Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 45 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 | #11756910 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11756774 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #66171⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#5431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11751630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751621 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11751618 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10612018 | — | 3 | 1 | no | maximal, Hall |
| 9 | C5×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C5⋊#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #91956 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #91955 | C22 | 1 | 1 | yes | characteristic |
| 13 | #91953 | — | 2 | 1 | no | — |
| 14 | C2×C5⋊GL(2,𝔽3) | — | 2 | 1 | no | — |
| 15 | C5×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #91894 | — | 2 | 1 | no | — |
| 17 | #91892 | — | 2 | 1 | no | — |
| 18 | #91500 | — | 4 | 1 | no | maximal |
| 19 | #4094⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C5×GU(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #85470 | — | 5 | 1 | no | maximal, Hall |
| 22 | #66171 | — | 3 | 1 | no | — |
| 23 | #66171 | D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | #66108 | — | 3 | 1 | no | — |
| 25 | #66108 | — | 3 | 1 | no | — |
| 26 | C5×#454 | — | 3 | 1 | no | — |
| 27 | #65488 | — | 3 | 1 | no | — |
| 28 | #65488 | — | 3 | 1 | no | — |
| 29 | #65350 | — | 3 | 1 | no | — |
| 30 | #65347 | — | 3 | 1 | no | — |
| 31 | #65112 | — | 3 | 1 | no | — |
| 32 | #65112 | — | 3 | 1 | no | — |
| 33 | #65111 | — | 3 | 1 | no | — |
| 34 | #65111 | — | 3 | 1 | no | — |
| 35 | #65043 | — | 3 | 1 | no | — |
| 36 | #65043 | — | 3 | 1 | no | — |
| 37 | D4×D15 | — | 4 | 1 | no | — |
| 38 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×C5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 40 | #6768 | — | 4 | 1 | no | — |
| 41 | C5⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 42 | C5⋊GL(2,𝔽3) | — | 2 | 1 | no | — |
| 43 | C5⋊GL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic, complemented |
| 44 | C5⋊#226 | D4 | 1 | 1 | yes | characteristic, complemented |
| 45 | C5×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 46 | C5×#213 | — | 4 | 1 | no | — |
| 47 | C3×#687 | — | 4 | 1 | no | — |
| 48 | #6658 | — | 4 | 1 | no | — |
| 49 | #6654 | — | 4 | 1 | no | — |
| 50 | #6651 | — | 4 | 1 | no | — |
| 51 | #5926 | — | 5 | 1 | no | — |
| 52 | #5925 | — | 5 | 1 | no | — |
| 53 | #577⋊C3 | — | 5 | 1 | no | — |
| 54 | #5431 | D5 | 1 | 1 | yes | characteristic, complemented |
| 55 | #5429 | — | 5 | 1 | no | — |
| 56 | #5407 | — | 5 | 1 | no | — |
| 57 | #5405 | — | 5 | 1 | no | — |
| 58 | C5×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 59 | #4149 | — | 3 | 1 | no | — |
| 60 | #4149 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 61 | #4144 | — | 3 | 1 | no | — |
| 62 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 63 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 64 | C5×#124 | — | 3 | 1 | no | — |
| 65 | #4096 | — | 3 | 1 | no | — |
| 66 | #4096 | — | 3 | 1 | no | — |
| 67 | #4096 | — | 6 | 1 | no | — |
| 68 | #4095 | — | 3 | 1 | no | — |
| 69 | #4095 | — | 3 | 1 | no | — |
| 70 | #4095 | — | 6 | 1 | no | — |
| 71 | #4094 | — | 3 | 1 | no | — |
| 72 | #4094 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 73 | #4088 | — | 3 | 1 | no | — |
| 74 | #4088 | — | 3 | 1 | no | — |
| 75 | #4088 | — | 6 | 1 | no | — |
| 76 | C2×#688 | — | 3 | 1 | no | — |
| 77 | C2×#688 | — | 3 | 1 | no | — |
| 78 | C2×#688 | — | 6 | 1 | no | — |
| 79 | C2×#686 | — | 3 | 1 | no | — |
| 80 | C2×#686 | — | 3 | 1 | no | — |
| 81 | #4062 | — | 6 | 1 | no | — |
| 82 | #4062 | — | 6 | 1 | no | — |
| 83 | #4060 | — | 6 | 1 | no | — |
| 84 | #4060 | — | 6 | 1 | no | — |
| 85 | #4057 | — | 6 | 1 | no | — |
| 86 | #4057 | — | 6 | 1 | no | — |
| 87 | D5×D8 | — | 6 | 1 | no | — |
| 88 | D5×D8 | — | 6 | 1 | no | — |
| 89 | #4054 | — | 3 | 1 | no | — |
| 90 | #4054 | — | 3 | 1 | no | — |
| 91 | #4053 | — | 3 | 1 | no | — |
| 92 | #4053 | — | 3 | 1 | no | — |
| 93 | #4020 | — | 3 | 1 | no | — |
| 94 | C5×#104 | — | 3 | 1 | no | — |
| 95 | C5×#104 | — | 3 | 1 | no | — |
| 96 | C5×#101 | — | 3 | 1 | no | — |
| 97 | #3965 | — | 3 | 1 | no | — |
| 98 | #3955 | — | 3 | 1 | no | — |
| 99 | #3955 | — | 3 | 1 | no | — |
| 100 | #3954 | — | 3 | 1 | no | — |
| 101 | #3954 | — | 3 | 1 | no | — |
| 102 | #3937 | — | 3 | 1 | no | — |
| 103 | #3937 | — | 3 | 1 | no | — |
| 104 | #3935 | — | 3 | 1 | no | — |
| 105 | #3288 | — | 15 | 1 | no | Sylow |
| 106 | C22×D15 | — | 8 | 1 | no | — |
| 107 | C3×C5×D4 | — | 4 | 1 | no | — |
| 108 | #1220 | — | 8 | 1 | no | — |
| 109 | D60 | — | 4 | 1 | no | — |
| 110 | C4×D15 | — | 4 | 1 | no | — |
| 111 | C5×D12 | — | 4 | 1 | no | — |
| 112 | C3×Dic10 | — | 4 | 1 | no | — |
| 113 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | #1203 | — | 8 | 1 | no | — |
| 115 | D3×Dic5 | — | 8 | 1 | no | — |
| 116 | C3×#168 | — | 4 | 1 | no | — |
| 117 | C5×C3⋊C8 | — | 4 | 1 | no | — |
| 118 | 2−1+4⋊C3 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 119 | #994 | — | 5 | 1 | no | — |
| 120 | #986 | — | 5 | 1 | no | — |
| 121 | #986 | — | 10 | 1 | no | — |
| 122 | #986 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 123 | #985 | — | 5 | 1 | no | — |
| 124 | #985 | — | 10 | 1 | no | — |
| 125 | #983 | — | 10 | 1 | no | — |
| 126 | C2×GL(2,𝔽3) | — | 10 | 1 | no | — |
| 127 | #914 | — | 20 | 1 | no | — |
| 128 | #131⋊C3 | — | 5 | 1 | no | — |
| 129 | GU(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 130 | C5×#41 | — | 3 | 1 | no | — |
| 131 | C5×#41 | — | 6 | 1 | no | — |
| 132 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 133 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 134 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 135 | C2×C5×D4 | — | 3 | 1 | no | — |
| 136 | C2×C22⋊D5 | — | 12 | 1 | no | — |
| 137 | #713 | — | 2 | 1 | no | — |
| 138 | #713 | — | 6 | 1 | no | — |
| 139 | #711 | — | 6 | 1 | no | — |
| 140 | #711 | — | 6 | 1 | no | — |
| 141 | D4×D5 | — | 6 | 1 | no | — |
| 142 | D4×D5 | — | 6 | 1 | no | — |
| 143 | D4×D5 | — | 6 | 1 | no | — |
| 144 | D4×D5 | — | 6 | 1 | no | — |
| 145 | D4×D5 | — | 12 | 1 | no | — |
| 146 | #709 | — | 3 | 1 | no | — |
| 147 | #709 | — | 3 | 1 | no | — |
| 148 | #709 | — | 6 | 1 | no | — |
| 149 | C2×D20 | — | 3 | 1 | no | — |
| 150 | C2×D20 | — | 3 | 1 | no | — |
| 151 | C2×D20 | — | 6 | 1 | no | — |
| 152 | C2×D20 | — | 12 | 1 | no | — |
| 153 | C5×SD16 | — | 6 | 1 | no | — |
| 154 | C5×SD16 | — | 6 | 1 | no | — |
| 155 | C5×D8 | — | 6 | 1 | no | — |
| 156 | C5×D8 | — | 6 | 1 | no | — |
| 157 | C5×M16 | — | 3 | 1 | no | — |
| 158 | C5×M16 | — | 3 | 1 | no | — |
| 159 | C5×C22⋊C4 | — | 12 | 1 | no | — |
| 160 | C42×C5 | — | 3 | 1 | no | — |
| 161 | #689 | — | 3 | 1 | no | — |
| 162 | #689 | — | 3 | 1 | no | — |
| 163 | #689 | — | 6 | 1 | no | — |
| 164 | #688 | — | 3 | 1 | no | — |
| 165 | #688 | — | 3 | 1 | no | — |
| 166 | #688 | — | 6 | 1 | no | — |
| 167 | #688 | — | 6 | 1 | no | — |
| 168 | #688 | — | 6 | 1 | no | — |
| 169 | #688 | — | 6 | 1 | no | — |
| 170 | #688 | — | 6 | 1 | no | — |
| 171 | #687 | — | 3 | 1 | no | — |
| 172 | #687 | S4 | 1 | 1 | yes | characteristic |
| 173 | #686 | — | 3 | 1 | no | — |
| 174 | #686 | — | 3 | 1 | no | — |
| 175 | #686 | — | 6 | 1 | no | — |
| 176 | #686 | — | 6 | 1 | no | — |
| 177 | #686 | — | 6 | 1 | no | — |
| 178 | #686 | — | 6 | 1 | no | — |
| 179 | #686 | — | 6 | 1 | no | — |
| 180 | #681 | — | 3 | 1 | no | — |
| 181 | #681 | — | 3 | 1 | no | — |
| 182 | #681 | — | 6 | 1 | no | — |
| 183 | C2×#168 | — | 3 | 1 | no | — |
| 184 | C2×#168 | — | 3 | 1 | no | — |
| 185 | C2×#168 | — | 6 | 1 | no | — |
| 186 | D40 | — | 6 | 1 | no | — |
| 187 | D40 | — | 6 | 1 | no | — |
| 188 | #677 | — | 6 | 1 | no | — |
| 189 | #677 | — | 6 | 1 | no | — |
| 190 | #676 | — | 6 | 1 | no | — |
| 191 | #676 | — | 6 | 1 | no | — |
| 192 | C8×D5 | — | 6 | 1 | no | — |
| 193 | C8×D5 | — | 6 | 1 | no | — |
| 194 | #577 | — | 5 | 1 | no | — |
| 195 | #577 | — | 15 | 1 | no | — |
| 196 | #576 | — | 15 | 1 | no | — |
| 197 | #576 | — | 15 | 1 | no | — |
| 198 | #496 | — | 15 | 1 | no | — |
| 199 | #472 | — | 15 | 1 | no | — |
| 200 | #472 | — | 15 | 1 | no | — |
| 201 | #471 | — | 15 | 1 | no | — |
| 202 | #471 | — | 15 | 1 | no | — |
| 203 | #455 | — | 15 | 1 | no | — |
| 204 | #454 | — | 3 | 1 | no | — |
| 205 | #453 | — | 15 | 1 | no | — |
| 206 | #453 | — | 15 | 1 | no | — |
| 207 | #444 | — | 15 | 1 | no | — |
| 208 | #444 | — | 15 | 1 | no | — |
| 209 | C22×C3×C5 | — | 8 | 1 | no | — |
| 210 | C2×D15 | — | 4 | 1 | no | — |
| 211 | C2×D15 | — | 8 | 1 | no | — |
| 212 | C2×D15 | — | 16 | 2 | no | — |
| 213 | C2×C5×D3 | — | 8 | 1 | no | — |
| 214 | C3×C4×C5 | — | 4 | 1 | no | — |
| 215 | Dic15 | — | 4 | 1 | no | — |
| 216 | C3×Dic5 | — | 8 | 1 | no | — |
| 217 | #239 | — | 20 | 1 | no | — |
| 218 | D3×D4 | — | 20 | 1 | no | — |
| 219 | #41⋊C3 | — | 10 | 1 | no | — |
| 220 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 221 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 222 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 223 | GL(2,𝔽3) | — | 5 | 1 | no | — |
| 224 | GL(2,𝔽3) | — | 10 | 1 | no | — |
| 225 | #226 | — | 5 | 1 | no | — |
| 226 | C3×SD16 | — | 20 | 1 | no | — |
| 227 | #215 | — | 20 | 1 | no | — |
| 228 | #213 | — | 4 | 1 | no | — |
| 229 | D24 | — | 20 | 1 | no | — |
| 230 | ΓL(1,𝔽25) | — | 20 | 1 | no | — |
| 231 | C23×C5 | — | 6 | 1 | no | — |
| 232 | C22×D5 | — | 6 | 1 | no | — |
| 233 | C22×D5 | — | 6 | 1 | no | — |
| 234 | C22×D5 | — | 12 | 1 | no | — |
| 235 | C22×D5 | — | 12 | 1 | no | — |
| 236 | C5×Q8 | — | 3 | 1 | no | — |
| 237 | C5×Q8 | — | 6 | 1 | no | — |
| 238 | C5×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 239 | C5×D4 | — | 3 | 1 | no | — |
| 240 | C5×D4 | — | 6 | 1 | no | — |
| 241 | C5×D4 | — | 6 | 1 | no | — |
| 242 | C5×D4 | — | 6 | 1 | no | — |
| 243 | C5×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 244 | C2×C4×C5 | — | 3 | 1 | no | — |
| 245 | C2×C4×C5 | — | 6 | 1 | no | — |
| 246 | C2×C4×C5 | — | 6 | 1 | no | — |
| 247 | C2×C4×C5 | — | 6 | 1 | no | — |
| 248 | C22⋊D5 | — | 6 | 1 | no | — |
| 249 | C22⋊D5 | — | 6 | 1 | no | — |
| 250 | C22⋊D5 | — | 12 | 1 | no | — |
| 251 | C22⋊D5 | — | 12 | 1 | no | — |
| 252 | C22⋊D5 | — | 12 | 1 | no | — |
| 253 | C2×Dic5 | — | 12 | 1 | no | — |
| 254 | D20 | — | 3 | 1 | no | — |
| 255 | D20 | — | 3 | 1 | no | — |
| 256 | D20 | — | 6 | 1 | no | — |
| 257 | D20 | — | 6 | 1 | no | — |
| 258 | D20 | — | 6 | 1 | no | — |
| 259 | D20 | — | 12 | 1 | no | — |
| 260 | D20 | — | 24 | 2 | no | — |
| 261 | C4×D5 | — | 6 | 1 | no | — |
| 262 | C4×D5 | — | 6 | 1 | no | — |
| 263 | C4×D5 | — | 12 | 1 | no | — |
| 264 | Dic10 | — | 3 | 1 | no | — |
| 265 | Dic10 | C2×S4 | 1 | 1 | yes | characteristic |
| 266 | C5×C8 | — | 6 | 1 | no | — |
| 267 | C5×C8 | — | 6 | 1 | no | — |
| 268 | #168 | — | 3 | 1 | no | — |
| 269 | #168 | — | 3 | 1 | no | — |
| 270 | #168 | — | 3 | 1 | no | — |
| 271 | #168 | — | 6 | 1 | no | — |
| 272 | #168 | C2×S4 | 1 | 1 | yes | characteristic |
| 273 | 2−1+4 | D3×D5 | 1 | 1 | yes | characteristic |
| 274 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 275 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 276 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 277 | #137 | — | 15 | 1 | no | — |
| 278 | #137 | — | 15 | 1 | no | — |
| 279 | #137 | — | 30 | 1 | no | — |
| 280 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 281 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 282 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 283 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 284 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 285 | AGL(1,ℤ/8) | — | 15 | 1 | no | — |
| 286 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 287 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 288 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 289 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 290 | AGL(1,ℤ/8) | — | 30 | 1 | no | — |
| 291 | #135 | — | 15 | 1 | no | — |
| 292 | #135 | — | 15 | 1 | no | — |
| 293 | #135 | — | 30 | 1 | no | — |
| 294 | #135 | — | 30 | 1 | no | — |
| 295 | #135 | — | 30 | 1 | no | — |
| 296 | C2×SD16 | — | 15 | 1 | no | — |
| 297 | C2×SD16 | — | 15 | 1 | no | — |
| 298 | C2×SD16 | — | 30 | 1 | no | — |
| 299 | C2×D8 | — | 15 | 1 | no | — |
| 300 | C2×D8 | — | 15 | 1 | no | — |
| 301 | C2×D8 | — | 30 | 1 | no | — |
| 302 | C2×D8 | — | 30 | 1 | no | — |
| 303 | #131 | — | 5 | 1 | no | — |
| 304 | #131 | — | 15 | 1 | no | — |
| 305 | #131 | — | 15 | 1 | no | — |
| 306 | #131 | — | 15 | 1 | no | — |
| 307 | #127 | — | 15 | 1 | no | — |
| 308 | #124 | — | 3 | 1 | no | — |
| 309 | #108 | — | 15 | 1 | no | — |
| 310 | #108 | — | 15 | 1 | no | — |
| 311 | #104 | — | 3 | 1 | no | — |
| 312 | #104 | — | 3 | 1 | no | — |
| 313 | #104 | — | 15 | 1 | no | — |
| 314 | #104 | — | 15 | 1 | no | — |
| 315 | #101 | — | 3 | 1 | no | — |
| 316 | #100 | — | 15 | 1 | no | — |
| 317 | #100 | — | 15 | 1 | no | — |
| 318 | #100 | — | 15 | 1 | no | — |
| 319 | #97 | — | 15 | 1 | no | — |
| 320 | C2×C3×C5 | — | 4 | 1 | no | — |
| 321 | C2×C3×C5 | — | 16 | 1 | no | — |
| 322 | D15 | — | 8 | 1 | no | — |
| 323 | D15 | — | 16 | 1 | no | — |
| 324 | C5×D3 | — | 16 | 1 | no | — |
| 325 | C22×D3 | — | 40 | 1 | no | — |
| 326 | C3×Q8 | — | 20 | 1 | no | — |
| 327 | C3×D4 | — | 4 | 1 | no | — |
| 328 | #67 | — | 40 | 1 | no | — |
| 329 | D12 | — | 4 | 1 | no | — |
| 330 | D12 | — | 20 | 1 | no | — |
| 331 | D12 | — | 40 | 1 | no | — |
| 332 | C4×D3 | — | 20 | 1 | no | — |
| 333 | C4×D3 | — | 40 | 1 | no | — |
| 334 | SL(2,𝔽3) | D4×D5 | 1 | 1 | yes | characteristic |
| 335 | C3×C8 | — | 20 | 1 | no | — |
| 336 | C3⋊C8 | — | 4 | 1 | no | — |
| 337 | C22×C5 | — | 2 | 1 | no | — |
| 338 | C22×C5 | — | 3 | 1 | no | — |
| 339 | C22×C5 | — | 12 | 1 | no | — |
| 340 | C22×C5 | — | 24 | 1 | no | — |
| 341 | C2×D5 | — | 6 | 1 | no | — |
| 342 | C2×D5 | — | 6 | 1 | no | — |
| 343 | C2×D5 | — | 12 | 1 | no | — |
| 344 | C2×D5 | — | 24 | 1 | no | — |
| 345 | C2×D5 | — | 24 | 1 | no | — |
| 346 | C2×D5 | — | 48 | 1 | no | — |
| 347 | C2×D5 | — | 48 | 1 | no | — |
| 348 | C4×C5 | — | 3 | 1 | no | — |
| 349 | C4×C5 | — | 6 | 1 | no | — |
| 350 | C4×C5 | — | 12 | 1 | no | — |
| 351 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 352 | Dic5 | — | 2 | 1 | no | — |
| 353 | Dic5 | — | 6 | 1 | no | — |
| 354 | #41 | — | 3 | 1 | no | — |
| 355 | #41 | — | 6 | 1 | no | — |
| 356 | #41 | — | 10 | 1 | no | — |
| 357 | #41 | — | 15 | 1 | no | — |
| 358 | #41 | — | 15 | 1 | no | — |
| 359 | #41 | — | 30 | 1 | no | — |
| 360 | #41 | — | 30 | 1 | no | — |
| 361 | #41 | — | 30 | 1 | no | — |
| 362 | #41 | — | 30 | 1 | no | — |
| 363 | #41 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 364 | C2×Q8 | — | 2 | 1 | no | — |
| 365 | C2×Q8 | — | 3 | 1 | no | — |
| 366 | C2×D4 | — | 3 | 1 | no | — |
| 367 | C2×D4 | — | 15 | 1 | no | — |
| 368 | C2×D4 | — | 15 | 1 | no | — |
| 369 | C2×D4 | — | 30 | 1 | no | — |
| 370 | C2×D4 | — | 30 | 1 | no | — |
| 371 | C2×D4 | — | 30 | 1 | no | — |
| 372 | C2×D4 | — | 30 | 1 | no | — |
| 373 | C2×D4 | — | 30 | 1 | no | — |
| 374 | C2×D4 | — | 60 | 1 | no | — |
| 375 | C2×D4 | — | 60 | 1 | no | — |
| 376 | C2×D4 | — | 60 | 1 | no | — |
| 377 | Q16 | — | 15 | 1 | no | — |
| 378 | Q16 | — | 15 | 1 | no | — |
| 379 | Q16 | — | 30 | 1 | no | — |
| 380 | SD16 | — | 5 | 1 | no | — |
| 381 | SD16 | — | 6 | 1 | no | — |
| 382 | SD16 | — | 6 | 1 | no | — |
| 383 | SD16 | — | 15 | 1 | no | — |
| 384 | SD16 | — | 15 | 1 | no | — |
| 385 | SD16 | — | 15 | 1 | no | — |
| 386 | SD16 | — | 30 | 1 | no | — |
| 387 | SD16 | — | 30 | 1 | no | — |
| 388 | SD16 | — | 30 | 1 | no | — |
| 389 | SD16 | — | 30 | 1 | no | — |
| 390 | SD16 | — | 30 | 1 | no | — |
| 391 | SD16 | — | 30 | 1 | no | — |
| 392 | SD16 | — | 30 | 1 | no | — |
| 393 | D8 | — | 6 | 1 | no | — |
| 394 | D8 | — | 6 | 1 | no | — |
| 395 | D8 | — | 15 | 1 | no | — |
| 396 | D8 | — | 15 | 1 | no | — |
| 397 | D8 | — | 30 | 1 | no | — |
| 398 | D8 | — | 30 | 1 | no | — |
| 399 | D8 | — | 30 | 1 | no | — |
| 400 | D8 | — | 30 | 1 | no | — |
| 401 | D8 | — | 30 | 1 | no | — |
| 402 | D8 | — | 30 | 1 | no | — |
| 403 | D8 | — | 30 | 1 | no | — |
| 404 | M16 | — | 3 | 1 | no | — |
| 405 | M16 | — | 3 | 1 | no | — |
| 406 | M16 | — | 15 | 1 | no | — |
| 407 | M16 | — | 15 | 1 | no | — |
| 408 | M16 | — | 30 | 1 | no | — |
| 409 | M16 | — | 30 | 1 | no | — |
| 410 | M16 | — | 30 | 1 | no | — |
| 411 | C2×C8 | — | 15 | 1 | no | — |
| 412 | C2×C8 | — | 15 | 1 | no | — |
| 413 | C2×C8 | — | 30 | 1 | no | — |
| 414 | C2×C8 | — | 30 | 1 | no | — |
| 415 | C2×C8 | — | 30 | 1 | no | — |
| 416 | C22⋊C4 | — | 12 | 1 | no | — |
| 417 | C42 | — | 3 | 1 | no | — |
| 418 | C3×C5 | — | 4 | 1 | no | Hall |
| 419 | C22×C3 | — | 8 | 1 | no | — |
| 420 | C2×D3 | — | 8 | 1 | no | — |
| 421 | C2×D3 | — | 20 | 1 | no | — |
| 422 | C2×D3 | — | 40 | 1 | no | — |
| 423 | C2×D3 | — | 80 | 2 | no | — |
| 424 | C3×C4 | — | 4 | 1 | no | — |
| 425 | C3×C4 | — | 40 | 1 | no | — |
| 426 | Dic3 | — | 20 | 1 | no | — |
| 427 | C2×C5 | — | 4 | 1 | no | — |
| 428 | C2×C5 | — | 6 | 1 | no | — |
| 429 | C2×C5 | — | 24 | 1 | no | — |
| 430 | C2×C5 | D4×S4 | 1 | 1 | yes | characteristic |
| 431 | D5 | — | 12 | 1 | no | — |
| 432 | D5 | — | 12 | 1 | no | — |
| 433 | D5 | — | 24 | 1 | no | — |
| 434 | C23 | — | 6 | 1 | no | — |
| 435 | C23 | — | 30 | 1 | no | — |
| 436 | C23 | — | 30 | 1 | no | — |
| 437 | C23 | — | 60 | 1 | no | — |
| 438 | C23 | — | 60 | 1 | no | — |
| 439 | Q8 | — | 3 | 1 | no | — |
| 440 | Q8 | — | 5 | 1 | no | — |
| 441 | Q8 | — | 6 | 1 | no | — |
| 442 | Q8 | — | 15 | 1 | no | — |
| 443 | Q8 | #6790 | 1 | 1 | yes | characteristic |
| 444 | D4 | — | 3 | 1 | no | — |
| 445 | D4 | — | 6 | 1 | no | — |
| 446 | D4 | — | 6 | 1 | no | — |
| 447 | D4 | — | 6 | 1 | no | — |
| 448 | D4 | — | 15 | 1 | no | — |
| 449 | D4 | — | 15 | 1 | no | — |
| 450 | D4 | — | 30 | 1 | no | — |
| 451 | D4 | — | 30 | 1 | no | — |
| 452 | D4 | — | 30 | 1 | no | — |
| 453 | D4 | — | 30 | 1 | no | — |
| 454 | D4 | — | 30 | 1 | no | — |
| 455 | D4 | — | 60 | 1 | no | — |
| 456 | D4 | — | 60 | 1 | no | — |
| 457 | D4 | — | 60 | 1 | no | — |
| 458 | D4 | — | 60 | 1 | no | — |
| 459 | D4 | — | 120 | 2 | no | — |
| 460 | D4 | D5×S4 | 1 | 1 | yes | characteristic |
| 461 | C2×C4 | — | 3 | 1 | no | — |
| 462 | C2×C4 | — | 6 | 1 | no | — |
| 463 | C2×C4 | — | 6 | 1 | no | — |
| 464 | C2×C4 | — | 6 | 1 | no | — |
| 465 | C2×C4 | — | 30 | 1 | no | — |
| 466 | C2×C4 | — | 30 | 1 | no | — |
| 467 | C2×C4 | — | 60 | 1 | no | — |
| 468 | C2×C4 | — | 60 | 1 | no | — |
| 469 | C8 | — | 5 | 1 | no | — |
| 470 | C8 | — | 6 | 1 | no | — |
| 471 | C8 | — | 6 | 1 | no | — |
| 472 | C8 | — | 15 | 1 | no | — |
| 473 | C8 | — | 15 | 1 | no | — |
| 474 | C8 | — | 15 | 1 | no | — |
| 475 | C8 | — | 30 | 1 | no | — |
| 476 | C2×C3 | — | 4 | 1 | no | — |
| 477 | C2×C3 | — | 16 | 1 | no | — |
| 478 | D3 | — | 16 | 1 | no | — |
| 479 | D3 | — | 40 | 1 | no | — |
| 480 | D3 | — | 80 | 1 | no | — |
| 481 | C5 | #85470 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 482 | C22 | — | 2 | 1 | no | — |
| 483 | C22 | — | 3 | 1 | no | — |
| 484 | C22 | — | 12 | 1 | no | — |
| 485 | C22 | — | 24 | 1 | no | — |
| 486 | C22 | — | 30 | 1 | no | — |
| 487 | C22 | — | 30 | 1 | no | — |
| 488 | C22 | — | 60 | 1 | no | — |
| 489 | C22 | — | 120 | 1 | no | — |
| 490 | C22 | — | 120 | 1 | no | — |
| 491 | C22 | — | 240 | 1 | no | — |
| 492 | C22 | — | 240 | 1 | no | — |
| 493 | C4 | — | 3 | 1 | no | — |
| 494 | C4 | — | 6 | 1 | no | — |
| 495 | C4 | — | 10 | 1 | no | — |
| 496 | C4 | — | 12 | 1 | no | — |
| 497 | C4 | — | 30 | 1 | no | — |
| 498 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 499 | C3 | — | 4 | 1 | no | Sylow |
| 500 | C2 | — | 4 | 1 | no | — |
| 501 | C2 | — | 6 | 1 | no | — |
| 502 | C2 | — | 24 | 1 | no | — |
| 503 | C2 | — | 60 | 1 | no | — |
| 504 | C2 | — | 60 | 1 | no | — |
| 505 | C2 | — | 120 | 1 | no | — |
| 506 | C2 | #11756799 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11756910 | C2 | semidirect |
| 2. #11756774 | C2 | semidirect |
| 3. #66171⋊C3 | C2 | semidirect |
| 4. C5×#5431 | C2 | semidirect |
| 5. #11751630 | C2 | semidirect |
| 6. #11751621 | C2 | semidirect |
| 7. #11751618 | C2 | semidirect |
| 9. C5×2−1+4⋊C3 | C22 | semidirect |
| 10. C5⋊#994 | C22 | semidirect |
| 11. #91956 | C22 | semidirect |
| 15. C5×#986 | C22 | semidirect |
| 19. #4094⋊C3 | C22 | semidirect |
| 20. C5×GU(2,𝔽3) | C22 | semidirect |
| 23. #66171 | D3 | semidirect |
| 43. C5⋊GL(2,𝔽3) | D4 | semidirect |
| 44. C5⋊#226 | D4 | semidirect |
| 54. #5431 | D5 | semidirect |
| 60. #4149 | C2×D3 | semidirect |
| 72. #4094 | C2×D3 | semidirect |
| 118. 2−1+4⋊C3 | C2×D5 | semidirect |
| 122. #986 | C2×D5 | semidirect |
| 129. GU(2,𝔽3) | C2×D5 | semidirect |
| 481. C5 | #85470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756910 | 2 |
| #11756774 | 2 |
| #66171⋊C3 | 2 |
| C5×#5431 | 2 |
| #11751630 | 2 |
| #11751621 | 2 |
| #11751618 | 2 |
| #10612018 | 3 |
| #91500 | 4 |
| #85470 | 5 |