Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
546 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 75 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 | C2×C5×#983 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #66146⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#91184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | Dic5×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11751600 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11751594 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | Dic5×#226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10615696 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×C5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 10 | C5×#983 | C4 | 1 | 4 | yes | complemented |
| 11 | C2×C5×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C5×#226 | C22 | 1 | 1 | yes | characteristic |
| 13 | #67⋊Dic5 | — | 4 | 1 | no | maximal |
| 14 | Dic5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 15 | Dic5×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 16 | #91184 | C22 | 1 | 1 | yes | characteristic |
| 17 | #91184 | C22 | 1 | 1 | yes | characteristic |
| 18 | #85354 | — | 5 | 1 | no | maximal, Hall |
| 19 | C2×C5×#137 | — | 3 | 1 | no | — |
| 20 | #66161 | — | 3 | 1 | no | — |
| 21 | #66146 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #65522 | — | 3 | 1 | no | — |
| 23 | C2×#3967 | — | 3 | 1 | no | — |
| 24 | #65473 | — | 3 | 1 | no | — |
| 25 | #65473 | — | 3 | 1 | no | — |
| 26 | Q16×Dic5 | — | 3 | 1 | no | — |
| 27 | Q16×Dic5 | — | 3 | 1 | no | — |
| 28 | #65453 | — | 3 | 1 | no | — |
| 29 | #65453 | — | 3 | 1 | no | — |
| 30 | SD16×Dic5 | — | 3 | 1 | no | — |
| 31 | SD16×Dic5 | — | 3 | 1 | no | — |
| 32 | #65411 | — | 3 | 1 | no | — |
| 33 | #65410 | — | 3 | 1 | no | — |
| 34 | C22×Dic15 | — | 4 | 1 | no | — |
| 35 | C2×C5×#67 | — | 4 | 1 | no | — |
| 36 | C2×C5×SL(2,𝔽3) | C2×C4 | 1 | 2 | yes | complemented |
| 37 | C2×C5×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×D3×Dic5 | — | 4 | 1 | no | — |
| 39 | C5×GL(2,𝔽3) | C2×C4 | 1 | 2 | yes | complemented |
| 40 | C5×#226 | C2×C4 | 1 | 2 | yes | complemented |
| 41 | C3×C22⋊Dic5 | — | 4 | 1 | no | — |
| 42 | Dic3⋊Dic5 | — | 4 | 1 | no | — |
| 43 | (C2×D3)⋊Dic5 | — | 4 | 1 | no | — |
| 44 | Dic3×Dic5 | — | 4 | 1 | no | — |
| 45 | C2×#983 | D5 | 1 | 1 | yes | characteristic |
| 46 | #519⋊C3 | — | 5 | 1 | no | — |
| 47 | C2×#859 | — | 5 | 1 | no | — |
| 48 | #5394 | — | 5 | 1 | no | — |
| 49 | C4×GL(2,𝔽3) | — | 5 | 1 | no | — |
| 50 | #5388 | — | 5 | 1 | no | — |
| 51 | C4×#226 | — | 5 | 1 | no | — |
| 52 | C2×C5×#41 | — | 3 | 1 | no | — |
| 53 | C22×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 54 | C5×#137 | — | 3 | 4 | no | — |
| 55 | C5×#137 | — | 3 | 4 | no | — |
| 56 | C2×C5×Q16 | — | 3 | 1 | no | — |
| 57 | C2×C5×Q16 | — | 3 | 1 | no | — |
| 58 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 59 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 60 | C2×C5×M16 | — | 3 | 1 | no | — |
| 61 | Q8×Dic5 | — | 3 | 1 | no | — |
| 62 | Q8×Dic5 | — | 3 | 1 | no | — |
| 63 | Q8×Dic5 | — | 3 | 1 | no | — |
| 64 | Q8×Dic5 | — | 3 | 1 | no | — |
| 65 | Q8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 66 | Q8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 67 | D4×Dic5 | — | 3 | 1 | no | — |
| 68 | D4×Dic5 | — | 3 | 1 | no | — |
| 69 | D4×Dic5 | — | 6 | 1 | no | — |
| 70 | D4×Dic5 | — | 6 | 1 | no | — |
| 71 | #4072 | — | 3 | 1 | no | — |
| 72 | #4072 | — | 3 | 1 | no | — |
| 73 | #4072 | — | 6 | 1 | no | — |
| 74 | C2×C4⋊Dic5 | — | 3 | 1 | no | — |
| 75 | C2×C4⋊Dic5 | — | 6 | 1 | no | — |
| 76 | C22×#168 | — | 3 | 1 | no | — |
| 77 | #3967 | — | 3 | 1 | no | — |
| 78 | #3967 | — | 3 | 1 | no | — |
| 79 | #3967 | — | 3 | 1 | no | — |
| 80 | #3967 | — | 3 | 1 | no | — |
| 81 | #3967 | — | 3 | 1 | no | — |
| 82 | #3967 | — | 3 | 1 | no | — |
| 83 | #3964 | — | 3 | 1 | no | — |
| 84 | #3964 | — | 3 | 1 | no | — |
| 85 | #3950 | — | 3 | 1 | no | — |
| 86 | #3950 | — | 3 | 1 | no | — |
| 87 | #3949 | — | 3 | 1 | no | — |
| 88 | #3949 | — | 3 | 1 | no | — |
| 89 | #3947 | — | 3 | 1 | no | — |
| 90 | #3947 | — | 3 | 1 | no | — |
| 91 | C8×Dic5 | — | 3 | 1 | no | — |
| 92 | C8×Dic5 | — | 3 | 1 | no | — |
| 93 | #2947 | — | 15 | 1 | no | Sylow |
| 94 | C23×C3×C5 | — | 4 | 1 | no | — |
| 95 | C22×C5×D3 | — | 4 | 1 | no | — |
| 96 | C2×Dic15 | — | 4 | 1 | no | — |
| 97 | C2×Dic15 | — | 4 | 1 | no | — |
| 98 | C2×Dic15 | — | 8 | 2 | no | — |
| 99 | C5×#67 | — | 4 | 4 | no | — |
| 100 | C2×C5×Dic3 | — | 4 | 1 | no | — |
| 101 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 102 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 103 | C5×SL(2,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 104 | D3×Dic5 | — | 8 | 2 | no | — |
| 105 | C22×SL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic |
| 106 | #983 | Dic5 | 1 | 4 | yes | complemented |
| 107 | C2×GL(2,𝔽3) | C2×D5 | 1 | 1 | yes | characteristic |
| 108 | C2×#226 | C2×D5 | 1 | 1 | yes | characteristic |
| 109 | #67⋊C4 | — | 20 | 1 | no | — |
| 110 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 111 | C4×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 112 | #859 | — | 5 | 1 | no | — |
| 113 | #859 | — | 5 | 1 | no | — |
| 114 | C5×#41 | — | 3 | 4 | no | — |
| 115 | C5×#41 | — | 6 | 2 | no | — |
| 116 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 117 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 118 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 119 | C2×C5×Q8 | C4×D3 | 1 | 2 | yes | complemented |
| 120 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 121 | C2×C5×D4 | — | 3 | 1 | no | — |
| 122 | C2×C5×D4 | — | 6 | 1 | no | — |
| 123 | C22×C4×C5 | — | 3 | 1 | no | — |
| 124 | C22×C4×C5 | — | 6 | 1 | no | — |
| 125 | C22×Dic5 | — | 6 | 1 | no | — |
| 126 | C22×Dic5 | — | 6 | 1 | no | — |
| 127 | C22×Dic5 | — | 6 | 1 | no | — |
| 128 | C5×Q16 | — | 3 | 4 | no | — |
| 129 | C5×Q16 | — | 3 | 2 | no | — |
| 130 | C5×Q16 | — | 3 | 2 | no | — |
| 131 | C5×SD16 | — | 3 | 4 | no | — |
| 132 | C5×SD16 | — | 3 | 2 | no | — |
| 133 | C5×SD16 | — | 3 | 2 | no | — |
| 134 | C5×M16 | — | 3 | 4 | no | — |
| 135 | C2×C5×C8 | — | 3 | 1 | no | — |
| 136 | C2×C5×C8 | — | 3 | 1 | no | — |
| 137 | C22⋊Dic5 | — | 3 | 1 | no | — |
| 138 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 139 | C22⋊Dic5 | — | 6 | 1 | no | — |
| 140 | C22⋊Dic5 | S4 | 1 | 1 | yes | characteristic |
| 141 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 142 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 143 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 144 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 145 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 146 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 147 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 148 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 149 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 150 | C4×Dic5 | — | 3 | 1 | no | — |
| 151 | C4×Dic5 | — | 3 | 1 | no | — |
| 152 | C4×Dic5 | — | 6 | 1 | no | — |
| 153 | C4×Dic5 | — | 6 | 1 | no | — |
| 154 | C4×Dic5 | — | 6 | 1 | no | — |
| 155 | C2×#168 | — | 3 | 1 | no | — |
| 156 | C2×#168 | — | 3 | 1 | no | — |
| 157 | C2×#168 | — | 6 | 2 | no | — |
| 158 | C2×#137 | — | 3 | 1 | no | — |
| 159 | #520 | — | 15 | 1 | no | — |
| 160 | #519 | — | 5 | 1 | no | — |
| 161 | #441 | — | 15 | 1 | no | — |
| 162 | #441 | — | 15 | 1 | no | — |
| 163 | #440 | — | 15 | 1 | no | — |
| 164 | #440 | — | 15 | 1 | no | — |
| 165 | C4×Q16 | — | 15 | 1 | no | — |
| 166 | C4×Q16 | — | 15 | 1 | no | — |
| 167 | C4×SD16 | — | 15 | 1 | no | — |
| 168 | C4×SD16 | — | 15 | 1 | no | — |
| 169 | #428 | — | 15 | 1 | no | — |
| 170 | #416 | — | 15 | 1 | no | — |
| 171 | C2×#103 | — | 15 | 1 | no | — |
| 172 | #405 | — | 15 | 1 | no | — |
| 173 | C22×C3×C5 | — | 4 | 2 | no | — |
| 174 | C22×C3×C5 | — | 4 | 1 | no | — |
| 175 | C22×C3×C5 | — | 8 | 1 | no | — |
| 176 | C22×C3×C5 | — | 8 | 1 | no | — |
| 177 | C2×C5×D3 | — | 4 | 2 | no | — |
| 178 | C2×C5×D3 | — | 8 | 1 | no | — |
| 179 | C2×C5×D3 | — | 8 | 1 | no | — |
| 180 | Dic15 | — | 4 | 2 | no | — |
| 181 | Dic15 | — | 8 | 1 | no | — |
| 182 | C3×Dic5 | — | 8 | 1 | no | — |
| 183 | C3×Dic5 | — | 8 | 1 | no | — |
| 184 | C5×Dic3 | — | 4 | 2 | no | — |
| 185 | C2×#67 | — | 4 | 1 | no | — |
| 186 | C22×Dic3 | — | 20 | 1 | no | — |
| 187 | C2×C4×D3 | — | 20 | 1 | no | — |
| 188 | C2×SL(2,𝔽3) | C2×Dic5 | 1 | 2 | yes | complemented |
| 189 | C2×SL(2,𝔽3) | C22×D5 | 1 | 1 | yes | characteristic |
| 190 | GL(2,𝔽3) | C2×Dic5 | 1 | 2 | yes | complemented |
| 191 | #226 | C2×Dic5 | 1 | 2 | yes | complemented |
| 192 | C3×C22⋊C4 | — | 20 | 1 | no | — |
| 193 | (C2×D3)⋊C4 | — | 20 | 1 | no | — |
| 194 | Dic3⋊C4 | — | 20 | 1 | no | — |
| 195 | C4×Dic3 | — | 20 | 1 | no | — |
| 196 | C23×C5 | — | 6 | 1 | no | — |
| 197 | C23×C5 | C2×S4 | 1 | 1 | yes | characteristic |
| 198 | C5×Q8 | — | 3 | 2 | no | — |
| 199 | C5×Q8 | — | 3 | 1 | no | — |
| 200 | C5×Q8 | — | 3 | 2 | no | — |
| 201 | C5×Q8 | — | 6 | 1 | no | — |
| 202 | C5×Q8 | — | 6 | 1 | no | — |
| 203 | C5×Q8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 204 | C5×D4 | — | 3 | 2 | no | — |
| 205 | C5×D4 | — | 6 | 1 | no | — |
| 206 | C5×D4 | — | 6 | 4 | no | — |
| 207 | C2×C4×C5 | — | 3 | 2 | no | — |
| 208 | C2×C4×C5 | — | 3 | 2 | no | — |
| 209 | C2×C4×C5 | — | 3 | 1 | no | — |
| 210 | C2×C4×C5 | — | 3 | 1 | no | — |
| 211 | C2×C4×C5 | — | 6 | 4 | no | — |
| 212 | C2×C4×C5 | — | 6 | 1 | no | — |
| 213 | C2×Dic5 | — | 3 | 1 | no | — |
| 214 | C2×Dic5 | — | 3 | 1 | no | — |
| 215 | C2×Dic5 | — | 6 | 1 | no | — |
| 216 | C2×Dic5 | — | 6 | 1 | no | — |
| 217 | C2×Dic5 | — | 24 | 1 | no | — |
| 218 | C2×Dic5 | — | 24 | 1 | no | — |
| 219 | C2×Dic5 | — | 24 | 1 | no | — |
| 220 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 221 | C2×Dic5 | C2×S4 | 1 | 1 | yes | characteristic |
| 222 | C5×C8 | — | 3 | 2 | no | — |
| 223 | C5×C8 | — | 3 | 2 | no | — |
| 224 | #168 | — | 6 | 1 | no | — |
| 225 | #168 | — | 6 | 1 | no | — |
| 226 | C2×#41 | — | 3 | 1 | no | — |
| 227 | C22×Q8 | D3×D5 | 1 | 1 | yes | characteristic |
| 228 | #137 | — | 3 | 4 | no | — |
| 229 | #137 | — | 3 | 4 | no | — |
| 230 | C2×Q16 | — | 3 | 1 | no | — |
| 231 | C2×Q16 | — | 3 | 1 | no | — |
| 232 | C2×SD16 | — | 3 | 1 | no | — |
| 233 | C2×SD16 | — | 3 | 1 | no | — |
| 234 | C2×M16 | — | 3 | 1 | no | — |
| 235 | C22×C8 | — | 15 | 1 | no | — |
| 236 | C4×Q8 | — | 5 | 1 | no | — |
| 237 | C4×Q8 | — | 5 | 1 | no | — |
| 238 | C4×Q8 | — | 15 | 1 | no | — |
| 239 | C4×Q8 | — | 15 | 1 | no | — |
| 240 | C4×Q8 | — | 15 | 1 | no | — |
| 241 | C4×Q8 | — | 15 | 1 | no | — |
| 242 | C4×D4 | — | 15 | 1 | no | — |
| 243 | C4×D4 | — | 15 | 1 | no | — |
| 244 | C4×D4 | — | 30 | 1 | no | — |
| 245 | C4×D4 | — | 30 | 1 | no | — |
| 246 | #117 | — | 15 | 1 | no | — |
| 247 | #117 | — | 15 | 1 | no | — |
| 248 | #117 | — | 30 | 1 | no | — |
| 249 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 250 | C2×C4⋊C4 | — | 30 | 1 | no | — |
| 251 | #107 | — | 15 | 1 | no | — |
| 252 | #107 | — | 15 | 1 | no | — |
| 253 | #106 | — | 15 | 1 | no | — |
| 254 | #106 | — | 15 | 1 | no | — |
| 255 | #103 | — | 15 | 1 | no | — |
| 256 | #103 | — | 15 | 1 | no | — |
| 257 | #103 | — | 15 | 1 | no | — |
| 258 | #103 | — | 15 | 1 | no | — |
| 259 | #103 | — | 15 | 1 | no | — |
| 260 | #103 | — | 15 | 1 | no | — |
| 261 | #102 | — | 15 | 1 | no | — |
| 262 | #102 | — | 15 | 1 | no | — |
| 263 | #97 | — | 15 | 1 | no | — |
| 264 | #97 | — | 15 | 1 | no | — |
| 265 | C4×C8 | — | 15 | 1 | no | — |
| 266 | C4×C8 | — | 15 | 1 | no | — |
| 267 | C2×C3×C5 | — | 4 | 1 | no | — |
| 268 | C2×C3×C5 | — | 4 | 1 | no | — |
| 269 | C2×C3×C5 | — | 4 | 1 | no | — |
| 270 | C2×C3×C5 | — | 8 | 2 | no | — |
| 271 | C5×D3 | — | 8 | 2 | no | — |
| 272 | C23×C3 | — | 4 | 1 | no | — |
| 273 | C22×D3 | — | 4 | 1 | no | — |
| 274 | C2×C3×C4 | — | 20 | 1 | no | — |
| 275 | C2×C3×C4 | — | 20 | 1 | no | — |
| 276 | #67 | — | 4 | 4 | no | — |
| 277 | C2×Dic3 | — | 4 | 1 | no | — |
| 278 | C2×Dic3 | — | 20 | 1 | no | — |
| 279 | C2×Dic3 | — | 20 | 1 | no | — |
| 280 | C2×Dic3 | — | 40 | 2 | no | — |
| 281 | C4×D3 | — | 40 | 2 | no | — |
| 282 | SL(2,𝔽3) | C22×Dic5 | 1 | 1 | yes | characteristic |
| 283 | C22×C5 | — | 2 | 1 | no | — |
| 284 | C22×C5 | — | 2 | 1 | no | — |
| 285 | C22×C5 | — | 6 | 2 | no | — |
| 286 | C22×C5 | — | 12 | 1 | no | — |
| 287 | C22×C5 | — | 12 | 1 | no | — |
| 288 | C22×C5 | C4×S4 | 1 | 2 | yes | — |
| 289 | C22×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 290 | C4×C5 | — | 3 | 1 | no | — |
| 291 | C4×C5 | — | 3 | 1 | no | — |
| 292 | C4×C5 | — | 3 | 2 | no | — |
| 293 | C4×C5 | — | 6 | 2 | no | — |
| 294 | Dic5 | — | 2 | 1 | no | — |
| 295 | Dic5 | — | 2 | 1 | no | — |
| 296 | Dic5 | — | 6 | 1 | no | — |
| 297 | Dic5 | — | 6 | 1 | no | — |
| 298 | Dic5 | — | 12 | 1 | no | — |
| 299 | Dic5 | — | 12 | 1 | no | — |
| 300 | #41 | — | 3 | 4 | no | — |
| 301 | #41 | — | 6 | 2 | no | — |
| 302 | C2×Q8 | — | 3 | 1 | no | — |
| 303 | C2×Q8 | — | 3 | 2 | no | — |
| 304 | C2×Q8 | — | 3 | 1 | no | — |
| 305 | C2×Q8 | D3×Dic5 | 1 | 2 | yes | complemented |
| 306 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 307 | C2×D4 | — | 3 | 1 | no | — |
| 308 | C2×D4 | — | 6 | 1 | no | — |
| 309 | C22×C4 | — | 3 | 1 | no | — |
| 310 | C22×C4 | — | 6 | 1 | no | — |
| 311 | C22×C4 | — | 30 | 1 | no | — |
| 312 | C22×C4 | — | 30 | 1 | no | — |
| 313 | C22×C4 | — | 30 | 1 | no | — |
| 314 | Q16 | — | 3 | 4 | no | — |
| 315 | Q16 | — | 3 | 2 | no | — |
| 316 | Q16 | — | 3 | 2 | no | — |
| 317 | SD16 | — | 3 | 4 | no | — |
| 318 | SD16 | — | 3 | 2 | no | — |
| 319 | SD16 | — | 3 | 2 | no | — |
| 320 | M16 | — | 3 | 4 | no | — |
| 321 | C2×C8 | — | 3 | 1 | no | — |
| 322 | C2×C8 | — | 3 | 1 | no | — |
| 323 | C2×C8 | — | 15 | 1 | no | — |
| 324 | C2×C8 | — | 15 | 1 | no | — |
| 325 | C2×C8 | — | 30 | 2 | no | — |
| 326 | C4⋊C4 | — | 15 | 1 | no | — |
| 327 | C4⋊C4 | — | 15 | 1 | no | — |
| 328 | C4⋊C4 | — | 15 | 1 | no | — |
| 329 | C4⋊C4 | — | 15 | 1 | no | — |
| 330 | C4⋊C4 | — | 15 | 1 | no | — |
| 331 | C4⋊C4 | — | 15 | 1 | no | — |
| 332 | C4⋊C4 | — | 30 | 1 | no | — |
| 333 | C4⋊C4 | — | 30 | 1 | no | — |
| 334 | C4⋊C4 | — | 30 | 1 | no | — |
| 335 | C22⋊C4 | — | 5 | 1 | no | — |
| 336 | C22⋊C4 | — | 15 | 1 | no | — |
| 337 | C22⋊C4 | — | 30 | 1 | no | — |
| 338 | C22⋊C4 | — | 30 | 1 | no | — |
| 339 | C42 | — | 15 | 1 | no | — |
| 340 | C42 | — | 15 | 1 | no | — |
| 341 | C42 | — | 30 | 1 | no | — |
| 342 | C42 | — | 30 | 1 | no | — |
| 343 | C42 | — | 30 | 1 | no | — |
| 344 | C3×C5 | — | 4 | 1 | no | Hall |
| 345 | C22×C3 | — | 4 | 1 | no | — |
| 346 | C22×C3 | — | 4 | 2 | no | — |
| 347 | C22×C3 | — | 8 | 1 | no | — |
| 348 | C22×C3 | — | 8 | 1 | no | — |
| 349 | C2×D3 | — | 4 | 2 | no | — |
| 350 | C2×D3 | — | 8 | 1 | no | — |
| 351 | C2×D3 | — | 8 | 1 | no | — |
| 352 | C3×C4 | — | 40 | 1 | no | — |
| 353 | C3×C4 | — | 40 | 1 | no | — |
| 354 | Dic3 | — | 4 | 2 | no | — |
| 355 | Dic3 | — | 20 | 2 | no | — |
| 356 | Dic3 | — | 40 | 1 | no | — |
| 357 | C2×C5 | — | 2 | 2 | no | — |
| 358 | C2×C5 | — | 12 | 2 | no | — |
| 359 | C2×C5 | C2×C4×S4 | 1 | 1 | yes | characteristic |
| 360 | C2×C5 | #5926 | 1 | 1 | yes | characteristic |
| 361 | C2×C5 | #5927 | 1 | 1 | yes | characteristic |
| 362 | C23 | — | 6 | 1 | no | — |
| 363 | C23 | D5×S4 | 1 | 1 | yes | characteristic |
| 364 | Q8 | — | 3 | 2 | no | — |
| 365 | Q8 | — | 3 | 1 | no | — |
| 366 | Q8 | — | 3 | 2 | no | — |
| 367 | Q8 | — | 6 | 1 | no | — |
| 368 | Q8 | — | 6 | 1 | no | — |
| 369 | Q8 | C2×D3×Dic5 | 1 | 1 | yes | characteristic |
| 370 | D4 | — | 3 | 2 | no | — |
| 371 | D4 | — | 6 | 1 | no | — |
| 372 | D4 | — | 6 | 4 | no | — |
| 373 | C2×C4 | — | 3 | 1 | no | — |
| 374 | C2×C4 | — | 3 | 1 | no | — |
| 375 | C2×C4 | — | 3 | 2 | no | — |
| 376 | C2×C4 | — | 3 | 2 | no | — |
| 377 | C2×C4 | — | 5 | 1 | no | — |
| 378 | C2×C4 | — | 5 | 1 | no | — |
| 379 | C2×C4 | — | 6 | 4 | no | — |
| 380 | C2×C4 | — | 6 | 1 | no | — |
| 381 | C2×C4 | — | 15 | 1 | no | — |
| 382 | C2×C4 | — | 15 | 1 | no | — |
| 383 | C2×C4 | — | 30 | 1 | no | — |
| 384 | C2×C4 | — | 30 | 1 | no | — |
| 385 | C2×C4 | — | 120 | 1 | no | — |
| 386 | C2×C4 | — | 120 | 1 | no | — |
| 387 | C2×C4 | — | 120 | 1 | no | — |
| 388 | C8 | — | 3 | 2 | no | — |
| 389 | C8 | — | 3 | 2 | no | — |
| 390 | C8 | — | 30 | 1 | no | — |
| 391 | C8 | — | 30 | 1 | no | — |
| 392 | C2×C3 | — | 4 | 1 | no | — |
| 393 | C2×C3 | — | 4 | 1 | no | — |
| 394 | C2×C3 | — | 4 | 1 | no | — |
| 395 | C2×C3 | — | 8 | 2 | no | — |
| 396 | D3 | — | 8 | 2 | no | — |
| 397 | C5 | #85354 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 398 | C22 | — | 2 | 1 | no | — |
| 399 | C22 | — | 2 | 1 | no | — |
| 400 | C22 | — | 6 | 2 | no | — |
| 401 | C22 | — | 12 | 1 | no | — |
| 402 | C22 | — | 12 | 1 | no | — |
| 403 | C22 | Dic5×S4 | 1 | 2 | yes | — |
| 404 | C22 | C2×D5×S4 | 1 | 1 | yes | characteristic |
| 405 | C4 | — | 3 | 1 | no | — |
| 406 | C4 | — | 3 | 1 | no | — |
| 407 | C4 | — | 3 | 2 | no | — |
| 408 | C4 | — | 6 | 2 | no | — |
| 409 | C4 | — | 10 | 1 | no | — |
| 410 | C4 | — | 10 | 1 | no | — |
| 411 | C4 | — | 30 | 1 | no | — |
| 412 | C4 | — | 30 | 1 | no | — |
| 413 | C4 | — | 60 | 1 | no | — |
| 414 | C4 | — | 60 | 1 | no | — |
| 415 | C3 | — | 4 | 1 | no | Sylow |
| 416 | C2 | — | 2 | 2 | no | — |
| 417 | C2 | — | 12 | 2 | no | — |
| 418 | C2 | #11756766 | 1 | 1 | yes | characteristic |
| 419 | C2 | #11756772 | 1 | 1 | yes | characteristic |
| 420 | C2 | C2×Dic5×S4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #66146⋊C3 | C2 | semidirect |
| 3. C2×#91184 | C2 | semidirect |
| 4. Dic5×GL(2,𝔽3) | C2 | semidirect |
| 5. #11751600 | C2 | semidirect |
| 6. #11751594 | C2 | semidirect |
| 7. Dic5×#226 | C2 | semidirect |
| 10. C5×#983 | C4 | semidirect |
| 21. #66146 | D3 | semidirect |
| 36. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 39. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 40. C5×#226 | C2×C4 | semidirect |
| 106. #983 | Dic5 | semidirect |
| 119. C2×C5×Q8 | C4×D3 | semidirect |
| 188. C2×SL(2,𝔽3) | C2×Dic5 | semidirect |
| 190. GL(2,𝔽3) | C2×Dic5 | semidirect |
| 191. #226 | C2×Dic5 | semidirect |
| 305. C2×Q8 | D3×Dic5 | semidirect |
| 397. C5 | #85354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#983 | 2 |
| #66146⋊C3 | 2 |
| C2×#91184 | 2 |
| Dic5×GL(2,𝔽3) | 2 |
| #11751600 | 2 |
| #11751594 | 2 |
| Dic5×#226 | 2 |
| #10615696 | 3 |
| #67⋊Dic5 | 4 |
| #85354 | 5 |