Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1720 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1720 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 | C2×C4⋊(C5⋊S4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#5912 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11756799 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | S4×D20 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | D5×C4⋊S4 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11756754 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11756747 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10617942 | — | 3 | 1 | no | maximal, Hall |
| 10 | C22×C5⋊S4 | C22 | 1 | 2 | yes | complemented |
| 11 | C2×D5×S4 | C22 | 1 | 4 | yes | complemented |
| 12 | C2×C4×C5×A4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #92019 | — | 4 | 1 | no | maximal |
| 14 | A4×C22⋊D5 | C22 | 1 | 2 | yes | complemented |
| 15 | A4×D20 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C4×D5×A4 | C22 | 1 | 2 | yes | complemented |
| 17 | A4×Dic10 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C4⋊(C5⋊S4) | C22 | 1 | 2 | yes | complemented |
| 19 | C4⋊(C5⋊S4) | C22 | 1 | 2 | yes | complemented |
| 20 | C5×GL(2,ℤ/4) | C22 | 1 | 2 | yes | complemented |
| 21 | C5×C4⋊S4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C4×C5×S4 | C22 | 1 | 2 | yes | complemented |
| 23 | C5×A4⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #91905 | C22 | 1 | 4 | yes | complemented |
| 25 | #91902 | C22 | 1 | 4 | yes | complemented |
| 26 | #91901 | C22 | 1 | 4 | yes | complemented |
| 27 | #87489 | — | 5 | 1 | no | maximal, Hall |
| 28 | C2×#4149 | — | 3 | 1 | no | — |
| 29 | C22×#709 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C5×#525 | — | 3 | 1 | no | — |
| 31 | #66167 | — | 3 | 1 | no | — |
| 32 | C2×#4076 | — | 3 | 1 | no | — |
| 33 | #65988 | — | 3 | 4 | no | — |
| 34 | #65963 | — | 3 | 2 | no | — |
| 35 | #65961 | — | 3 | 2 | no | — |
| 36 | #65941 | — | 3 | 2 | no | — |
| 37 | D5×#121 | — | 3 | 2 | no | — |
| 38 | #65924 | — | 3 | 4 | no | — |
| 39 | #65887 | — | 3 | 2 | no | — |
| 40 | #65886 | — | 3 | 2 | no | — |
| 41 | #65884 | — | 3 | 2 | no | — |
| 42 | D4×D20 | — | 3 | 2 | no | — |
| 43 | #65859 | — | 3 | 1 | no | — |
| 44 | #65857 | — | 3 | 1 | no | — |
| 45 | C22×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×D5×A4 | C23 | 1 | 2 | yes | — |
| 47 | C2×C5⋊S4 | — | 4 | 2 | no | — |
| 48 | C2×C5⋊S4 | C23 | 1 | 4 | yes | — |
| 49 | C2×C5×S4 | C23 | 1 | 2 | yes | — |
| 50 | D5×S4 | — | 4 | 4 | no | — |
| 51 | C2×D60 | — | 4 | 1 | no | — |
| 52 | C5×#235 | — | 4 | 1 | no | — |
| 53 | C3×#709 | — | 4 | 1 | no | — |
| 54 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 55 | C4×C5×A4 | C23 | 1 | 1 | yes | characteristic |
| 56 | #6790 | — | 4 | 4 | no | — |
| 57 | D3×D20 | — | 4 | 2 | no | — |
| 58 | D5×D12 | — | 4 | 2 | no | — |
| 59 | #6773 | — | 4 | 2 | no | — |
| 60 | #6769 | — | 4 | 2 | no | — |
| 61 | A4×Dic5 | C23 | 1 | 2 | yes | — |
| 62 | C5×SL(2,ℤ/4) | C23 | 1 | 2 | yes | — |
| 63 | A4×#41 | — | 5 | 1 | no | — |
| 64 | #5919 | — | 5 | 2 | no | — |
| 65 | D4×S4 | — | 5 | 4 | no | — |
| 66 | D4×S4 | — | 5 | 2 | no | — |
| 67 | #5912 | — | 5 | 2 | no | — |
| 68 | #5912 | D5 | 1 | 1 | yes | characteristic, complemented |
| 69 | C2×C4⋊S4 | — | 5 | 1 | no | — |
| 70 | C2×C4⋊S4 | — | 5 | 2 | no | — |
| 71 | C2×C5×#41 | — | 3 | 1 | no | — |
| 72 | C23×C4×C5 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 73 | C22×C22⋊D5 | — | 3 | 2 | no | — |
| 74 | C22×C22⋊D5 | C2×D3 | 1 | 2 | yes | complemented |
| 75 | #4149 | — | 6 | 2 | no | — |
| 76 | #4149 | — | 6 | 2 | no | — |
| 77 | #4149 | — | 6 | 1 | no | — |
| 78 | #4149 | — | 6 | 1 | no | — |
| 79 | #4149 | — | 6 | 1 | no | — |
| 80 | #4149 | — | 6 | 1 | no | — |
| 81 | C2×#713 | — | 3 | 2 | no | — |
| 82 | C2×D4×D5 | — | 3 | 4 | no | — |
| 83 | C2×D4×D5 | — | 3 | 2 | no | — |
| 84 | C2×D4×D5 | — | 3 | 4 | no | — |
| 85 | C2×#709 | — | 3 | 1 | no | — |
| 86 | C2×#709 | — | 3 | 1 | no | — |
| 87 | C2×#709 | — | 3 | 1 | no | — |
| 88 | C2×#709 | — | 3 | 1 | no | — |
| 89 | C2×#709 | — | 3 | 2 | no | — |
| 90 | C2×#709 | — | 3 | 2 | no | — |
| 91 | C2×#709 | — | 3 | 2 | no | — |
| 92 | C22×D20 | — | 3 | 1 | no | — |
| 93 | C22×D20 | — | 3 | 2 | no | — |
| 94 | C22×D20 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 95 | C22×C4×D5 | C2×D3 | 1 | 2 | yes | complemented |
| 96 | C22×Dic10 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 97 | C5×#123 | — | 3 | 2 | no | — |
| 98 | C5×C22⋊Q8 | — | 3 | 1 | no | — |
| 99 | C5×C22⋊Q8 | — | 3 | 1 | no | — |
| 100 | C5×#121 | — | 3 | 1 | no | — |
| 101 | C5×#121 | — | 3 | 1 | no | — |
| 102 | C5×#120 | — | 3 | 2 | no | — |
| 103 | C4×C5×D4 | — | 3 | 2 | no | — |
| 104 | C4×C5×D4 | — | 3 | 2 | no | — |
| 105 | C5×#117 | — | 3 | 1 | no | — |
| 106 | #4092 | — | 3 | 2 | no | — |
| 107 | #4086 | — | 3 | 4 | no | — |
| 108 | #4085 | — | 3 | 4 | no | — |
| 109 | #4085 | — | 3 | 4 | no | — |
| 110 | #4084 | — | 3 | 2 | no | — |
| 111 | #4083 | — | 3 | 4 | no | — |
| 112 | #4076 | — | 3 | 2 | no | — |
| 113 | #4076 | — | 3 | 2 | no | — |
| 114 | #4076 | — | 3 | 2 | no | — |
| 115 | #4076 | — | 3 | 2 | no | — |
| 116 | #4076 | — | 3 | 2 | no | — |
| 117 | C2×#685 | — | 3 | 2 | no | — |
| 118 | C2×C4⋊Dic5 | — | 3 | 1 | no | — |
| 119 | #4070 | — | 3 | 2 | no | — |
| 120 | #4042 | — | 3 | 4 | no | — |
| 121 | #4041 | — | 3 | 2 | no | — |
| 122 | #4041 | — | 3 | 2 | no | — |
| 123 | #4041 | — | 3 | 4 | no | — |
| 124 | #4040 | — | 3 | 4 | no | — |
| 125 | #4039 | — | 3 | 4 | no | — |
| 126 | #4038 | — | 3 | 2 | no | — |
| 127 | D5×C4⋊C4 | — | 3 | 2 | no | — |
| 128 | #4031 | — | 3 | 4 | no | — |
| 129 | #4030 | — | 3 | 4 | no | — |
| 130 | #4030 | — | 3 | 4 | no | — |
| 131 | #4030 | — | 3 | 4 | no | — |
| 132 | #4028 | — | 3 | 4 | no | — |
| 133 | #4028 | — | 3 | 4 | no | — |
| 134 | #4028 | — | 3 | 4 | no | — |
| 135 | #4027 | — | 3 | 4 | no | — |
| 136 | #4027 | — | 3 | 4 | no | — |
| 137 | D5×C22⋊C4 | — | 3 | 4 | no | — |
| 138 | #4021 | — | 3 | 2 | no | — |
| 139 | #4020 | — | 3 | 2 | no | — |
| 140 | C4×D20 | — | 3 | 2 | no | — |
| 141 | C4×Dic10 | — | 3 | 2 | no | — |
| 142 | #3488 | — | 15 | 1 | no | Sylow |
| 143 | C22×D15 | — | 4 | 2 | no | — |
| 144 | C2×C5×A4 | — | 2 | 1 | no | — |
| 145 | C2×C5×A4 | C24 | 1 | 1 | yes | characteristic |
| 146 | C2×D3×D5 | — | 4 | 4 | no | — |
| 147 | D5×A4 | — | 2 | 2 | no | — |
| 148 | C5⋊S4 | — | 2 | 4 | no | — |
| 149 | C5×S4 | — | 2 | 2 | no | — |
| 150 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 151 | D60 | — | 4 | 2 | no | — |
| 152 | D60 | — | 4 | 2 | no | — |
| 153 | C5×#67 | — | 4 | 2 | no | — |
| 154 | C5×D12 | — | 4 | 1 | no | — |
| 155 | C4×C5×D3 | — | 4 | 2 | no | — |
| 156 | C5×Dic6 | — | 4 | 1 | no | — |
| 157 | C3×C22⋊D5 | — | 4 | 2 | no | — |
| 158 | C3×D20 | — | 4 | 1 | no | — |
| 159 | C3×C4×D5 | — | 4 | 2 | no | — |
| 160 | C3×Dic10 | — | 4 | 1 | no | — |
| 161 | #1203 | — | 4 | 4 | no | — |
| 162 | #1202 | — | 4 | 4 | no | — |
| 163 | #1200 | — | 4 | 4 | no | — |
| 164 | C22×S4 | — | 5 | 2 | no | — |
| 165 | C22×S4 | — | 5 | 4 | no | — |
| 166 | #1009 | — | 20 | 1 | no | — |
| 167 | Q8×A4 | — | 5 | 1 | no | — |
| 168 | D4×A4 | — | 5 | 2 | no | — |
| 169 | D4×A4 | — | 5 | 1 | no | — |
| 170 | C2×C4×A4 | — | 5 | 2 | no | — |
| 171 | C2×C4×A4 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 172 | GL(2,ℤ/4) | — | 5 | 4 | no | — |
| 173 | GL(2,ℤ/4) | C2×D5 | 1 | 2 | yes | complemented |
| 174 | C4⋊S4 | — | 5 | 4 | no | — |
| 175 | C4⋊S4 | — | 5 | 2 | no | — |
| 176 | C4⋊S4 | — | 5 | 2 | no | — |
| 177 | C4⋊S4 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 178 | C4×S4 | — | 5 | 4 | no | — |
| 179 | C4×S4 | C2×D5 | 1 | 2 | yes | complemented |
| 180 | A4⋊Q8 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 181 | C24×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 182 | C23×D5 | — | 3 | 4 | no | — |
| 183 | C23×D5 | — | 3 | 2 | no | — |
| 184 | C23×D5 | C22×D3 | 1 | 2 | yes | — |
| 185 | C5×#41 | — | 6 | 1 | no | — |
| 186 | C5×#41 | — | 6 | 1 | no | — |
| 187 | C5×#41 | — | 6 | 1 | no | — |
| 188 | C5×#41 | — | 6 | 1 | no | — |
| 189 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 190 | C2×C5×D4 | — | 3 | 2 | no | — |
| 191 | C2×C5×D4 | — | 3 | 1 | no | — |
| 192 | C2×C5×D4 | — | 3 | 2 | no | — |
| 193 | C2×C5×D4 | — | 3 | 2 | no | — |
| 194 | C22×C4×C5 | — | 3 | 1 | no | — |
| 195 | C22×C4×C5 | — | 3 | 1 | no | — |
| 196 | C22×C4×C5 | — | 3 | 1 | no | — |
| 197 | C22×C4×C5 | — | 3 | 1 | no | — |
| 198 | C22×C4×C5 | — | 3 | 2 | no | — |
| 199 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 200 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 201 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 202 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 203 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 204 | C2×C22⋊D5 | — | 3 | 2 | no | — |
| 205 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 206 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 207 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 208 | C2×C22⋊D5 | — | 3 | 4 | no | — |
| 209 | C2×C22⋊D5 | — | 12 | 2 | no | — |
| 210 | C2×C22⋊D5 | — | 12 | 2 | no | — |
| 211 | C22×Dic5 | — | 3 | 2 | no | — |
| 212 | C22×Dic5 | C22×D3 | 1 | 2 | yes | — |
| 213 | #713 | — | 6 | 2 | no | — |
| 214 | #713 | — | 6 | 2 | no | — |
| 215 | #713 | — | 6 | 2 | no | — |
| 216 | #713 | — | 6 | 2 | no | — |
| 217 | D4×D5 | — | 6 | 2 | no | — |
| 218 | D4×D5 | — | 6 | 2 | no | — |
| 219 | D4×D5 | — | 6 | 2 | no | — |
| 220 | D4×D5 | — | 6 | 4 | no | — |
| 221 | D4×D5 | — | 6 | 4 | no | — |
| 222 | D4×D5 | — | 6 | 4 | no | — |
| 223 | D4×D5 | — | 6 | 4 | no | — |
| 224 | D4×D5 | — | 6 | 2 | no | — |
| 225 | D4×D5 | — | 12 | 4 | no | — |
| 226 | D4×D5 | — | 12 | 4 | no | — |
| 227 | #709 | — | 3 | 1 | no | — |
| 228 | #709 | — | 3 | 2 | no | — |
| 229 | #709 | — | 3 | 1 | no | — |
| 230 | #709 | — | 3 | 2 | no | — |
| 231 | #709 | — | 3 | 1 | no | — |
| 232 | #709 | — | 6 | 2 | no | — |
| 233 | #709 | — | 6 | 1 | no | — |
| 234 | #709 | — | 6 | 2 | no | — |
| 235 | #709 | — | 6 | 4 | no | — |
| 236 | #709 | — | 6 | 1 | no | — |
| 237 | #709 | — | 6 | 2 | no | — |
| 238 | #709 | — | 6 | 1 | no | — |
| 239 | #709 | — | 6 | 2 | no | — |
| 240 | #709 | S4 | 1 | 1 | yes | characteristic, complemented |
| 241 | C2×D20 | — | 3 | 1 | no | — |
| 242 | C2×D20 | — | 3 | 1 | no | — |
| 243 | C2×D20 | — | 3 | 2 | no | — |
| 244 | C2×D20 | — | 3 | 2 | no | — |
| 245 | C2×D20 | — | 3 | 4 | no | — |
| 246 | C2×D20 | — | 3 | 2 | no | — |
| 247 | C2×D20 | — | 3 | 4 | no | — |
| 248 | C2×D20 | — | 3 | 4 | no | — |
| 249 | C2×D20 | — | 6 | 4 | no | — |
| 250 | C2×D20 | — | 6 | 2 | no | — |
| 251 | C2×D20 | — | 6 | 1 | no | — |
| 252 | C2×D20 | — | 6 | 1 | no | — |
| 253 | C2×D20 | — | 6 | 1 | no | — |
| 254 | C2×D20 | — | 6 | 1 | no | — |
| 255 | C2×D20 | — | 6 | 2 | no | — |
| 256 | C2×C4×D5 | — | 3 | 2 | no | — |
| 257 | C2×C4×D5 | — | 3 | 2 | no | — |
| 258 | C2×C4×D5 | — | 3 | 2 | no | — |
| 259 | C2×C4×D5 | — | 3 | 2 | no | — |
| 260 | C2×C4×D5 | — | 3 | 4 | no | — |
| 261 | C2×C4×D5 | — | 3 | 4 | no | — |
| 262 | C2×Dic10 | — | 3 | 1 | no | — |
| 263 | C2×Dic10 | — | 3 | 1 | no | — |
| 264 | C2×Dic10 | — | 3 | 2 | no | — |
| 265 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 266 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 267 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 268 | C5×C4⋊C4 | — | 3 | 2 | no | — |
| 269 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 270 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 271 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 272 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 273 | C5×C22⋊C4 | — | 3 | 2 | no | — |
| 274 | C42×C5 | — | 3 | 2 | no | — |
| 275 | C22⋊Dic5 | — | 3 | 4 | no | — |
| 276 | #685 | — | 3 | 4 | no | — |
| 277 | #685 | — | 3 | 4 | no | — |
| 278 | #685 | — | 3 | 4 | no | — |
| 279 | #685 | — | 3 | 4 | no | — |
| 280 | #685 | — | 3 | 4 | no | — |
| 281 | #685 | — | 3 | 4 | no | — |
| 282 | C4⋊Dic5 | — | 3 | 2 | no | — |
| 283 | C4⋊Dic5 | — | 3 | 2 | no | — |
| 284 | #683 | — | 3 | 4 | no | — |
| 285 | #683 | — | 3 | 4 | no | — |
| 286 | C4×Dic5 | — | 3 | 4 | no | — |
| 287 | C2×H(5,𝔽2) | — | 15 | 1 | no | — |
| 288 | C22×#41 | — | 5 | 1 | no | — |
| 289 | #550 | — | 15 | 2 | no | — |
| 290 | #548 | — | 15 | 2 | no | — |
| 291 | #546 | — | 15 | 2 | no | — |
| 292 | #546 | — | 15 | 4 | no | — |
| 293 | D42 | — | 15 | 2 | no | — |
| 294 | D42 | — | 15 | 4 | no | — |
| 295 | #537 | — | 15 | 2 | no | — |
| 296 | #537 | — | 15 | 1 | no | — |
| 297 | #535 | — | 15 | 1 | no | — |
| 298 | #535 | — | 15 | 2 | no | — |
| 299 | #525 | — | 3 | 1 | no | — |
| 300 | #525 | — | 15 | 2 | no | — |
| 301 | C2×#121 | — | 15 | 2 | no | — |
| 302 | C2×#121 | — | 15 | 1 | no | — |
| 303 | #520 | — | 15 | 1 | no | — |
| 304 | C22×C3×C5 | — | 4 | 1 | no | — |
| 305 | C2×D15 | — | 4 | 4 | no | — |
| 306 | C2×D15 | — | 16 | 2 | no | — |
| 307 | C2×C5×D3 | — | 4 | 2 | no | — |
| 308 | C2×C3×D5 | — | 4 | 2 | no | — |
| 309 | C5×A4 | H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 310 | D3×D5 | — | 16 | 4 | no | — |
| 311 | C3×C4×C5 | — | 4 | 1 | no | — |
| 312 | C3×C4×C5 | — | 4 | 1 | no | — |
| 313 | C3×Dic5 | — | 4 | 2 | no | — |
| 314 | C5×Dic3 | — | 4 | 2 | no | — |
| 315 | C22×A4 | — | 5 | 2 | no | — |
| 316 | C22×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 317 | C2×S4 | — | 5 | 4 | no | — |
| 318 | C2×S4 | — | 20 | 4 | no | — |
| 319 | C2×S4 | — | 20 | 2 | no | — |
| 320 | C2×S4 | C22×D5 | 1 | 2 | yes | — |
| 321 | C3×#41 | — | 20 | 1 | no | — |
| 322 | #239 | — | 20 | 2 | no | — |
| 323 | D3×D4 | — | 20 | 2 | no | — |
| 324 | D3×D4 | — | 20 | 4 | no | — |
| 325 | #235 | — | 4 | 1 | no | — |
| 326 | #235 | — | 20 | 2 | no | — |
| 327 | C2×D12 | — | 20 | 2 | no | — |
| 328 | C2×D12 | — | 20 | 1 | no | — |
| 329 | C4×A4 | — | 5 | 2 | no | — |
| 330 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 331 | C4×A4 | C22×D5 | 1 | 1 | yes | characteristic |
| 332 | SL(2,ℤ/4) | C22×D5 | 1 | 2 | yes | — |
| 333 | C23×C5 | — | 2 | 1 | no | — |
| 334 | C23×C5 | — | 3 | 1 | no | — |
| 335 | C23×C5 | — | 3 | 1 | no | — |
| 336 | C23×C5 | — | 3 | 2 | no | — |
| 337 | C23×C5 | — | 6 | 1 | no | — |
| 338 | C23×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 339 | C22×D5 | — | 2 | 2 | no | — |
| 340 | C22×D5 | — | 3 | 2 | no | — |
| 341 | C22×D5 | — | 3 | 2 | no | — |
| 342 | C22×D5 | — | 3 | 4 | no | — |
| 343 | C22×D5 | — | 6 | 4 | no | — |
| 344 | C22×D5 | — | 6 | 2 | no | — |
| 345 | C22×D5 | — | 6 | 2 | no | — |
| 346 | C22×D5 | — | 6 | 2 | no | — |
| 347 | C22×D5 | — | 6 | 4 | no | — |
| 348 | C22×D5 | — | 12 | 4 | no | — |
| 349 | C22×D5 | — | 12 | 2 | no | — |
| 350 | C22×D5 | — | 12 | 4 | no | — |
| 351 | C22×D5 | — | 12 | 2 | no | — |
| 352 | C5×Q8 | — | 6 | 1 | no | — |
| 353 | C5×Q8 | — | 6 | 1 | no | — |
| 354 | C5×D4 | — | 6 | 1 | no | — |
| 355 | C5×D4 | — | 6 | 2 | no | — |
| 356 | C5×D4 | — | 6 | 2 | no | — |
| 357 | C5×D4 | — | 6 | 2 | no | — |
| 358 | C5×D4 | — | 6 | 2 | no | — |
| 359 | C5×D4 | — | 6 | 1 | no | — |
| 360 | C5×D4 | — | 12 | 2 | no | — |
| 361 | C2×C4×C5 | — | 3 | 1 | no | — |
| 362 | C2×C4×C5 | — | 3 | 1 | no | — |
| 363 | C2×C4×C5 | — | 3 | 1 | no | — |
| 364 | C2×C4×C5 | — | 3 | 1 | no | — |
| 365 | C2×C4×C5 | — | 3 | 1 | no | — |
| 366 | C2×C4×C5 | — | 3 | 1 | no | — |
| 367 | C2×C4×C5 | — | 3 | 1 | no | — |
| 368 | C2×C4×C5 | — | 3 | 2 | no | — |
| 369 | C2×C4×C5 | — | 3 | 2 | no | — |
| 370 | C2×C4×C5 | — | 3 | 2 | no | — |
| 371 | C2×C4×C5 | — | 6 | 1 | no | — |
| 372 | C2×C4×C5 | — | 6 | 2 | no | — |
| 373 | C2×C4×C5 | — | 6 | 2 | no | — |
| 374 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 375 | C22⋊D5 | — | 3 | 2 | no | — |
| 376 | C22⋊D5 | — | 3 | 2 | no | — |
| 377 | C22⋊D5 | — | 3 | 2 | no | — |
| 378 | C22⋊D5 | — | 6 | 2 | no | — |
| 379 | C22⋊D5 | — | 6 | 4 | no | — |
| 380 | C22⋊D5 | — | 6 | 4 | no | — |
| 381 | C22⋊D5 | — | 6 | 4 | no | — |
| 382 | C22⋊D5 | — | 6 | 4 | no | — |
| 383 | C22⋊D5 | — | 12 | 4 | no | — |
| 384 | C22⋊D5 | — | 12 | 4 | no | — |
| 385 | C22⋊D5 | C2×S4 | 1 | 2 | yes | complemented |
| 386 | C2×Dic5 | — | 3 | 2 | no | — |
| 387 | C2×Dic5 | — | 3 | 2 | no | — |
| 388 | C2×Dic5 | — | 3 | 4 | no | — |
| 389 | C2×Dic5 | — | 12 | 2 | no | — |
| 390 | D20 | — | 3 | 2 | no | — |
| 391 | D20 | — | 3 | 1 | no | — |
| 392 | D20 | — | 6 | 1 | no | — |
| 393 | D20 | — | 6 | 2 | no | — |
| 394 | D20 | — | 6 | 2 | no | — |
| 395 | D20 | — | 6 | 4 | no | — |
| 396 | D20 | — | 6 | 4 | no | — |
| 397 | D20 | — | 6 | 2 | no | — |
| 398 | D20 | — | 6 | 2 | no | — |
| 399 | D20 | — | 12 | 4 | no | — |
| 400 | D20 | — | 12 | 4 | no | — |
| 401 | D20 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 402 | C4×D5 | — | 3 | 2 | no | — |
| 403 | C4×D5 | — | 3 | 2 | no | — |
| 404 | C4×D5 | — | 3 | 2 | no | — |
| 405 | C4×D5 | — | 6 | 2 | no | — |
| 406 | C4×D5 | — | 6 | 4 | no | — |
| 407 | C4×D5 | — | 6 | 4 | no | — |
| 408 | C4×D5 | — | 12 | 4 | no | — |
| 409 | C4×D5 | C2×S4 | 1 | 2 | yes | complemented |
| 410 | Dic10 | — | 3 | 1 | no | — |
| 411 | Dic10 | — | 3 | 2 | no | — |
| 412 | Dic10 | — | 6 | 1 | no | — |
| 413 | Dic10 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 414 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 415 | H(5,𝔽2) | — | 30 | 2 | no | — |
| 416 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 417 | H(5,𝔽2) | — | 30 | 2 | no | — |
| 418 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 419 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 420 | C2×#41 | — | 3 | 1 | no | — |
| 421 | C2×#41 | — | 15 | 1 | no | — |
| 422 | C2×#41 | — | 15 | 1 | no | — |
| 423 | C2×#41 | — | 15 | 2 | no | — |
| 424 | C2×#41 | — | 15 | 2 | no | — |
| 425 | C2×#41 | — | 15 | 1 | no | — |
| 426 | C2×#41 | — | 15 | 1 | no | — |
| 427 | C2×#41 | — | 15 | 2 | no | — |
| 428 | C2×#41 | — | 15 | 2 | no | — |
| 429 | C22×Q8 | — | 5 | 1 | no | — |
| 430 | C22×D4 | — | 5 | 2 | no | — |
| 431 | C22×D4 | — | 5 | 1 | no | — |
| 432 | C22×D4 | — | 15 | 1 | no | — |
| 433 | C22×D4 | — | 15 | 2 | no | — |
| 434 | C22×D4 | — | 15 | 2 | no | — |
| 435 | C22×D4 | — | 15 | 4 | no | — |
| 436 | C22×D4 | — | 15 | 4 | no | — |
| 437 | C22×D4 | — | 15 | 2 | no | — |
| 438 | C23×C4 | — | 5 | 2 | no | — |
| 439 | C23×C4 | D3×D5 | 1 | 1 | yes | characteristic, complemented |
| 440 | #127 | — | 15 | 2 | no | — |
| 441 | #127 | — | 15 | 4 | no | — |
| 442 | #124 | — | 15 | 2 | no | — |
| 443 | #124 | — | 15 | 4 | no | — |
| 444 | #123 | — | 3 | 2 | no | — |
| 445 | #123 | — | 15 | 4 | no | — |
| 446 | C22⋊Q8 | — | 3 | 1 | no | — |
| 447 | C22⋊Q8 | — | 3 | 1 | no | — |
| 448 | C22⋊Q8 | — | 15 | 4 | no | — |
| 449 | C22⋊Q8 | — | 15 | 2 | no | — |
| 450 | C22⋊Q8 | — | 15 | 2 | no | — |
| 451 | #121 | — | 3 | 1 | no | — |
| 452 | #121 | — | 3 | 1 | no | — |
| 453 | #121 | — | 15 | 4 | no | — |
| 454 | #121 | — | 15 | 4 | no | — |
| 455 | #121 | — | 15 | 4 | no | — |
| 456 | #121 | — | 15 | 2 | no | — |
| 457 | #121 | — | 15 | 2 | no | — |
| 458 | #121 | — | 15 | 4 | no | — |
| 459 | #121 | — | 15 | 2 | no | — |
| 460 | #121 | — | 15 | 2 | no | — |
| 461 | #121 | — | 15 | 2 | no | — |
| 462 | #121 | — | 15 | 4 | no | — |
| 463 | #121 | — | 15 | 2 | no | — |
| 464 | #121 | — | 15 | 4 | no | — |
| 465 | #121 | — | 15 | 2 | no | — |
| 466 | #121 | — | 15 | 2 | no | — |
| 467 | #120 | — | 3 | 2 | no | — |
| 468 | #120 | — | 15 | 4 | no | — |
| 469 | #120 | — | 15 | 4 | no | — |
| 470 | #120 | — | 15 | 4 | no | — |
| 471 | #120 | — | 15 | 4 | no | — |
| 472 | C4×Q8 | — | 15 | 2 | no | — |
| 473 | C4×D4 | — | 3 | 2 | no | — |
| 474 | C4×D4 | — | 3 | 2 | no | — |
| 475 | C4×D4 | — | 15 | 2 | no | — |
| 476 | C4×D4 | — | 15 | 4 | no | — |
| 477 | C4×D4 | — | 15 | 4 | no | — |
| 478 | C4×D4 | — | 15 | 4 | no | — |
| 479 | #117 | — | 3 | 1 | no | — |
| 480 | #117 | — | 15 | 2 | no | — |
| 481 | C2×C4⋊C4 | — | 15 | 2 | no | — |
| 482 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 483 | C2×C22⋊C4 | — | 15 | 4 | no | — |
| 484 | C2×C22⋊C4 | — | 15 | 2 | no | — |
| 485 | C2×C3×C5 | — | 4 | 1 | no | — |
| 486 | C2×C3×C5 | — | 8 | 1 | no | — |
| 487 | D15 | — | 8 | 4 | no | — |
| 488 | C3×D5 | — | 8 | 2 | no | — |
| 489 | C5×D3 | — | 8 | 2 | no | — |
| 490 | C22×D3 | — | 20 | 4 | no | — |
| 491 | C22×D3 | — | 20 | 2 | no | — |
| 492 | C2×A4 | — | 2 | 1 | no | — |
| 493 | C2×A4 | — | 10 | 2 | no | — |
| 494 | C2×A4 | C23×D5 | 1 | 1 | yes | characteristic |
| 495 | S4 | — | 2 | 2 | no | — |
| 496 | S4 | — | 10 | 4 | no | — |
| 497 | C3×Q8 | — | 20 | 1 | no | — |
| 498 | C3×D4 | — | 20 | 1 | no | — |
| 499 | C3×D4 | — | 20 | 2 | no | — |
| 500 | C2×C3×C4 | — | 4 | 1 | no | — |
| 501 | C2×C3×C4 | — | 20 | 2 | no | — |
| 502 | #67 | — | 4 | 2 | no | — |
| 503 | #67 | — | 20 | 4 | no | — |
| 504 | D12 | — | 4 | 1 | no | — |
| 505 | D12 | — | 20 | 2 | no | — |
| 506 | D12 | — | 20 | 2 | no | — |
| 507 | D12 | — | 20 | 4 | no | — |
| 508 | C4×D3 | — | 4 | 2 | no | — |
| 509 | C4×D3 | — | 20 | 4 | no | — |
| 510 | Dic6 | — | 4 | 1 | no | — |
| 511 | C22×C5 | — | 3 | 1 | no | — |
| 512 | C22×C5 | — | 3 | 1 | no | — |
| 513 | C22×C5 | — | 3 | 1 | no | — |
| 514 | C22×C5 | — | 6 | 1 | no | — |
| 515 | C22×C5 | — | 6 | 1 | no | — |
| 516 | C22×C5 | — | 6 | 1 | no | — |
| 517 | C22×C5 | — | 6 | 1 | no | — |
| 518 | C22×C5 | — | 6 | 2 | no | — |
| 519 | C22×C5 | — | 6 | 2 | no | — |
| 520 | C22×C5 | — | 6 | 2 | no | — |
| 521 | C22×C5 | #1009 | 1 | 1 | yes | characteristic, complemented |
| 522 | C22×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 523 | C2×D5 | — | 3 | 2 | no | — |
| 524 | C2×D5 | — | 6 | 2 | no | — |
| 525 | C2×D5 | — | 6 | 2 | no | — |
| 526 | C2×D5 | — | 6 | 2 | no | — |
| 527 | C2×D5 | — | 6 | 2 | no | — |
| 528 | C2×D5 | — | 6 | 4 | no | — |
| 529 | C2×D5 | — | 6 | 4 | no | — |
| 530 | C2×D5 | — | 6 | 4 | no | — |
| 531 | C2×D5 | — | 24 | 4 | no | — |
| 532 | C2×D5 | — | 24 | 4 | no | — |
| 533 | C2×D5 | — | 24 | 2 | no | — |
| 534 | C2×D5 | — | 24 | 2 | no | — |
| 535 | C2×D5 | C22×S4 | 1 | 2 | yes | — |
| 536 | C4×C5 | — | 3 | 1 | no | — |
| 537 | C4×C5 | — | 3 | 1 | no | — |
| 538 | C4×C5 | — | 6 | 2 | no | — |
| 539 | C4×C5 | — | 6 | 2 | no | — |
| 540 | C4×C5 | — | 6 | 2 | no | — |
| 541 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 542 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 543 | Dic5 | — | 3 | 2 | no | — |
| 544 | Dic5 | — | 6 | 4 | no | — |
| 545 | Dic5 | C22×S4 | 1 | 2 | yes | — |
| 546 | C24 | — | 5 | 2 | no | — |
| 547 | C24 | — | 15 | 2 | no | — |
| 548 | C24 | — | 15 | 4 | no | — |
| 549 | C24 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 550 | #41 | — | 5 | 1 | no | — |
| 551 | #41 | — | 6 | 1 | no | — |
| 552 | #41 | — | 6 | 1 | no | — |
| 553 | #41 | — | 6 | 1 | no | — |
| 554 | #41 | — | 6 | 1 | no | — |
| 555 | #41 | — | 15 | 2 | no | — |
| 556 | #41 | — | 15 | 2 | no | — |
| 557 | #41 | — | 15 | 1 | no | — |
| 558 | #41 | — | 15 | 1 | no | — |
| 559 | #41 | — | 15 | 1 | no | — |
| 560 | #41 | — | 30 | 1 | no | — |
| 561 | #41 | — | 30 | 1 | no | — |
| 562 | #41 | — | 30 | 1 | no | — |
| 563 | #41 | — | 30 | 2 | no | — |
| 564 | #41 | — | 30 | 2 | no | — |
| 565 | #41 | — | 30 | 2 | no | — |
| 566 | #41 | — | 30 | 2 | no | — |
| 567 | #41 | — | 30 | 4 | no | — |
| 568 | #41 | — | 30 | 2 | no | — |
| 569 | #41 | — | 30 | 2 | no | — |
| 570 | #41 | — | 30 | 2 | no | — |
| 571 | #41 | — | 30 | 2 | no | — |
| 572 | C2×Q8 | — | 3 | 1 | no | — |
| 573 | C2×Q8 | — | 15 | 1 | no | — |
| 574 | C2×Q8 | — | 15 | 1 | no | — |
| 575 | C2×Q8 | — | 15 | 2 | no | — |
| 576 | C2×D4 | — | 3 | 2 | no | — |
| 577 | C2×D4 | — | 3 | 1 | no | — |
| 578 | C2×D4 | — | 3 | 2 | no | — |
| 579 | C2×D4 | — | 3 | 2 | no | — |
| 580 | C2×D4 | — | 15 | 1 | no | — |
| 581 | C2×D4 | — | 15 | 2 | no | — |
| 582 | C2×D4 | — | 15 | 1 | no | — |
| 583 | C2×D4 | — | 15 | 4 | no | — |
| 584 | C2×D4 | — | 15 | 2 | no | — |
| 585 | C2×D4 | — | 15 | 2 | no | — |
| 586 | C2×D4 | — | 15 | 4 | no | — |
| 587 | C2×D4 | — | 15 | 4 | no | — |
| 588 | C2×D4 | — | 15 | 2 | no | — |
| 589 | C2×D4 | — | 15 | 2 | no | — |
| 590 | C2×D4 | — | 15 | 2 | no | — |
| 591 | C2×D4 | — | 15 | 2 | no | — |
| 592 | C2×D4 | — | 15 | 4 | no | — |
| 593 | C2×D4 | — | 15 | 4 | no | — |
| 594 | C2×D4 | — | 15 | 4 | no | — |
| 595 | C2×D4 | — | 15 | 4 | no | — |
| 596 | C2×D4 | — | 30 | 1 | no | — |
| 597 | C2×D4 | — | 30 | 1 | no | — |
| 598 | C2×D4 | — | 30 | 1 | no | — |
| 599 | C2×D4 | — | 30 | 2 | no | — |
| 600 | C2×D4 | — | 30 | 2 | no | — |
| 601 | C2×D4 | — | 30 | 4 | no | — |
| 602 | C2×D4 | — | 30 | 2 | no | — |
| 603 | C2×D4 | — | 30 | 2 | no | — |
| 604 | C2×D4 | — | 30 | 2 | no | — |
| 605 | C2×D4 | — | 30 | 2 | no | — |
| 606 | C2×D4 | — | 30 | 4 | no | — |
| 607 | C2×D4 | — | 30 | 4 | no | — |
| 608 | C2×D4 | — | 30 | 4 | no | — |
| 609 | C2×D4 | — | 30 | 4 | no | — |
| 610 | C2×D4 | — | 30 | 1 | no | — |
| 611 | C2×D4 | — | 60 | 4 | no | — |
| 612 | C2×D4 | — | 60 | 4 | no | — |
| 613 | C2×D4 | — | 60 | 2 | no | — |
| 614 | C2×D4 | — | 60 | 2 | no | — |
| 615 | C22×C4 | — | 3 | 1 | no | — |
| 616 | C22×C4 | — | 3 | 1 | no | — |
| 617 | C22×C4 | — | 3 | 1 | no | — |
| 618 | C22×C4 | — | 3 | 1 | no | — |
| 619 | C22×C4 | — | 3 | 2 | no | — |
| 620 | C22×C4 | — | 5 | 2 | no | — |
| 621 | C22×C4 | — | 15 | 2 | no | — |
| 622 | C22×C4 | — | 15 | 2 | no | — |
| 623 | C22×C4 | — | 15 | 2 | no | — |
| 624 | C22×C4 | — | 15 | 2 | no | — |
| 625 | C22×C4 | — | 15 | 4 | no | — |
| 626 | C22×C4 | — | 15 | 4 | no | — |
| 627 | C22×C4 | — | 15 | 2 | no | — |
| 628 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 629 | C22×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 630 | C4⋊C4 | — | 3 | 1 | no | — |
| 631 | C4⋊C4 | — | 3 | 1 | no | — |
| 632 | C4⋊C4 | — | 3 | 2 | no | — |
| 633 | C4⋊C4 | — | 3 | 2 | no | — |
| 634 | C4⋊C4 | — | 15 | 2 | no | — |
| 635 | C4⋊C4 | — | 15 | 4 | no | — |
| 636 | C4⋊C4 | — | 15 | 2 | no | — |
| 637 | C4⋊C4 | — | 15 | 4 | no | — |
| 638 | C22⋊C4 | — | 3 | 2 | no | — |
| 639 | C22⋊C4 | — | 3 | 2 | no | — |
| 640 | C22⋊C4 | — | 3 | 2 | no | — |
| 641 | C22⋊C4 | — | 3 | 2 | no | — |
| 642 | C22⋊C4 | — | 3 | 2 | no | — |
| 643 | C22⋊C4 | — | 15 | 4 | no | — |
| 644 | C22⋊C4 | — | 15 | 4 | no | — |
| 645 | C22⋊C4 | — | 15 | 4 | no | — |
| 646 | C22⋊C4 | — | 15 | 4 | no | — |
| 647 | C22⋊C4 | — | 15 | 4 | no | — |
| 648 | C22⋊C4 | — | 15 | 4 | no | — |
| 649 | C22⋊C4 | — | 15 | 4 | no | — |
| 650 | C42 | — | 3 | 2 | no | — |
| 651 | C42 | — | 15 | 4 | no | — |
| 652 | C3×C5 | — | 4 | 1 | no | Hall |
| 653 | C22×C3 | — | 4 | 1 | no | — |
| 654 | C22×C3 | — | 20 | 2 | no | — |
| 655 | C2×D3 | — | 4 | 2 | no | — |
| 656 | C2×D3 | — | 20 | 4 | no | — |
| 657 | C2×D3 | — | 80 | 4 | no | — |
| 658 | C2×D3 | — | 80 | 2 | no | — |
| 659 | A4 | #4149 | 1 | 1 | yes | characteristic, complemented |
| 660 | C3×C4 | — | 4 | 1 | no | — |
| 661 | C3×C4 | — | 4 | 1 | no | — |
| 662 | C3×C4 | — | 20 | 2 | no | — |
| 663 | Dic3 | — | 4 | 2 | no | — |
| 664 | C2×C5 | — | 2 | 1 | no | — |
| 665 | C2×C5 | — | 3 | 1 | no | — |
| 666 | C2×C5 | — | 3 | 1 | no | — |
| 667 | C2×C5 | — | 6 | 1 | no | — |
| 668 | C2×C5 | — | 12 | 2 | no | — |
| 669 | C2×C5 | C23×S4 | 1 | 1 | yes | characteristic |
| 670 | D5 | — | 2 | 2 | no | — |
| 671 | D5 | — | 6 | 2 | no | — |
| 672 | D5 | — | 12 | 4 | no | — |
| 673 | C23 | — | 2 | 1 | no | — |
| 674 | C23 | — | 3 | 1 | no | — |
| 675 | C23 | — | 3 | 1 | no | — |
| 676 | C23 | — | 3 | 2 | no | — |
| 677 | C23 | — | 6 | 1 | no | — |
| 678 | C23 | — | 10 | 2 | no | — |
| 679 | C23 | — | 15 | 2 | no | — |
| 680 | C23 | — | 15 | 2 | no | — |
| 681 | C23 | — | 15 | 4 | no | — |
| 682 | C23 | — | 30 | 2 | no | — |
| 683 | C23 | — | 30 | 2 | no | — |
| 684 | C23 | — | 30 | 4 | no | — |
| 685 | C23 | — | 30 | 4 | no | — |
| 686 | C23 | — | 30 | 2 | no | — |
| 687 | C23 | — | 60 | 2 | no | — |
| 688 | C23 | — | 60 | 4 | no | — |
| 689 | C23 | — | 60 | 2 | no | — |
| 690 | C23 | — | 60 | 4 | no | — |
| 691 | C23 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 692 | Q8 | — | 5 | 1 | no | — |
| 693 | Q8 | — | 6 | 1 | no | — |
| 694 | Q8 | — | 6 | 1 | no | — |
| 695 | Q8 | — | 15 | 2 | no | — |
| 696 | Q8 | — | 15 | 1 | no | — |
| 697 | Q8 | — | 30 | 1 | no | — |
| 698 | D4 | — | 5 | 2 | no | — |
| 699 | D4 | — | 5 | 1 | no | — |
| 700 | D4 | — | 6 | 1 | no | — |
| 701 | D4 | — | 6 | 2 | no | — |
| 702 | D4 | — | 6 | 2 | no | — |
| 703 | D4 | — | 6 | 2 | no | — |
| 704 | D4 | — | 6 | 2 | no | — |
| 705 | D4 | — | 6 | 1 | no | — |
| 706 | D4 | — | 12 | 2 | no | — |
| 707 | D4 | — | 15 | 2 | no | — |
| 708 | D4 | — | 15 | 2 | no | — |
| 709 | D4 | — | 15 | 2 | no | — |
| 710 | D4 | — | 15 | 2 | no | — |
| 711 | D4 | — | 15 | 1 | no | — |
| 712 | D4 | — | 30 | 1 | no | — |
| 713 | D4 | — | 30 | 2 | no | — |
| 714 | D4 | — | 30 | 2 | no | — |
| 715 | D4 | — | 30 | 4 | no | — |
| 716 | D4 | — | 30 | 4 | no | — |
| 717 | D4 | — | 30 | 4 | no | — |
| 718 | D4 | — | 30 | 2 | no | — |
| 719 | D4 | — | 30 | 4 | no | — |
| 720 | D4 | — | 30 | 4 | no | — |
| 721 | D4 | — | 30 | 4 | no | — |
| 722 | D4 | — | 30 | 2 | no | — |
| 723 | D4 | — | 30 | 2 | no | — |
| 724 | D4 | — | 60 | 4 | no | — |
| 725 | D4 | — | 60 | 4 | no | — |
| 726 | D4 | — | 60 | 4 | no | — |
| 727 | D4 | — | 60 | 4 | no | — |
| 728 | C2×C4 | — | 3 | 1 | no | — |
| 729 | C2×C4 | — | 3 | 1 | no | — |
| 730 | C2×C4 | — | 3 | 1 | no | — |
| 731 | C2×C4 | — | 3 | 1 | no | — |
| 732 | C2×C4 | — | 3 | 1 | no | — |
| 733 | C2×C4 | — | 3 | 1 | no | — |
| 734 | C2×C4 | — | 3 | 1 | no | — |
| 735 | C2×C4 | — | 3 | 2 | no | — |
| 736 | C2×C4 | — | 3 | 2 | no | — |
| 737 | C2×C4 | — | 3 | 2 | no | — |
| 738 | C2×C4 | — | 5 | 2 | no | — |
| 739 | C2×C4 | — | 6 | 1 | no | — |
| 740 | C2×C4 | — | 6 | 2 | no | — |
| 741 | C2×C4 | — | 6 | 2 | no | — |
| 742 | C2×C4 | — | 15 | 2 | no | — |
| 743 | C2×C4 | — | 15 | 2 | no | — |
| 744 | C2×C4 | — | 15 | 2 | no | — |
| 745 | C2×C4 | — | 15 | 2 | no | — |
| 746 | C2×C4 | — | 15 | 2 | no | — |
| 747 | C2×C4 | — | 15 | 4 | no | — |
| 748 | C2×C4 | — | 30 | 2 | no | — |
| 749 | C2×C4 | — | 30 | 4 | no | — |
| 750 | C2×C4 | — | 30 | 4 | no | — |
| 751 | C2×C4 | — | 60 | 4 | no | — |
| 752 | C2×C4 | — | 60 | 2 | no | — |
| 753 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic, complemented |
| 754 | C2×C3 | — | 4 | 1 | no | — |
| 755 | C2×C3 | — | 8 | 1 | no | — |
| 756 | C2×C3 | — | 40 | 2 | no | — |
| 757 | D3 | — | 8 | 2 | no | — |
| 758 | D3 | — | 40 | 4 | no | — |
| 759 | C5 | #87489 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 760 | C22 | — | 3 | 1 | no | — |
| 761 | C22 | — | 3 | 1 | no | — |
| 762 | C22 | — | 3 | 1 | no | — |
| 763 | C22 | — | 5 | 2 | no | — |
| 764 | C22 | — | 6 | 1 | no | — |
| 765 | C22 | — | 6 | 1 | no | — |
| 766 | C22 | — | 6 | 1 | no | — |
| 767 | C22 | — | 6 | 1 | no | — |
| 768 | C22 | — | 6 | 2 | no | — |
| 769 | C22 | — | 6 | 2 | no | — |
| 770 | C22 | — | 6 | 2 | no | — |
| 771 | C22 | — | 15 | 2 | no | — |
| 772 | C22 | — | 30 | 2 | no | — |
| 773 | C22 | — | 30 | 2 | no | — |
| 774 | C22 | — | 30 | 2 | no | — |
| 775 | C22 | — | 30 | 2 | no | — |
| 776 | C22 | — | 30 | 4 | no | — |
| 777 | C22 | — | 30 | 4 | no | — |
| 778 | C22 | — | 30 | 4 | no | — |
| 779 | C22 | — | 120 | 2 | no | — |
| 780 | C22 | — | 120 | 2 | no | — |
| 781 | C22 | — | 120 | 4 | no | — |
| 782 | C22 | — | 120 | 4 | no | — |
| 783 | C22 | #92019 | 1 | 1 | yes | characteristic, complemented |
| 784 | C22 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 785 | C4 | — | 3 | 1 | no | — |
| 786 | C4 | — | 3 | 1 | no | — |
| 787 | C4 | — | 5 | 2 | no | — |
| 788 | C4 | — | 6 | 2 | no | — |
| 789 | C4 | — | 6 | 2 | no | — |
| 790 | C4 | — | 6 | 2 | no | — |
| 791 | C4 | — | 15 | 2 | no | — |
| 792 | C4 | — | 30 | 4 | no | — |
| 793 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 794 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 795 | C3 | — | 4 | 1 | no | Sylow |
| 796 | C2 | — | 2 | 1 | no | — |
| 797 | C2 | — | 3 | 1 | no | — |
| 798 | C2 | — | 3 | 1 | no | — |
| 799 | C2 | — | 6 | 1 | no | — |
| 800 | C2 | — | 10 | 2 | no | — |
| 801 | C2 | — | 12 | 2 | no | — |
| 802 | C2 | — | 30 | 2 | no | — |
| 803 | C2 | — | 60 | 4 | no | — |
| 804 | 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 | H(5,𝔽2) |
| 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. C2×C4⋊(C5⋊S4) | C2 | semidirect |
| 3. C5×#5912 | C2 | semidirect |
| 4. #11756799 | C2 | semidirect |
| 5. S4×D20 | C2 | semidirect |
| 6. D5×C4⋊S4 | C2 | semidirect |
| 7. #11756754 | C2 | semidirect |
| 8. #11756747 | C2 | semidirect |
| 10. C22×C5⋊S4 | C22 | semidirect |
| 11. C2×D5×S4 | C22 | semidirect |
| 12. C2×C4×C5×A4 | C22 | semidirect |
| 14. A4×C22⋊D5 | C22 | semidirect |
| 15. A4×D20 | C22 | semidirect |
| 16. C4×D5×A4 | C22 | semidirect |
| 17. A4×Dic10 | C22 | semidirect |
| 18. C4⋊(C5⋊S4) | C22 | semidirect |
| 19. C4⋊(C5⋊S4) | C22 | semidirect |
| 20. C5×GL(2,ℤ/4) | C22 | semidirect |
| 21. C5×C4⋊S4 | C22 | semidirect |
| 22. C4×C5×S4 | C22 | semidirect |
| 23. C5×A4⋊Q8 | C22 | semidirect |
| 24. #91905 | C22 | semidirect |
| 25. #91902 | C22 | semidirect |
| 26. #91901 | C22 | semidirect |
| 29. C22×#709 | D3 | semidirect |
| 68. #5912 | D5 | semidirect |
| 72. C23×C4×C5 | C2×D3 | semidirect |
| 74. C22×C22⋊D5 | C2×D3 | semidirect |
| 94. C22×D20 | C2×D3 | semidirect |
| 95. C22×C4×D5 | C2×D3 | semidirect |
| 96. C22×Dic10 | C2×D3 | semidirect |
| 171. C2×C4×A4 | C2×D5 | semidirect |
| 173. GL(2,ℤ/4) | C2×D5 | semidirect |
| 177. C4⋊S4 | C2×D5 | semidirect |
| 179. C4×S4 | C2×D5 | semidirect |
| 180. A4⋊Q8 | C2×D5 | semidirect |
| 240. #709 | S4 | semidirect |
| 309. C5×A4 | H(5,𝔽2) | semidirect |
| 374. C2×C4×C5 | C2×S4 | semidirect |
| 385. C22⋊D5 | C2×S4 | semidirect |
| 401. D20 | C2×S4 | semidirect |
| 409. C4×D5 | C2×S4 | semidirect |
| 413. Dic10 | C2×S4 | semidirect |
| 439. C23×C4 | D3×D5 | semidirect |
| 521. C22×C5 | #1009 | semidirect |
| 659. A4 | #4149 | semidirect |
| 753. C2×C4 | D5×S4 | semidirect |
| 759. C5 | #87489 | semidirect |
| 783. C22 | #92019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#709 | 2 |
| C2×C4⋊(C5⋊S4) | 2 |
| C5×#5912 | 2 |
| #11756799 | 2 |
| S4×D20 | 2 |
| D5×C4⋊S4 | 2 |
| #11756754 | 2 |
| #11756747 | 2 |
| #10617942 | 3 |
| #92019 | 4 |
| #87489 | 5 |