Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 71 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×#5923 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #66153⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#91185 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11751617 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11751615 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10615731 | — | 3 | 1 | no | maximal, Hall |
| 7 | C2×C5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 8 | C5×#986 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C5×#985 | C22 | 1 | 2 | yes | — |
| 10 | C5×#984 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×#983 | C4 | 1 | 2 | yes | complemented |
| 12 | #91288 | — | 4 | 1 | no | maximal |
| 13 | #4094⋊C3 | C22 | 1 | 2 | yes | complemented |
| 14 | #91185 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #91185 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #85453 | — | 5 | 1 | no | maximal, Hall |
| 17 | C5×#575 | — | 3 | 1 | no | — |
| 18 | #66153 | — | 3 | 1 | no | — |
| 19 | #66153 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×#3969 | — | 3 | 1 | no | — |
| 21 | C2×#3969 | — | 3 | 1 | no | — |
| 22 | #65486 | — | 3 | 2 | no | — |
| 23 | #65486 | — | 3 | 2 | no | — |
| 24 | #65485 | — | 3 | 2 | no | — |
| 25 | #65485 | — | 3 | 2 | no | — |
| 26 | #65414 | — | 3 | 1 | no | — |
| 27 | M16×Dic5 | — | 3 | 1 | no | — |
| 28 | C5×#235 | — | 4 | 1 | no | — |
| 29 | C5×#41⋊C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 31 | C2×C5×SL(2,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C5×GL(2,𝔽3) | C2×C4 | 1 | 2 | yes | complemented |
| 33 | C5×#226 | C2×C4 | 1 | 2 | yes | complemented |
| 34 | C2×C3⋊#168 | — | 4 | 1 | no | — |
| 35 | C3×#681 | — | 4 | 1 | no | — |
| 36 | #6650 | — | 4 | 2 | no | — |
| 37 | D3×#168 | — | 4 | 2 | no | — |
| 38 | #5923 | D5 | 1 | 1 | yes | characteristic |
| 39 | #568⋊C3 | — | 5 | 1 | no | — |
| 40 | C2×GU(2,𝔽3) | — | 5 | 1 | no | — |
| 41 | #5405 | — | 5 | 2 | no | — |
| 42 | #5404 | — | 5 | 2 | no | — |
| 43 | C2×C5×#41 | — | 3 | 1 | no | — |
| 44 | C2×C5×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 45 | C5×#137 | — | 3 | 1 | no | — |
| 46 | C5×#137 | — | 3 | 1 | no | — |
| 47 | C5×#137 | — | 3 | 2 | no | — |
| 48 | C5×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 49 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 50 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 51 | C5×#135 | — | 3 | 2 | no | — |
| 52 | C5×#135 | — | 3 | 2 | no | — |
| 53 | C2×C5×M16 | — | 3 | 1 | no | — |
| 54 | #4094 | — | 3 | 2 | no | — |
| 55 | #4094 | — | 3 | 2 | no | — |
| 56 | #4094 | — | 3 | 2 | no | — |
| 57 | #4094 | — | 6 | 1 | no | — |
| 58 | #4094 | — | 6 | 1 | no | — |
| 59 | #4094 | C2×D3 | 1 | 2 | yes | — |
| 60 | C2×C4×Dic5 | — | 3 | 1 | no | — |
| 61 | C2×#681 | — | 3 | 1 | no | — |
| 62 | C2×#681 | — | 3 | 1 | no | — |
| 63 | C2×#681 | — | 3 | 1 | no | — |
| 64 | C2×#681 | — | 6 | 2 | no | — |
| 65 | #3969 | — | 3 | 2 | no | — |
| 66 | #3969 | — | 3 | 1 | no | — |
| 67 | #3969 | — | 3 | 2 | no | — |
| 68 | #3969 | — | 3 | 1 | no | — |
| 69 | #3969 | — | 3 | 1 | no | — |
| 70 | #3969 | — | 3 | 1 | no | — |
| 71 | #3951 | — | 3 | 2 | no | — |
| 72 | #3951 | — | 3 | 2 | no | — |
| 73 | #3947 | — | 3 | 2 | no | — |
| 74 | C8×Dic5 | — | 3 | 2 | no | — |
| 75 | #2956 | — | 15 | 1 | no | Sylow |
| 76 | C2×C3×C4×C5 | — | 4 | 1 | no | — |
| 77 | C5×#67 | — | 4 | 2 | no | — |
| 78 | C5×D12 | — | 4 | 1 | no | — |
| 79 | C4×C5×D3 | — | 4 | 2 | no | — |
| 80 | C5×Dic6 | — | 4 | 1 | no | — |
| 81 | C5×SL(2,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 82 | C3⋊#168 | — | 4 | 1 | no | — |
| 83 | C3⋊#168 | — | 4 | 1 | no | — |
| 84 | C3×#168 | — | 4 | 2 | no | — |
| 85 | C2×#41⋊C3 | C2×D5 | 1 | 1 | yes | characteristic |
| 86 | #986 | Dic5 | 1 | 1 | yes | characteristic, complemented |
| 87 | #985 | C2×D5 | 1 | 2 | yes | — |
| 88 | #984 | Dic5 | 1 | 1 | yes | characteristic, complemented |
| 89 | #983 | Dic5 | 1 | 2 | yes | complemented |
| 90 | #907 | — | 20 | 1 | no | — |
| 91 | #131⋊C3 | — | 5 | 2 | no | — |
| 92 | GU(2,𝔽3) | — | 5 | 1 | no | — |
| 93 | GU(2,𝔽3) | — | 5 | 1 | no | — |
| 94 | C5×#41 | — | 3 | 1 | no | — |
| 95 | C5×#41 | — | 3 | 1 | no | — |
| 96 | C5×#41 | — | 3 | 2 | no | — |
| 97 | C5×#41 | — | 3 | 2 | no | — |
| 98 | C5×#41 | — | 6 | 1 | no | — |
| 99 | C5×#41 | — | 6 | 1 | no | — |
| 100 | C5×#41 | C4×D3 | 1 | 1 | yes | characteristic |
| 101 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 102 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 103 | C2×C5×Q8 | C4×D3 | 1 | 1 | yes | characteristic |
| 104 | C2×C5×D4 | — | 3 | 1 | no | — |
| 105 | C2×C5×D4 | — | 3 | 1 | no | — |
| 106 | C2×C5×D4 | — | 6 | 1 | no | — |
| 107 | C22×C4×C5 | — | 3 | 1 | no | — |
| 108 | C22×C4×C5 | — | 6 | 1 | no | — |
| 109 | C22×Dic5 | — | 6 | 1 | no | — |
| 110 | C5×Q16 | — | 3 | 2 | no | — |
| 111 | C5×Q16 | — | 3 | 2 | no | — |
| 112 | C5×SD16 | — | 3 | 2 | no | — |
| 113 | C5×SD16 | — | 3 | 2 | no | — |
| 114 | C5×SD16 | — | 3 | 2 | no | — |
| 115 | C5×SD16 | — | 3 | 2 | no | — |
| 116 | C5×D8 | — | 3 | 2 | no | — |
| 117 | C5×D8 | — | 3 | 2 | no | — |
| 118 | C5×M16 | — | 3 | 2 | no | — |
| 119 | C5×M16 | — | 3 | 1 | no | — |
| 120 | C5×M16 | — | 3 | 1 | no | — |
| 121 | C2×C5×C8 | — | 3 | 2 | no | — |
| 122 | C4×Dic5 | — | 3 | 1 | no | — |
| 123 | C4×Dic5 | — | 3 | 1 | no | — |
| 124 | C4×Dic5 | — | 6 | 1 | no | — |
| 125 | #681 | — | 3 | 1 | no | — |
| 126 | #681 | — | 3 | 2 | no | — |
| 127 | #681 | — | 3 | 2 | no | — |
| 128 | #681 | — | 3 | 1 | no | — |
| 129 | #681 | — | 3 | 1 | no | — |
| 130 | #681 | — | 6 | 2 | no | — |
| 131 | #681 | — | 6 | 1 | no | — |
| 132 | #681 | — | 6 | 2 | no | — |
| 133 | #681 | S4 | 1 | 1 | yes | characteristic |
| 134 | C2×#168 | — | 3 | 2 | no | — |
| 135 | C2×#168 | — | 6 | 1 | no | — |
| 136 | C2×#168 | — | 6 | 2 | no | — |
| 137 | C2×#168 | — | 6 | 1 | no | — |
| 138 | C2×#168 | — | 6 | 2 | no | — |
| 139 | #575 | — | 3 | 1 | no | — |
| 140 | #568 | — | 5 | 1 | no | — |
| 141 | #568 | — | 15 | 1 | no | — |
| 142 | #444 | — | 15 | 2 | no | — |
| 143 | #444 | — | 15 | 2 | no | — |
| 144 | #443 | — | 15 | 2 | no | — |
| 145 | #443 | — | 15 | 2 | no | — |
| 146 | #430 | — | 15 | 1 | no | — |
| 147 | C2×#104 | — | 15 | 1 | no | — |
| 148 | C2×#104 | — | 15 | 1 | no | — |
| 149 | C4×M16 | — | 15 | 1 | no | — |
| 150 | C22×C3×C5 | — | 4 | 1 | no | — |
| 151 | C2×C5×D3 | — | 4 | 2 | no | — |
| 152 | C3×C4×C5 | — | 4 | 1 | no | — |
| 153 | C3×C4×C5 | — | 4 | 1 | no | — |
| 154 | C5×Dic3 | — | 4 | 2 | no | — |
| 155 | #235 | — | 4 | 1 | no | — |
| 156 | #41⋊C3 | C2×Dic5 | 1 | 1 | yes | characteristic |
| 157 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 158 | C2×SL(2,𝔽3) | C2×Dic5 | 1 | 1 | yes | characteristic |
| 159 | GL(2,𝔽3) | C2×Dic5 | 1 | 2 | yes | complemented |
| 160 | #226 | C2×Dic5 | 1 | 2 | yes | complemented |
| 161 | C3×M16 | — | 20 | 1 | no | — |
| 162 | C2×C3⋊C8 | — | 20 | 1 | no | — |
| 163 | ΓL(1,𝔽25) | — | 20 | 2 | no | — |
| 164 | D3×C8 | — | 20 | 2 | no | — |
| 165 | C23×C5 | — | 3 | 1 | no | — |
| 166 | C23×C5 | — | 6 | 1 | no | — |
| 167 | C5×Q8 | — | 3 | 1 | no | — |
| 168 | C5×Q8 | — | 3 | 2 | no | — |
| 169 | C5×Q8 | — | 6 | 1 | no | — |
| 170 | C5×Q8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 171 | C5×D4 | — | 3 | 1 | no | — |
| 172 | C5×D4 | — | 3 | 1 | no | — |
| 173 | C5×D4 | — | 3 | 2 | no | — |
| 174 | C5×D4 | — | 6 | 1 | no | — |
| 175 | C5×D4 | — | 6 | 2 | no | — |
| 176 | C5×D4 | — | 6 | 2 | no | — |
| 177 | C5×D4 | — | 6 | 1 | no | — |
| 178 | C2×C4×C5 | — | 3 | 1 | no | — |
| 179 | C2×C4×C5 | — | 3 | 1 | no | — |
| 180 | C2×C4×C5 | — | 3 | 1 | no | — |
| 181 | C2×C4×C5 | — | 3 | 1 | no | — |
| 182 | C2×C4×C5 | — | 3 | 1 | no | — |
| 183 | C2×C4×C5 | — | 6 | 2 | no | — |
| 184 | C2×C4×C5 | — | 6 | 1 | no | — |
| 185 | C2×C4×C5 | — | 6 | 2 | no | — |
| 186 | C2×C4×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 187 | C2×Dic5 | — | 6 | 1 | no | — |
| 188 | C2×Dic5 | — | 6 | 1 | no | — |
| 189 | C2×Dic5 | — | 12 | 2 | no | — |
| 190 | C5×C8 | — | 3 | 2 | no | — |
| 191 | C5×C8 | — | 3 | 2 | no | — |
| 192 | #168 | — | 3 | 2 | no | — |
| 193 | #168 | — | 6 | 1 | no | — |
| 194 | #168 | — | 6 | 1 | no | — |
| 195 | #168 | C2×S4 | 1 | 2 | yes | — |
| 196 | C2×#41 | — | 3 | 1 | no | — |
| 197 | C2×#41 | D3×D5 | 1 | 1 | yes | characteristic |
| 198 | #137 | — | 3 | 1 | no | — |
| 199 | #137 | — | 3 | 1 | no | — |
| 200 | #137 | — | 3 | 2 | no | — |
| 201 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 202 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 203 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 204 | #135 | — | 3 | 2 | no | — |
| 205 | #135 | — | 3 | 2 | no | — |
| 206 | #131 | — | 5 | 2 | no | — |
| 207 | #131 | — | 15 | 2 | no | — |
| 208 | #131 | — | 15 | 2 | no | — |
| 209 | #131 | — | 15 | 2 | no | — |
| 210 | #131 | — | 30 | 1 | no | — |
| 211 | #131 | — | 30 | 1 | no | — |
| 212 | C2×M16 | — | 3 | 1 | no | — |
| 213 | C2×M16 | — | 15 | 1 | no | — |
| 214 | C2×M16 | — | 15 | 1 | no | — |
| 215 | C2×M16 | — | 15 | 1 | no | — |
| 216 | C2×M16 | — | 30 | 2 | no | — |
| 217 | C2×C42 | — | 15 | 1 | no | — |
| 218 | #108 | — | 15 | 2 | no | — |
| 219 | #108 | — | 15 | 2 | no | — |
| 220 | #104 | — | 15 | 2 | no | — |
| 221 | #104 | — | 15 | 1 | no | — |
| 222 | #104 | — | 15 | 2 | no | — |
| 223 | #104 | — | 15 | 1 | no | — |
| 224 | #104 | — | 15 | 1 | no | — |
| 225 | #104 | — | 15 | 1 | no | — |
| 226 | #97 | — | 15 | 2 | no | — |
| 227 | C4×C8 | — | 15 | 2 | no | — |
| 228 | C2×C3×C5 | — | 4 | 1 | no | — |
| 229 | C2×C3×C5 | — | 8 | 1 | no | — |
| 230 | C5×D3 | — | 8 | 2 | no | — |
| 231 | C2×C3×C4 | — | 4 | 1 | no | — |
| 232 | #67 | — | 4 | 2 | no | — |
| 233 | D12 | — | 4 | 1 | no | — |
| 234 | C4×D3 | — | 4 | 2 | no | — |
| 235 | Dic6 | — | 4 | 1 | no | — |
| 236 | SL(2,𝔽3) | C22×Dic5 | 1 | 1 | yes | characteristic |
| 237 | C3×C8 | — | 20 | 2 | no | — |
| 238 | C3⋊C8 | — | 20 | 1 | no | — |
| 239 | C3⋊C8 | — | 20 | 1 | no | — |
| 240 | C22×C5 | — | 3 | 1 | no | — |
| 241 | C22×C5 | — | 3 | 1 | no | — |
| 242 | C22×C5 | — | 6 | 2 | no | — |
| 243 | C22×C5 | — | 12 | 1 | no | — |
| 244 | C22×C5 | — | 24 | 1 | no | — |
| 245 | C22×C5 | C4×S4 | 1 | 1 | yes | characteristic |
| 246 | C4×C5 | — | 3 | 1 | no | — |
| 247 | C4×C5 | — | 3 | 1 | no | — |
| 248 | C4×C5 | — | 6 | 2 | no | — |
| 249 | C4×C5 | C4×S4 | 1 | 1 | yes | characteristic |
| 250 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 251 | Dic5 | — | 6 | 2 | no | — |
| 252 | Dic5 | — | 12 | 1 | no | — |
| 253 | #41 | — | 3 | 1 | no | — |
| 254 | #41 | — | 3 | 1 | no | — |
| 255 | #41 | — | 3 | 2 | no | — |
| 256 | #41 | — | 3 | 2 | no | — |
| 257 | #41 | — | 6 | 1 | no | — |
| 258 | #41 | — | 6 | 1 | no | — |
| 259 | #41 | D3×Dic5 | 1 | 1 | yes | characteristic |
| 260 | #41 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 261 | C2×Q8 | — | 3 | 1 | no | — |
| 262 | C2×Q8 | D3×Dic5 | 1 | 1 | yes | characteristic |
| 263 | C2×D4 | — | 3 | 1 | no | — |
| 264 | C2×D4 | — | 3 | 1 | no | — |
| 265 | C2×D4 | — | 6 | 1 | no | — |
| 266 | C22×C4 | — | 3 | 1 | no | — |
| 267 | C22×C4 | — | 6 | 1 | no | — |
| 268 | C22×C4 | — | 30 | 1 | no | — |
| 269 | Q16 | — | 3 | 2 | no | — |
| 270 | Q16 | — | 3 | 2 | no | — |
| 271 | SD16 | — | 3 | 2 | no | — |
| 272 | SD16 | — | 3 | 2 | no | — |
| 273 | SD16 | — | 3 | 2 | no | — |
| 274 | SD16 | — | 3 | 2 | no | — |
| 275 | D8 | — | 3 | 2 | no | — |
| 276 | D8 | — | 3 | 2 | no | — |
| 277 | M16 | — | 3 | 2 | no | — |
| 278 | M16 | — | 3 | 1 | no | — |
| 279 | M16 | — | 3 | 1 | no | — |
| 280 | M16 | — | 5 | 1 | no | — |
| 281 | M16 | — | 15 | 2 | no | — |
| 282 | M16 | — | 15 | 1 | no | — |
| 283 | M16 | — | 15 | 2 | no | — |
| 284 | M16 | — | 15 | 1 | no | — |
| 285 | M16 | — | 15 | 1 | no | — |
| 286 | M16 | — | 30 | 2 | no | — |
| 287 | M16 | — | 30 | 2 | no | — |
| 288 | M16 | — | 30 | 1 | no | — |
| 289 | C2×C8 | — | 3 | 2 | no | — |
| 290 | C2×C8 | — | 15 | 2 | no | — |
| 291 | C2×C8 | — | 30 | 2 | no | — |
| 292 | C2×C8 | — | 30 | 1 | no | — |
| 293 | C2×C8 | — | 30 | 2 | no | — |
| 294 | C2×C8 | — | 30 | 1 | no | — |
| 295 | C42 | — | 15 | 1 | no | — |
| 296 | C42 | — | 15 | 1 | no | — |
| 297 | C42 | — | 30 | 1 | no | — |
| 298 | C3×C5 | — | 4 | 1 | no | Hall |
| 299 | C22×C3 | — | 4 | 1 | no | — |
| 300 | C2×D3 | — | 4 | 2 | no | — |
| 301 | C3×C4 | — | 4 | 1 | no | — |
| 302 | C3×C4 | — | 4 | 1 | no | — |
| 303 | Dic3 | — | 4 | 2 | no | — |
| 304 | C2×C5 | — | 2 | 1 | no | — |
| 305 | C2×C5 | — | 6 | 1 | no | — |
| 306 | C2×C5 | — | 6 | 1 | no | — |
| 307 | C2×C5 | — | 12 | 2 | no | — |
| 308 | C2×C5 | C2×C4×S4 | 1 | 1 | yes | characteristic |
| 309 | C23 | — | 3 | 1 | no | — |
| 310 | C23 | — | 6 | 1 | no | — |
| 311 | Q8 | — | 3 | 1 | no | — |
| 312 | Q8 | — | 3 | 2 | no | — |
| 313 | Q8 | — | 6 | 1 | no | — |
| 314 | Q8 | C2×D3×Dic5 | 1 | 1 | yes | characteristic |
| 315 | D4 | — | 3 | 1 | no | — |
| 316 | D4 | — | 3 | 1 | no | — |
| 317 | D4 | — | 3 | 2 | no | — |
| 318 | D4 | — | 6 | 1 | no | — |
| 319 | D4 | — | 6 | 2 | no | — |
| 320 | D4 | — | 6 | 2 | no | — |
| 321 | D4 | — | 6 | 1 | no | — |
| 322 | C2×C4 | — | 3 | 1 | no | — |
| 323 | C2×C4 | — | 3 | 1 | no | — |
| 324 | C2×C4 | — | 3 | 1 | no | — |
| 325 | C2×C4 | — | 3 | 1 | no | — |
| 326 | C2×C4 | — | 3 | 1 | no | — |
| 327 | C2×C4 | — | 6 | 2 | no | — |
| 328 | C2×C4 | — | 6 | 1 | no | — |
| 329 | C2×C4 | — | 6 | 2 | no | — |
| 330 | C2×C4 | — | 30 | 1 | no | — |
| 331 | C2×C4 | — | 30 | 1 | no | — |
| 332 | C2×C4 | — | 60 | 2 | no | — |
| 333 | C2×C4 | D5×S4 | 1 | 1 | yes | characteristic |
| 334 | C8 | — | 3 | 2 | no | — |
| 335 | C8 | — | 3 | 2 | no | — |
| 336 | C8 | — | 5 | 2 | no | — |
| 337 | C8 | — | 15 | 2 | no | — |
| 338 | C8 | — | 30 | 1 | no | — |
| 339 | C8 | — | 30 | 1 | no | — |
| 340 | C2×C3 | — | 4 | 1 | no | — |
| 341 | C2×C3 | — | 8 | 1 | no | — |
| 342 | D3 | — | 8 | 2 | no | — |
| 343 | C5 | #85453 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 344 | C22 | — | 3 | 1 | no | — |
| 345 | C22 | — | 3 | 1 | no | — |
| 346 | C22 | — | 6 | 2 | no | — |
| 347 | C22 | — | 12 | 1 | no | — |
| 348 | C22 | — | 24 | 1 | no | — |
| 349 | C22 | Dic5×S4 | 1 | 1 | yes | characteristic |
| 350 | C4 | — | 3 | 1 | no | — |
| 351 | C4 | — | 3 | 1 | no | — |
| 352 | C4 | — | 6 | 2 | no | — |
| 353 | C4 | — | 30 | 2 | no | — |
| 354 | C4 | — | 60 | 1 | no | — |
| 355 | C4 | Dic5×S4 | 1 | 1 | yes | characteristic |
| 356 | C4 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 357 | C3 | — | 4 | 1 | no | Sylow |
| 358 | C2 | — | 2 | 1 | no | — |
| 359 | C2 | — | 6 | 1 | no | — |
| 360 | C2 | — | 6 | 1 | no | — |
| 361 | C2 | — | 12 | 2 | no | — |
| 362 | C2 | C2×Dic5×S4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #66153⋊C3 | C2 | semidirect |
| 3. C2×#91185 | C2 | semidirect |
| 4. #11751617 | C2 | semidirect |
| 5. #11751615 | C2 | semidirect |
| 8. C5×#986 | C4 | semidirect |
| 10. C5×#984 | C4 | semidirect |
| 11. C5×#983 | C4 | semidirect |
| 13. #4094⋊C3 | C22 | semidirect |
| 14. #91185 | C22 | semidirect |
| 15. #91185 | C22 | semidirect |
| 19. #66153 | D3 | semidirect |
| 32. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 33. C5×#226 | C2×C4 | semidirect |
| 86. #986 | Dic5 | semidirect |
| 88. #984 | Dic5 | semidirect |
| 89. #983 | Dic5 | semidirect |
| 159. GL(2,𝔽3) | C2×Dic5 | semidirect |
| 160. #226 | C2×Dic5 | semidirect |
| 343. C5 | #85453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5923 | 2 |
| #66153⋊C3 | 2 |
| C2×#91185 | 2 |
| #11751617 | 2 |
| #11751615 | 2 |
| #10615731 | 3 |
| #91288 | 4 |
| #85453 | 5 |