Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
386 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 46 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 | D5×#994 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #66266⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D5⋊(#131⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10617559 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 5 | C5×#994 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | D5×#41⋊C3 | — | 2 | 1 | no | — |
| 7 | D5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 8 | C5⋊#994 | — | 2 | 1 | no | — |
| 9 | C5⋊#994 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | AGL(1,𝔽5)×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 11 | #4133⋊C3 | — | 2 | 1 | no | — |
| 12 | C3×#4009 | — | 4 | 1 | no | maximal |
| 13 | #2897⋊C3 | — | 5 | 1 | no | maximal, Hall |
| 14 | D5×H(5,𝔽2) | C2×C3 | 1 | 1 | yes | characteristic |
| 15 | #66266 | C2×C3 | 1 | 1 | yes | characteristic |
| 16 | D5⋊#131 | C2×C3 | 1 | 1 | yes | characteristic |
| 17 | #65794 | — | 3 | 1 | no | — |
| 18 | #65793 | — | 3 | 1 | no | — |
| 19 | #65767 | — | 3 | 1 | no | — |
| 20 | C2×#4007 | — | 3 | 1 | no | — |
| 21 | C3×Q8×D5 | — | 4 | 1 | no | — |
| 22 | C5×#41⋊C3 | — | 2 | 1 | no | — |
| 23 | C5×#41⋊C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 24 | C3×C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 25 | C3×D5⋊C8 | — | 4 | 1 | no | — |
| 26 | D5×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 27 | C5⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 28 | C5⋊(#41⋊C3) | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×#994 | — | 5 | 1 | no | — |
| 30 | C2×#131⋊C3 | — | 5 | 1 | no | — |
| 31 | #520⋊C3 | — | 5 | 1 | no | — |
| 32 | C5×H(5,𝔽2) | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | #4149 | — | 2 | 1 | no | — |
| 34 | #4149 | — | 3 | 1 | no | — |
| 35 | #4149 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 36 | D5×#41 | — | 2 | 1 | no | — |
| 37 | D5×#41 | — | 3 | 1 | no | — |
| 38 | D5×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 39 | #4144 | — | 3 | 1 | no | — |
| 40 | #4144 | — | 6 | 1 | no | — |
| 41 | C2×D4×D5 | — | 3 | 1 | no | — |
| 42 | C2×D4×D5 | — | 6 | 1 | no | — |
| 43 | Q8×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 44 | #4133 | — | 2 | 1 | no | — |
| 45 | D4×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 46 | #4131 | — | 6 | 1 | no | — |
| 47 | #4130 | — | 3 | 1 | no | — |
| 48 | C2×C4⋊AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 49 | D5⋊M16 | — | 3 | 1 | no | — |
| 50 | C2×D5⋊C8 | — | 3 | 1 | no | — |
| 51 | #4009 | — | 3 | 1 | no | — |
| 52 | #4009 | A4 | 1 | 1 | yes | characteristic |
| 53 | #4007 | — | 3 | 2 | no | — |
| 54 | #4007 | — | 3 | 1 | no | — |
| 55 | #4007 | — | 3 | 1 | no | — |
| 56 | #2897 | — | 5 | 1 | no | Sylow |
| 57 | C2×C3×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 58 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 59 | C3×C4×D5 | — | 4 | 1 | no | — |
| 60 | C3×C4×D5 | — | 8 | 1 | no | — |
| 61 | C3×Dic10 | — | 4 | 1 | no | — |
| 62 | C3×Dic10 | — | 8 | 1 | no | — |
| 63 | C5×SL(2,𝔽3) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 64 | C3×#170 | — | 8 | 1 | no | — |
| 65 | #994 | — | 5 | 1 | no | — |
| 66 | #994 | — | 10 | 1 | no | — |
| 67 | #994 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 68 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 69 | C2×#41⋊C3 | — | 10 | 1 | no | — |
| 70 | #131⋊C3 | — | 10 | 1 | no | — |
| 71 | C4×SL(2,𝔽3) | — | 10 | 1 | no | — |
| 72 | C3×#103 | — | 20 | 1 | no | — |
| 73 | C23×D5 | — | 6 | 1 | no | — |
| 74 | C22×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 75 | C5×#41 | — | 2 | 1 | no | — |
| 76 | C5×#41 | — | 3 | 1 | no | — |
| 77 | C5×#41 | C2×C3×C4 | 1 | 1 | yes | characteristic |
| 78 | C2×C5×D4 | — | 3 | 1 | no | — |
| 79 | C2×C5×D4 | — | 6 | 1 | no | — |
| 80 | C2×C22⋊D5 | — | 6 | 1 | no | — |
| 81 | C2×C22⋊D5 | — | 6 | 2 | no | — |
| 82 | #713 | — | 2 | 1 | no | — |
| 83 | #713 | — | 3 | 1 | no | — |
| 84 | #713 | C3×D4 | 1 | 1 | yes | characteristic |
| 85 | Q8×D5 | C3×D4 | 1 | 1 | yes | characteristic |
| 86 | Q8×D5 | C2×A4 | 1 | 1 | yes | characteristic |
| 87 | #711 | — | 3 | 1 | no | — |
| 88 | #711 | — | 3 | 1 | no | — |
| 89 | #711 | — | 6 | 1 | no | — |
| 90 | #711 | — | 6 | 1 | no | — |
| 91 | D4×D5 | — | 3 | 1 | no | — |
| 92 | D4×D5 | — | 3 | 2 | no | — |
| 93 | D4×D5 | — | 3 | 1 | no | — |
| 94 | D4×D5 | — | 6 | 1 | no | — |
| 95 | D4×D5 | — | 6 | 1 | no | — |
| 96 | D4×D5 | — | 6 | 1 | no | — |
| 97 | D4×D5 | — | 6 | 1 | no | — |
| 98 | D4×D5 | — | 6 | 2 | no | — |
| 99 | D4×D5 | — | 6 | 1 | no | — |
| 100 | #709 | — | 3 | 1 | no | — |
| 101 | #709 | — | 3 | 1 | no | — |
| 102 | #709 | — | 6 | 1 | no | — |
| 103 | #709 | — | 6 | 1 | no | — |
| 104 | C2×D20 | — | 3 | 1 | no | — |
| 105 | C2×D20 | — | 6 | 1 | no | — |
| 106 | C2×C4×D5 | — | 3 | 1 | no | — |
| 107 | C2×C4×D5 | — | 6 | 1 | no | — |
| 108 | C22⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 109 | #704 | — | 6 | 1 | no | — |
| 110 | C2×#170 | — | 6 | 1 | no | — |
| 111 | C4⋊AGL(1,𝔽5) | — | 3 | 1 | no | — |
| 112 | C4⋊AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 113 | C4⋊AGL(1,𝔽5) | C2×A4 | 1 | 1 | yes | characteristic |
| 114 | C4×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 115 | #700 | — | 6 | 1 | no | — |
| 116 | D5⋊C8 | — | 3 | 1 | no | — |
| 117 | D5⋊C8 | — | 6 | 1 | no | — |
| 118 | D5⋊C8 | C2×A4 | 1 | 1 | yes | characteristic |
| 119 | C2×H(5,𝔽2) | — | 5 | 1 | no | — |
| 120 | C2×#131 | — | 5 | 1 | no | — |
| 121 | #520 | — | 5 | 1 | no | — |
| 122 | #418 | — | 15 | 1 | no | — |
| 123 | #417 | — | 15 | 1 | no | — |
| 124 | #416 | — | 15 | 1 | no | — |
| 125 | C2×#102 | — | 15 | 1 | no | — |
| 126 | C2×C3×D5 | — | 4 | 1 | no | — |
| 127 | C3×AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 128 | C3×C4×C5 | — | 4 | 1 | no | — |
| 129 | C3×C4×C5 | — | 8 | 1 | no | — |
| 130 | C3×Dic5 | — | 4 | 1 | no | — |
| 131 | C3×Dic5 | — | 8 | 1 | no | — |
| 132 | C2×C3×Q8 | — | 20 | 1 | no | — |
| 133 | #41⋊C3 | — | 2 | 1 | no | — |
| 134 | #41⋊C3 | — | 5 | 1 | no | — |
| 135 | #41⋊C3 | — | 10 | 1 | no | — |
| 136 | #41⋊C3 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 137 | C2×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 138 | C2×C3×C8 | — | 20 | 1 | no | — |
| 139 | C3×C4⋊C4 | — | 20 | 1 | no | — |
| 140 | C23×C5 | — | 6 | 1 | no | — |
| 141 | C22×D5 | — | 3 | 1 | no | — |
| 142 | C22×D5 | — | 6 | 2 | no | — |
| 143 | C22×D5 | — | 6 | 1 | no | — |
| 144 | C22×D5 | — | 6 | 1 | no | — |
| 145 | C22×D5 | — | 24 | 1 | no | — |
| 146 | C22×D5 | — | 24 | 1 | no | — |
| 147 | C2×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 148 | C2×AGL(1,𝔽5) | — | 6 | 1 | no | — |
| 149 | C2×AGL(1,𝔽5) | — | 24 | 1 | no | — |
| 150 | C5×Q8 | C3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 151 | C5×Q8 | C4×A4 | 1 | 1 | yes | characteristic |
| 152 | C5×D4 | — | 3 | 1 | no | — |
| 153 | C5×D4 | — | 3 | 1 | no | — |
| 154 | C5×D4 | — | 6 | 1 | no | — |
| 155 | C5×D4 | — | 6 | 1 | no | — |
| 156 | C2×C4×C5 | — | 3 | 1 | no | — |
| 157 | C2×C4×C5 | — | 6 | 1 | no | — |
| 158 | C22⋊D5 | — | 3 | 2 | no | — |
| 159 | C22⋊D5 | — | 6 | 1 | no | — |
| 160 | C22⋊D5 | — | 6 | 1 | no | — |
| 161 | C22⋊D5 | — | 6 | 2 | no | — |
| 162 | C22⋊D5 | — | 6 | 1 | no | — |
| 163 | C2×Dic5 | — | 3 | 1 | no | — |
| 164 | C2×Dic5 | — | 6 | 1 | no | — |
| 165 | D20 | — | 3 | 1 | no | — |
| 166 | D20 | — | 3 | 1 | no | — |
| 167 | D20 | — | 6 | 1 | no | — |
| 168 | D20 | — | 6 | 1 | no | — |
| 169 | C4×D5 | — | 2 | 1 | no | — |
| 170 | C4×D5 | — | 3 | 1 | no | — |
| 171 | C4×D5 | — | 3 | 1 | no | — |
| 172 | C4×D5 | — | 3 | 1 | no | — |
| 173 | C4×D5 | — | 6 | 1 | no | — |
| 174 | C4×D5 | — | 6 | 1 | no | — |
| 175 | C4×D5 | C22×A4 | 1 | 1 | yes | characteristic |
| 176 | Dic10 | — | 2 | 1 | no | — |
| 177 | Dic10 | — | 3 | 1 | no | — |
| 178 | Dic10 | C4×A4 | 1 | 1 | yes | characteristic |
| 179 | #170 | — | 2 | 1 | no | — |
| 180 | #170 | — | 6 | 1 | no | — |
| 181 | H(5,𝔽2) | — | 5 | 1 | no | — |
| 182 | H(5,𝔽2) | — | 10 | 1 | no | — |
| 183 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 184 | H(5,𝔽2) | — | 15 | 1 | no | — |
| 185 | H(5,𝔽2) | — | 30 | 1 | no | — |
| 186 | H(5,𝔽2) | C3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 187 | C2×#41 | — | 5 | 1 | no | — |
| 188 | C2×#41 | — | 10 | 1 | no | — |
| 189 | C2×#41 | — | 15 | 1 | no | — |
| 190 | C22×D4 | — | 15 | 1 | no | — |
| 191 | C22×D4 | — | 30 | 1 | no | — |
| 192 | #131 | — | 10 | 1 | no | — |
| 193 | #131 | — | 30 | 1 | no | — |
| 194 | C2×M16 | — | 15 | 1 | no | — |
| 195 | C22×C8 | — | 15 | 1 | no | — |
| 196 | C4×Q8 | — | 10 | 1 | no | — |
| 197 | C4×D4 | — | 30 | 1 | no | — |
| 198 | #117 | — | 15 | 1 | no | — |
| 199 | C2×C4⋊C4 | — | 15 | 1 | no | — |
| 200 | #103 | — | 5 | 1 | no | — |
| 201 | #103 | — | 15 | 1 | no | — |
| 202 | #102 | — | 15 | 1 | no | — |
| 203 | #102 | — | 15 | 1 | no | — |
| 204 | #102 | — | 15 | 2 | no | — |
| 205 | C2×C3×C5 | — | 4 | 1 | no | — |
| 206 | C3×D5 | — | 4 | 1 | no | — |
| 207 | C3×D5 | — | 4 | 1 | no | — |
| 208 | C3×Q8 | — | 4 | 1 | no | — |
| 209 | C3×Q8 | — | 20 | 1 | no | — |
| 210 | C3×Q8 | — | 40 | 1 | no | — |
| 211 | C2×C3×C4 | — | 20 | 1 | no | — |
| 212 | C2×C3×C4 | — | 40 | 1 | no | — |
| 213 | C2×C3×C4 | — | 40 | 1 | no | — |
| 214 | SL(2,𝔽3) | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 215 | C3×C8 | — | 40 | 1 | no | — |
| 216 | C22×C5 | — | 3 | 1 | no | — |
| 217 | C22×C5 | — | 6 | 1 | no | — |
| 218 | C22×C5 | — | 24 | 1 | no | — |
| 219 | C2×D5 | — | 3 | 1 | no | — |
| 220 | C2×D5 | — | 6 | 1 | no | — |
| 221 | C2×D5 | — | 6 | 1 | no | — |
| 222 | C2×D5 | — | 6 | 1 | no | — |
| 223 | C2×D5 | — | 12 | 1 | no | — |
| 224 | C2×D5 | — | 12 | 1 | no | — |
| 225 | C2×D5 | — | 24 | 2 | no | — |
| 226 | C2×D5 | — | 24 | 1 | no | — |
| 227 | C2×D5 | D4×A4 | 1 | 1 | yes | characteristic |
| 228 | AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 229 | AGL(1,𝔽5) | — | 12 | 1 | no | — |
| 230 | C4×C5 | — | 2 | 1 | no | — |
| 231 | C4×C5 | — | 3 | 1 | no | — |
| 232 | C4×C5 | C2×C4×A4 | 1 | 1 | yes | characteristic |
| 233 | Dic5 | — | 2 | 1 | no | — |
| 234 | Dic5 | — | 3 | 1 | no | — |
| 235 | Dic5 | D4×A4 | 1 | 1 | yes | characteristic |
| 236 | C24 | — | 30 | 1 | no | — |
| 237 | #41 | — | 2 | 1 | no | — |
| 238 | #41 | — | 3 | 1 | no | — |
| 239 | #41 | — | 5 | 1 | no | — |
| 240 | #41 | — | 10 | 1 | no | — |
| 241 | #41 | — | 15 | 1 | no | — |
| 242 | #41 | — | 15 | 1 | no | — |
| 243 | #41 | — | 15 | 1 | no | — |
| 244 | #41 | — | 15 | 1 | no | — |
| 245 | #41 | — | 15 | 1 | no | — |
| 246 | #41 | — | 30 | 1 | no | — |
| 247 | #41 | — | 30 | 1 | no | — |
| 248 | #41 | — | 30 | 1 | no | — |
| 249 | #41 | — | 30 | 1 | no | — |
| 250 | #41 | C2×C3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 251 | C2×Q8 | — | 5 | 1 | no | — |
| 252 | C2×Q8 | — | 5 | 1 | no | — |
| 253 | C2×D4 | — | 3 | 1 | no | — |
| 254 | C2×D4 | — | 6 | 1 | no | — |
| 255 | C2×D4 | — | 15 | 1 | no | — |
| 256 | C2×D4 | — | 15 | 1 | no | — |
| 257 | C2×D4 | — | 15 | 1 | no | — |
| 258 | C2×D4 | — | 15 | 2 | no | — |
| 259 | C2×D4 | — | 30 | 1 | no | — |
| 260 | C2×D4 | — | 30 | 1 | no | — |
| 261 | C2×D4 | — | 30 | 1 | no | — |
| 262 | C2×D4 | — | 30 | 1 | no | — |
| 263 | C2×D4 | — | 30 | 1 | no | — |
| 264 | C2×D4 | — | 30 | 1 | no | — |
| 265 | C2×D4 | — | 30 | 2 | no | — |
| 266 | C2×D4 | — | 30 | 1 | no | — |
| 267 | C2×D4 | — | 30 | 2 | no | — |
| 268 | C22×C4 | — | 15 | 1 | no | — |
| 269 | C22×C4 | — | 30 | 1 | no | — |
| 270 | C22×C4 | — | 30 | 1 | no | — |
| 271 | M16 | — | 30 | 1 | no | — |
| 272 | M16 | — | 30 | 1 | no | — |
| 273 | C2×C8 | — | 5 | 1 | no | — |
| 274 | C2×C8 | — | 15 | 1 | no | — |
| 275 | C2×C8 | — | 30 | 1 | no | — |
| 276 | C2×C8 | — | 30 | 1 | no | — |
| 277 | C4⋊C4 | — | 5 | 1 | no | — |
| 278 | C4⋊C4 | — | 15 | 1 | no | — |
| 279 | C4⋊C4 | — | 30 | 1 | no | — |
| 280 | C22⋊C4 | — | 30 | 1 | no | — |
| 281 | C42 | — | 30 | 1 | no | — |
| 282 | C3×C5 | — | 4 | 1 | no | Hall |
| 283 | C22×C3 | — | 20 | 1 | no | — |
| 284 | C3×C4 | — | 4 | 1 | no | — |
| 285 | C3×C4 | — | 8 | 1 | no | — |
| 286 | C3×C4 | — | 20 | 1 | no | — |
| 287 | C3×C4 | — | 40 | 1 | no | — |
| 288 | C3×C4 | — | 80 | 1 | no | — |
| 289 | C2×C5 | — | 6 | 1 | no | — |
| 290 | C2×C5 | — | 12 | 1 | no | — |
| 291 | C2×C5 | A4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 292 | D5 | — | 6 | 1 | no | — |
| 293 | D5 | — | 12 | 1 | no | — |
| 294 | D5 | #576⋊C3 | 1 | 1 | yes | characteristic |
| 295 | D5 | #577⋊C3 | 1 | 1 | yes | characteristic |
| 296 | C23 | — | 6 | 1 | no | — |
| 297 | C23 | — | 15 | 1 | no | — |
| 298 | C23 | — | 30 | 1 | no | — |
| 299 | C23 | — | 30 | 1 | no | — |
| 300 | C23 | — | 30 | 2 | no | — |
| 301 | C23 | — | 120 | 1 | no | — |
| 302 | C23 | — | 120 | 1 | no | — |
| 303 | Q8 | — | 5 | 1 | no | — |
| 304 | Q8 | — | 10 | 1 | no | — |
| 305 | Q8 | — | 15 | 1 | no | — |
| 306 | Q8 | C3×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 307 | Q8 | A4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 308 | D4 | — | 3 | 1 | no | — |
| 309 | D4 | — | 3 | 1 | no | — |
| 310 | D4 | — | 6 | 1 | no | — |
| 311 | D4 | — | 6 | 1 | no | — |
| 312 | D4 | — | 15 | 1 | no | — |
| 313 | D4 | — | 15 | 2 | no | — |
| 314 | D4 | — | 15 | 1 | no | — |
| 315 | D4 | — | 30 | 1 | no | — |
| 316 | D4 | — | 30 | 1 | no | — |
| 317 | D4 | — | 30 | 1 | no | — |
| 318 | D4 | — | 30 | 1 | no | — |
| 319 | D4 | — | 30 | 1 | no | — |
| 320 | D4 | — | 30 | 2 | no | — |
| 321 | C2×C4 | — | 3 | 1 | no | — |
| 322 | C2×C4 | — | 5 | 1 | no | — |
| 323 | C2×C4 | — | 6 | 1 | no | — |
| 324 | C2×C4 | — | 10 | 1 | no | — |
| 325 | C2×C4 | — | 10 | 1 | no | — |
| 326 | C2×C4 | — | 15 | 1 | no | — |
| 327 | C2×C4 | — | 15 | 1 | no | — |
| 328 | C2×C4 | — | 15 | 1 | no | — |
| 329 | C2×C4 | — | 15 | 1 | no | — |
| 330 | C2×C4 | — | 30 | 1 | no | — |
| 331 | C2×C4 | — | 30 | 1 | no | — |
| 332 | C2×C4 | — | 30 | 1 | no | — |
| 333 | C2×C4 | — | 30 | 1 | no | — |
| 334 | C2×C4 | — | 120 | 1 | no | — |
| 335 | C8 | — | 10 | 1 | no | — |
| 336 | C8 | — | 30 | 1 | no | — |
| 337 | C2×C3 | — | 4 | 1 | no | — |
| 338 | C2×C3 | — | 20 | 1 | no | — |
| 339 | C2×C3 | — | 20 | 1 | no | — |
| 340 | C5 | #2897⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 341 | C22 | — | 3 | 1 | no | — |
| 342 | C22 | — | 5 | 1 | no | — |
| 343 | C22 | — | 6 | 1 | no | — |
| 344 | C22 | — | 15 | 1 | no | — |
| 345 | C22 | — | 24 | 1 | no | — |
| 346 | C22 | — | 30 | 1 | no | — |
| 347 | C22 | — | 30 | 1 | no | — |
| 348 | C22 | — | 30 | 1 | no | — |
| 349 | C22 | — | 60 | 1 | no | — |
| 350 | C22 | — | 60 | 1 | no | — |
| 351 | C22 | — | 120 | 1 | no | — |
| 352 | C22 | — | 120 | 2 | no | — |
| 353 | C4 | — | 2 | 1 | no | — |
| 354 | C4 | — | 3 | 1 | no | — |
| 355 | C4 | — | 5 | 1 | no | — |
| 356 | C4 | — | 10 | 1 | no | — |
| 357 | C4 | — | 15 | 1 | no | — |
| 358 | C4 | — | 20 | 1 | no | — |
| 359 | C4 | — | 60 | 1 | no | — |
| 360 | C4 | C2×A4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 361 | C3 | — | 4 | 1 | no | Sylow |
| 362 | C2 | — | 5 | 1 | no | — |
| 363 | C2 | — | 5 | 1 | no | — |
| 364 | C2 | — | 6 | 1 | no | — |
| 365 | C2 | — | 12 | 1 | no | — |
| 366 | C2 | — | 30 | 1 | no | — |
| 367 | C2 | — | 60 | 1 | no | — |
| 368 | C2 | A4×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #66266⋊C3 | C2 | semidirect |
| 3. D5⋊(#131⋊C3) | C2 | semidirect |
| 4. #10617559 | C3 | semidirect |
| 5. C5×#994 | C4 | semidirect |
| 9. C5⋊#994 | C4 | semidirect |
| 32. C5×H(5,𝔽2) | C3×C4 | semidirect |
| 35. #4149 | C3×C4 | semidirect |
| 67. #994 | AGL(1,𝔽5) | semidirect |
| 186. H(5,𝔽2) | C3×AGL(1,𝔽5) | semidirect |
| 340. C5 | #2897⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#994 | 2 |
| #66266⋊C3 | 2 |
| D5⋊(#131⋊C3) | 2 |
| #10617559 | 3 |
| C3×#4009 | 4 |
| #2897⋊C3 | 5 |