Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1518 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1518 conjugacy classes of subgroups — too many to draw. Only its 149 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 | C5×#5945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11756910 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #11756909 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11756907 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×#91956 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10619199 | — | 3 | 1 | no | maximal, Hall |
| 7 | #92100 | — | 4 | 1 | no | maximal |
| 8 | C5×2−1+4⋊C3 | C22 | 1 | 3 | yes | complemented |
| 9 | C5×#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×C5×#41⋊C3 | C22 | 1 | 3 | yes | complemented |
| 11 | #91956 | C22 | 1 | 3 | yes | complemented |
| 12 | #91956 | C22 | 1 | 6 | yes | complemented |
| 13 | #91955 | C22 | 1 | 6 | yes | complemented |
| 14 | #91954 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #91953 | C22 | 1 | 6 | yes | complemented |
| 16 | C2×C5⋊GL(2,𝔽3) | C22 | 1 | 6 | yes | complemented |
| 17 | #87498 | — | 5 | 1 | no | maximal, Hall |
| 18 | C5×#585 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#4149 | — | 3 | 1 | no | — |
| 20 | #66171 | — | 3 | 2 | no | — |
| 21 | #66171 | — | 3 | 6 | no | — |
| 22 | #66169 | — | 3 | 6 | no | — |
| 23 | #66169 | — | 3 | 2 | no | — |
| 24 | #66156 | — | 3 | 3 | no | — |
| 25 | #66156 | — | 3 | 3 | no | — |
| 26 | C2×#4095 | — | 3 | 3 | no | — |
| 27 | C2×#4095 | — | 3 | 3 | no | — |
| 28 | #66153 | — | 3 | 1 | no | — |
| 29 | C3×C5×#41 | — | 4 | 1 | no | — |
| 30 | #6821 | — | 4 | 2 | no | — |
| 31 | D4×D15 | — | 4 | 6 | no | — |
| 32 | #6817 | — | 4 | 3 | no | — |
| 33 | C2×D60 | — | 4 | 3 | no | — |
| 34 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 35 | C5×#41⋊C3 | C23 | 1 | 3 | yes | complemented |
| 36 | C2×C5×SL(2,𝔽3) | C23 | 1 | 3 | yes | complemented |
| 37 | C5⋊GL(2,𝔽3) | C23 | 1 | 6 | yes | complemented |
| 38 | C5⋊#226 | C23 | 1 | 2 | yes | complemented |
| 39 | #5945 | D5 | 1 | 1 | yes | characteristic, complemented |
| 40 | #5926 | — | 5 | 6 | no | — |
| 41 | #5925 | — | 5 | 2 | no | — |
| 42 | #5923 | — | 5 | 3 | no | — |
| 43 | C2×#986 | — | 5 | 3 | no | — |
| 44 | C5×2−1+4 | — | 3 | 1 | no | — |
| 45 | C5×2−1+4 | C2×D3 | 1 | 3 | yes | complemented |
| 46 | C5×H(5,𝔽2) | — | 3 | 3 | no | — |
| 47 | C5×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 48 | C2×C5×#41 | — | 3 | 1 | no | — |
| 49 | C2×C5×#41 | — | 3 | 3 | no | — |
| 50 | C2×C5×#41 | C2×D3 | 1 | 3 | yes | complemented |
| 51 | #4149 | — | 3 | 2 | no | — |
| 52 | #4149 | — | 3 | 6 | no | — |
| 53 | #4149 | — | 6 | 3 | no | — |
| 54 | #4149 | — | 6 | 1 | no | — |
| 55 | C2×#713 | — | 6 | 1 | no | — |
| 56 | C2×D4×D5 | — | 6 | 3 | no | — |
| 57 | C2×#709 | — | 3 | 3 | no | — |
| 58 | C22×D20 | — | 3 | 3 | no | — |
| 59 | #4097 | — | 3 | 3 | no | — |
| 60 | #4097 | — | 3 | 1 | no | — |
| 61 | #4096 | — | 3 | 6 | no | — |
| 62 | #4096 | — | 3 | 12 | no | — |
| 63 | #4096 | — | 3 | 6 | no | — |
| 64 | #4095 | — | 3 | 3 | no | — |
| 65 | #4095 | — | 3 | 6 | no | — |
| 66 | #4095 | — | 3 | 6 | no | — |
| 67 | #4095 | — | 3 | 12 | no | — |
| 68 | #4095 | — | 3 | 3 | no | — |
| 69 | #4095 | — | 3 | 6 | no | — |
| 70 | #4094 | — | 3 | 2 | no | — |
| 71 | #4094 | — | 3 | 6 | no | — |
| 72 | #4088 | — | 3 | 6 | no | — |
| 73 | #4088 | — | 3 | 6 | no | — |
| 74 | C2×#688 | — | 3 | 6 | no | — |
| 75 | C2×#688 | — | 3 | 6 | no | — |
| 76 | #4078 | — | 3 | 6 | no | — |
| 77 | #4078 | — | 3 | 6 | no | — |
| 78 | C2×#686 | — | 3 | 6 | no | — |
| 79 | C2×#686 | — | 3 | 6 | no | — |
| 80 | C2×#681 | — | 3 | 3 | no | — |
| 81 | C2×#681 | — | 3 | 3 | no | — |
| 82 | #3585 | — | 15 | 1 | no | Sylow |
| 83 | C22×D15 | — | 4 | 6 | no | — |
| 84 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 85 | C3×C5×D4 | — | 4 | 3 | no | — |
| 86 | C2×C3×C4×C5 | — | 4 | 3 | no | — |
| 87 | #1220 | — | 4 | 6 | no | — |
| 88 | D60 | — | 4 | 3 | no | — |
| 89 | D60 | — | 4 | 6 | no | — |
| 90 | C4×D15 | — | 4 | 6 | no | — |
| 91 | Dic30 | — | 4 | 1 | no | — |
| 92 | C5×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 93 | #1009 | — | 20 | 1 | no | — |
| 94 | 2−1+4⋊C3 | C2×D5 | 1 | 3 | yes | complemented |
| 95 | #994 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 96 | C2×#41⋊C3 | C2×D5 | 1 | 3 | yes | complemented |
| 97 | #986 | — | 5 | 3 | no | — |
| 98 | #986 | — | 5 | 6 | no | — |
| 99 | #985 | — | 5 | 6 | no | — |
| 100 | #984 | — | 5 | 1 | no | — |
| 101 | #983 | — | 5 | 6 | no | — |
| 102 | C2×GL(2,𝔽3) | — | 5 | 6 | no | — |
| 103 | C23×D5 | — | 6 | 3 | no | — |
| 104 | C5×#41 | — | 3 | 1 | no | — |
| 105 | C5×#41 | — | 3 | 3 | no | — |
| 106 | C5×#41 | — | 3 | 3 | no | — |
| 107 | C5×#41 | — | 3 | 3 | no | — |
| 108 | C5×#41 | — | 3 | 3 | no | — |
| 109 | C5×#41 | — | 3 | 6 | no | — |
| 110 | C5×#41 | — | 6 | 3 | no | — |
| 111 | C5×#41 | S4 | 1 | 1 | yes | characteristic |
| 112 | C5×#41 | C22×D3 | 1 | 3 | yes | — |
| 113 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 114 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 115 | C2×C5×Q8 | — | 3 | 3 | no | — |
| 116 | C2×C5×Q8 | C22×D3 | 1 | 3 | yes | — |
| 117 | C2×C5×D4 | — | 3 | 3 | no | — |
| 118 | C2×C5×D4 | — | 3 | 3 | no | — |
| 119 | C2×C5×D4 | — | 3 | 3 | no | — |
| 120 | C2×C5×D4 | — | 6 | 3 | no | — |
| 121 | C22×C4×C5 | — | 3 | 3 | no | — |
| 122 | C22×C4×C5 | — | 6 | 1 | no | — |
| 123 | C2×C22⋊D5 | — | 6 | 3 | no | — |
| 124 | #713 | — | 6 | 6 | no | — |
| 125 | #713 | — | 6 | 2 | no | — |
| 126 | D4×D5 | — | 6 | 12 | no | — |
| 127 | D4×D5 | — | 6 | 6 | no | — |
| 128 | D4×D5 | — | 6 | 6 | no | — |
| 129 | #709 | — | 3 | 6 | no | — |
| 130 | #709 | — | 3 | 6 | no | — |
| 131 | #709 | — | 6 | 3 | no | — |
| 132 | #709 | — | 6 | 3 | no | — |
| 133 | C2×D20 | — | 3 | 3 | no | — |
| 134 | C2×D20 | — | 3 | 6 | no | — |
| 135 | C2×D20 | — | 3 | 6 | no | — |
| 136 | C2×D20 | — | 6 | 3 | no | — |
| 137 | C2×D20 | — | 6 | 3 | no | — |
| 138 | C2×D20 | — | 6 | 3 | no | — |
| 139 | C2×C4×D5 | — | 6 | 3 | no | — |
| 140 | C2×Dic10 | — | 3 | 1 | no | — |
| 141 | #689 | — | 3 | 6 | no | — |
| 142 | #689 | — | 3 | 2 | no | — |
| 143 | #688 | — | 3 | 6 | no | — |
| 144 | #688 | — | 3 | 12 | no | — |
| 145 | #688 | — | 3 | 6 | no | — |
| 146 | #687 | — | 3 | 2 | no | — |
| 147 | #687 | — | 3 | 6 | no | — |
| 148 | #686 | — | 3 | 12 | no | — |
| 149 | #686 | — | 3 | 6 | no | — |
| 150 | #686 | — | 3 | 6 | no | — |
| 151 | #681 | — | 3 | 3 | no | — |
| 152 | #681 | — | 3 | 1 | no | — |
| 153 | #681 | — | 3 | 6 | no | — |
| 154 | #681 | — | 3 | 6 | no | — |
| 155 | C2×#168 | — | 3 | 6 | no | — |
| 156 | C2×#168 | — | 3 | 6 | no | — |
| 157 | #585 | D15 | 1 | 1 | yes | characteristic, complemented |
| 158 | C2×H(5,𝔽2) | — | 15 | 1 | no | — |
| 159 | #577 | — | 15 | 2 | no | — |
| 160 | #577 | — | 15 | 6 | no | — |
| 161 | #576 | — | 15 | 6 | no | — |
| 162 | #576 | — | 15 | 2 | no | — |
| 163 | #575 | — | 15 | 3 | no | — |
| 164 | #575 | — | 15 | 3 | no | — |
| 165 | C2×AGL(1,ℤ/8) | — | 15 | 3 | no | — |
| 166 | C2×AGL(1,ℤ/8) | — | 15 | 3 | no | — |
| 167 | #568 | — | 15 | 1 | no | — |
| 168 | C22×C3×C5 | — | 4 | 3 | no | — |
| 169 | C2×D15 | — | 4 | 6 | no | — |
| 170 | C2×D15 | — | 16 | 6 | no | — |
| 171 | C3×C4×C5 | — | 4 | 1 | no | — |
| 172 | C3×C4×C5 | — | 4 | 3 | no | — |
| 173 | Dic15 | — | 4 | 2 | no | — |
| 174 | C3×#41 | — | 4 | 1 | no | — |
| 175 | #239 | — | 20 | 2 | no | — |
| 176 | D3×D4 | — | 20 | 6 | no | — |
| 177 | #235 | — | 20 | 3 | no | — |
| 178 | C2×D12 | — | 20 | 3 | no | — |
| 179 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 180 | #41⋊C3 | C22×D5 | 1 | 3 | yes | complemented |
| 181 | C2×SL(2,𝔽3) | C22×D5 | 1 | 3 | yes | complemented |
| 182 | GL(2,𝔽3) | — | 5 | 6 | no | — |
| 183 | #226 | — | 5 | 2 | no | — |
| 184 | C23×C5 | — | 3 | 3 | no | — |
| 185 | C23×C5 | — | 6 | 1 | no | — |
| 186 | C22×D5 | — | 6 | 3 | no | — |
| 187 | C22×D5 | — | 6 | 6 | no | — |
| 188 | C22×D5 | — | 6 | 6 | no | — |
| 189 | C22×D5 | — | 24 | 6 | no | — |
| 190 | C5×Q8 | — | 3 | 3 | no | — |
| 191 | C5×Q8 | — | 3 | 3 | no | — |
| 192 | C5×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 193 | C5×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 194 | C5×D4 | — | 3 | 1 | no | — |
| 195 | C5×D4 | — | 3 | 3 | no | — |
| 196 | C5×D4 | — | 3 | 6 | no | — |
| 197 | C5×D4 | — | 3 | 3 | no | — |
| 198 | C5×D4 | — | 6 | 3 | no | — |
| 199 | C5×D4 | C2×S4 | 1 | 3 | yes | — |
| 200 | C2×C4×C5 | — | 3 | 3 | no | — |
| 201 | C2×C4×C5 | — | 3 | 3 | no | — |
| 202 | C2×C4×C5 | — | 3 | 1 | no | — |
| 203 | C2×C4×C5 | — | 3 | 3 | no | — |
| 204 | C2×C4×C5 | — | 3 | 3 | no | — |
| 205 | C2×C4×C5 | — | 6 | 3 | no | — |
| 206 | C2×C4×C5 | C2×S4 | 1 | 3 | yes | — |
| 207 | C22⋊D5 | — | 6 | 6 | no | — |
| 208 | C22⋊D5 | — | 6 | 6 | no | — |
| 209 | C2×Dic5 | — | 6 | 1 | no | — |
| 210 | D20 | — | 3 | 6 | no | — |
| 211 | D20 | — | 6 | 6 | no | — |
| 212 | D20 | — | 6 | 3 | no | — |
| 213 | D20 | — | 6 | 6 | no | — |
| 214 | C4×D5 | — | 6 | 6 | no | — |
| 215 | C4×D5 | — | 6 | 6 | no | — |
| 216 | Dic10 | — | 3 | 2 | no | — |
| 217 | Dic10 | — | 6 | 1 | no | — |
| 218 | #168 | — | 3 | 2 | no | — |
| 219 | #168 | — | 3 | 6 | no | — |
| 220 | 2−1+4 | — | 3 | 1 | no | — |
| 221 | 2−1+4 | C2×D15 | 1 | 3 | yes | complemented |
| 222 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 223 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 224 | H(5,𝔽2) | — | 15 | 6 | no | — |
| 225 | H(5,𝔽2) | — | 30 | 3 | no | — |
| 226 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 227 | H(5,𝔽2) | C2×D15 | 1 | 1 | yes | characteristic, complemented |
| 228 | C2×#41 | — | 3 | 1 | no | — |
| 229 | C2×#41 | — | 3 | 3 | no | — |
| 230 | C2×#41 | — | 15 | 3 | no | — |
| 231 | C2×#41 | — | 30 | 1 | no | — |
| 232 | C2×#41 | C2×D15 | 1 | 3 | yes | complemented |
| 233 | C22×D4 | — | 15 | 3 | no | — |
| 234 | C22×D4 | — | 30 | 3 | no | — |
| 235 | #137 | — | 15 | 6 | no | — |
| 236 | #137 | — | 15 | 3 | no | — |
| 237 | #137 | — | 15 | 1 | no | — |
| 238 | #137 | — | 15 | 6 | no | — |
| 239 | AGL(1,ℤ/8) | — | 15 | 6 | no | — |
| 240 | AGL(1,ℤ/8) | — | 15 | 6 | no | — |
| 241 | AGL(1,ℤ/8) | — | 15 | 3 | no | — |
| 242 | AGL(1,ℤ/8) | — | 15 | 6 | no | — |
| 243 | AGL(1,ℤ/8) | — | 15 | 6 | no | — |
| 244 | AGL(1,ℤ/8) | — | 15 | 12 | no | — |
| 245 | AGL(1,ℤ/8) | — | 15 | 3 | no | — |
| 246 | AGL(1,ℤ/8) | — | 15 | 6 | no | — |
| 247 | #135 | — | 15 | 6 | no | — |
| 248 | #135 | — | 15 | 12 | no | — |
| 249 | #135 | — | 15 | 6 | no | — |
| 250 | C2×SD16 | — | 15 | 6 | no | — |
| 251 | C2×SD16 | — | 15 | 6 | no | — |
| 252 | C2×D8 | — | 15 | 6 | no | — |
| 253 | C2×D8 | — | 15 | 6 | no | — |
| 254 | #131 | — | 15 | 2 | no | — |
| 255 | #131 | — | 15 | 6 | no | — |
| 256 | C2×M16 | — | 15 | 3 | no | — |
| 257 | C2×M16 | — | 15 | 3 | no | — |
| 258 | C2×C3×C5 | — | 4 | 1 | no | — |
| 259 | C2×C3×C5 | — | 8 | 3 | no | — |
| 260 | D15 | — | 8 | 6 | no | — |
| 261 | C22×D3 | — | 20 | 6 | no | — |
| 262 | C3×Q8 | — | 4 | 1 | no | — |
| 263 | C3×D4 | — | 4 | 3 | no | — |
| 264 | C2×C3×C4 | — | 4 | 3 | no | — |
| 265 | #67 | — | 20 | 6 | no | — |
| 266 | D12 | — | 20 | 3 | no | — |
| 267 | D12 | — | 20 | 6 | no | — |
| 268 | C4×D3 | — | 20 | 6 | no | — |
| 269 | Dic6 | — | 20 | 1 | no | — |
| 270 | SL(2,𝔽3) | C23×D5 | 1 | 1 | yes | characteristic |
| 271 | C22×C5 | — | 3 | 1 | no | — |
| 272 | C22×C5 | — | 3 | 3 | no | — |
| 273 | C22×C5 | — | 12 | 3 | no | — |
| 274 | C22×C5 | — | 24 | 1 | no | — |
| 275 | C22×C5 | C22×S4 | 1 | 3 | yes | — |
| 276 | C2×D5 | — | 6 | 6 | no | — |
| 277 | C2×D5 | — | 12 | 6 | no | — |
| 278 | C2×D5 | — | 24 | 6 | no | — |
| 279 | C2×D5 | — | 24 | 6 | no | — |
| 280 | C4×C5 | — | 3 | 1 | no | — |
| 281 | C4×C5 | — | 3 | 3 | no | — |
| 282 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 283 | C4×C5 | C22×S4 | 1 | 3 | yes | — |
| 284 | Dic5 | — | 6 | 2 | no | — |
| 285 | C24 | — | 30 | 3 | no | — |
| 286 | #41 | — | 3 | 1 | no | — |
| 287 | #41 | — | 3 | 3 | no | — |
| 288 | #41 | — | 3 | 3 | no | — |
| 289 | #41 | — | 3 | 3 | no | — |
| 290 | #41 | — | 3 | 3 | no | — |
| 291 | #41 | — | 3 | 6 | no | — |
| 292 | #41 | — | 6 | 3 | no | — |
| 293 | #41 | — | 15 | 6 | no | — |
| 294 | #41 | — | 15 | 6 | no | — |
| 295 | #41 | — | 30 | 3 | no | — |
| 296 | #41 | — | 30 | 6 | no | — |
| 297 | #41 | — | 30 | 2 | no | — |
| 298 | #41 | — | 30 | 3 | no | — |
| 299 | #41 | C5⋊S4 | 1 | 1 | yes | characteristic |
| 300 | #41 | C22×D15 | 1 | 3 | yes | — |
| 301 | #41 | C22×D15 | 1 | 1 | yes | characteristic |
| 302 | C2×Q8 | — | 3 | 1 | no | — |
| 303 | C2×Q8 | — | 3 | 3 | no | — |
| 304 | C2×Q8 | — | 15 | 1 | no | — |
| 305 | C2×Q8 | C22×D15 | 1 | 3 | yes | — |
| 306 | C2×D4 | — | 3 | 3 | no | — |
| 307 | C2×D4 | — | 3 | 3 | no | — |
| 308 | C2×D4 | — | 3 | 3 | no | — |
| 309 | C2×D4 | — | 6 | 3 | no | — |
| 310 | C2×D4 | — | 15 | 6 | no | — |
| 311 | C2×D4 | — | 15 | 6 | no | — |
| 312 | C2×D4 | — | 15 | 3 | no | — |
| 313 | C2×D4 | — | 30 | 3 | no | — |
| 314 | C2×D4 | — | 30 | 3 | no | — |
| 315 | C2×D4 | — | 30 | 12 | no | — |
| 316 | C2×D4 | — | 30 | 6 | no | — |
| 317 | C2×D4 | — | 30 | 3 | no | — |
| 318 | C2×D4 | — | 30 | 6 | no | — |
| 319 | C2×D4 | — | 30 | 3 | no | — |
| 320 | C22×C4 | — | 3 | 3 | no | — |
| 321 | C22×C4 | — | 6 | 1 | no | — |
| 322 | C22×C4 | — | 30 | 3 | no | — |
| 323 | Q16 | — | 15 | 6 | no | — |
| 324 | Q16 | — | 15 | 2 | no | — |
| 325 | SD16 | — | 15 | 2 | no | — |
| 326 | SD16 | — | 15 | 6 | no | — |
| 327 | SD16 | — | 15 | 6 | no | — |
| 328 | SD16 | — | 15 | 12 | no | — |
| 329 | SD16 | — | 15 | 6 | no | — |
| 330 | D8 | — | 15 | 12 | no | — |
| 331 | D8 | — | 15 | 6 | no | — |
| 332 | D8 | — | 15 | 6 | no | — |
| 333 | M16 | — | 15 | 1 | no | — |
| 334 | M16 | — | 15 | 3 | no | — |
| 335 | M16 | — | 15 | 6 | no | — |
| 336 | M16 | — | 15 | 6 | no | — |
| 337 | C2×C8 | — | 15 | 6 | no | — |
| 338 | C2×C8 | — | 15 | 6 | no | — |
| 339 | C3×C5 | — | 4 | 1 | no | Hall |
| 340 | C22×C3 | — | 4 | 3 | no | — |
| 341 | C2×D3 | — | 20 | 6 | no | — |
| 342 | C2×D3 | — | 80 | 6 | no | — |
| 343 | C3×C4 | — | 4 | 1 | no | — |
| 344 | C3×C4 | — | 4 | 3 | no | — |
| 345 | Dic3 | — | 20 | 2 | no | — |
| 346 | C2×C5 | — | 2 | 3 | no | — |
| 347 | C2×C5 | — | 6 | 1 | no | — |
| 348 | C2×C5 | — | 6 | 3 | no | — |
| 349 | C2×C5 | C23×S4 | 1 | 1 | yes | characteristic |
| 350 | D5 | — | 12 | 6 | no | — |
| 351 | C23 | — | 3 | 3 | no | — |
| 352 | C23 | — | 6 | 1 | no | — |
| 353 | C23 | — | 30 | 3 | no | — |
| 354 | C23 | — | 30 | 6 | no | — |
| 355 | C23 | — | 30 | 6 | no | — |
| 356 | C23 | — | 120 | 6 | no | — |
| 357 | Q8 | — | 3 | 3 | no | — |
| 358 | Q8 | — | 3 | 3 | no | — |
| 359 | Q8 | — | 15 | 2 | no | — |
| 360 | Q8 | — | 30 | 1 | no | — |
| 361 | Q8 | C2×C5⋊S4 | 1 | 1 | yes | characteristic |
| 362 | Q8 | C23×D15 | 1 | 1 | yes | characteristic |
| 363 | D4 | — | 3 | 1 | no | — |
| 364 | D4 | — | 3 | 3 | no | — |
| 365 | D4 | — | 3 | 6 | no | — |
| 366 | D4 | — | 3 | 3 | no | — |
| 367 | D4 | — | 6 | 3 | no | — |
| 368 | D4 | — | 15 | 6 | no | — |
| 369 | D4 | — | 30 | 6 | no | — |
| 370 | D4 | — | 30 | 6 | no | — |
| 371 | D4 | — | 30 | 6 | no | — |
| 372 | D4 | — | 30 | 3 | no | — |
| 373 | D4 | — | 30 | 6 | no | — |
| 374 | D4 | C2×C5⋊S4 | 1 | 3 | yes | — |
| 375 | C2×C4 | — | 3 | 3 | no | — |
| 376 | C2×C4 | — | 3 | 3 | no | — |
| 377 | C2×C4 | — | 3 | 1 | no | — |
| 378 | C2×C4 | — | 3 | 3 | no | — |
| 379 | C2×C4 | — | 3 | 3 | no | — |
| 380 | C2×C4 | — | 6 | 3 | no | — |
| 381 | C2×C4 | — | 30 | 6 | no | — |
| 382 | C2×C4 | — | 30 | 1 | no | — |
| 383 | C2×C4 | — | 30 | 6 | no | — |
| 384 | C2×C4 | C2×C5⋊S4 | 1 | 3 | yes | — |
| 385 | C8 | — | 15 | 2 | no | — |
| 386 | C8 | — | 15 | 6 | no | — |
| 387 | C2×C3 | — | 4 | 1 | no | — |
| 388 | C2×C3 | — | 8 | 3 | no | — |
| 389 | D3 | — | 40 | 6 | no | — |
| 390 | C5 | #87498 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 391 | C22 | — | 3 | 1 | no | — |
| 392 | C22 | — | 3 | 3 | no | — |
| 393 | C22 | — | 12 | 3 | no | — |
| 394 | C22 | — | 24 | 1 | no | — |
| 395 | C22 | — | 30 | 6 | no | — |
| 396 | C22 | — | 60 | 6 | no | — |
| 397 | C22 | — | 120 | 6 | no | — |
| 398 | C22 | — | 120 | 6 | no | — |
| 399 | C22 | C22×C5⋊S4 | 1 | 3 | yes | — |
| 400 | C4 | — | 3 | 1 | no | — |
| 401 | C4 | — | 3 | 3 | no | — |
| 402 | C4 | — | 30 | 2 | no | — |
| 403 | C4 | C22×C5⋊S4 | 1 | 1 | yes | characteristic |
| 404 | C4 | C22×C5⋊S4 | 1 | 3 | yes | — |
| 405 | C3 | — | 4 | 1 | no | Sylow |
| 406 | C2 | — | 2 | 3 | no | — |
| 407 | C2 | — | 6 | 1 | no | — |
| 408 | C2 | — | 6 | 3 | no | — |
| 409 | C2 | — | 60 | 6 | no | — |
| 410 | C2 | C23×C5⋊S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×C5⋊S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C24 |
| Fitting | C5×#585 | D3 |
| socle | C2×C5 | C23×S4 |
| hypercenter | #41 | C5⋊S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#5945 | C2 | semidirect |
| 2. #11756910 | C2 | semidirect |
| 3. #11756909 | C2 | semidirect |
| 4. #11756907 | C2 | semidirect |
| 5. C2×#91956 | C2 | semidirect |
| 8. C5×2−1+4⋊C3 | C22 | semidirect |
| 9. C5×#994 | C22 | semidirect |
| 10. C2×C5×#41⋊C3 | C22 | semidirect |
| 11. #91956 | C22 | semidirect |
| 12. #91956 | C22 | semidirect |
| 13. #91955 | C22 | semidirect |
| 14. #91954 | C22 | semidirect |
| 15. #91953 | C22 | semidirect |
| 16. C2×C5⋊GL(2,𝔽3) | C22 | semidirect |
| 18. C5×#585 | D3 | semidirect |
| 35. C5×#41⋊C3 | C23 | semidirect |
| 36. C2×C5×SL(2,𝔽3) | C23 | semidirect |
| 37. C5⋊GL(2,𝔽3) | C23 | semidirect |
| 38. C5⋊#226 | C23 | semidirect |
| 39. #5945 | D5 | semidirect |
| 45. C5×2−1+4 | C2×D3 | semidirect |
| 47. C5×H(5,𝔽2) | C2×D3 | semidirect |
| 50. C2×C5×#41 | C2×D3 | semidirect |
| 94. 2−1+4⋊C3 | C2×D5 | semidirect |
| 95. #994 | C2×D5 | semidirect |
| 96. C2×#41⋊C3 | C2×D5 | semidirect |
| 157. #585 | D15 | semidirect |
| 180. #41⋊C3 | C22×D5 | semidirect |
| 181. C2×SL(2,𝔽3) | C22×D5 | semidirect |
| 221. 2−1+4 | C2×D15 | semidirect |
| 227. H(5,𝔽2) | C2×D15 | semidirect |
| 232. C2×#41 | C2×D15 | semidirect |
| 390. C5 | #87498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5945 | 2 |
| #11756910 | 2 |
| #11756909 | 2 |
| #11756907 | 2 |
| C2×#91956 | 2 |
| #10619199 | 3 |
| #92100 | 4 |
| #87498 | 5 |