← #13045337
Subgroups — #13045337
Order 1280.
1790 conjugacy classes of subgroups.
The subgroup lattice has 656 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10618396 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617373 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10617354 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #10617353 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10617342 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10617341 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10617331 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10617258 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10617257 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10617190 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10617186 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10617110 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | D5⋊#424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#4133 | C22 | 1 | 2 | yes | — |
| 15 | C2×#4133 | C22 | 1 | 2 | yes | — |
| 16 | C2×D5⋊M16 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×D5⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 18 | C5×#541 | C4 | 1 | 1 | yes | characteristic |
| 19 | #66065 | C4 | 1 | 1 | yes | characteristic |
| 20 | #66059 | C22 | 1 | 1 | yes | characteristic |
| 21 | #66040 | C22 | 1 | 4 | yes | — |
| 22 | #66038 | C4 | 1 | 4 | yes | — |
| 23 | #66032 | C4 | 1 | 1 | yes | characteristic |
| 24 | #66026 | C4 | 1 | 4 | yes | — |
| 25 | #66025 | C22 | 1 | 4 | yes | — |
| 26 | #66022 | C22 | 1 | 1 | yes | characteristic |
| 27 | #65977 | C4 | 1 | 2 | yes | — |
| 28 | #65961 | C22 | 1 | 2 | yes | — |
| 29 | #65916 | C4 | 1 | 2 | yes | — |
| 30 | C4×#713 | C22 | 1 | 2 | yes | — |
| 31 | #65869 | C4 | 1 | 1 | yes | characteristic |
| 32 | D5×#117 | C22 | 1 | 1 | yes | characteristic |
| 33 | #65787 | C22 | 1 | 2 | yes | — |
| 34 | #65787 | C22 | 1 | 2 | yes | — |
| 35 | #65756 | C22 | 1 | 2 | yes | — |
| 36 | #65709 | C22 | 1 | 4 | yes | complemented |
| 37 | #65708 | C22 | 1 | 2 | yes | — |
| 38 | #65708 | C22 | 1 | 2 | yes | — |
| 39 | #65708 | C22 | 1 | 2 | yes | — |
| 40 | #65708 | C22 | 1 | 2 | yes | — |
| 41 | #65708 | C22 | 1 | 4 | yes | complemented |
| 42 | #65708 | C22 | 1 | 4 | yes | complemented |
| 43 | #65707 | C22 | 1 | 4 | yes | complemented |
| 44 | #65707 | C22 | 1 | 4 | yes | complemented |
| 45 | #65706 | C22 | 1 | 4 | yes | — |
| 46 | #65706 | C22 | 1 | 4 | yes | complemented |
| 47 | #65706 | C22 | 1 | 4 | yes | complemented |
| 48 | #65705 | C22 | 1 | 4 | yes | — |
| 49 | #65705 | C22 | 1 | 4 | yes | complemented |
| 50 | #65704 | C22 | 1 | 4 | yes | — |
| 51 | #65704 | C22 | 1 | 4 | yes | — |
| 52 | #65704 | C22 | 1 | 4 | yes | complemented |
| 53 | #65704 | C22 | 1 | 4 | yes | complemented |
| 54 | #65703 | C22 | 1 | 4 | yes | complemented |
| 55 | #65702 | C22 | 1 | 4 | yes | — |
| 56 | #65702 | C22 | 1 | 4 | yes | complemented |
| 57 | #65701 | C22 | 1 | 2 | yes | — |
| 58 | #65701 | C22 | 1 | 2 | yes | — |
| 59 | #65697 | C22 | 1 | 4 | yes | — |
| 60 | #65696 | C22 | 1 | 2 | yes | — |
| 61 | #65696 | C22 | 1 | 2 | yes | — |
| 62 | #65695 | C22 | 1 | 4 | yes | — |
| 63 | #65694 | C22 | 1 | 4 | yes | — |
| 64 | #65693 | C22 | 1 | 4 | yes | — |
| 65 | #65692 | C22 | 1 | 4 | yes | — |
| 66 | #65683 | C22 | 1 | 4 | yes | complemented |
| 67 | #65682 | C22 | 1 | 1 | yes | characteristic |
| 68 | #65682 | C22 | 1 | 4 | yes | complemented |
| 69 | #65681 | C22 | 1 | 1 | yes | characteristic |
| 70 | #65680 | C22 | 1 | 4 | yes | complemented |
| 71 | D5⋊(C4⋊C8) | C22 | 1 | 2 | yes | — |
| 72 | D5⋊(C4⋊C8) | C22 | 1 | 2 | yes | — |
| 73 | D5⋊(C4⋊C8) | C22 | 1 | 4 | yes | complemented |
| 74 | C4×#700 | C22 | 1 | 2 | yes | — |
| 75 | #60267 | — | 5 | 1 | no | maximal, Sylow |
| 76 | C2×#713 | C23 | 1 | 2 | yes | — |
| 77 | C22×C4×D5 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×#704 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#704 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×#170 | C23 | 1 | 2 | yes | — |
| 81 | #4133 | — | 4 | 4 | no | — |
| 82 | #4133 | — | 4 | 4 | no | — |
| 83 | D5⋊M16 | — | 4 | 2 | no | — |
| 84 | C2×#700 | C23 | 1 | 2 | yes | — |
| 85 | C2×#700 | C23 | 1 | 2 | yes | — |
| 86 | C2×#700 | C23 | 1 | 4 | yes | — |
| 87 | C2×#700 | C23 | 1 | 4 | yes | — |
| 88 | C2×#700 | C23 | 1 | 2 | yes | — |
| 89 | C2×D5⋊C8 | — | 4 | 2 | no | — |
| 90 | C2×D5⋊C8 | C23 | 1 | 2 | yes | — |
| 91 | C2×D5⋊C8 | C23 | 1 | 2 | yes | — |
| 92 | C2×D5⋊C8 | C23 | 1 | 4 | yes | — |
| 93 | C2×D5⋊C8 | C23 | 1 | 4 | yes | — |
| 94 | C2×D5⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×D5⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 96 | C5×C4⋊Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 97 | C5×#126 | C2×C4 | 1 | 4 | yes | — |
| 98 | C5×#125 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | C5×#125 | C2×C4 | 1 | 4 | yes | — |
| 100 | C5×C22⋊Q8 | C2×C4 | 1 | 2 | yes | — |
| 101 | C4×C5×Q8 | C2×C4 | 1 | 2 | yes | — |
| 102 | C5×#117 | C2×C4 | 1 | 1 | yes | characteristic |
| 103 | #4093 | C2×C4 | 1 | 2 | yes | — |
| 104 | #4092 | C2×C4 | 1 | 2 | yes | — |
| 105 | Q8×Dic5 | C2×C4 | 1 | 2 | yes | — |
| 106 | #4076 | C2×C4 | 1 | 2 | yes | — |
| 107 | #4072 | C2×C4 | 1 | 1 | yes | characteristic |
| 108 | #4044 | C2×C4 | 1 | 4 | yes | — |
| 109 | #4044 | C2×C4 | 1 | 4 | yes | — |
| 110 | #4043 | C2×C4 | 1 | 4 | yes | — |
| 111 | #4042 | C2×C4 | 1 | 4 | yes | — |
| 112 | #4042 | C2×C4 | 1 | 4 | yes | — |
| 113 | #4041 | C2×C4 | 1 | 4 | yes | — |
| 114 | #4041 | C2×C4 | 1 | 2 | yes | — |
| 115 | #4041 | C2×C4 | 1 | 4 | yes | — |
| 116 | #4040 | C2×C4 | 1 | 4 | yes | — |
| 117 | #4040 | C2×C4 | 1 | 4 | yes | — |
| 118 | #4040 | C2×C4 | 1 | 4 | yes | — |
| 119 | #4040 | C2×C4 | 1 | 4 | yes | — |
| 120 | #4039 | C2×C4 | 1 | 2 | yes | — |
| 121 | #4039 | C2×C4 | 1 | 4 | yes | — |
| 122 | #4039 | C23 | 1 | 4 | yes | — |
| 123 | #4039 | C23 | 1 | 4 | yes | — |
| 124 | #4038 | C23 | 1 | 2 | yes | — |
| 125 | #4038 | C23 | 1 | 2 | yes | — |
| 126 | #4038 | C23 | 1 | 4 | yes | — |
| 127 | D5×C4⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 128 | #4035 | C2×C4 | 1 | 4 | yes | — |
| 129 | #4034 | C2×C4 | 1 | 2 | yes | — |
| 130 | #4033 | C23 | 1 | 4 | yes | — |
| 131 | #4031 | C2×C4 | 1 | 4 | yes | — |
| 132 | #4030 | C2×C4 | 1 | 4 | yes | — |
| 133 | #4029 | C2×C4 | 1 | 4 | yes | — |
| 134 | #4028 | C2×C4 | 1 | 4 | yes | — |
| 135 | #4027 | C23 | 1 | 4 | yes | — |
| 136 | D5×C22⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 137 | #4023 | C23 | 1 | 2 | yes | — |
| 138 | #4022 | C2×C4 | 1 | 4 | yes | — |
| 139 | #4021 | C2×C4 | 1 | 4 | yes | — |
| 140 | #4020 | C2×C4 | 1 | 1 | yes | characteristic |
| 141 | C4×D20 | C2×C4 | 1 | 2 | yes | — |
| 142 | C4×D20 | C2×C4 | 1 | 4 | yes | — |
| 143 | #4018 | C2×C4 | 1 | 1 | yes | characteristic |
| 144 | #4018 | C2×C4 | 1 | 1 | yes | characteristic |
| 145 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 146 | C42×D5 | C23 | 1 | 1 | yes | characteristic |
| 147 | C42×D5 | C23 | 1 | 4 | yes | — |
| 148 | #4016 | C2×C4 | 1 | 1 | yes | characteristic |
| 149 | C22⋊#170 | C23 | 1 | 4 | yes | — |
| 150 | #4004 | C23 | 1 | 2 | yes | — |
| 151 | #4004 | C23 | 1 | 2 | yes | — |
| 152 | #4004 | C23 | 1 | 2 | yes | — |
| 153 | #4004 | C23 | 1 | 2 | yes | — |
| 154 | #4004 | C23 | 1 | 4 | yes | — |
| 155 | #4004 | C23 | 1 | 4 | yes | — |
| 156 | #4004 | C23 | 1 | 4 | yes | — |
| 157 | #4003 | C23 | 1 | 4 | yes | — |
| 158 | #4003 | C23 | 1 | 4 | yes | — |
| 159 | #4003 | C23 | 1 | 4 | yes | — |
| 160 | #4003 | C23 | 1 | 4 | yes | — |
| 161 | #4003 | C23 | 1 | 4 | yes | — |
| 162 | #4002 | C23 | 1 | 4 | yes | — |
| 163 | #4002 | C23 | 1 | 4 | yes | — |
| 164 | #4002 | C23 | 1 | 4 | yes | — |
| 165 | C4⋊#170 | C23 | 1 | 2 | yes | — |
| 166 | C4⋊#170 | C23 | 1 | 2 | yes | — |
| 167 | C4⋊#170 | C23 | 1 | 2 | yes | — |
| 168 | C4⋊#170 | C23 | 1 | 2 | yes | — |
| 169 | C4⋊#170 | C23 | 1 | 4 | yes | — |
| 170 | C4⋊#170 | C23 | 1 | 4 | yes | — |
| 171 | C4⋊#170 | C23 | 1 | 4 | yes | — |
| 172 | C4×#170 | C23 | 1 | 4 | yes | — |
| 173 | C4×#170 | C23 | 1 | 4 | yes | — |
| 174 | C4×#170 | C23 | 1 | 4 | yes | — |
| 175 | #3455 | — | 5 | 1 | no | — |
| 176 | #2995 | — | 5 | 4 | no | — |
| 177 | #2994 | — | 5 | 4 | no | — |
| 178 | #2993 | — | 5 | 4 | no | — |
| 179 | #2992 | — | 5 | 4 | no | — |
| 180 | #2962 | — | 5 | 2 | no | — |
| 181 | #2935 | — | 5 | 2 | no | — |
| 182 | #2930 | — | 5 | 2 | no | — |
| 183 | #2929 | — | 5 | 2 | no | — |
| 184 | #2925 | — | 5 | 2 | no | — |
| 185 | #2921 | — | 5 | 1 | no | — |
| 186 | #2906 | — | 5 | 2 | no | — |
| 187 | C2×#424 | — | 5 | 1 | no | — |
| 188 | C23×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 189 | C2×C5×Q8 | C22×C4 | 1 | 2 | yes | — |
| 190 | C22×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 191 | C2×C22⋊D5 | C22×C4 | 1 | 4 | yes | — |
| 192 | C22×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 193 | #713 | — | 2 | 4 | no | — |
| 194 | #713 | — | 2 | 4 | no | — |
| 195 | C2×D20 | C22×C4 | 1 | 2 | yes | — |
| 196 | C2×D20 | C22×C4 | 1 | 4 | yes | — |
| 197 | C2×D20 | C22×C4 | 1 | 4 | yes | — |
| 198 | C2×D20 | C22×C4 | 1 | 4 | yes | — |
| 199 | C2×C4×D5 | — | 2 | 2 | no | — |
| 200 | C2×C4×D5 | — | 2 | 2 | no | — |
| 201 | C2×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 202 | C2×C4×D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 203 | C2×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 204 | C2×C4×D5 | C22×C4 | 1 | 4 | yes | — |
| 205 | C2×C4×D5 | C22×C4 | 1 | 2 | yes | — |
| 206 | C2×C4×D5 | C22×C4 | 1 | 4 | yes | — |
| 207 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×D5 | C24 | 1 | 4 | yes | — |
| 209 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 210 | C2×Dic10 | C22×C4 | 1 | 4 | yes | — |
| 211 | #704 | — | 4 | 1 | no | — |
| 212 | #704 | — | 4 | 1 | no | — |
| 213 | C2×#170 | — | 4 | 2 | no | — |
| 214 | C2×#170 | C24 | 1 | 2 | yes | — |
| 215 | C2×#170 | C24 | 1 | 2 | yes | — |
| 216 | C2×#170 | C24 | 1 | 4 | yes | — |
| 217 | C2×#170 | C24 | 1 | 2 | yes | — |
| 218 | C2×#170 | C24 | 1 | 2 | yes | — |
| 219 | C2×#170 | C24 | 1 | 4 | yes | — |
| 220 | #700 | — | 2 | 4 | no | — |
| 221 | #700 | — | 2 | 4 | no | — |
| 222 | #700 | — | 4 | 2 | no | — |
| 223 | #700 | — | 4 | 4 | no | — |
| 224 | #700 | — | 4 | 4 | no | — |
| 225 | D5⋊C8 | — | 2 | 4 | no | — |
| 226 | D5⋊C8 | — | 2 | 4 | no | — |
| 227 | D5⋊C8 | — | 4 | 1 | no | — |
| 228 | D5⋊C8 | — | 4 | 1 | no | — |
| 229 | D5⋊C8 | — | 4 | 4 | no | — |
| 230 | D5⋊C8 | — | 4 | 4 | no | — |
| 231 | C5×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 232 | C5×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 233 | C5×C4⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 234 | C5×C4⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 235 | C5×C4⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 236 | C5×C4⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 237 | C5×C22⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 238 | C5×C22⋊C4 | C22×C4 | 1 | 4 | yes | — |
| 239 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 240 | C42×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 241 | C42×C5 | C22×C4 | 1 | 4 | yes | — |
| 242 | C22⋊Dic5 | C22×C4 | 1 | 2 | yes | — |
| 243 | #685 | C22×C4 | 1 | 2 | yes | — |
| 244 | #685 | C22×C4 | 1 | 2 | yes | — |
| 245 | #685 | C22×C4 | 1 | 4 | yes | — |
| 246 | #685 | C22×C4 | 1 | 4 | yes | — |
| 247 | #685 | C22×C4 | 1 | 4 | yes | — |
| 248 | #685 | C22×C4 | 1 | 4 | yes | — |
| 249 | #685 | C22×C4 | 1 | 4 | yes | — |
| 250 | #685 | C22×C4 | 1 | 4 | yes | — |
| 251 | #685 | C22×C4 | 1 | 4 | yes | — |
| 252 | #685 | C22×C4 | 1 | 4 | yes | — |
| 253 | C4⋊Dic5 | C22×C4 | 1 | 2 | yes | — |
| 254 | C4⋊Dic5 | C22×C4 | 1 | 4 | yes | — |
| 255 | C4⋊Dic5 | C22×C4 | 1 | 2 | yes | — |
| 256 | #683 | C22×C4 | 1 | 4 | yes | — |
| 257 | #683 | C22×C4 | 1 | 2 | yes | — |
| 258 | #683 | C22×C4 | 1 | 2 | yes | — |
| 259 | #683 | C22×C4 | 1 | 4 | yes | — |
| 260 | #683 | C22×C4 | 1 | 4 | yes | — |
| 261 | C4×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 262 | C4×Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 263 | C4×Dic5 | C22×C4 | 1 | 4 | yes | — |
| 264 | C4×Dic5 | C24 | 1 | 2 | yes | — |
| 265 | C4×Dic5 | C24 | 1 | 4 | yes | — |
| 266 | C4×Dic5 | C24 | 1 | 2 | yes | — |
| 267 | C2×#131 | — | 5 | 2 | no | — |
| 268 | C2×#131 | — | 5 | 2 | no | — |
| 269 | C22×M16 | — | 5 | 1 | no | — |
| 270 | C23×C8 | — | 5 | 1 | no | — |
| 271 | #542 | — | 5 | 2 | no | — |
| 272 | #542 | — | 5 | 2 | no | — |
| 273 | #541 | — | 5 | 1 | no | — |
| 274 | #541 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 275 | #540 | — | 5 | 1 | no | — |
| 276 | #540 | — | 5 | 1 | no | — |
| 277 | #539 | — | 5 | 4 | no | — |
| 278 | #538 | — | 5 | 4 | no | — |
| 279 | #533 | — | 5 | 1 | no | — |
| 280 | #532 | — | 5 | 1 | no | — |
| 281 | #529 | — | 5 | 4 | no | — |
| 282 | #529 | — | 5 | 4 | no | — |
| 283 | #525 | — | 5 | 2 | no | — |
| 284 | C4×#41 | — | 5 | 2 | no | — |
| 285 | C2×#117 | — | 5 | 1 | no | — |
| 286 | #446 | — | 5 | 4 | no | — |
| 287 | #446 | — | 5 | 4 | no | — |
| 288 | #446 | — | 5 | 4 | no | — |
| 289 | C8×Q8 | — | 5 | 4 | no | — |
| 290 | #436 | — | 5 | 4 | no | — |
| 291 | #436 | — | 5 | 4 | no | — |
| 292 | #436 | — | 5 | 4 | no | — |
| 293 | #435 | — | 5 | 4 | no | — |
| 294 | #435 | — | 5 | 4 | no | — |
| 295 | #435 | — | 5 | 4 | no | — |
| 296 | #435 | — | 5 | 4 | no | — |
| 297 | #435 | — | 5 | 4 | no | — |
| 298 | #435 | — | 5 | 4 | no | — |
| 299 | C8×D4 | — | 5 | 4 | no | — |
| 300 | C8×D4 | — | 5 | 4 | no | — |
| 301 | C8×D4 | — | 5 | 4 | no | — |
| 302 | #433 | — | 5 | 4 | no | — |
| 303 | #433 | — | 5 | 4 | no | — |
| 304 | #433 | — | 5 | 4 | no | — |
| 305 | #433 | — | 5 | 4 | no | — |
| 306 | #432 | — | 5 | 4 | no | — |
| 307 | #431 | — | 5 | 4 | no | — |
| 308 | #424 | — | 5 | 2 | no | — |
| 309 | #424 | — | 5 | 2 | no | — |
| 310 | #424 | — | 5 | 2 | no | — |
| 311 | #424 | — | 5 | 2 | no | — |
| 312 | #424 | — | 5 | 2 | no | — |
| 313 | #424 | — | 5 | 2 | no | — |
| 314 | #424 | — | 5 | 4 | no | — |
| 315 | #424 | — | 5 | 4 | no | — |
| 316 | #423 | — | 5 | 1 | no | — |
| 317 | #423 | — | 5 | 4 | no | — |
| 318 | #423 | — | 5 | 1 | no | — |
| 319 | C2×C4⋊C8 | — | 5 | 2 | no | — |
| 320 | C2×C4⋊C8 | — | 5 | 2 | no | — |
| 321 | C2×C4⋊C8 | — | 5 | 4 | no | — |
| 322 | #408 | — | 5 | 2 | no | — |
| 323 | #408 | — | 5 | 2 | no | — |
| 324 | #407 | — | 5 | 2 | no | — |
| 325 | #405 | — | 5 | 2 | no | — |
| 326 | #405 | — | 5 | 2 | no | — |
| 327 | C4×M16 | — | 5 | 2 | no | — |
| 328 | C23×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 329 | C22×D5 | — | 2 | 2 | no | — |
| 330 | C22×D5 | — | 4 | 2 | no | — |
| 331 | C22×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 332 | C22×D5 | C23×C4 | 1 | 4 | yes | — |
| 333 | C22×D5 | C23×C4 | 1 | 1 | yes | characteristic |
| 334 | C5×Q8 | — | 2 | 4 | no | — |
| 335 | C2×C4×C5 | — | 2 | 2 | no | — |
| 336 | C2×C4×C5 | C23×C4 | 1 | 4 | yes | — |
| 337 | C2×C4×C5 | C23×C4 | 1 | 2 | yes | — |
| 338 | C2×C4×C5 | C23×C4 | 1 | 2 | yes | — |
| 339 | C2×C4×C5 | C23×C4 | 1 | 4 | yes | — |
| 340 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 341 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 342 | C22⋊D5 | — | 4 | 4 | no | — |
| 343 | C2×Dic5 | — | 2 | 1 | no | — |
| 344 | C2×Dic5 | — | 2 | 1 | no | — |
| 345 | C2×Dic5 | C23×C4 | 1 | 2 | yes | — |
| 346 | C2×Dic5 | C23×C4 | 1 | 4 | yes | — |
| 347 | C2×Dic5 | C23×C4 | 1 | 2 | yes | — |
| 348 | C2×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 349 | C2×Dic5 | C25 | 1 | 1 | yes | characteristic |
| 350 | D20 | — | 2 | 8 | no | — |
| 351 | D20 | — | 2 | 4 | no | — |
| 352 | D20 | — | 4 | 4 | no | — |
| 353 | D20 | — | 4 | 4 | no | — |
| 354 | C4×D5 | — | 2 | 2 | no | — |
| 355 | C4×D5 | — | 2 | 2 | no | — |
| 356 | C4×D5 | — | 2 | 1 | no | — |
| 357 | C4×D5 | — | 2 | 4 | no | — |
| 358 | C4×D5 | — | 2 | 1 | no | — |
| 359 | C4×D5 | — | 2 | 4 | no | — |
| 360 | C4×D5 | — | 4 | 2 | no | — |
| 361 | C4×D5 | — | 4 | 4 | no | — |
| 362 | C4×D5 | — | 4 | 4 | no | — |
| 363 | C4×D5 | — | 4 | 2 | no | — |
| 364 | C4×D5 | H(5,𝔽2) | 1 | 2 | yes | — |
| 365 | C4×D5 | 2−1+4 | 1 | 2 | yes | — |
| 366 | Dic10 | — | 4 | 4 | no | — |
| 367 | #170 | — | 2 | 2 | no | — |
| 368 | #170 | — | 2 | 2 | no | — |
| 369 | #170 | — | 2 | 2 | no | — |
| 370 | #170 | — | 2 | 2 | no | — |
| 371 | #170 | — | 2 | 4 | no | — |
| 372 | #170 | — | 2 | 4 | no | — |
| 373 | C2×#41 | — | 5 | 2 | no | — |
| 374 | C23×C4 | — | 5 | 1 | no | — |
| 375 | #131 | — | 20 | 4 | no | — |
| 376 | #131 | — | 20 | 4 | no | — |
| 377 | C2×M16 | — | 5 | 2 | no | — |
| 378 | C2×M16 | — | 5 | 2 | no | — |
| 379 | C2×M16 | — | 5 | 2 | no | — |
| 380 | C2×M16 | — | 5 | 4 | no | — |
| 381 | C2×M16 | — | 5 | 4 | no | — |
| 382 | C2×M16 | — | 5 | 1 | no | — |
| 383 | C2×M16 | — | 5 | 1 | no | — |
| 384 | C2×M16 | — | 20 | 2 | no | — |
| 385 | C22×C8 | — | 5 | 2 | no | — |
| 386 | C22×C8 | — | 5 | 2 | no | — |
| 387 | C22×C8 | — | 5 | 1 | no | — |
| 388 | C22×C8 | — | 5 | 1 | no | — |
| 389 | C22×C8 | — | 5 | 4 | no | — |
| 390 | C22×C8 | — | 5 | 4 | no | — |
| 391 | C22×C8 | — | 5 | 2 | no | — |
| 392 | C22×C8 | — | 20 | 2 | no | — |
| 393 | C4⋊Q8 | — | 5 | 2 | no | — |
| 394 | C4⋊Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 395 | #127 | — | 5 | 1 | no | — |
| 396 | #126 | — | 5 | 4 | no | — |
| 397 | #126 | — | 5 | 4 | no | — |
| 398 | #126 | — | 5 | 4 | no | — |
| 399 | #126 | C2×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 400 | #125 | — | 5 | 4 | no | — |
| 401 | #125 | — | 5 | 1 | no | — |
| 402 | #125 | C2×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 403 | #125 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 404 | #124 | — | 5 | 2 | no | — |
| 405 | #124 | — | 5 | 4 | no | — |
| 406 | #124 | — | 5 | 4 | no | — |
| 407 | #123 | — | 5 | 4 | no | — |
| 408 | #123 | — | 5 | 4 | no | — |
| 409 | #123 | — | 5 | 4 | no | — |
| 410 | #123 | — | 5 | 4 | no | — |
| 411 | #123 | — | 5 | 4 | no | — |
| 412 | C22⋊Q8 | — | 5 | 2 | no | — |
| 413 | C22⋊Q8 | — | 5 | 4 | no | — |
| 414 | C22⋊Q8 | — | 5 | 4 | no | — |
| 415 | C22⋊Q8 | — | 5 | 4 | no | — |
| 416 | C22⋊Q8 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 417 | #121 | — | 5 | 2 | no | — |
| 418 | #121 | — | 5 | 2 | no | — |
| 419 | #121 | — | 5 | 4 | no | — |
| 420 | #121 | — | 5 | 4 | no | — |
| 421 | #121 | — | 5 | 4 | no | — |
| 422 | #120 | — | 5 | 4 | no | — |
| 423 | C4×Q8 | — | 5 | 2 | no | — |
| 424 | C4×Q8 | — | 5 | 4 | no | — |
| 425 | C4×Q8 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 426 | C4×D4 | — | 5 | 4 | no | — |
| 427 | C4×D4 | — | 5 | 2 | no | — |
| 428 | C4×D4 | — | 5 | 4 | no | — |
| 429 | C4×D4 | — | 5 | 4 | no | — |
| 430 | C4×D4 | — | 5 | 4 | no | — |
| 431 | C4×D4 | — | 5 | 4 | no | — |
| 432 | C4×D4 | — | 5 | 2 | no | — |
| 433 | #117 | — | 5 | 1 | no | — |
| 434 | #117 | — | 5 | 2 | no | — |
| 435 | #117 | — | 5 | 2 | no | — |
| 436 | #117 | — | 5 | 4 | no | — |
| 437 | #117 | — | 5 | 2 | no | — |
| 438 | #117 | — | 5 | 1 | no | — |
| 439 | #117 | — | 5 | 1 | no | — |
| 440 | #117 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 441 | C2×C4⋊C4 | — | 5 | 2 | no | — |
| 442 | C2×C22⋊C4 | — | 5 | 2 | no | — |
| 443 | C2×C42 | — | 5 | 1 | no | — |
| 444 | C2×C42 | — | 5 | 1 | no | — |
| 445 | C2×C42 | — | 5 | 4 | no | — |
| 446 | C4⋊C8 | — | 5 | 2 | no | — |
| 447 | C4⋊C8 | — | 5 | 2 | no | — |
| 448 | C4⋊C8 | — | 5 | 2 | no | — |
| 449 | C4⋊C8 | — | 5 | 4 | no | — |
| 450 | C4⋊C8 | — | 5 | 4 | no | — |
| 451 | C4⋊C8 | — | 5 | 2 | no | — |
| 452 | C4⋊C8 | — | 5 | 4 | no | — |
| 453 | C4⋊C8 | — | 5 | 2 | no | — |
| 454 | C4⋊C8 | — | 5 | 2 | no | — |
| 455 | C4⋊C8 | — | 5 | 4 | no | — |
| 456 | C4⋊C8 | — | 5 | 2 | no | — |
| 457 | C4⋊C8 | — | 5 | 2 | no | — |
| 458 | C4⋊C8 | — | 5 | 4 | no | — |
| 459 | C4⋊C8 | — | 5 | 4 | no | — |
| 460 | C22⋊C8 | — | 5 | 4 | no | — |
| 461 | C22⋊C8 | — | 5 | 4 | no | — |
| 462 | C22⋊C8 | — | 5 | 4 | no | — |
| 463 | C22⋊C8 | — | 5 | 4 | no | — |
| 464 | C22⋊C8 | — | 5 | 4 | no | — |
| 465 | C22⋊C8 | — | 5 | 4 | no | — |
| 466 | #97 | — | 5 | 4 | no | — |
| 467 | #97 | — | 5 | 4 | no | — |
| 468 | #97 | — | 5 | 4 | no | — |
| 469 | C4×C8 | — | 5 | 4 | no | — |
| 470 | C4×C8 | — | 5 | 4 | no | — |
| 471 | C4×C8 | — | 5 | 4 | no | — |
| 472 | C22×C5 | — | 2 | 1 | no | — |
| 473 | C22×C5 | — | 2 | 2 | no | — |
| 474 | C22×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 475 | C2×D5 | — | 2 | 2 | no | — |
| 476 | C2×D5 | — | 2 | 1 | no | — |
| 477 | C2×D5 | — | 2 | 4 | no | — |
| 478 | C2×D5 | — | 2 | 4 | no | — |
| 479 | C2×D5 | — | 2 | 4 | no | — |
| 480 | C2×D5 | — | 2 | 2 | no | — |
| 481 | C2×D5 | — | 4 | 4 | no | — |
| 482 | C2×D5 | #520 | 1 | 2 | yes | — |
| 483 | C4×C5 | — | 2 | 1 | no | — |
| 484 | C4×C5 | — | 2 | 4 | no | — |
| 485 | C4×C5 | — | 2 | 4 | no | — |
| 486 | C4×C5 | — | 2 | 2 | no | — |
| 487 | C4×C5 | — | 2 | 2 | no | — |
| 488 | C4×C5 | #520 | 1 | 2 | yes | — |
| 489 | Dic5 | — | 2 | 1 | no | — |
| 490 | Dic5 | — | 2 | 2 | no | — |
| 491 | Dic5 | — | 2 | 4 | no | — |
| 492 | Dic5 | — | 2 | 2 | no | — |
| 493 | Dic5 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 494 | Dic5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 495 | C24 | — | 5 | 1 | no | — |
| 496 | #41 | — | 10 | 4 | no | — |
| 497 | #41 | — | 10 | 4 | no | — |
| 498 | C2×Q8 | — | 5 | 4 | no | — |
| 499 | C2×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 500 | C2×D4 | — | 5 | 4 | no | — |
| 501 | C2×D4 | — | 5 | 4 | no | — |
| 502 | C2×D4 | — | 5 | 2 | no | — |
| 503 | C2×D4 | — | 5 | 4 | no | — |
| 504 | C2×D4 | — | 5 | 4 | no | — |
| 505 | C22×C4 | — | 5 | 1 | no | — |
| 506 | C22×C4 | — | 5 | 1 | no | — |
| 507 | C22×C4 | — | 5 | 4 | no | — |
| 508 | C22×C4 | — | 5 | 1 | no | — |
| 509 | C22×C4 | — | 5 | 1 | no | — |
| 510 | C22×C4 | — | 5 | 1 | no | — |
| 511 | C22×C4 | — | 5 | 2 | no | — |
| 512 | C22×C4 | — | 5 | 2 | no | — |
| 513 | C22×C4 | — | 5 | 4 | no | — |
| 514 | C22×C4 | — | 5 | 4 | no | — |
| 515 | C22×C4 | — | 10 | 2 | no | — |
| 516 | C22×C4 | — | 10 | 2 | no | — |
| 517 | C22×C4 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 518 | M16 | — | 10 | 4 | no | — |
| 519 | M16 | — | 10 | 4 | no | — |
| 520 | M16 | — | 20 | 2 | no | — |
| 521 | M16 | — | 20 | 1 | no | — |
| 522 | M16 | — | 20 | 1 | no | — |
| 523 | M16 | — | 20 | 4 | no | — |
| 524 | M16 | — | 20 | 4 | no | — |
| 525 | C2×C8 | — | 5 | 4 | no | — |
| 526 | C2×C8 | — | 5 | 2 | no | — |
| 527 | C2×C8 | — | 5 | 2 | no | — |
| 528 | C2×C8 | — | 5 | 4 | no | — |
| 529 | C2×C8 | — | 5 | 2 | no | — |
| 530 | C2×C8 | — | 5 | 2 | no | — |
| 531 | C2×C8 | — | 10 | 4 | no | — |
| 532 | C2×C8 | — | 10 | 4 | no | — |
| 533 | C2×C8 | — | 20 | 1 | no | — |
| 534 | C2×C8 | — | 20 | 1 | no | — |
| 535 | C2×C8 | — | 20 | 2 | no | — |
| 536 | C2×C8 | — | 20 | 4 | no | — |
| 537 | C2×C8 | — | 20 | 4 | no | — |
| 538 | C4⋊C4 | — | 5 | 2 | no | — |
| 539 | C4⋊C4 | — | 5 | 2 | no | — |
| 540 | C4⋊C4 | — | 5 | 2 | no | — |
| 541 | C4⋊C4 | — | 5 | 2 | no | — |
| 542 | C4⋊C4 | — | 5 | 4 | no | — |
| 543 | C4⋊C4 | — | 5 | 4 | no | — |
| 544 | C4⋊C4 | — | 5 | 4 | no | — |
| 545 | C4⋊C4 | — | 5 | 4 | no | — |
| 546 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 547 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 548 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 549 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 550 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 551 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 552 | C22⋊C4 | — | 5 | 2 | no | — |
| 553 | C22⋊C4 | — | 5 | 2 | no | — |
| 554 | C22⋊C4 | — | 5 | 2 | no | — |
| 555 | C22⋊C4 | — | 5 | 4 | no | — |
| 556 | C22⋊C4 | — | 5 | 4 | no | — |
| 557 | C22⋊C4 | — | 5 | 4 | no | — |
| 558 | C22⋊C4 | — | 5 | 4 | no | — |
| 559 | C22⋊C4 | — | 5 | 4 | no | — |
| 560 | C22⋊C4 | — | 5 | 4 | no | — |
| 561 | C22⋊C4 | — | 5 | 4 | no | — |
| 562 | C22⋊C4 | — | 5 | 4 | no | — |
| 563 | C22⋊C4 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 564 | C22⋊C4 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 565 | C42 | — | 5 | 2 | no | — |
| 566 | C42 | — | 5 | 4 | no | — |
| 567 | C42 | — | 5 | 2 | no | — |
| 568 | C42 | — | 5 | 1 | no | — |
| 569 | C42 | — | 5 | 1 | no | — |
| 570 | C42 | — | 5 | 4 | no | — |
| 571 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 572 | C42 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 573 | C42 | C22×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 574 | C2×C5 | — | 4 | 1 | no | — |
| 575 | C2×C5 | C2×#520 | 1 | 1 | yes | characteristic |
| 576 | C2×C5 | #3573 | 1 | 2 | yes | — |
| 577 | D5 | — | 2 | 2 | no | — |
| 578 | D5 | — | 4 | 4 | no | — |
| 579 | D5 | — | 4 | 1 | no | — |
| 580 | C23 | — | 5 | 1 | no | — |
| 581 | C23 | — | 5 | 1 | no | — |
| 582 | C23 | — | 5 | 4 | no | — |
| 583 | C23 | — | 10 | 2 | no | — |
| 584 | C23 | — | 20 | 2 | no | — |
| 585 | C23 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 586 | Q8 | — | 2 | 4 | no | — |
| 587 | Q8 | — | 20 | 4 | no | — |
| 588 | D4 | — | 10 | 8 | no | — |
| 589 | D4 | — | 10 | 4 | no | — |
| 590 | D4 | — | 20 | 4 | no | — |
| 591 | D4 | — | 20 | 4 | no | — |
| 592 | D4 | — | 20 | 4 | no | — |
| 593 | C2×C4 | — | 2 | 2 | no | — |
| 594 | C2×C4 | — | 5 | 1 | no | — |
| 595 | C2×C4 | — | 5 | 2 | no | — |
| 596 | C2×C4 | — | 5 | 2 | no | — |
| 597 | C2×C4 | — | 5 | 2 | no | — |
| 598 | C2×C4 | — | 5 | 2 | no | — |
| 599 | C2×C4 | — | 5 | 4 | no | — |
| 600 | C2×C4 | — | 5 | 1 | no | — |
| 601 | C2×C4 | — | 10 | 1 | no | — |
| 602 | C2×C4 | — | 10 | 4 | no | — |
| 603 | C2×C4 | — | 10 | 1 | no | — |
| 604 | C2×C4 | — | 10 | 4 | no | — |
| 605 | C2×C4 | — | 10 | 2 | no | — |
| 606 | C2×C4 | — | 10 | 1 | no | — |
| 607 | C2×C4 | — | 10 | 1 | no | — |
| 608 | C2×C4 | — | 10 | 2 | no | — |
| 609 | C2×C4 | — | 20 | 2 | no | — |
| 610 | C2×C4 | — | 20 | 4 | no | — |
| 611 | C2×C4 | — | 20 | 2 | no | — |
| 612 | C2×C4 | — | 20 | 4 | no | — |
| 613 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 614 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 615 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 616 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 617 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 618 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 619 | C8 | — | 10 | 2 | no | — |
| 620 | C8 | — | 10 | 2 | no | — |
| 621 | C8 | — | 10 | 2 | no | — |
| 622 | C8 | — | 10 | 2 | no | — |
| 623 | C8 | — | 10 | 4 | no | — |
| 624 | C8 | — | 10 | 4 | no | — |
| 625 | C5 | #60267 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 626 | C22 | — | 2 | 1 | no | — |
| 627 | C22 | — | 2 | 2 | no | — |
| 628 | C22 | — | 5 | 2 | no | — |
| 629 | C22 | — | 10 | 2 | no | — |
| 630 | C22 | — | 10 | 1 | no | — |
| 631 | C22 | — | 10 | 4 | no | — |
| 632 | C22 | — | 10 | 4 | no | — |
| 633 | C22 | — | 10 | 4 | no | — |
| 634 | C22 | — | 10 | 2 | no | — |
| 635 | C22 | — | 20 | 4 | no | — |
| 636 | C22 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 637 | C4 | — | 2 | 1 | no | — |
| 638 | C4 | — | 2 | 4 | no | — |
| 639 | C4 | — | 2 | 2 | no | — |
| 640 | C4 | — | 2 | 2 | no | — |
| 641 | C4 | — | 2 | 4 | no | — |
| 642 | C4 | — | 5 | 1 | no | — |
| 643 | C4 | — | 5 | 1 | no | — |
| 644 | C4 | — | 10 | 1 | no | — |
| 645 | C4 | — | 10 | 2 | no | — |
| 646 | C4 | — | 10 | 4 | no | — |
| 647 | C4 | — | 10 | 2 | no | — |
| 648 | C4 | #66266 | 1 | 2 | yes | — |
| 649 | C2 | — | 4 | 1 | no | — |
| 650 | C2 | — | 10 | 2 | no | — |
| 651 | C2 | — | 20 | 1 | no | — |
| 652 | C2 | — | 20 | 4 | no | — |
| 653 | C2 | C2×#66266 | 1 | 1 | yes | characteristic |
| 654 | C2 | #10619415 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta