Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
668 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #66287⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C5×#578⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #66171⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #66086⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D5×#131⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10619111 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 7 | C5×2−1+4⋊C3 | C22 | 1 | 2 | yes | complemented |
| 8 | D5×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 9 | C5⋊#994 | C22 | 1 | 2 | yes | complemented |
| 10 | #4147⋊C3 | — | 2 | 2 | no | — |
| 11 | C2×C5⋊(#41⋊C3) | — | 2 | 2 | no | — |
| 12 | C3×#4058 | — | 4 | 1 | no | maximal |
| 13 | C5×#131⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #4094⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #3584⋊C3 | — | 5 | 1 | no | maximal, Hall |
| 16 | #66287 | C2×C3 | 1 | 2 | yes | complemented |
| 17 | C5×#578 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 18 | #66171 | C2×C3 | 1 | 2 | yes | complemented |
| 19 | #66112 | — | 3 | 2 | no | — |
| 20 | #66111 | — | 3 | 2 | no | — |
| 21 | #66103 | — | 3 | 1 | no | — |
| 22 | D5×#135 | — | 3 | 1 | no | — |
| 23 | #66100 | — | 3 | 1 | no | — |
| 24 | C2×#4065 | — | 3 | 1 | no | — |
| 25 | #66086 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | D5×#131 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×#711 | — | 4 | 2 | no | — |
| 28 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 29 | C2×C5×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 30 | D5×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 31 | C5⋊(#41⋊C3) | — | 2 | 2 | no | — |
| 32 | C5⋊(#41⋊C3) | D4 | 1 | 1 | yes | characteristic |
| 33 | C3×C5×D8 | — | 4 | 1 | no | — |
| 34 | C3×#687 | — | 4 | 2 | no | — |
| 35 | C3×Dic20 | — | 4 | 1 | no | — |
| 36 | C3×C8×D5 | — | 4 | 1 | no | — |
| 37 | #5945 | — | 5 | 2 | no | — |
| 38 | #578⋊C3 | D5 | 1 | 1 | yes | characteristic, complemented |
| 39 | #577⋊C3 | — | 5 | 2 | no | — |
| 40 | #576⋊C3 | — | 5 | 1 | no | — |
| 41 | C2×#131⋊C3 | — | 5 | 1 | no | — |
| 42 | C5×2−1+4 | C22×C3 | 1 | 2 | yes | — |
| 43 | #4149 | — | 3 | 2 | no | — |
| 44 | #4149 | — | 6 | 2 | no | — |
| 45 | #4149 | C22×C3 | 1 | 2 | yes | — |
| 46 | D5×#41 | — | 3 | 2 | no | — |
| 47 | D5×#41 | — | 6 | 2 | no | — |
| 48 | D5×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 49 | #4147 | — | 2 | 2 | no | — |
| 50 | #4147 | — | 3 | 2 | no | — |
| 51 | C2×#713 | — | 2 | 2 | no | — |
| 52 | C2×#713 | — | 3 | 2 | no | — |
| 53 | C5×#137 | — | 3 | 2 | no | — |
| 54 | C5×#135 | — | 3 | 1 | no | — |
| 55 | C2×C5×Q16 | — | 3 | 1 | no | — |
| 56 | C5×#131 | C22×C3 | 1 | 1 | yes | characteristic |
| 57 | #4096 | — | 3 | 2 | no | — |
| 58 | #4095 | — | 3 | 2 | no | — |
| 59 | #4094 | C22×C3 | 1 | 1 | yes | characteristic |
| 60 | #4088 | — | 3 | 2 | no | — |
| 61 | C2×#688 | — | 3 | 2 | no | — |
| 62 | #4065 | — | 3 | 2 | no | — |
| 63 | #4065 | — | 3 | 2 | no | — |
| 64 | #4065 | — | 3 | 2 | no | — |
| 65 | #4065 | — | 3 | 1 | no | — |
| 66 | #4064 | — | 3 | 4 | no | — |
| 67 | D5×Q16 | — | 3 | 1 | no | — |
| 68 | #4062 | — | 3 | 2 | no | — |
| 69 | #4060 | — | 3 | 4 | no | — |
| 70 | D5×SD16 | — | 3 | 2 | no | — |
| 71 | #4058 | A4 | 1 | 1 | yes | characteristic |
| 72 | D5×D8 | — | 3 | 1 | no | — |
| 73 | #4054 | — | 3 | 2 | no | — |
| 74 | #4053 | — | 3 | 1 | no | — |
| 75 | D5×M16 | — | 3 | 1 | no | — |
| 76 | #4050 | — | 3 | 1 | no | — |
| 77 | C2×D40 | — | 3 | 1 | no | — |
| 78 | #4047 | — | 3 | 1 | no | — |
| 79 | C2×C8×D5 | — | 3 | 1 | no | — |
| 80 | #3584 | — | 5 | 1 | no | Sylow |
| 81 | C3×C5×D4 | — | 4 | 2 | no | — |
| 82 | C3×C22⋊D5 | — | 8 | 2 | no | — |
| 83 | C2×C3×Dic5 | — | 8 | 2 | no | — |
| 84 | C3×C4×D5 | — | 4 | 1 | no | — |
| 85 | C3×Dic10 | — | 4 | 2 | no | — |
| 86 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C3×C5×C8 | — | 4 | 1 | no | — |
| 88 | C3×#168 | — | 4 | 1 | no | — |
| 89 | 2−1+4⋊C3 | — | 10 | 2 | no | — |
| 90 | 2−1+4⋊C3 | C2×D5 | 1 | 2 | yes | complemented |
| 91 | #994 | — | 5 | 2 | no | — |
| 92 | C2×#41⋊C3 | — | 5 | 1 | no | — |
| 93 | C2×#41⋊C3 | — | 10 | 2 | no | — |
| 94 | C3×#135 | — | 20 | 1 | no | — |
| 95 | #131⋊C3 | — | 5 | 1 | no | — |
| 96 | #131⋊C3 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 97 | C5×#41 | — | 3 | 2 | no | — |
| 98 | C5×#41 | — | 6 | 2 | no | — |
| 99 | C5×#41 | C23×C3 | 1 | 1 | yes | characteristic |
| 100 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 101 | C2×C5×Q8 | — | 3 | 2 | no | — |
| 102 | #713 | — | 2 | 2 | no | — |
| 103 | #713 | — | 3 | 4 | no | — |
| 104 | #713 | — | 3 | 2 | no | — |
| 105 | #713 | — | 6 | 2 | no | — |
| 106 | #713 | — | 6 | 2 | no | — |
| 107 | #713 | — | 6 | 2 | no | — |
| 108 | #713 | C3×D4 | 1 | 1 | yes | characteristic |
| 109 | Q8×D5 | — | 3 | 2 | no | — |
| 110 | Q8×D5 | — | 6 | 2 | no | — |
| 111 | Q8×D5 | C3×D4 | 1 | 1 | yes | characteristic |
| 112 | #711 | — | 3 | 1 | no | — |
| 113 | #711 | — | 6 | 2 | no | — |
| 114 | #711 | C2×A4 | 1 | 2 | yes | — |
| 115 | D4×D5 | — | 3 | 1 | no | — |
| 116 | D4×D5 | — | 3 | 2 | no | — |
| 117 | D4×D5 | — | 6 | 2 | no | — |
| 118 | D4×D5 | — | 6 | 4 | no | — |
| 119 | D4×D5 | — | 6 | 2 | no | — |
| 120 | #709 | — | 3 | 1 | no | — |
| 121 | #709 | — | 3 | 2 | no | — |
| 122 | #709 | — | 6 | 2 | no | — |
| 123 | #709 | — | 6 | 2 | no | — |
| 124 | #709 | — | 6 | 4 | no | — |
| 125 | C2×D20 | — | 3 | 2 | no | — |
| 126 | C2×D20 | — | 6 | 2 | no | — |
| 127 | C2×D20 | — | 6 | 2 | no | — |
| 128 | C2×C4×D5 | — | 3 | 1 | no | — |
| 129 | C2×C4×D5 | — | 6 | 2 | no | — |
| 130 | C2×C4×D5 | — | 6 | 2 | no | — |
| 131 | C5×Q16 | — | 3 | 2 | no | — |
| 132 | C5×Q16 | — | 3 | 1 | no | — |
| 133 | C5×SD16 | — | 3 | 2 | no | — |
| 134 | C5×D8 | C2×A4 | 1 | 1 | yes | characteristic |
| 135 | C5×M16 | — | 3 | 1 | no | — |
| 136 | C2×C5×C8 | — | 3 | 1 | no | — |
| 137 | #689 | — | 3 | 2 | no | — |
| 138 | #688 | — | 3 | 4 | no | — |
| 139 | #688 | — | 3 | 2 | no | — |
| 140 | #687 | C2×A4 | 1 | 2 | yes | — |
| 141 | #686 | — | 3 | 2 | no | — |
| 142 | #681 | — | 3 | 1 | no | — |
| 143 | C2×#168 | — | 3 | 1 | no | — |
| 144 | Dic20 | C2×A4 | 1 | 1 | yes | characteristic |
| 145 | D40 | — | 3 | 2 | no | — |
| 146 | D40 | — | 3 | 1 | no | — |
| 147 | #677 | — | 3 | 2 | no | — |
| 148 | #676 | — | 3 | 2 | no | — |
| 149 | C8×D5 | — | 3 | 1 | no | — |
| 150 | C8×D5 | — | 3 | 1 | no | — |
| 151 | C8×D5 | — | 3 | 1 | no | — |
| 152 | C8×D5 | C2×A4 | 1 | 1 | yes | characteristic |
| 153 | #585 | — | 5 | 2 | no | — |
| 154 | #578 | — | 15 | 1 | no | — |
| 155 | #578 | C3×D5 | 1 | 1 | yes | characteristic, complemented |
| 156 | #577 | — | 5 | 2 | no | — |
| 157 | #577 | — | 15 | 2 | no | — |
| 158 | #576 | — | 5 | 1 | no | — |
| 159 | #576 | — | 15 | 1 | no | — |
| 160 | #575 | — | 15 | 2 | no | — |
| 161 | C2×#135 | — | 15 | 1 | no | — |
| 162 | C2×#135 | — | 15 | 1 | no | — |
| 163 | C2×#131 | — | 5 | 1 | no | — |
| 164 | C22×C3×C5 | — | 8 | 2 | no | — |
| 165 | C2×C3×D5 | — | 4 | 1 | no | — |
| 166 | C3×C4×C5 | — | 4 | 1 | no | — |
| 167 | C3×Dic5 | — | 4 | 1 | no | — |
| 168 | C3×Dic5 | — | 8 | 2 | no | — |
| 169 | C3×#41 | — | 20 | 2 | no | — |
| 170 | #41⋊C3 | — | 5 | 1 | no | — |
| 171 | #41⋊C3 | — | 10 | 2 | no | — |
| 172 | #41⋊C3 | C22×D5 | 1 | 1 | yes | characteristic |
| 173 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 174 | C2×SL(2,𝔽3) | — | 5 | 1 | no | — |
| 175 | C3×Q16 | — | 20 | 1 | no | — |
| 176 | C3×SD16 | — | 20 | 2 | no | — |
| 177 | C3×D8 | — | 4 | 1 | no | — |
| 178 | C2×C3×C8 | — | 20 | 1 | no | — |
| 179 | C22×D5 | — | 3 | 1 | no | — |
| 180 | C22×D5 | — | 6 | 2 | no | — |
| 181 | C22×D5 | — | 6 | 2 | no | — |
| 182 | C5×Q8 | — | 3 | 2 | no | — |
| 183 | C5×Q8 | — | 6 | 2 | no | — |
| 184 | C5×Q8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 185 | C5×D4 | — | 3 | 1 | no | — |
| 186 | C5×D4 | — | 6 | 2 | no | — |
| 187 | C5×D4 | C22×A4 | 1 | 2 | yes | — |
| 188 | C2×C4×C5 | — | 3 | 1 | no | — |
| 189 | C2×C4×C5 | — | 6 | 2 | no | — |
| 190 | C2×C4×C5 | — | 6 | 2 | no | — |
| 191 | C22⋊D5 | — | 2 | 2 | no | — |
| 192 | C22⋊D5 | — | 3 | 2 | no | — |
| 193 | C22⋊D5 | — | 6 | 2 | no | — |
| 194 | C22⋊D5 | — | 6 | 2 | no | — |
| 195 | C2×Dic5 | — | 2 | 2 | no | — |
| 196 | C2×Dic5 | — | 3 | 1 | no | — |
| 197 | D20 | — | 3 | 1 | no | — |
| 198 | D20 | — | 3 | 2 | no | — |
| 199 | D20 | — | 6 | 2 | no | — |
| 200 | D20 | — | 6 | 4 | no | — |
| 201 | D20 | — | 6 | 2 | no | — |
| 202 | C4×D5 | — | 3 | 1 | no | — |
| 203 | C4×D5 | — | 3 | 1 | no | — |
| 204 | C4×D5 | — | 3 | 1 | no | — |
| 205 | C4×D5 | — | 6 | 2 | no | — |
| 206 | C4×D5 | — | 6 | 2 | no | — |
| 207 | C4×D5 | — | 6 | 4 | no | — |
| 208 | C4×D5 | — | 6 | 2 | no | — |
| 209 | C4×D5 | C22×A4 | 1 | 1 | yes | characteristic |
| 210 | Dic10 | — | 3 | 1 | no | — |
| 211 | Dic10 | — | 6 | 2 | no | — |
| 212 | Dic10 | C22×A4 | 1 | 2 | yes | — |
| 213 | C5×C8 | — | 3 | 1 | no | — |
| 214 | C5×C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 215 | #168 | — | 3 | 1 | no | — |
| 216 | #168 | C22×A4 | 1 | 1 | yes | characteristic |
| 217 | 2−1+4 | — | 10 | 2 | no | — |
| 218 | 2−1+4 | — | 15 | 2 | no | — |
| 219 | 2−1+4 | C2×C3×D5 | 1 | 2 | yes | — |
| 220 | H(5,𝔽2) | — | 5 | 2 | no | — |
| 221 | H(5,𝔽2) | — | 15 | 2 | no | — |
| 222 | H(5,𝔽2) | — | 30 | 2 | no | — |
| 223 | C2×#41 | — | 5 | 1 | no | — |
| 224 | C2×#41 | — | 10 | 2 | no | — |
| 225 | C2×#41 | — | 15 | 2 | no | — |
| 226 | C2×#41 | — | 15 | 2 | no | — |
| 227 | C2×#41 | — | 30 | 2 | no | — |
| 228 | #137 | — | 3 | 2 | no | — |
| 229 | #137 | — | 15 | 4 | no | — |
| 230 | #137 | — | 15 | 2 | no | — |
| 231 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 232 | AGL(1,ℤ/8) | — | 15 | 4 | no | — |
| 233 | AGL(1,ℤ/8) | — | 15 | 2 | no | — |
| 234 | #135 | — | 3 | 1 | no | — |
| 235 | #135 | — | 5 | 1 | no | — |
| 236 | #135 | — | 15 | 1 | no | — |
| 237 | #135 | — | 15 | 1 | no | — |
| 238 | #135 | — | 15 | 2 | no | — |
| 239 | #135 | — | 15 | 2 | no | — |
| 240 | #135 | — | 15 | 2 | no | — |
| 241 | #135 | — | 15 | 2 | no | — |
| 242 | #135 | — | 15 | 2 | no | — |
| 243 | C2×Q16 | — | 3 | 1 | no | — |
| 244 | C2×Q16 | — | 15 | 1 | no | — |
| 245 | C2×SD16 | — | 15 | 2 | no | — |
| 246 | C2×SD16 | — | 15 | 2 | no | — |
| 247 | C2×D8 | — | 15 | 1 | no | — |
| 248 | C2×D8 | — | 15 | 1 | no | — |
| 249 | #131 | — | 5 | 1 | no | — |
| 250 | #131 | — | 15 | 1 | no | — |
| 251 | #131 | — | 15 | 1 | no | — |
| 252 | #131 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 253 | C2×M16 | — | 15 | 1 | no | — |
| 254 | C22×C8 | — | 15 | 1 | no | — |
| 255 | C2×C3×C5 | — | 4 | 1 | no | — |
| 256 | C2×C3×C5 | — | 16 | 2 | no | — |
| 257 | C3×D5 | — | 8 | 1 | no | — |
| 258 | C3×Q8 | — | 20 | 2 | no | — |
| 259 | C3×D4 | — | 4 | 2 | no | — |
| 260 | C3×D4 | — | 40 | 2 | no | — |
| 261 | C2×C3×C4 | — | 20 | 1 | no | — |
| 262 | C2×C3×C4 | — | 40 | 2 | no | — |
| 263 | SL(2,𝔽3) | D4×D5 | 1 | 1 | yes | characteristic |
| 264 | C3×C8 | — | 4 | 1 | no | — |
| 265 | C3×C8 | — | 20 | 1 | no | — |
| 266 | C22×C5 | — | 2 | 2 | no | — |
| 267 | C22×C5 | — | 3 | 1 | no | — |
| 268 | C2×D5 | — | 3 | 1 | no | — |
| 269 | C2×D5 | — | 6 | 2 | no | — |
| 270 | C2×D5 | — | 12 | 1 | no | — |
| 271 | C2×D5 | — | 24 | 2 | no | — |
| 272 | C2×D5 | — | 24 | 2 | no | — |
| 273 | C2×D5 | D4×A4 | 1 | 1 | yes | characteristic |
| 274 | C4×C5 | — | 3 | 1 | no | — |
| 275 | C4×C5 | — | 6 | 2 | no | — |
| 276 | C4×C5 | C23×A4 | 1 | 1 | yes | characteristic |
| 277 | Dic5 | — | 2 | 2 | no | — |
| 278 | Dic5 | — | 3 | 1 | no | — |
| 279 | Dic5 | D4×A4 | 1 | 1 | yes | characteristic |
| 280 | #41 | — | 3 | 2 | no | — |
| 281 | #41 | — | 5 | 2 | no | — |
| 282 | #41 | — | 5 | 1 | no | — |
| 283 | #41 | — | 6 | 2 | no | — |
| 284 | #41 | — | 10 | 2 | no | — |
| 285 | #41 | — | 15 | 1 | no | — |
| 286 | #41 | — | 15 | 2 | no | — |
| 287 | #41 | — | 15 | 2 | no | — |
| 288 | #41 | — | 15 | 1 | no | — |
| 289 | #41 | — | 15 | 4 | no | — |
| 290 | #41 | — | 30 | 2 | no | — |
| 291 | #41 | — | 30 | 4 | no | — |
| 292 | #41 | — | 30 | 2 | no | — |
| 293 | #41 | — | 30 | 2 | no | — |
| 294 | #41 | — | 30 | 2 | no | — |
| 295 | #41 | — | 30 | 2 | no | — |
| 296 | #41 | — | 30 | 2 | no | — |
| 297 | #41 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 298 | C2×Q8 | — | 2 | 2 | no | — |
| 299 | C2×Q8 | — | 3 | 2 | no | — |
| 300 | C2×Q8 | — | 5 | 1 | no | — |
| 301 | C2×Q8 | — | 15 | 2 | no | — |
| 302 | C2×Q8 | — | 30 | 2 | no | — |
| 303 | C2×D4 | — | 15 | 2 | no | — |
| 304 | C2×D4 | — | 15 | 1 | no | — |
| 305 | C2×D4 | — | 15 | 2 | no | — |
| 306 | C2×D4 | — | 30 | 2 | no | — |
| 307 | C2×D4 | — | 30 | 2 | no | — |
| 308 | C2×D4 | — | 30 | 2 | no | — |
| 309 | C2×D4 | — | 30 | 2 | no | — |
| 310 | C2×D4 | — | 30 | 4 | no | — |
| 311 | C22×C4 | — | 15 | 1 | no | — |
| 312 | C22×C4 | — | 30 | 2 | no | — |
| 313 | C22×C4 | — | 30 | 2 | no | — |
| 314 | Q16 | — | 3 | 2 | no | — |
| 315 | Q16 | — | 3 | 1 | no | — |
| 316 | Q16 | — | 5 | 1 | no | — |
| 317 | Q16 | — | 15 | 2 | no | — |
| 318 | SD16 | — | 3 | 2 | no | — |
| 319 | SD16 | — | 5 | 2 | no | — |
| 320 | SD16 | — | 15 | 2 | no | — |
| 321 | SD16 | — | 15 | 2 | no | — |
| 322 | SD16 | — | 15 | 4 | no | — |
| 323 | D8 | — | 15 | 2 | no | — |
| 324 | D8 | — | 15 | 2 | no | — |
| 325 | D8 | — | 15 | 1 | no | — |
| 326 | D8 | D5×A4 | 1 | 1 | yes | characteristic |
| 327 | M16 | — | 3 | 1 | no | — |
| 328 | M16 | — | 15 | 2 | no | — |
| 329 | M16 | — | 15 | 1 | no | — |
| 330 | C2×C8 | — | 3 | 1 | no | — |
| 331 | C2×C8 | — | 5 | 1 | no | — |
| 332 | C2×C8 | — | 15 | 1 | no | — |
| 333 | C2×C8 | — | 15 | 1 | no | — |
| 334 | C2×C8 | — | 15 | 1 | no | — |
| 335 | C2×C8 | — | 15 | 1 | no | — |
| 336 | C3×C5 | — | 4 | 1 | no | Hall |
| 337 | C22×C3 | — | 8 | 2 | no | — |
| 338 | C22×C3 | — | 20 | 1 | no | — |
| 339 | C3×C4 | — | 4 | 1 | no | — |
| 340 | C3×C4 | — | 20 | 1 | no | — |
| 341 | C3×C4 | — | 40 | 2 | no | — |
| 342 | C2×C5 | — | 4 | 2 | no | — |
| 343 | C2×C5 | — | 6 | 1 | no | — |
| 344 | C2×C5 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 345 | D5 | — | 2 | 1 | no | — |
| 346 | D5 | — | 6 | 1 | no | — |
| 347 | D5 | — | 12 | 2 | no | — |
| 348 | C23 | — | 15 | 1 | no | — |
| 349 | C23 | — | 30 | 2 | no | — |
| 350 | C23 | — | 30 | 2 | no | — |
| 351 | Q8 | — | 3 | 2 | no | — |
| 352 | Q8 | — | 5 | 2 | no | — |
| 353 | Q8 | — | 6 | 2 | no | — |
| 354 | Q8 | — | 15 | 1 | no | — |
| 355 | Q8 | — | 30 | 2 | no | — |
| 356 | Q8 | C3×D4×D5 | 1 | 1 | yes | characteristic |
| 357 | D4 | — | 3 | 1 | no | — |
| 358 | D4 | — | 6 | 2 | no | — |
| 359 | D4 | — | 10 | 2 | no | — |
| 360 | D4 | — | 15 | 1 | no | — |
| 361 | D4 | — | 15 | 2 | no | — |
| 362 | D4 | — | 15 | 2 | no | — |
| 363 | D4 | — | 30 | 2 | no | — |
| 364 | D4 | — | 30 | 2 | no | — |
| 365 | D4 | — | 30 | 4 | no | — |
| 366 | D4 | — | 30 | 2 | no | — |
| 367 | D4 | — | 30 | 2 | no | — |
| 368 | D4 | C2×D5×A4 | 1 | 2 | yes | — |
| 369 | C2×C4 | — | 3 | 1 | no | — |
| 370 | C2×C4 | — | 5 | 1 | no | — |
| 371 | C2×C4 | — | 6 | 2 | no | — |
| 372 | C2×C4 | — | 6 | 2 | no | — |
| 373 | C2×C4 | — | 10 | 2 | no | — |
| 374 | C2×C4 | — | 15 | 1 | no | — |
| 375 | C2×C4 | — | 15 | 1 | no | — |
| 376 | C2×C4 | — | 15 | 1 | no | — |
| 377 | C2×C4 | — | 15 | 1 | no | — |
| 378 | C2×C4 | — | 30 | 2 | no | — |
| 379 | C2×C4 | — | 30 | 2 | no | — |
| 380 | C2×C4 | — | 30 | 2 | no | — |
| 381 | C2×C4 | — | 30 | 4 | no | — |
| 382 | C8 | — | 3 | 1 | no | — |
| 383 | C8 | — | 5 | 1 | no | — |
| 384 | C8 | — | 15 | 1 | no | — |
| 385 | C8 | C2×D5×A4 | 1 | 1 | yes | characteristic |
| 386 | C2×C3 | — | 4 | 1 | no | — |
| 387 | C2×C3 | — | 16 | 2 | no | — |
| 388 | C2×C3 | — | 40 | 1 | no | — |
| 389 | C5 | #3584⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 390 | C22 | — | 2 | 2 | no | — |
| 391 | C22 | — | 3 | 1 | no | — |
| 392 | C22 | — | 5 | 1 | no | — |
| 393 | C22 | — | 15 | 1 | no | — |
| 394 | C22 | — | 30 | 2 | no | — |
| 395 | C22 | — | 60 | 1 | no | — |
| 396 | C22 | — | 120 | 2 | no | — |
| 397 | C22 | — | 120 | 2 | no | — |
| 398 | C4 | — | 3 | 1 | no | — |
| 399 | C4 | — | 5 | 1 | no | — |
| 400 | C4 | — | 6 | 2 | no | — |
| 401 | C4 | — | 10 | 2 | no | — |
| 402 | C4 | — | 15 | 1 | no | — |
| 403 | C4 | C22×D5×A4 | 1 | 1 | yes | characteristic |
| 404 | C3 | — | 4 | 1 | no | Sylow |
| 405 | C2 | — | 4 | 2 | no | — |
| 406 | C2 | — | 6 | 1 | no | — |
| 407 | C2 | — | 10 | 1 | no | — |
| 408 | C2 | — | 30 | 1 | no | — |
| 409 | C2 | — | 60 | 2 | no | — |
| 410 | C2 | D4×D5×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D5×A4 |
| commutator, cosocle | C5×#41 | C23×C3 |
| Frattini | C4 | C22×D5×A4 |
| Fitting | C5×#578 | C2×C3 |
| socle | C2×C5 | C2×D4×A4 |
| hypercenter | D8 | D5×A4 |
| hypocenter | C5×Q8 | C2×C3×D4 |
| LCS | G ▷ C5×#41 ▷ C5×Q8 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #66287⋊C3 | C2 | semidirect |
| 2. C5×#578⋊C3 | C2 | semidirect |
| 3. #66171⋊C3 | C2 | semidirect |
| 4. #66086⋊C3 | C2 | semidirect |
| 5. D5×#131⋊C3 | C2 | semidirect |
| 6. #10619111 | C3 | semidirect |
| 7. C5×2−1+4⋊C3 | C22 | semidirect |
| 9. C5⋊#994 | C22 | semidirect |
| 13. C5×#131⋊C3 | C22 | semidirect |
| 14. #4094⋊C3 | C22 | semidirect |
| 16. #66287 | C2×C3 | semidirect |
| 17. C5×#578 | C2×C3 | semidirect |
| 18. #66171 | C2×C3 | semidirect |
| 25. #66086 | C2×C3 | semidirect |
| 26. D5×#131 | C2×C3 | semidirect |
| 38. #578⋊C3 | D5 | semidirect |
| 90. 2−1+4⋊C3 | C2×D5 | semidirect |
| 96. #131⋊C3 | C2×D5 | semidirect |
| 155. #578 | C3×D5 | semidirect |
| 389. C5 | #3584⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66287⋊C3 | 2 |
| C5×#578⋊C3 | 2 |
| #66171⋊C3 | 2 |
| #66086⋊C3 | 2 |
| D5×#131⋊C3 | 2 |
| #10619111 | 3 |
| C3×#4058 | 4 |
| #3584⋊C3 | 5 |