #1204 | — | 4 | 4 | no | — |
| 158 | #1202 | — | 4 | 4 | no | — |
| 159 | #1200 | — | 4 | 4 | no | — |
| 160 | D5×Dic3 | — | 4 | 4 | no | — |
| 161 | #1010 | — | 20 | 1 | no | — |
| 162 | Q8×A4 | — | 5 | 1 | no | — |
| 163 | D4×A4 | — | 5 | 2 | no | — |
| 164 | D4×A4 | — | 5 | 1 | no | — |
| 165 | C2×C4×A4 | — | 5 | 2 | no | — |
| 166 | C2×C4×A4 | C2×D5 | 1 | 1 | yes | characteristic |
| 167 | GL(2,ℤ/4) | — | 5 | 2 | no | — |
| 168 | GL(2,ℤ/4) | — | 5 | 4 | no | — |
| 169 | C2×SL(2,ℤ/4) | — | 5 | 4 | no | — |
| 170 | C2×SL(2,ℤ/4) | C2×D5 | 1 | 2 | yes | — |
| 171 | C4⋊S4 | — | 5 | 1 | no | — |
| 172 | C4×S4 | — | 5 | 2 | no | — |
| 173 | C4×S4 | — | 5 | 4 | no | — |
| 174 | A4⋊Q8 | — | 5 | 1 | no | — |
| 175 | A4⋊Q8 | — | 5 | 4 | no | — |
| 176 | A4⋊Q8 | C2×D5 | 1 | 2 | yes | — |
| 177 | A4⋊Q8 | C2×D5 | 1 | 2 | yes | — |
| 178 | C24×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 179 | C23×D5 | C22×D3 | 1 | 2 | yes | — |
| 180 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 181 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 182 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 183 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 184 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 185 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 186 | C22×C4×C5 | — | 3 | 1 | no | — |
| 187 | C22×C4×C5 | — | 3 | 1 | no | — |
| 188 | C22×C4×C5 | — | 3 | 1 | no | — |
| 189 | C22×C4×C5 | — | 3 | 1 | no | — |
| 190 | C22×C4×C5 | — | 3 | 2 | no | — |
| 191 | C22×C4×C5 | — | 3 | 2 | no | — |
| 192 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 193 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 194 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 195 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 196 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 197 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 198 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 199 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 200 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 201 | C22×Dic5 | C22×D3 | 1 | 2 | yes | — |
| 202 | #713 | — | 6 | 2 | no | — |
| 203 | #713 | — | 6 | 2 | no | — |
| 204 | #713 | — | 6 | 2 | no | — |
| 205 | #713 | — | 6 | 4 | no | — |
| 206 | #713 | — | 6 | 2 | no | — |
| 207 | #713 | — | 6 | 2 | no | — |
| 208 | #713 | — | 6 | 2 | no | — |
| 209 | Q8×D5 | — | 6 | 2 | no | — |
| 210 | Q8×D5 | — | 6 | 4 | no | — |
| 211 | Q8×D5 | — | 6 | 2 | no | — |
| 212 | Q8×D5 | — | 6 | 2 | no | — |
| 213 | Q8×D5 | — | 6 | 2 | no | — |
| 214 | Q8×D5 | — | 6 | 2 | no | — |
| 215 | Q8×D5 | — | 6 | 2 | no | — |
| 216 | #709 | — | 3 | 1 | no | — |
| 217 | #709 | — | 3 | 2 | no | — |
| 218 | #709 | — | 3 | 1 | no | — |
| 219 | #709 | — | 3 | 2 | no | — |
| 220 | #709 | — | 3 | 1 | no | — |
| 221 | #709 | — | 6 | 2 | no | — |
| 222 | #709 | — | 6 | 1 | no | — |
| 223 | #709 | — | 6 | 1 | no | — |
| 224 | #709 | — | 6 | 2 | no | — |
| 225 | #709 | — | 6 | 1 | no | — |
| 226 | #709 | — | 6 | 4 | no | — |
| 227 | #709 | — | 6 | 4 | no | — |
| 228 | #709 | — | 6 | 4 | no | — |
| 229 | #709 | — | 6 | 1 | no | — |
| 230 | #709 | — | 6 | 1 | no | — |
| 231 | #709 | — | 6 | 1 | no | — |
| 232 | #709 | — | 6 | 1 | no | — |
| 233 | #709 | — | 6 | 4 | no | — |
| 234 | #709 | S4 | 1 | 1 | yes | characteristic, complemented |
| 235 | C2×D20 | — | 3 | 1 | no | — |
| 236 | C2×D20 | — | 3 | 2 | no | — |
| 237 | C2×D20 | — | 3 | 1 | no | — |
| 238 | C2×D20 | — | 3 | 4 | no | — |
| 239 | C2×D20 | — | 3 | 1 | no | — |
| 240 | C2×D20 | — | 3 | 4 | no | — |
| 241 | C2×C4×D5 | — | 3 | 2 | no | — |
| 242 | C2×C4×D5 | — | 3 | 2 | no | — |
| 243 | C2×C4×D5 | — | 3 | 2 | no | — |
| 244 | C2×C4×D5 | — | 3 | 2 | no | — |
| 245 | C2×C4×D5 | — | 3 | 4 | no | — |
| 246 | C2×C4×D5 | — | 3 | 4 | no | — |
| 247 | C2×C4×D5 | — | 3 | 2 | no | — |
| 248 | C2×C4×D5 | — | 3 | 4 | no | — |
| 249 | C2×Dic10 | — | 3 | 1 | no | — |
| 250 | C2×Dic10 | — | 3 | 2 | no | — |
| 251 | C2×Dic10 | — | 3 | 1 | no | — |
| 252 | C2×Dic10 | — | 3 | 4 | no | — |
| 253 | C2×Dic10 | — | 3 | 1 | no | — |
| 254 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 255 | C5×C4⋊C4 | — | 3 | 4 | no | — |
| 256 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 257 | C5×C4⋊C4 | — | 3 | 4 | no | — |
| 258 | C5×C22⋊C4 | — | 3 | 4 | no | — |
| 259 | C5×C22⋊C4 | — | 3 | 4 | no | — |
| 260 | C22⋊Dic5 | — | 3 | 2 | no | — |
| 261 | C22⋊Dic5 | — | 3 | 2 | no | — |
| 262 | C22⋊Dic5 | — | 3 | 2 | no | — |
| 263 | #685 | — | 3 | 4 | no | — |
| 264 | #685 | — | 3 | 4 | no | — |
| 265 | #685 | — | 3 | 4 | no | — |
| 266 | #685 | — | 3 | 4 | no | — |
| 267 | #685 | — | 3 | 4 | no | — |
| 268 | #685 | — | 3 | 2 | no | — |
| 269 | #685 | — | 3 | 2 | no | — |
| 270 | C4⋊Dic5 | — | 3 | 4 | no | — |
| 271 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 272 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 273 | #683 | — | 3 | 4 | no | — |
| 274 | #683 | — | 3 | 4 | no | — |
| 275 | #683 | — | 3 | 4 | no | — |
| 276 | #683 | — | 3 | 2 | no | — |
| 277 | #683 | — | 3 | 2 | no | — |
| 278 | C4×Dic5 | — | 3 | 4 | no | — |
| 279 | C4×Dic5 | — | 3 | 2 | no | — |
| 280 | C2×2−1+4 | — | 15 | 1 | no | — |
| 281 | C22×#41 | — | 5 | 1 | no | — |
| 282 | D4×Q8 | — | 15 | 2 | no | — |
| 283 | #548 | — | 15 | 2 | no | — |
| 284 | #547 | — | 15 | 4 | no | — |
| 285 | #547 | — | 15 | 2 | no | — |
| 286 | #546 | — | 15 | 4 | no | — |
| 287 | #546 | — | 15 | 2 | no | — |
| 288 | #537 | — | 15 | 1 | no | — |
| 289 | #537 | — | 15 | 2 | no | — |
| 290 | #536 | — | 15 | 2 | no | — |
| 291 | #536 | — | 15 | 1 | no | — |
| 292 | #525 | — | 15 | 2 | no | — |
| 293 | #525 | — | 15 | 1 | no | — |
| 294 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 295 | C2×C22⋊Q8 | — | 15 | 2 | no | — |
| 296 | #520 | — | 15 | 1 | no | — |
| 297 | C22×C3×C5 | — | 4 | 1 | no | — |
| 298 | C2×D15 | — | 4 | 2 | no | — |
| 299 | C2×C3×D5 | — | 4 | 2 | no | — |
| 300 | C5×A4 | 2−1+4 | 1 | 1 | yes | characteristic, complemented |
| 301 | C3×C4×C5 | — | 4 | 1 | no | — |
| 302 | C3×C4×C5 | — | 4 | 1 | no | — |
| 303 | Dic15 | — | 4 | 2 | no | — |
| 304 | C3×Dic5 | — | 4 | 2 | no | — |
| 305 | C5×Dic3 | — | 4 | 4 | no | — |
| 306 | C22×A4 | — | 5 | 2 | no | — |
| 307 | C22×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 308 | C2×S4 | — | 5 | 2 | no | — |
| 309 | C3×#41 | — | 20 | 1 | no | — |
| 310 | D3×Q8 | — | 20 | 2 | no | — |
| 311 | #237 | — | 20 | 2 | no | — |
| 312 | #237 | — | 20 | 4 | no | — |
| 313 | #235 | — | 20 | 2 | no | — |
| 314 | #235 | — | 20 | 1 | no | — |
| 315 | C2×Dic6 | — | 4 | 1 | no | — |
| 316 | C2×Dic6 | — | 20 | 2 | no | — |
| 317 | C4×A4 | — | 5 | 2 | no | — |
| 318 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 319 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 320 | SL(2,ℤ/4) | — | 5 | 2 | no | — |
| 321 | SL(2,ℤ/4) | C22×D5 | 1 | 4 | yes | — |
| 322 | C23×C5 | — | 2 | 1 | no | — |
| 323 | C23×C5 | — | 3 | 1 | no | — |
| 324 | C23×C5 | — | 3 | 1 | no | — |
| 325 | C23×C5 | — | 6 | 1 | no | — |
| 326 | C23×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 327 | C22×D5 | — | 2 | 2 | no | — |
| 328 | C22×D5 | — | 3 | 2 | no | — |
| 329 | C22×D5 | — | 3 | 2 | no | — |
| 330 | C22×D5 | — | 3 | 2 | no | — |
| 331 | C22×D5 | — | 6 | 2 | no | — |
| 332 | C5×Q8 | — | 6 | 2 | no | — |
| 333 | C5×Q8 | — | 6 | 2 | no | — |
| 334 | C5×Q8 | — | 6 | 2 | no | — |
| 335 | C5×Q8 | — | 6 | 2 | no | — |
| 336 | C2×C4×C5 | — | 3 | 1 | no | — |
| 337 | C2×C4×C5 | — | 3 | 1 | no | — |
| 338 | C2×C4×C5 | — | 3 | 1 | no | — |
| 339 | C2×C4×C5 | — | 3 | 1 | no | — |
| 340 | C2×C4×C5 | — | 3 | 1 | no | — |
| 341 | C2×C4×C5 | — | 3 | 1 | no | — |
| 342 | C2×C4×C5 | — | 3 | 1 | no | — |
| 343 | C2×C4×C5 | — | 3 | 4 | no | — |
| 344 | C2×C4×C5 | — | 3 | 4 | no | — |
| 345 | C2×C4×C5 | — | 6 | 1 | no | — |
| 346 | C2×C4×C5 | — | 6 | 2 | no | — |
| 347 | C2×C4×C5 | — | 6 | 2 | no | — |
| 348 | C2×C4×C5 | — | 12 | 2 | no | — |
| 349 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 350 | C22⋊D5 | — | 3 | 2 | no | — |
| 351 | C22⋊D5 | — | 3 | 2 | no | — |
| 352 | C22⋊D5 | — | 3 | 2 | no | — |
| 353 | C22⋊D5 | — | 6 | 2 | no | — |
| 354 | C22⋊D5 | — | 6 | 2 | no | — |
| 355 | C22⋊D5 | — | 6 | 2 | no | — |
| 356 | C22⋊D5 | — | 6 | 2 | no | — |
| 357 | C22⋊D5 | — | 6 | 2 | no | — |
| 358 | C22⋊D5 | — | 12 | 2 | no | — |
| 359 | C22⋊D5 | C2×S4 | 1 | 2 | yes | — |
| 360 | C2×Dic5 | — | 3 | 2 | no | — |
| 361 | C2×Dic5 | — | 3 | 2 | no | — |
| 362 | C2×Dic5 | — | 3 | 2 | no | — |
| 363 | C2×Dic5 | — | 3 | 2 | no | — |
| 364 | C2×Dic5 | — | 3 | 2 | no | — |
| 365 | D20 | — | 3 | 2 | no | — |
| 366 | D20 | — | 3 | 1 | no | — |
| 367 | D20 | — | 6 | 1 | no | — |
| 368 | D20 | — | 6 | 1 | no | — |
| 369 | D20 | — | 6 | 4 | no | — |
| 370 | D20 | — | 6 | 4 | no | — |
| 371 | D20 | — | 6 | 1 | no | — |
| 372 | D20 | — | 12 | 4 | no | — |
| 373 | D20 | C2×S4 | 1 | 1 | yes | characteristic |
| 374 | C4×D5 | — | 3 | 2 | no | — |
| 375 | C4×D5 | — | 3 | 2 | no | — |
| 376 | C4×D5 | — | 3 | 2 | no | — |
| 377 | C4×D5 | — | 6 | 2 | no | — |
| 378 | C4×D5 | — | 6 | 4 | no | — |
| 379 | C4×D5 | — | 6 | 2 | no | — |
| 380 | C4×D5 | — | 6 | 4 | no | — |
| 381 | C4×D5 | — | 6 | 4 | no | — |
| 382 | C4×D5 | — | 6 | 2 | no | — |
| 383 | C4×D5 | — | 6 | 4 | no | — |
| 384 | C4×D5 | — | 12 | 4 | no | — |
| 385 | C4×D5 | C2×S4 | 1 | 2 | yes | — |
| 386 | Dic10 | — | 3 | 1 | no | — |
| 387 | Dic10 | — | 3 | 2 | no | — |
| 388 | Dic10 | — | 6 | 1 | no | — |
| 389 | Dic10 | — | 6 | 4 | no | — |
| 390 | Dic10 | — | 6 | 1 | no | — |
| 391 | Dic10 | — | 6 | 1 | no | — |
| 392 | Dic10 | — | 6 | 4 | no | — |
| 393 | Dic10 | C2×S4 | 1 | 1 | yes | characteristic |
| 394 | 2−1+4 | — | 30 | 1 | no | — |
| 395 | 2−1+4 | — | 30 | 2 | no | — |
| 396 | 2−1+4 | — | 30 | 1 | no | — |
| 397 | 2−1+4 | — | 30 | 2 | no | — |
| 398 | 2−1+4 | — | 30 | 1 | no | — |
| 399 | 2−1+4 | — | 30 | 1 | no | — |
| 400 | C2×#41 | — | 15 | 1 | no | — |
| 401 | C2×#41 | — | 15 | 1 | no | — |
| 402 | C2×#41 | — | 15 | 2 | no | — |
| 403 | C2×#41 | — | 15 | 2 | no | — |
| 404 | C2×#41 | — | 15 | 1 | no | — |
| 405 | C2×#41 | — | 15 | 1 | no | — |
| 406 | C2×#41 | — | 15 | 1 | no | — |
| 407 | C2×#41 | — | 15 | 4 | no | — |
| 408 | C2×#41 | — | 15 | 2 | no | — |
| 409 | C2×#41 | — | 15 | 2 | no | — |
| 410 | C22×Q8 | — | 3 | 1 | no | — |
| 411 | C22×Q8 | — | 5 | 1 | no | — |
| 412 | C22×Q8 | — | 15 | 2 | no | — |
| 413 | C22×Q8 | — | 15 | 2 | no | — |
| 414 | C22×D4 | — | 5 | 2 | no | — |
| 415 | C22×D4 | — | 5 | 1 | no | — |
| 416 | C23×C4 | — | 5 | 2 | no | — |
| 417 | C23×C4 | D3×D5 | 1 | 1 | yes | characteristic |
| 418 | C4⋊Q8 | — | 15 | 4 | no | — |
| 419 | C4⋊Q8 | — | 15 | 2 | no | — |
| 420 | #124 | — | 15 | 4 | no | — |
| 421 | #124 | — | 15 | 2 | no | — |
| 422 | #123 | — | 15 | 4 | no | — |
| 423 | #123 | — | 15 | 4 | no | — |
| 424 | #123 | — | 15 | 4 | no | — |
| 425 | #123 | — | 15 | 2 | no | — |
| 426 | #123 | — | 15 | 4 | no | — |
| 427 | C22⋊Q8 | — | 3 | 2 | no | — |
| 428 | C22⋊Q8 | — | 3 | 2 | no | — |
| 429 | C22⋊Q8 | — | 3 | 2 | no | — |
| 430 | C22⋊Q8 | — | 3 | 2 | no | — |
| 431 | C22⋊Q8 | — | 15 | 4 | no | — |
| 432 | C22⋊Q8 | — | 15 | 2 | no | — |
| 433 | C22⋊Q8 | — | 15 | 4 | no | — |
| 434 | C22⋊Q8 | — | 15 | 4 | no | — |
| 435 | C22⋊Q8 | — | 15 | 2 | no | — |
| 436 | C22⋊Q8 | — | 15 | 1 | no | — |
| 437 | C22⋊Q8 | — | 15 | 2 | no | — |
| 438 | C22⋊Q8 | — | 15 | 2 | no | — |
| 439 | C22⋊Q8 | — | 15 | 1 | no | — |
| 440 | #121 | — | 15 | 4 | no | — |
| 441 | #121 | — | 15 | 4 | no | — |
| 442 | #121 | — | 15 | 2 | no | — |
| 443 | #121 | — | 15 | 4 | no | — |
| 444 | #121 | — | 15 | 2 | no | — |
| 445 | #121 | — | 15 | 1 | no | — |
| 446 | #121 | — | 15 | 4 | no | — |
| 447 | #121 | — | 15 | 1 | no | — |
| 448 | #120 | — | 15 | 4 | no | — |
| 449 | #120 | — | 15 | 2 | no | — |
| 450 | C4×Q8 | — | 15 | 2 | no | — |
| 451 | C4×D4 | — | 15 | 4 | no | — |
| 452 | C4×D4 | — | 15 | 2 | no | — |
| 453 | C4×D4 | — | 15 | 4 | no | — |
| 454 | C4×D4 | — | 15 | 4 | no | — |
| 455 | C4×D4 | — | 15 | 2 | no | — |
| 456 | C4×D4 | — | 15 | 2 | no | — |
| 457 | #117 | — | 15 | 2 | no | — |
| 458 | #117 | — | 15 | 1 | no | — |
| 459 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 460 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 461 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 462 | C2×C4⋊C4 | — | 15 | 4 | no | — |
| 463 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 464 | C2×C22⋊C4 | — | 15 | 4 | no | — |
| 465 | C2×C3×C5 | — | 4 | 1 | no | — |
| 466 | C2×C3×C5 | — | 8 | 1 | no | — |
| 467 | D15 | — | 8 | 2 | no | — |
| 468 | C3×D5 | — | 8 | 2 | no | — |
| 469 | C2×A4 | — | 2 | 1 | no | — |
| 470 | C2×A4 | — | 10 | 2 | no | — |
| 471 | C2×A4 | C23×D5 | 1 | 1 | yes | characteristic |
| 472 | S4 | — | 10 | 2 | no | — |
| 473 | C3×Q8 | — | 20 | 1 | no | — |
| 474 | C3×D4 | — | 20 | 1 | no | — |
| 475 | C3×D4 | — | 20 | 2 | no | — |
| 476 | C2×C3×C4 | — | 4 | 1 | no | — |
| 477 | C2×C3×C4 | — | 20 | 2 | no | — |
| 478 | #67 | — | 20 | 4 | no | — |
| 479 | #67 | — | 20 | 2 | no | — |
| 480 | C2×Dic3 | — | 4 | 2 | no | — |
| 481 | C2×Dic3 | — | 20 | 4 | no | — |
| 482 | D12 | — | 20 | 1 | no | — |
| 483 | C4×D3 | — | 20 | 4 | no | — |
| 484 | C4×D3 | — | 20 | 2 | no | — |
| 485 | Dic6 | — | 4 | 2 | no | — |
| 486 | Dic6 | — | 4 | 2 | no | — |
| 487 | Dic6 | — | 20 | 4 | no | — |
| 488 | Dic6 | — | 20 | 1 | no | — |
| 489 | C22×C5 | — | 3 | 1 | no | — |
| 490 | C22×C5 | — | 3 | 1 | no | — |
| 491 | C22×C5 | — | 3 | 1 | no | — |
| 492 | C22×C5 | — | 6 | 1 | no | — |
| 493 | C22×C5 | — | 6 | 1 | no | — |
| 494 | C22×C5 | — | 6 | 1 | no | — |
| 495 | C22×C5 | — | 6 | 1 | no | — |
| 496 | C22×C5 | #1010 | 1 | 1 | yes | characteristic, complemented |
| 497 | C22×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 498 | C2×D5 | — | 3 | 2 | no | — |
| 499 | C2×D5 | — | 6 | 2 | no | — |
| 500 | C2×D5 | — | 6 | 2 | no | — |
| 501 | C2×D5 | — | 6 | 2 | no | — |
| 502 | C2×D5 | — | 6 | 2 | no | — |
| 503 | C2×D5 | — | 6 | 2 | no | — |
| 504 | C2×D5 | — | 6 | 2 | no | — |
| 505 | C2×D5 | — | 6 | 2 | no | — |
| 506 | C2×D5 | C22×S4 | 1 | 2 | yes | — |
| 507 | C4×C5 | — | 3 | 1 | no | — |
| 508 | C4×C5 | — | 3 | 1 | no | — |
| 509 | C4×C5 | — | 6 | 4 | no | — |
| 510 | C4×C5 | — | 6 | 4 | no | — |
| 511 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 512 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 513 | Dic5 | — | 3 | 2 | no | — |
| 514 | Dic5 | — | 6 | 2 | no | — |
| 515 | Dic5 | — | 6 | 2 | no | — |
| 516 | Dic5 | — | 6 | 2 | no | — |
| 517 | Dic5 | C22×S4 | 1 | 2 | yes | — |
| 518 | C24 | — | 5 | 2 | no | — |
| 519 | C24 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 520 | #41 | — | 5 | 1 | no | — |
| 521 | #41 | — | 15 | 2 | no | — |
| 522 | #41 | — | 15 | 2 | no | — |
| 523 | #41 | — | 15 | 1 | no | — |
| 524 | #41 | — | 15 | 1 | no | — |
| 525 | #41 | — | 15 | 1 | no | — |
| 526 | #41 | — | 30 | 1 | no | — |
| 527 | #41 | — | 30 | 1 | no | — |
| 528 | #41 | — | 30 | 1 | no | — |
| 529 | #41 | — | 30 | 1 | no | — |
| 530 | #41 | — | 30 | 1 | no | — |
| 531 | #41 | — | 30 | 1 | no | — |
| 532 | #41 | — | 30 | 2 | no | — |
| 533 | #41 | — | 30 | 2 | no | — |
| 534 | #41 | — | 30 | 2 | no | — |
| 535 | #41 | — | 30 | 4 | no | — |
| 536 | #41 | — | 30 | 4 | no | — |
| 537 | #41 | — | 30 | 4 | no | — |
| 538 | #41 | — | 30 | 4 | no | — |
| 539 | #41 | — | 30 | 2 | no | — |
| 540 | #41 | — | 30 | 2 | no | — |
| 541 | #41 | — | 30 | 2 | no | — |
| 542 | #41 | — | 30 | 2 | no | — |
| 543 | #41 | — | 30 | 4 | no | — |
| 544 | #41 | — | 30 | 2 | no | — |
| 545 | #41 | — | 30 | 1 | no | — |
| 546 | C2×Q8 | — | 3 | 2 | no | — |
| 547 | C2×Q8 | — | 3 | 2 | no | — |
| 548 | C2×Q8 | — | 6 | 1 | no | — |
| 549 | C2×Q8 | — | 6 | 1 | no | — |
| 550 | C2×Q8 | — | 6 | 1 | no | — |
| 551 | C2×Q8 | — | 6 | 1 | no | — |
| 552 | C2×Q8 | — | 15 | 1 | no | — |
| 553 | C2×Q8 | — | 15 | 1 | no | — |
| 554 | C2×Q8 | — | 15 | 2 | no | — |
| 555 | C2×Q8 | — | 15 | 1 | no | — |
| 556 | C2×Q8 | — | 15 | 4 | no | — |
| 557 | C2×Q8 | — | 30 | 2 | no | — |
| 558 | C2×Q8 | — | 30 | 2 | no | — |
| 559 | C2×Q8 | — | 30 | 2 | no | — |
| 560 | C2×Q8 | — | 30 | 2 | no | — |
| 561 | C2×Q8 | — | 30 | 2 | no | — |
| 562 | C2×Q8 | — | 30 | 4 | no | — |
| 563 | C2×Q8 | — | 30 | 2 | no | — |
| 564 | C2×D4 | — | 15 | 1 | no | — |
| 565 | C2×D4 | — | 15 | 2 | no | — |
| 566 | C2×D4 | — | 15 | 1 | no | — |
| 567 | C2×D4 | — | 15 | 4 | no | — |
| 568 | C2×D4 | — | 15 | 1 | no | — |
| 569 | C2×D4 | — | 15 | 4 | no | — |
| 570 | C2×D4 | — | 15 | 2 | no | — |
| 571 | C2×D4 | — | 15 | 2 | no | — |
| 572 | C2×D4 | — | 15 | 2 | no | — |
| 573 | C2×D4 | — | 15 | 2 | no | — |
| 574 | C2×D4 | — | 15 | 2 | no | — |
| 575 | C2×D4 | — | 15 | 2 | no | — |
| 576 | C2×D4 | — | 15 | 2 | no | — |
| 577 | C22×C4 | — | 3 | 1 | no | — |
| 578 | C22×C4 | — | 3 | 1 | no | — |
| 579 | C22×C4 | — | 3 | 1 | no | — |
| 580 | C22×C4 | — | 3 | 1 | no | — |
| 581 | C22×C4 | — | 3 | 2 | no | — |
| 582 | C22×C4 | — | 3 | 2 | no | — |
| 583 | C22×C4 | — | 5 | 2 | no | — |
| 584 | C22×C4 | — | 15 | 2 | no | — |
| 585 | C22×C4 | — | 15 | 2 | no | — |
| 586 | C22×C4 | — | 15 | 2 | no | — |
| 587 | C22×C4 | — | 15 | 2 | no | — |
| 588 | C22×C4 | — | 15 | 4 | no | — |
| 589 | C22×C4 | — | 15 | 2 | no | — |
| 590 | C22×C4 | — | 15 | 4 | no | — |
| 591 | C22×C4 | — | 15 | 4 | no | — |
| 592 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 593 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 594 | C4⋊C4 | — | 3 | 2 | no | — |
| 595 | C4⋊C4 | — | 3 | 4 | no | — |
| 596 | C4⋊C4 | — | 3 | 2 | no | — |
| 597 | C4⋊C4 | — | 3 | 4 | no | — |
| 598 | C4⋊C4 | — | 15 | 1 | no | — |
| 599 | C4⋊C4 | — | 15 | 2 | no | — |
| 600 | C4⋊C4 | — | 15 | 4 | no | — |
| 601 | C4⋊C4 | — | 15 | 4 | no | — |
| 602 | C4⋊C4 | — | 15 | 4 | no | — |
| 603 | C4⋊C4 | — | 15 | 1 | no | — |
| 604 | C4⋊C4 | — | 15 | 2 | no | — |
| 605 | C4⋊C4 | — | 15 | 4 | no | — |
| 606 | C22⋊C4 | — | 3 | 4 | no | — |
| 607 | C22⋊C4 | — | 3 | 4 | no | — |
| 608 | C22⋊C4 | — | 15 | 4 | no | — |
| 609 | C22⋊C4 | — | 15 | 4 | no | — |
| 610 | C22⋊C4 | — | 15 | 4 | no | — |
| 611 | C22⋊C4 | — | 15 | 2 | no | — |
| 612 | C22⋊C4 | — | 15 | 4 | no | — |
| 613 | C22⋊C4 | — | 15 | 2 | no | — |
| 614 | C22⋊C4 | — | 15 | 4 | no | — |
| 615 | C22⋊C4 | — | 15 | 2 | no | — |
| 616 | C22⋊C4 | — | 15 | 2 | no | — |
| 617 | C22⋊C4 | — | 15 | 2 | no | — |
| 618 | C42 | — | 15 | 2 | no | — |
| 619 | C42 | — | 15 | 4 | no | — |
| 620 | C3×C5 | — | 4 | 1 | no | Hall |
| 621 | C22×C3 | — | 4 | 1 | no | — |
| 622 | C22×C3 | — | 20 | 2 | no | — |
| 623 | C2×D3 | — | 20 | 2 | no | — |
| 624 | A4 | #4147 | 1 | 1 | yes | characteristic, complemented |
| 625 | C3×C4 | — | 4 | 1 | no | — |
| 626 | C3×C4 | — | 4 | 1 | no | — |
| 627 | C3×C4 | — | 20 | 2 | no | — |
| 628 | Dic3 | — | 4 | 4 | no | — |
| 629 | Dic3 | — | 20 | 2 | no | — |
| 630 | C2×C5 | — | 2 | 1 | no | — |
| 631 | C2×C5 | — | 3 | 1 | no | — |
| 632 | C2×C5 | — | 3 | 1 | no | — |
| 633 | C2×C5 | — | 6 | 1 | no | — |
| 634 | C2×C5 | C23×S4 | 1 | 1 | yes | characteristic |
| 635 | D5 | — | 2 | 2 | no | — |
| 636 | D5 | — | 6 | 2 | no | — |
| 637 | D5 | — | 12 | 2 | no | — |
| 638 | C23 | — | 2 | 1 | no | — |
| 639 | C23 | — | 3 | 1 | no | — |
| 640 | C23 | — | 3 | 1 | no | — |
| 641 | C23 | — | 6 | 1 | no | — |
| 642 | C23 | — | 10 | 2 | no | — |
| 643 | C23 | — | 15 | 2 | no | — |
| 644 | C23 | — | 15 | 2 | no | — |
| 645 | C23 | — | 15 | 2 | no | — |
| 646 | C23 | — | 30 | 2 | no | — |
| 647 | C23 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 648 | Q8 | — | 5 | 1 | no | — |
| 649 | Q8 | — | 6 | 2 | no | — |
| 650 | Q8 | — | 6 | 2 | no | — |
| 651 | Q8 | — | 6 | 2 | no | — |
| 652 | Q8 | — | 6 | 2 | no | — |
| 653 | Q8 | — | 15 | 2 | no | — |
| 654 | Q8 | — | 15 | 1 | no | — |
| 655 | Q8 | — | 30 | 1 | no | — |
| 656 | Q8 | — | 30 | 1 | no | — |
| 657 | Q8 | — | 30 | 4 | no | — |
| 658 | Q8 | — | 30 | 4 | no | — |
| 659 | Q8 | — | 30 | 1 | no | — |
| 660 | D4 | — | 5 | 2 | no | — |
| 661 | D4 | — | 5 | 1 | no | — |
| 662 | D4 | — | 15 | 2 | no | — |
| 663 | D4 | — | 15 | 2 | no | — |
| 664 | D4 | — | 15 | 2 | no | — |
| 665 | D4 | — | 15 | 2 | no | — |
| 666 | D4 | — | 15 | 1 | no | — |
| 667 | D4 | — | 30 | 1 | no | — |
| 668 | D4 | — | 30 | 1 | no | — |
| 669 | D4 | — | 30 | 4 | no | — |
| 670 | D4 | — | 30 | 4 | no | — |
| 671 | D4 | — | 30 | 2 | no | — |
| 672 | D4 | — | 30 | 2 | no | — |
| 673 | D4 | — | 30 | 2 | no | — |
| 674 | D4 | — | 30 | 2 | no | — |
| 675 | D4 | — | 30 | 2 | no | — |
| 676 | D4 | — | 30 | 1 | no | — |
| 677 | D4 | — | 60 | 4 | no | — |
| 678 | D4 | — | 60 | 2 | no | — |
| 679 | C2×C4 | — | 3 | 1 | no | — |
| 680 | C2×C4 | — | 3 | 1 | no | — |
| 681 | C2×C4 | — | 3 | 1 | no | — |
| 682 | C2×C4 | — | 3 | 1 | no | — |
| 683 | C2×C4 | — | 3 | 1 | no | — |
| 684 | C2×C4 | — | 3 | 1 | no | — |
| 685 | C2×C4 | — | 3 | 1 | no | — |
| 686 | C2×C4 | — | 3 | 4 | no | — |
| 687 | C2×C4 | — | 3 | 4 | no | — |
| 688 | C2×C4 | — | 5 | 2 | no | — |
| 689 | C2×C4 | — | 6 | 1 | no | — |
| 690 | C2×C4 | — | 6 | 2 | no | — |
| 691 | C2×C4 | — | 6 | 2 | no | — |
| 692 | C2×C4 | — | 12 | 2 | no | — |
| 693 | C2×C4 | — | 15 | 2 | no | — |
| 694 | C2×C4 | — | 15 | 2 | no | — |
| 695 | C2×C4 | — | 15 | 2 | no | — |
| 696 | C2×C4 | — | 15 | 2 | no | — |
| 697 | C2×C4 | — | 15 | 2 | no | — |
| 698 | C2×C4 | — | 15 | 2 | no | — |
| 699 | C2×C4 | — | 15 | 2 | no | — |
| 700 | C2×C4 | — | 15 | 2 | no | — |
| 701 | C2×C4 | — | 30 | 2 | no | — |
| 702 | C2×C4 | — | 30 | 2 | no | — |
| 703 | C2×C4 | — | 30 | 4 | no | — |
| 704 | C2×C4 | — | 30 | 4 | no | — |
| 705 | C2×C4 | — | 30 | 4 | no | — |
| 706 | C2×C4 | — | 30 | 4 | no | — |
| 707 | C2×C4 | — | 30 | 2 | no | — |
| 708 | C2×C4 | — | 60 | 4 | no | — |
| 709 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 710 | C2×C3 | — | 4 | 1 | no | — |
| 711 | C2×C3 | — | 8 | 1 | no | — |
| 712 | C2×C3 | — | 40 | 2 | no | — |
| 713 | D3 | — | 40 | 2 | no | — |
| 714 | C5 | #87490 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 715 | C22 | — | 3 | 1 | no | — |
| 716 | C22 | — | 3 | 1 | no | — |
| 717 | C22 | — | 3 | 1 | no | — |
| 718 | C22 | — | 5 | 2 | no | — |
| 719 | C22 | — | 6 | 1 | no | — |
| 720 | C22 | — | 6 | 1 | no | — |
| 721 | C22 | — | 6 | 1 | no | — |
| 722 | C22 | — | 6 | 1 | no | — |
| 723 | C22 | — | 15 | 2 | no | — |
| 724 | C22 | — | 30 | 2 | no | — |
| 725 | C22 | — | 30 | 2 | no | — |
| 726 | C22 | — | 30 | 2 | no | — |
| 727 | C22 | — | 30 | 2 | no | — |
| 728 | C22 | — | 30 | 2 | no | — |
| 729 | C22 | — | 30 | 2 | no | — |
| 730 | C22 | — | 30 | 2 | no | — |
| 731 | C22 | #92000 | 1 | 1 | yes | characteristic, complemented |
| 732 | C22 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 733 | C4 | — | 3 | 1 | no | — |
| 734 | C4 | — | 3 | 1 | no | — |
| 735 | C4 | — | 5 | 2 | no | — |
| 736 | C4 | — | 6 | 4 | no | — |
| 737 | C4 | — | 6 | 4 | no | — |
| 738 | C4 | — | 15 | 2 | no | — |
| 739 | C4 | — | 30 | 2 | no | — |
| 740 | C4 | — | 30 | 2 | no | — |
| 741 | C4 | — | 30 | 2 | no | — |
| 742 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 743 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 744 | C3 | — | 4 | 1 | no | Sylow |
| 745 | C2 | — | 2 | 1 | no | — |
| 746 | C2 | — | 3 | 1 | no | — |
| 747 | C2 | — | 3 | 1 | no | — |
| 748 | C2 | — | 6 | 1 | no | — |
| 749 | C2 | — | 10 | 2 | no | — |
| 750 | C2 | — | 30 | 2 | no | — |
| 751 | C2 | — | 60 | 2 | no | — |
| 752 | C2 | C22×D5×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×S4 |
| commutator, cosocle | C2×C5×A4 | C24 |
| Fitting | C23×C4×C5 | C2×D3 |
| socle | C23×C5 | C23×D3 |
| hypercenter | C2×C4 | D5×S4 |
| hypocenter | C5×A4 | 2−1+4 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#709 | C2 | semidirect |
| 2. #11756896 | C2 | semidirect |
| 3. C2×C5×A4⋊Q8 | C2 | semidirect |
| 4. #11756793 | C2 | semidirect |
| 5. #11756754 | C2 | semidirect |
| 6. #11756751 | C2 | semidirect |
| 7. D5×A4⋊Q8 | C2 | semidirect |
| 8. (C5⋊S4)⋊Q8 | C2 | semidirect |
| 29. C22×#709 | D3 | semidirect |
| 68. C2×A4⋊Q8 | D5 | semidirect |
| 234. #709 | S4 | semidirect |
| 300. C5×A4 | 2−1+4 | semidirect |
| 496. C22×C5 | #1010 | semidirect |
| 624. A4 | #4147 | semidirect |
| 714. C5 | #87490 | semidirect |
| 731. C22 | #92000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#709 | 2 |
| #11756896 | 2 |
| C2×C5×A4⋊Q8 | 2 |
| #11756793 | 2 |
| #11756754 | 2 |
| #11756751 | 2 |
| D5×A4⋊Q8 | 2 |
| (C5⋊S4)⋊Q8 | 2 |
| #10617886 | 3 |
| #92000 | 4 |
| #87490 | 5 |