Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
678 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #11756944 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D5×#994 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#576⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #66169⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #66170⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #66085⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #66084⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10619105 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 9 | C5×#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C5×#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #4150⋊C3 | — | 2 | 1 | no | — |
| 12 | #4150⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | D5×#41⋊C3 | — | 2 | 1 | no | — |
| 14 | D5×#41⋊C3 | — | 2 | 1 | no | — |
| 15 | D5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 16 | C5⋊#994 | — | 2 | 1 | no | — |
| 17 | C5⋊#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C3×#4064 | — | 4 | 1 | no | maximal |
| 19 | C5×#131⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #4094⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #3585⋊C3 | — | 5 | 1 | no | maximal, Hall |
| 22 | #66285 | C2×C3 | 1 | 1 | yes | characteristic |
| 23 | D5×H(5,𝔽2) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C5×#576 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #66170 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | #66169 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | #66109 | — | 3 | 1 | no | — |
| 28 | #66108 | — | 3 | 1 | no | — |
| 29 | #66107 | — | 3 | 1 | no | — |
| 30 | D5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 31 | #66104 | — | 3 | 1 | no | — |
| 32 | #66102 | — | 3 | 1 | no | — |
| 33 | #66091 | — | 3 | 1 | no | — |
| 34 | C2×#4057 | — | 3 | 1 | no | — |
| 35 | #66085 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 36 | #66084 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#713 | — | 4 | 1 | no | — |
| 38 | C3×Q8×D5 | — | 4 | 1 | no | — |
| 39 | C5×#41⋊C3 | — | 2 | 1 | no | — |
| 40 | C5×#41⋊C3 | — | 2 | 1 | no | — |
| 41 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 42 | D5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 43 | D5×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 44 | C5⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 45 | C5⋊(#41⋊C3) | D4 | 1 | 1 | yes | characteristic |
| 46 | C3×C5×Q16 | — | 4 | 1 | no | — |
| 47 | C3×#689 | — | 4 | 1 | no | — |
| 48 | C3×#688 | — | 4 | 1 | no | — |
| 49 | C3×#677 | — | 4 | 1 | no | — |
| 50 | C3×#676 | — | 4 | 1 | no | — |
| 51 | #5945 | — | 5 | 1 | no | — |
| 52 | C2×#994 | — | 5 | 1 | no | — |
| 53 | #577⋊C3 | — | 5 | 1 | no | — |
| 54 | #577⋊C3 | — | 5 | 1 | no | — |
| 55 | #576⋊C3 | — | 5 | 1 | no | — |
| 56 | #576⋊C3 | D5 | 1 | 1 | yes | characteristic, complemented |
| 57 | #568⋊C3 | — | 5 | 1 | no | — |
| 58 | C5×H(5,𝔽2) | C22×C3 | 1 | 1 | yes | characteristic |
| 59 | C5×H(5,𝔽2) | C22×C3 | 1 | 1 | yes | characteristic |
| 60 | #4150 | — | 2 | 1 | no | — |
| 61 | #4150 | — | 3 | 1 | no | — |
| 62 | #4150 | C22×C3 | 1 | 1 | yes | characteristic |
| 63 | #4149 | — | 2 | 1 | no | — |
| 64 | #4149 | — | 3 | 1 | no | — |
| 65 | #4149 | C22×C3 | 1 | 1 | yes | characteristic |
| 66 | D5×#41 | — | 2 | 1 | no | — |
| 67 | D5×#41 | — | 2 | 1 | no | — |
| 68 | D5×#41 | — | 3 | 1 | no | — |
| 69 | D5×#41 | — | 3 | 1 | no | — |
| 70 | D5×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 71 | #4144 | — | 3 | 1 | no | — |
| 72 | #4144 | — | 3 | 1 | no | — |
| 73 | #4144 | — | 6 | 1 | no | — |
| 74 | #4144 | — | 6 | 1 | no | — |
| 75 | C2×#711 | — | 3 | 1 | no | — |
| 76 | C2×#711 | — | 6 | 1 | no | — |
| 77 | C2×D4×D5 | — | 3 | 1 | no | — |
| 78 | C2×D4×D5 | — | 6 | 1 | no | — |
| 79 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 80 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 81 | C5×#135 | — | 3 | 1 | no | — |
| 82 | C2×C5×D8 | — | 3 | 1 | no | — |
| 83 | C5×#131 | C22×C3 | 1 | 1 | yes | characteristic |
| 84 | #4097 | — | 3 | 1 | no | — |
| 85 | #4096 | — | 3 | 1 | no | — |
| 86 | #4096 | — | 3 | 1 | no | — |
| 87 | #4095 | — | 3 | 1 | no | — |
| 88 | #4094 | C22×C3 | 1 | 1 | yes | characteristic |
| 89 | C2×#687 | — | 3 | 1 | no | — |
| 90 | #4078 | — | 3 | 1 | no | — |
| 91 | #4078 | — | 3 | 1 | no | — |
| 92 | C2×#686 | — | 3 | 1 | no | — |
| 93 | #4064 | — | 3 | 1 | no | — |
| 94 | #4064 | A4 | 1 | 1 | yes | characteristic |
| 95 | #4062 | — | 3 | 2 | no | — |
| 96 | #4061 | — | 3 | 1 | no | — |
| 97 | #4061 | — | 3 | 1 | no | — |
| 98 | #4060 | — | 3 | 1 | no | — |
| 99 | #4060 | — | 3 | 1 | no | — |
| 100 | D5×SD16 | — | 3 | 2 | no | — |
| 101 | #4058 | — | 3 | 2 | no | — |
| 102 | #4057 | — | 3 | 2 | no | — |
| 103 | #4057 | — | 3 | 2 | no | — |
| 104 | #4057 | — | 3 | 2 | no | — |
| 105 | #4057 | — | 3 | 1 | no | — |
| 106 | #4057 | — | 3 | 1 | no | — |
| 107 | D5×D8 | — | 3 | 2 | no | — |
| 108 | #4055 | — | 3 | 1 | no | — |
| 109 | #4054 | — | 3 | 1 | no | — |
| 110 | #4053 | — | 3 | 1 | no | — |
| 111 | D5×M16 | — | 3 | 1 | no | — |
| 112 | #4050 | — | 3 | 1 | no | — |
| 113 | C2×#677 | — | 3 | 1 | no | — |
| 114 | #4047 | — | 3 | 1 | no | — |
| 115 | C2×#676 | — | 3 | 1 | no | — |
| 116 | #3585 | — | 5 | 1 | no | Sylow |
| 117 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 118 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 119 | C3×D20 | — | 4 | 1 | no | — |
| 120 | C3×D20 | — | 8 | 1 | no | — |
| 121 | C3×C4×D5 | — | 4 | 1 | no | — |
| 122 | C3×C4×D5 | — | 8 | 1 | no | — |
| 123 | C3×C4×D5 | — | 8 | 1 | no | — |
| 124 | C3×Dic10 | — | 4 | 1 | no | — |
| 125 | C3×Dic10 | — | 8 | 1 | no | — |
| 126 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C3×C5×C8 | — | 4 | 1 | no | — |
| 128 | C3×#168 | — | 4 | 1 | no | — |
| 129 | 2−1+4⋊C3 | — | 5 | 1 | no | — |
| 130 | 2−1+4⋊C3 | — | 10 | 1 | no | — |
| 131 | #994 | — | 5 | 1 | no | — |
| 132 | #994 | — | 10 | 1 | no | — |
| 133 | #994 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 134 | #994 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 135 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 136 | C2×#41⋊C3 | — | 10 | 1 | no | — |
| 137 | C2×#41⋊C3 | — | 10 | 1 | no | — |
| 138 | C3×#137 | — | 20 | 1 | no | — |
| 139 | #131⋊C3 | — | 5 | 1 | no | — |
| 140 | #131⋊C3 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 141 | C23×D5 | — | 6 | 1 | no | — |
| 142 | C5×#41 | — | 2 | 1 | no | — |
| 143 | C5×#41 | — | 2 | 1 | no | — |
| 144 | C5×#41 | — | 3 | 1 | no | — |
| 145 | C5×#41 | — | 3 | 1 | no | — |
| 146 | C5×#41 | C23×C3 | 1 | 1 | yes | characteristic |
| 147 | C2×C5×D4 | — | 3 | 1 | no | — |
| 148 | C2×C5×D4 | — | 3 | 1 | no | — |
| 149 | C2×C5×D4 | — | 6 | 1 | no | — |
| 150 | C2×C5×D4 | — | 6 | 1 | no | — |
| 151 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 152 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 153 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 154 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 155 | C22×Dic5 | — | 6 | 1 | no | — |
| 156 | #713 | — | 2 | 1 | no | — |
| 157 | #713 | — | 3 | 1 | no | — |
| 158 | #713 | C3×D4 | 1 | 1 | yes | characteristic |
| 159 | #713 | C2×A4 | 1 | 1 | yes | characteristic |
| 160 | Q8×D5 | — | 2 | 1 | no | — |
| 161 | Q8×D5 | — | 3 | 1 | no | — |
| 162 | Q8×D5 | C3×D4 | 1 | 1 | yes | characteristic |
| 163 | Q8×D5 | C2×A4 | 1 | 1 | yes | characteristic |
| 164 | #711 | — | 3 | 1 | no | — |
| 165 | #711 | — | 3 | 2 | no | — |
| 166 | #711 | — | 3 | 1 | no | — |
| 167 | #711 | — | 3 | 1 | no | — |
| 168 | #711 | — | 6 | 1 | no | — |
| 169 | #711 | — | 6 | 1 | no | — |
| 170 | #711 | — | 6 | 1 | no | — |
| 171 | #711 | — | 6 | 1 | no | — |
| 172 | #711 | — | 6 | 1 | no | — |
| 173 | #711 | — | 6 | 1 | no | — |
| 174 | #711 | — | 6 | 2 | no | — |
| 175 | #711 | — | 6 | 1 | no | — |
| 176 | D4×D5 | — | 3 | 1 | no | — |
| 177 | D4×D5 | — | 3 | 2 | no | — |
| 178 | D4×D5 | — | 3 | 1 | no | — |
| 179 | D4×D5 | — | 3 | 1 | no | — |
| 180 | D4×D5 | — | 6 | 1 | no | — |
| 181 | D4×D5 | — | 6 | 1 | no | — |
| 182 | D4×D5 | — | 6 | 1 | no | — |
| 183 | D4×D5 | — | 6 | 1 | no | — |
| 184 | D4×D5 | — | 6 | 1 | no | — |
| 185 | D4×D5 | — | 6 | 1 | no | — |
| 186 | D4×D5 | — | 6 | 2 | no | — |
| 187 | D4×D5 | — | 6 | 1 | no | — |
| 188 | #709 | — | 3 | 1 | no | — |
| 189 | #709 | — | 3 | 1 | no | — |
| 190 | #709 | — | 3 | 1 | no | — |
| 191 | #709 | — | 6 | 1 | no | — |
| 192 | #709 | — | 6 | 1 | no | — |
| 193 | #709 | — | 6 | 1 | no | — |
| 194 | #709 | — | 6 | 1 | no | — |
| 195 | C2×D20 | — | 3 | 1 | no | — |
| 196 | C2×D20 | — | 6 | 1 | no | — |
| 197 | C2×C4×D5 | — | 3 | 1 | no | — |
| 198 | C2×C4×D5 | — | 6 | 1 | no | — |
| 199 | C2×C4×D5 | — | 6 | 1 | no | — |
| 200 | C2×Dic10 | — | 3 | 1 | no | — |
| 201 | C2×Dic10 | — | 6 | 1 | no | — |
| 202 | C5×Q16 | C2×A4 | 1 | 1 | yes | characteristic |
| 203 | C5×SD16 | — | 3 | 1 | no | — |
| 204 | C5×SD16 | — | 3 | 1 | no | — |
| 205 | C5×D8 | — | 3 | 2 | no | — |
| 206 | C5×D8 | — | 3 | 1 | no | — |
| 207 | C5×M16 | — | 3 | 1 | no | — |
| 208 | C2×C5×C8 | — | 3 | 1 | no | — |
| 209 | #689 | — | 3 | 1 | no | — |
| 210 | #689 | C2×A4 | 1 | 1 | yes | characteristic |
| 211 | #688 | — | 3 | 1 | no | — |
| 212 | #688 | C2×A4 | 1 | 1 | yes | characteristic |
| 213 | #687 | — | 3 | 2 | no | — |
| 214 | #687 | — | 3 | 1 | no | — |
| 215 | #687 | — | 3 | 1 | no | — |
| 216 | #686 | — | 3 | 2 | no | — |
| 217 | #686 | — | 3 | 1 | no | — |
| 218 | #686 | — | 3 | 1 | no | — |
| 219 | #681 | — | 3 | 1 | no | — |
| 220 | C2×#168 | — | 3 | 1 | no | — |
| 221 | Dic20 | — | 3 | 1 | no | — |
| 222 | D40 | — | 3 | 1 | no | — |
| 223 | #677 | — | 3 | 2 | no | — |
| 224 | #677 | — | 3 | 1 | no | — |
| 225 | #677 | C2×A4 | 1 | 1 | yes | characteristic |
| 226 | #676 | — | 3 | 1 | no | — |
| 227 | #676 | — | 3 | 1 | no | — |
| 228 | #676 | — | 3 | 1 | no | — |
| 229 | #676 | C2×A4 | 1 | 1 | yes | characteristic |
| 230 | C8×D5 | — | 3 | 2 | no | — |
| 231 | #585 | — | 5 | 1 | no | — |
| 232 | C2×H(5,𝔽2) | — | 5 | 1 | no | — |
| 233 | #577 | — | 5 | 1 | no | — |
| 234 | #577 | — | 5 | 1 | no | — |
| 235 | #577 | — | 15 | 1 | no | — |
| 236 | #577 | — | 15 | 1 | no | — |
| 237 | #576 | — | 5 | 1 | no | — |
| 238 | #576 | — | 15 | 1 | no | — |
| 239 | #576 | — | 15 | 1 | no | — |
| 240 | #576 | C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 241 | #575 | — | 15 | 1 | no | — |
| 242 | #575 | — | 15 | 1 | no | — |
| 243 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 244 | C2×AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 245 | #568 | — | 5 | 1 | no | — |
| 246 | C2×C3×D5 | — | 4 | 1 | no | — |
| 247 | C2×C3×D5 | — | 8 | 1 | no | — |
| 248 | C3×C4×C5 | — | 4 | 1 | no | — |
| 249 | C3×C4×C5 | — | 8 | 1 | no | — |
| 250 | C3×C4×C5 | — | 8 | 1 | no | — |
| 251 | C3×Dic5 | — | 4 | 1 | no | — |
| 252 | C3×Dic5 | — | 8 | 1 | no | — |
| 253 | C3×#41 | — | 20 | 1 | no | — |
| 254 | C2×C3×Q8 | — | 20 | 1 | no | — |
| 255 | #41⋊C3 | — | 2 | 1 | no | — |
| 256 | #41⋊C3 | — | 2 | 1 | no | — |
| 257 | #41⋊C3 | — | 5 | 1 | no | — |
| 258 | #41⋊C3 | — | 10 | 1 | no | — |
| 259 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 260 | C2×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 261 | C2×SL(2,𝔽3) | — | 10 | 1 | no | — |
| 262 | C3×Q16 | — | 4 | 1 | no | — |
| 263 | C3×Q16 | — | 20 | 1 | no | — |
| 264 | C3×SD16 | — | 20 | 1 | no | — |
| 265 | C3×SD16 | — | 20 | 1 | no | — |
| 266 | C3×M16 | — | 20 | 1 | no | — |
| 267 | C23×C5 | — | 6 | 1 | no | — |
| 268 | C23×C5 | — | 6 | 1 | no | — |
| 269 | C22×D5 | — | 3 | 1 | no | — |
| 270 | C22×D5 | — | 6 | 1 | no | — |
| 271 | C22×D5 | — | 6 | 2 | no | — |
| 272 | C22×D5 | — | 6 | 1 | no | — |
| 273 | C22×D5 | — | 6 | 1 | no | — |
| 274 | C22×D5 | — | 24 | 2 | no | — |
| 275 | C5×Q8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 276 | C5×Q8 | C22×A4 | 1 | 1 | yes | characteristic |
| 277 | C5×Q8 | C22×A4 | 1 | 1 | yes | characteristic |
| 278 | C5×D4 | — | 3 | 1 | no | — |
| 279 | C5×D4 | — | 3 | 1 | no | — |
| 280 | C5×D4 | — | 3 | 1 | no | — |
| 281 | C5×D4 | — | 6 | 1 | no | — |
| 282 | C5×D4 | — | 6 | 1 | no | — |
| 283 | C5×D4 | — | 6 | 1 | no | — |
| 284 | C5×D4 | — | 6 | 1 | no | — |
| 285 | C2×C4×C5 | — | 3 | 1 | no | — |
| 286 | C2×C4×C5 | — | 6 | 1 | no | — |
| 287 | C2×C4×C5 | — | 6 | 1 | no | — |
| 288 | C22⋊D5 | — | 3 | 2 | no | — |
| 289 | C22⋊D5 | — | 6 | 1 | no | — |
| 290 | C22⋊D5 | — | 6 | 1 | no | — |
| 291 | C22⋊D5 | — | 6 | 1 | no | — |
| 292 | C22⋊D5 | — | 6 | 2 | no | — |
| 293 | C22⋊D5 | — | 6 | 1 | no | — |
| 294 | C22⋊D5 | — | 6 | 2 | no | — |
| 295 | C22⋊D5 | — | 6 | 1 | no | — |
| 296 | C22⋊D5 | — | 6 | 1 | no | — |
| 297 | C2×Dic5 | — | 3 | 1 | no | — |
| 298 | C2×Dic5 | — | 6 | 1 | no | — |
| 299 | C2×Dic5 | — | 6 | 2 | no | — |
| 300 | C2×Dic5 | — | 6 | 1 | no | — |
| 301 | C2×Dic5 | — | 6 | 1 | no | — |
| 302 | D20 | — | 2 | 1 | no | — |
| 303 | D20 | — | 3 | 1 | no | — |
| 304 | D20 | — | 3 | 1 | no | — |
| 305 | D20 | — | 6 | 1 | no | — |
| 306 | D20 | — | 6 | 1 | no | — |
| 307 | D20 | C22×A4 | 1 | 1 | yes | characteristic |
| 308 | C4×D5 | — | 2 | 1 | no | — |
| 309 | C4×D5 | — | 2 | 1 | no | — |
| 310 | C4×D5 | — | 3 | 1 | no | — |
| 311 | C4×D5 | — | 3 | 1 | no | — |
| 312 | C4×D5 | — | 3 | 1 | no | — |
| 313 | C4×D5 | — | 6 | 1 | no | — |
| 314 | C4×D5 | — | 6 | 1 | no | — |
| 315 | C4×D5 | — | 6 | 1 | no | — |
| 316 | C4×D5 | — | 6 | 1 | no | — |
| 317 | C4×D5 | C22×A4 | 1 | 1 | yes | characteristic |
| 318 | Dic10 | — | 2 | 1 | no | — |
| 319 | Dic10 | — | 3 | 1 | no | — |
| 320 | Dic10 | — | 3 | 1 | no | — |
| 321 | Dic10 | — | 6 | 1 | no | — |
| 322 | Dic10 | — | 6 | 1 | no | — |
| 323 | Dic10 | C22×A4 | 1 | 1 | yes | characteristic |
| 324 | C5×C8 | — | 3 | 1 | no | — |
| 325 | C5×C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 326 | #168 | — | 3 | 1 | no | — |
| 327 | #168 | C22×A4 | 1 | 1 | yes | characteristic |
| 328 | 2−1+4 | — | 5 | 1 | no | — |
| 329 | 2−1+4 | — | 10 | 1 | no | — |
| 330 | 2−1+4 | — | 15 | 1 | no | — |
| 331 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 332 | H(5,𝔽2) | — | 10 | 1 | no | — |
| 333 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 334 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 335 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 336 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 337 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 338 | H(5,𝔽2) | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 339 | H(5,𝔽2) | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 340 | C2×#41 | — | 5 | 1 | no | — |
| 341 | C2×#41 | — | 10 | 1 | no | — |
| 342 | C2×#41 | — | 10 | 1 | no | — |
| 343 | C2×#41 | — | 15 | 1 | no | — |
| 344 | C2×#41 | — | 15 | 1 | no | — |
| 345 | C2×#41 | — | 15 | 1 | no | — |
| 346 | C2×#41 | — | 30 | 1 | no | — |
| 347 | C22×D4 | — | 15 | 1 | no | — |
| 348 | C22×D4 | — | 30 | 1 | no | — |
| 349 | #137 | — | 5 | 1 | no | — |
| 350 | #137 | — | 15 | 1 | no | — |
| 351 | #137 | — | 15 | 1 | no | — |
| 352 | #137 | — | 15 | 1 | no | — |
| 353 | #137 | — | 15 | 1 | no | — |
| 354 | #137 | — | 15 | 1 | no | — |
| 355 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 356 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 357 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 358 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 359 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 360 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 361 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 362 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 363 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 364 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 365 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 366 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 367 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 368 | #135 | — | 3 | 1 | no | — |
| 369 | #135 | — | 15 | 1 | no | — |
| 370 | #135 | — | 15 | 2 | no | — |
| 371 | #135 | — | 15 | 2 | no | — |
| 372 | #135 | — | 15 | 1 | no | — |
| 373 | #135 | — | 15 | 1 | no | — |
| 374 | C2×SD16 | — | 15 | 1 | no | — |
| 375 | C2×SD16 | — | 15 | 2 | no | — |
| 376 | C2×SD16 | — | 15 | 1 | no | — |
| 377 | C2×D8 | — | 3 | 1 | no | — |
| 378 | C2×D8 | — | 15 | 2 | no | — |
| 379 | C2×D8 | — | 15 | 1 | no | — |
| 380 | #131 | — | 5 | 1 | no | — |
| 381 | #131 | — | 15 | 1 | no | — |
| 382 | #131 | — | 15 | 1 | no | — |
| 383 | #131 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 384 | C2×M16 | — | 15 | 1 | no | — |
| 385 | C2×M16 | — | 15 | 1 | no | — |
| 386 | C2×C3×C5 | — | 4 | 1 | no | — |
| 387 | C3×D5 | — | 8 | 1 | no | — |
| 388 | C3×D5 | — | 16 | 1 | no | — |
| 389 | C3×Q8 | — | 4 | 1 | no | — |
| 390 | C3×Q8 | — | 4 | 1 | no | — |
| 391 | C3×Q8 | — | 20 | 1 | no | — |
| 392 | C3×Q8 | — | 40 | 1 | no | — |
| 393 | C3×D4 | — | 20 | 1 | no | — |
| 394 | C3×D4 | — | 40 | 1 | no | — |
| 395 | C2×C3×C4 | — | 20 | 1 | no | — |
| 396 | C2×C3×C4 | — | 40 | 1 | no | — |
| 397 | C2×C3×C4 | — | 40 | 1 | no | — |
| 398 | SL(2,𝔽3) | D4×D5 | 1 | 1 | yes | characteristic |
| 399 | C3×C8 | — | 4 | 1 | no | — |
| 400 | C3×C8 | — | 20 | 1 | no | — |
| 401 | C22×C5 | — | 3 | 1 | no | — |
| 402 | C22×C5 | — | 6 | 1 | no | — |
| 403 | C22×C5 | — | 6 | 1 | no | — |
| 404 | C22×C5 | — | 24 | 1 | no | — |
| 405 | C22×C5 | — | 24 | 1 | no | — |
| 406 | C2×D5 | — | 2 | 1 | no | — |
| 407 | C2×D5 | — | 3 | 1 | no | — |
| 408 | C2×D5 | — | 6 | 1 | no | — |
| 409 | C2×D5 | — | 12 | 1 | no | — |
| 410 | C2×D5 | — | 12 | 2 | no | — |
| 411 | C2×D5 | — | 24 | 1 | no | — |
| 412 | C2×D5 | — | 24 | 2 | no | — |
| 413 | C2×D5 | — | 24 | 1 | no | — |
| 414 | C2×D5 | D4×A4 | 1 | 1 | yes | characteristic |
| 415 | C4×C5 | — | 2 | 1 | no | — |
| 416 | C4×C5 | — | 2 | 1 | no | — |
| 417 | C4×C5 | — | 3 | 1 | no | — |
| 418 | C4×C5 | C23×A4 | 1 | 1 | yes | characteristic |
| 419 | Dic5 | — | 2 | 1 | no | — |
| 420 | Dic5 | — | 3 | 1 | no | — |
| 421 | Dic5 | — | 6 | 1 | no | — |
| 422 | Dic5 | D4×A4 | 1 | 1 | yes | characteristic |
| 423 | C24 | — | 30 | 1 | no | — |
| 424 | #41 | — | 2 | 1 | no | — |
| 425 | #41 | — | 2 | 1 | no | — |
| 426 | #41 | — | 3 | 1 | no | — |
| 427 | #41 | — | 3 | 1 | no | — |
| 428 | #41 | — | 5 | 1 | no | — |
| 429 | #41 | — | 5 | 1 | no | — |
| 430 | #41 | — | 10 | 1 | no | — |
| 431 | #41 | — | 15 | 1 | no | — |
| 432 | #41 | — | 15 | 1 | no | — |
| 433 | #41 | — | 15 | 1 | no | — |
| 434 | #41 | — | 15 | 1 | no | — |
| 435 | #41 | — | 15 | 1 | no | — |
| 436 | #41 | — | 15 | 1 | no | — |
| 437 | #41 | — | 15 | 2 | no | — |
| 438 | #41 | — | 15 | 1 | no | — |
| 439 | #41 | — | 30 | 1 | no | — |
| 440 | #41 | — | 30 | 1 | no | — |
| 441 | #41 | — | 30 | 1 | no | — |
| 442 | #41 | — | 30 | 1 | no | — |
| 443 | #41 | — | 30 | 1 | no | — |
| 444 | #41 | — | 30 | 1 | no | — |
| 445 | #41 | — | 30 | 1 | no | — |
| 446 | #41 | — | 30 | 1 | no | — |
| 447 | #41 | — | 30 | 2 | no | — |
| 448 | #41 | — | 30 | 1 | no | — |
| 449 | #41 | — | 30 | 1 | no | — |
| 450 | #41 | — | 30 | 1 | no | — |
| 451 | #41 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 452 | C2×Q8 | — | 5 | 1 | no | — |
| 453 | C2×Q8 | — | 5 | 1 | no | — |
| 454 | C2×Q8 | — | 10 | 1 | no | — |
| 455 | C2×Q8 | — | 15 | 1 | no | — |
| 456 | C2×Q8 | — | 15 | 1 | no | — |
| 457 | C2×Q8 | — | 30 | 1 | no | — |
| 458 | C2×D4 | — | 3 | 1 | no | — |
| 459 | C2×D4 | — | 3 | 1 | no | — |
| 460 | C2×D4 | — | 6 | 1 | no | — |
| 461 | C2×D4 | — | 6 | 1 | no | — |
| 462 | C2×D4 | — | 15 | 1 | no | — |
| 463 | C2×D4 | — | 15 | 1 | no | — |
| 464 | C2×D4 | — | 15 | 1 | no | — |
| 465 | C2×D4 | — | 15 | 1 | no | — |
| 466 | C2×D4 | — | 15 | 2 | no | — |
| 467 | C2×D4 | — | 30 | 1 | no | — |
| 468 | C2×D4 | — | 30 | 1 | no | — |
| 469 | C2×D4 | — | 30 | 1 | no | — |
| 470 | C2×D4 | — | 30 | 1 | no | — |
| 471 | C2×D4 | — | 30 | 1 | no | — |
| 472 | C2×D4 | — | 30 | 1 | no | — |
| 473 | C2×D4 | — | 30 | 1 | no | — |
| 474 | C2×D4 | — | 30 | 1 | no | — |
| 475 | C2×D4 | — | 30 | 2 | no | — |
| 476 | C2×D4 | — | 30 | 1 | no | — |
| 477 | C2×D4 | — | 30 | 2 | no | — |
| 478 | C2×D4 | — | 30 | 2 | no | — |
| 479 | C2×D4 | — | 30 | 1 | no | — |
| 480 | C22×C4 | — | 15 | 1 | no | — |
| 481 | C22×C4 | — | 30 | 1 | no | — |
| 482 | C22×C4 | — | 30 | 1 | no | — |
| 483 | C22×C4 | — | 30 | 1 | no | — |
| 484 | Q16 | — | 5 | 1 | no | — |
| 485 | Q16 | — | 15 | 1 | no | — |
| 486 | Q16 | — | 15 | 1 | no | — |
| 487 | Q16 | D5×A4 | 1 | 1 | yes | characteristic |
| 488 | SD16 | — | 3 | 1 | no | — |
| 489 | SD16 | — | 3 | 1 | no | — |
| 490 | SD16 | — | 5 | 1 | no | — |
| 491 | SD16 | — | 5 | 1 | no | — |
| 492 | SD16 | — | 15 | 2 | no | — |
| 493 | SD16 | — | 15 | 1 | no | — |
| 494 | SD16 | — | 15 | 1 | no | — |
| 495 | SD16 | — | 15 | 2 | no | — |
| 496 | SD16 | — | 15 | 1 | no | — |
| 497 | SD16 | — | 15 | 1 | no | — |
| 498 | D8 | — | 3 | 2 | no | — |
| 499 | D8 | — | 3 | 1 | no | — |
| 500 | D8 | — | 15 | 1 | no | — |
| 501 | D8 | — | 15 | 1 | no | — |
| 502 | D8 | — | 15 | 1 | no | — |
| 503 | D8 | — | 15 | 2 | no | — |
| 504 | M16 | — | 3 | 1 | no | — |
| 505 | M16 | — | 5 | 1 | no | — |
| 506 | M16 | — | 15 | 1 | no | — |
| 507 | M16 | — | 15 | 1 | no | — |
| 508 | M16 | — | 15 | 1 | no | — |
| 509 | M16 | — | 15 | 1 | no | — |
| 510 | C2×C8 | — | 3 | 1 | no | — |
| 511 | C2×C8 | — | 15 | 2 | no | — |
| 512 | C2×C8 | — | 15 | 1 | no | — |
| 513 | C3×C5 | — | 4 | 1 | no | Hall |
| 514 | C22×C3 | — | 20 | 1 | no | — |
| 515 | C22×C3 | — | 40 | 1 | no | — |
| 516 | C3×C4 | — | 4 | 1 | no | — |
| 517 | C3×C4 | — | 8 | 1 | no | — |
| 518 | C3×C4 | — | 8 | 1 | no | — |
| 519 | C3×C4 | — | 20 | 1 | no | — |
| 520 | C3×C4 | — | 40 | 1 | no | — |
| 521 | C2×C5 | — | 6 | 1 | no | — |
| 522 | C2×C5 | — | 12 | 1 | no | — |
| 523 | C2×C5 | — | 12 | 1 | no | — |
| 524 | C2×C5 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 525 | D5 | — | 2 | 1 | no | — |
| 526 | D5 | — | 4 | 1 | no | — |
| 527 | D5 | — | 6 | 1 | no | — |
| 528 | D5 | — | 12 | 1 | no | — |
| 529 | C23 | — | 6 | 1 | no | — |
| 530 | C23 | — | 6 | 1 | no | — |
| 531 | C23 | — | 15 | 1 | no | — |
| 532 | C23 | — | 30 | 1 | no | — |
| 533 | C23 | — | 30 | 1 | no | — |
| 534 | C23 | — | 30 | 1 | no | — |
| 535 | C23 | — | 30 | 2 | no | — |
| 536 | C23 | — | 120 | 2 | no | — |
| 537 | Q8 | — | 5 | 1 | no | — |
| 538 | Q8 | — | 10 | 1 | no | — |
| 539 | Q8 | — | 15 | 1 | no | — |
| 540 | Q8 | — | 15 | 1 | no | — |
| 541 | Q8 | — | 30 | 1 | no | — |
| 542 | Q8 | — | 30 | 1 | no | — |
| 543 | Q8 | C3×D4×D5 | 1 | 1 | yes | characteristic |
| 544 | Q8 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 545 | Q8 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 546 | D4 | — | 3 | 1 | no | — |
| 547 | D4 | — | 3 | 1 | no | — |
| 548 | D4 | — | 3 | 1 | no | — |
| 549 | D4 | — | 5 | 1 | no | — |
| 550 | D4 | — | 6 | 1 | no | — |
| 551 | D4 | — | 6 | 1 | no | — |
| 552 | D4 | — | 6 | 1 | no | — |
| 553 | D4 | — | 6 | 1 | no | — |
| 554 | D4 | — | 10 | 1 | no | — |
| 555 | D4 | — | 15 | 1 | no | — |
| 556 | D4 | — | 15 | 2 | no | — |
| 557 | D4 | — | 15 | 1 | no | — |
| 558 | D4 | — | 30 | 1 | no | — |
| 559 | D4 | — | 30 | 1 | no | — |
| 560 | D4 | — | 30 | 1 | no | — |
| 561 | D4 | — | 30 | 1 | no | — |
| 562 | D4 | — | 30 | 1 | no | — |
| 563 | D4 | — | 30 | 1 | no | — |
| 564 | D4 | — | 30 | 2 | no | — |
| 565 | D4 | — | 30 | 1 | no | — |
| 566 | D4 | — | 30 | 1 | no | — |
| 567 | D4 | — | 30 | 2 | no | — |
| 568 | C2×C4 | — | 3 | 1 | no | — |
| 569 | C2×C4 | — | 5 | 1 | no | — |
| 570 | C2×C4 | — | 6 | 1 | no | — |
| 571 | C2×C4 | — | 6 | 1 | no | — |
| 572 | C2×C4 | — | 10 | 1 | no | — |
| 573 | C2×C4 | — | 10 | 1 | no | — |
| 574 | C2×C4 | — | 15 | 1 | no | — |
| 575 | C2×C4 | — | 15 | 1 | no | — |
| 576 | C2×C4 | — | 15 | 1 | no | — |
| 577 | C2×C4 | — | 15 | 1 | no | — |
| 578 | C2×C4 | — | 30 | 1 | no | — |
| 579 | C2×C4 | — | 30 | 1 | no | — |
| 580 | C2×C4 | — | 30 | 1 | no | — |
| 581 | C2×C4 | — | 30 | 1 | no | — |
| 582 | C2×C4 | — | 30 | 1 | no | — |
| 583 | C2×C4 | — | 30 | 1 | no | — |
| 584 | C2×C4 | — | 30 | 2 | no | — |
| 585 | C2×C4 | — | 30 | 1 | no | — |
| 586 | C8 | — | 3 | 1 | no | — |
| 587 | C8 | — | 5 | 1 | no | — |
| 588 | C8 | — | 15 | 1 | no | — |
| 589 | C8 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 590 | C2×C3 | — | 4 | 1 | no | — |
| 591 | C2×C3 | — | 40 | 1 | no | — |
| 592 | C2×C3 | — | 80 | 1 | no | — |
| 593 | C5 | #3585⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 594 | C22 | — | 3 | 1 | no | — |
| 595 | C22 | — | 5 | 1 | no | — |
| 596 | C22 | — | 6 | 1 | no | — |
| 597 | C22 | — | 6 | 1 | no | — |
| 598 | C22 | — | 10 | 1 | no | — |
| 599 | C22 | — | 15 | 1 | no | — |
| 600 | C22 | — | 24 | 1 | no | — |
| 601 | C22 | — | 24 | 1 | no | — |
| 602 | C22 | — | 30 | 1 | no | — |
| 603 | C22 | — | 60 | 1 | no | — |
| 604 | C22 | — | 60 | 2 | no | — |
| 605 | C22 | — | 120 | 1 | no | — |
| 606 | C22 | — | 120 | 1 | no | — |
| 607 | C22 | — | 120 | 2 | no | — |
| 608 | C4 | — | 2 | 1 | no | — |
| 609 | C4 | — | 2 | 1 | no | — |
| 610 | C4 | — | 3 | 1 | no | — |
| 611 | C4 | — | 5 | 1 | no | — |
| 612 | C4 | — | 10 | 1 | no | — |
| 613 | C4 | — | 15 | 1 | no | — |
| 614 | C4 | — | 30 | 1 | no | — |
| 615 | C4 | C22×D5×A4 | 1 | 1 | yes | characteristic |
| 616 | C3 | — | 4 | 1 | no | Sylow |
| 617 | C2 | — | 6 | 1 | no | — |
| 618 | C2 | — | 10 | 1 | no | — |
| 619 | C2 | — | 12 | 1 | no | — |
| 620 | C2 | — | 12 | 1 | no | — |
| 621 | C2 | — | 20 | 1 | no | — |
| 622 | C2 | — | 30 | 1 | no | — |
| 623 | C2 | — | 60 | 1 | no | — |
| 624 | C2 | D4×D5×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D5×A4 |
| commutator, cosocle | C5×#41 | C23×C3 |
| Frattini | C4 | C22×D5×A4 |
| Fitting | C5×#576 | C2×C3 |
| socle | C2×C5 | C2×D4×A4 |
| hypercenter | Q16 | D5×A4 |
| hypocenter | C5×Q8 | C2×C3×D4 |
| LCS | G ▷ C5×#41 ▷ C5×Q8 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11756944 | C2 | semidirect |
| 2. D5×#994 | C2 | semidirect |
| 3. C5×#576⋊C3 | C2 | semidirect |
| 4. #66169⋊C3 | C2 | semidirect |
| 5. #66170⋊C3 | C2 | semidirect |
| 6. #66085⋊C3 | C2 | semidirect |
| 7. #66084⋊C3 | C2 | semidirect |
| 8. #10619105 | C3 | semidirect |
| 9. C5×#994 | C22 | semidirect |
| 10. C5×#994 | C22 | semidirect |
| 12. #4150⋊C3 | C22 | semidirect |
| 17. C5⋊#994 | C22 | semidirect |
| 19. C5×#131⋊C3 | C22 | semidirect |
| 20. #4094⋊C3 | C22 | semidirect |
| 23. D5×H(5,𝔽2) | C2×C3 | semidirect |
| 24. C5×#576 | C2×C3 | semidirect |
| 25. #66170 | C2×C3 | semidirect |
| 26. #66169 | C2×C3 | semidirect |
| 35. #66085 | C2×C3 | semidirect |
| 36. #66084 | C2×C3 | semidirect |
| 56. #576⋊C3 | D5 | semidirect |
| 133. #994 | C2×D5 | semidirect |
| 134. #994 | C2×D5 | semidirect |
| 140. #131⋊C3 | C2×D5 | semidirect |
| 240. #576 | C3×D5 | semidirect |
| 593. C5 | #3585⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756944 | 2 |
| D5×#994 | 2 |
| C5×#576⋊C3 | 2 |
| #66169⋊C3 | 2 |
| #66170⋊C3 | 2 |
| #66085⋊C3 | 2 |
| #66084⋊C3 | 2 |
| #10619105 | 3 |
| C3×#4064 | 4 |
| #3585⋊C3 | 5 |