Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 64 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×#5927 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#5926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#578⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#5431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#5430 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C5×#5406 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C5×#5405 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C5×#3289 | — | 3 | 1 | no | maximal, Hall |
| 9 | C5×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 10 | C5×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×#986 | C22 | 1 | 1 | yes | characteristic |
| 12 | C5×#985 | C22 | 1 | 1 | yes | characteristic |
| 13 | C5×#984 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C5×#983 | — | 2 | 1 | no | — |
| 15 | C5×#983 | — | 2 | 1 | no | — |
| 16 | C2×C5×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 17 | C2×C5×#226 | — | 2 | 1 | no | — |
| 18 | C5×#911 | — | 4 | 1 | no | maximal |
| 19 | C5×#131⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C5×GU(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #85474 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 22 | C5×#578 | — | 3 | 1 | no | — |
| 23 | C5×#578 | D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C5×#577 | — | 3 | 1 | no | — |
| 25 | C5×#577 | — | 3 | 1 | no | — |
| 26 | C5×#497 | — | 3 | 1 | no | — |
| 27 | C5×#473 | — | 3 | 1 | no | — |
| 28 | C5×#473 | — | 3 | 1 | no | — |
| 29 | C5×#471 | — | 3 | 1 | no | — |
| 30 | C5×#471 | — | 3 | 1 | no | — |
| 31 | C5×#456 | — | 3 | 1 | no | — |
| 32 | C5×#456 | — | 3 | 1 | no | — |
| 33 | C5×#455 | — | 3 | 1 | no | — |
| 34 | C5×#454 | — | 3 | 1 | no | — |
| 35 | C5×#444 | — | 3 | 1 | no | — |
| 36 | C5×#444 | — | 3 | 1 | no | — |
| 37 | C5×#237 | — | 4 | 1 | no | — |
| 38 | C5×D3×D4 | — | 4 | 1 | no | — |
| 39 | C5×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×C5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 41 | C2×C5×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 42 | C5×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 43 | C5×GL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 44 | C5×#226 | — | 2 | 1 | no | — |
| 45 | C5×#226 | D4 | 1 | 1 | yes | characteristic |
| 46 | C3×C5×D8 | — | 4 | 1 | no | — |
| 47 | C5×#214 | — | 4 | 1 | no | — |
| 48 | C5×#213 | — | 4 | 1 | no | — |
| 49 | C5×#204 | — | 4 | 1 | no | — |
| 50 | C5×ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 51 | #5927 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 52 | #5926 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 53 | #578⋊C3 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 54 | #5431 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 55 | #5430 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 56 | #5406 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 57 | #5405 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 58 | C5×2−1+4 | — | 3 | 1 | no | — |
| 59 | C5×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 60 | C5×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 61 | C5×H(5,𝔽2) | — | 3 | 1 | no | — |
| 62 | C5×#137 | — | 3 | 1 | no | — |
| 63 | C5×#137 | — | 3 | 1 | no | — |
| 64 | C5×#137 | — | 3 | 1 | no | — |
| 65 | C5×#137 | — | 3 | 1 | no | — |
| 66 | C5×#137 | — | 3 | 1 | no | — |
| 67 | C5×#137 | — | 3 | 1 | no | — |
| 68 | C5×#137 | — | 6 | 1 | no | — |
| 69 | C5×#137 | — | 6 | 1 | no | — |
| 70 | C5×#137 | — | 6 | 1 | no | — |
| 71 | C5×#137 | — | 6 | 1 | no | — |
| 72 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 73 | C5×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 74 | C5×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 75 | C5×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 76 | C5×#135 | — | 3 | 1 | no | — |
| 77 | C5×#135 | — | 3 | 1 | no | — |
| 78 | C5×#135 | — | 6 | 1 | no | — |
| 79 | C5×#135 | — | 6 | 1 | no | — |
| 80 | C5×#135 | — | 6 | 1 | no | — |
| 81 | C2×C5×Q16 | — | 3 | 1 | no | — |
| 82 | C2×C5×Q16 | — | 3 | 1 | no | — |
| 83 | C2×C5×Q16 | — | 6 | 1 | no | — |
| 84 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 85 | C2×C5×SD16 | — | 3 | 1 | no | — |
| 86 | C2×C5×SD16 | — | 6 | 1 | no | — |
| 87 | C2×C5×SD16 | — | 6 | 1 | no | — |
| 88 | C5×#131 | — | 3 | 1 | no | — |
| 89 | C5×#131 | — | 3 | 1 | no | — |
| 90 | C5×#131 | — | 3 | 1 | no | — |
| 91 | C5×#131 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 92 | C5×C4⋊Q8 | — | 3 | 1 | no | — |
| 93 | C5×#124 | — | 3 | 1 | no | — |
| 94 | C5×#108 | — | 3 | 1 | no | — |
| 95 | C5×#108 | — | 3 | 1 | no | — |
| 96 | C5×#104 | — | 3 | 1 | no | — |
| 97 | C5×#104 | — | 3 | 1 | no | — |
| 98 | C5×#104 | — | 3 | 1 | no | — |
| 99 | C5×#104 | — | 3 | 1 | no | — |
| 100 | C5×#101 | — | 3 | 1 | no | — |
| 101 | C5×#101 | — | 3 | 1 | no | — |
| 102 | C5×#101 | — | 3 | 1 | no | — |
| 103 | C5×#100 | — | 3 | 1 | no | — |
| 104 | C5×#97 | — | 3 | 1 | no | — |
| 105 | #3289 | — | 3 | 1 | no | Sylow |
| 106 | C22×C5×D3 | — | 8 | 1 | no | — |
| 107 | C3×C5×D4 | — | 4 | 1 | no | — |
| 108 | C3×C5×D4 | — | 4 | 1 | no | — |
| 109 | C5×#67 | — | 8 | 1 | no | — |
| 110 | C5×#67 | — | 8 | 1 | no | — |
| 111 | C2×C5×Dic3 | — | 8 | 1 | no | — |
| 112 | C5×D12 | — | 4 | 1 | no | — |
| 113 | C4×C5×D3 | — | 4 | 1 | no | — |
| 114 | C5×Dic6 | — | 4 | 1 | no | — |
| 115 | C5×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C3×C5×C8 | — | 4 | 1 | no | — |
| 117 | C5×C3⋊C8 | — | 4 | 1 | no | — |
| 118 | 2−1+4⋊C3 | C22×C5 | 1 | 1 | yes | characteristic |
| 119 | 2−1+4⋊C3 | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 120 | #986 | C22×C5 | 1 | 1 | yes | characteristic |
| 121 | #985 | C22×C5 | 1 | 1 | yes | characteristic |
| 122 | #984 | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 123 | #983 | — | 2 | 1 | no | — |
| 124 | #983 | — | 2 | 1 | no | — |
| 125 | C2×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 126 | C2×#226 | — | 2 | 1 | no | — |
| 127 | #911 | — | 4 | 1 | no | — |
| 128 | #131⋊C3 | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 129 | GU(2,𝔽3) | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 130 | C5×#41 | — | 3 | 1 | no | — |
| 131 | C5×#41 | — | 3 | 1 | no | — |
| 132 | C5×#41 | — | 3 | 1 | no | — |
| 133 | C5×#41 | — | 6 | 1 | no | — |
| 134 | C5×#41 | — | 6 | 1 | no | — |
| 135 | C5×#41 | — | 6 | 1 | no | — |
| 136 | C5×#41 | — | 6 | 1 | no | — |
| 137 | C5×#41 | — | 6 | 1 | no | — |
| 138 | C5×#41 | — | 6 | 1 | no | — |
| 139 | C5×#41 | — | 12 | 1 | no | — |
| 140 | C5×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 141 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 142 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 143 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 144 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 145 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 146 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 147 | C2×C5×Q8 | — | 6 | 1 | no | — |
| 148 | C2×C5×D4 | — | 3 | 1 | no | — |
| 149 | C2×C5×D4 | — | 6 | 1 | no | — |
| 150 | C2×C5×D4 | — | 6 | 1 | no | — |
| 151 | C2×C5×D4 | — | 12 | 1 | no | — |
| 152 | C5×Q16 | — | 3 | 1 | no | — |
| 153 | C5×Q16 | — | 3 | 1 | no | — |
| 154 | C5×Q16 | — | 6 | 1 | no | — |
| 155 | C5×Q16 | — | 6 | 1 | no | — |
| 156 | C5×Q16 | — | 6 | 1 | no | — |
| 157 | C5×Q16 | — | 6 | 1 | no | — |
| 158 | C5×Q16 | — | 6 | 1 | no | — |
| 159 | C5×Q16 | — | 6 | 1 | no | — |
| 160 | C5×Q16 | — | 6 | 1 | no | — |
| 161 | C5×SD16 | — | 3 | 1 | no | — |
| 162 | C5×SD16 | — | 3 | 1 | no | — |
| 163 | C5×SD16 | — | 3 | 1 | no | — |
| 164 | C5×SD16 | — | 3 | 1 | no | — |
| 165 | C5×SD16 | — | 6 | 1 | no | — |
| 166 | C5×SD16 | — | 6 | 1 | no | — |
| 167 | C5×SD16 | — | 6 | 1 | no | — |
| 168 | C5×SD16 | — | 6 | 1 | no | — |
| 169 | C5×SD16 | — | 6 | 1 | no | — |
| 170 | C5×SD16 | — | 6 | 1 | no | — |
| 171 | C5×SD16 | — | 6 | 1 | no | — |
| 172 | C5×SD16 | — | 6 | 1 | no | — |
| 173 | C5×SD16 | — | 6 | 1 | no | — |
| 174 | C5×SD16 | — | 6 | 1 | no | — |
| 175 | C5×D8 | — | 3 | 1 | no | — |
| 176 | C5×D8 | — | 6 | 1 | no | — |
| 177 | C5×D8 | — | 6 | 1 | no | — |
| 178 | C5×D8 | S4 | 1 | 1 | yes | characteristic |
| 179 | C5×M16 | — | 3 | 1 | no | — |
| 180 | C5×M16 | — | 3 | 1 | no | — |
| 181 | C5×M16 | — | 3 | 1 | no | — |
| 182 | C5×M16 | — | 3 | 1 | no | — |
| 183 | C5×M16 | — | 6 | 1 | no | — |
| 184 | C5×M16 | — | 6 | 1 | no | — |
| 185 | C5×M16 | — | 6 | 1 | no | — |
| 186 | C2×C5×C8 | — | 3 | 1 | no | — |
| 187 | C2×C5×C8 | — | 3 | 1 | no | — |
| 188 | C2×C5×C8 | — | 6 | 1 | no | — |
| 189 | C2×C5×C8 | — | 6 | 1 | no | — |
| 190 | C2×C5×C8 | — | 6 | 1 | no | — |
| 191 | C5×C4⋊C4 | — | 12 | 1 | no | — |
| 192 | C5×C22⋊C4 | — | 12 | 1 | no | — |
| 193 | C42×C5 | — | 3 | 1 | no | — |
| 194 | #578 | — | 3 | 1 | no | — |
| 195 | #578 | C5×D3 | 1 | 1 | yes | characteristic, complemented |
| 196 | #577 | — | 3 | 1 | no | — |
| 197 | #577 | — | 3 | 1 | no | — |
| 198 | #497 | — | 3 | 1 | no | — |
| 199 | #473 | — | 3 | 1 | no | — |
| 200 | #473 | — | 3 | 1 | no | — |
| 201 | #471 | — | 3 | 1 | no | — |
| 202 | #471 | — | 3 | 1 | no | — |
| 203 | #456 | — | 3 | 1 | no | — |
| 204 | #456 | — | 3 | 1 | no | — |
| 205 | #455 | — | 3 | 1 | no | — |
| 206 | #454 | — | 3 | 1 | no | — |
| 207 | #444 | — | 3 | 1 | no | — |
| 208 | #444 | — | 3 | 1 | no | — |
| 209 | C22×C3×C5 | — | 8 | 1 | no | — |
| 210 | C22×C3×C5 | — | 8 | 1 | no | — |
| 211 | C2×C5×D3 | — | 4 | 1 | no | — |
| 212 | C2×C5×D3 | — | 8 | 1 | no | — |
| 213 | C2×C5×D3 | — | 16 | 2 | no | — |
| 214 | C3×C4×C5 | — | 4 | 1 | no | — |
| 215 | C5×Dic3 | — | 4 | 1 | no | — |
| 216 | C5×Dic3 | — | 8 | 1 | no | — |
| 217 | #237 | — | 4 | 1 | no | — |
| 218 | D3×D4 | — | 4 | 1 | no | — |
| 219 | #41⋊C3 | C23×C5 | 1 | 1 | yes | characteristic |
| 220 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 221 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 222 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 223 | GL(2,𝔽3) | C5×D4 | 1 | 1 | yes | characteristic |
| 224 | #226 | — | 2 | 1 | no | — |
| 225 | #226 | C5×D4 | 1 | 1 | yes | characteristic |
| 226 | C3×D8 | — | 4 | 1 | no | — |
| 227 | #214 | — | 4 | 1 | no | — |
| 228 | #213 | — | 4 | 1 | no | — |
| 229 | #204 | — | 4 | 1 | no | — |
| 230 | ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 231 | C23×C5 | — | 6 | 1 | no | — |
| 232 | C23×C5 | — | 12 | 1 | no | — |
| 233 | C5×Q8 | — | 3 | 1 | no | — |
| 234 | C5×Q8 | — | 3 | 1 | no | — |
| 235 | C5×Q8 | — | 3 | 1 | no | — |
| 236 | C5×Q8 | — | 6 | 1 | no | — |
| 237 | C5×Q8 | — | 6 | 1 | no | — |
| 238 | C5×Q8 | — | 6 | 1 | no | — |
| 239 | C5×Q8 | — | 6 | 1 | no | — |
| 240 | C5×Q8 | — | 12 | 1 | no | — |
| 241 | C5×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 242 | C5×D4 | — | 3 | 1 | no | — |
| 243 | C5×D4 | — | 3 | 1 | no | — |
| 244 | C5×D4 | — | 6 | 1 | no | — |
| 245 | C5×D4 | — | 6 | 1 | no | — |
| 246 | C5×D4 | — | 6 | 1 | no | — |
| 247 | C5×D4 | — | 6 | 1 | no | — |
| 248 | C5×D4 | — | 6 | 1 | no | — |
| 249 | C5×D4 | — | 12 | 1 | no | — |
| 250 | C5×D4 | — | 12 | 1 | no | — |
| 251 | C5×D4 | — | 12 | 1 | no | — |
| 252 | C5×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 253 | C5×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×C5 | — | 3 | 1 | no | — |
| 255 | C2×C4×C5 | — | 6 | 1 | no | — |
| 256 | C2×C4×C5 | — | 6 | 1 | no | — |
| 257 | C2×C4×C5 | — | 6 | 1 | no | — |
| 258 | C2×C4×C5 | — | 6 | 1 | no | — |
| 259 | C2×C4×C5 | — | 6 | 1 | no | — |
| 260 | C2×C4×C5 | — | 6 | 1 | no | — |
| 261 | C2×C4×C5 | — | 6 | 1 | no | — |
| 262 | C2×C4×C5 | — | 12 | 1 | no | — |
| 263 | C2×C4×C5 | — | 12 | 1 | no | — |
| 264 | C2×C4×C5 | — | 12 | 1 | no | — |
| 265 | C5×C8 | — | 3 | 1 | no | — |
| 266 | C5×C8 | — | 3 | 1 | no | — |
| 267 | C5×C8 | — | 3 | 1 | no | — |
| 268 | C5×C8 | — | 6 | 1 | no | — |
| 269 | C5×C8 | — | 6 | 1 | no | — |
| 270 | C5×C8 | — | 6 | 1 | no | — |
| 271 | C5×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 272 | 2−1+4 | — | 3 | 1 | no | — |
| 273 | 2−1+4 | C2×C5×D3 | 1 | 1 | yes | characteristic |
| 274 | 2−1+4 | C2×C5×D3 | 1 | 1 | yes | characteristic, complemented |
| 275 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 276 | #137 | — | 3 | 1 | no | — |
| 277 | #137 | — | 3 | 1 | no | — |
| 278 | #137 | — | 3 | 1 | no | — |
| 279 | #137 | — | 3 | 1 | no | — |
| 280 | #137 | — | 3 | 1 | no | — |
| 281 | #137 | — | 3 | 1 | no | — |
| 282 | #137 | — | 6 | 1 | no | — |
| 283 | #137 | — | 6 | 1 | no | — |
| 284 | #137 | — | 6 | 1 | no | — |
| 285 | #137 | — | 6 | 1 | no | — |
| 286 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 287 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 288 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 289 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 290 | #135 | — | 3 | 1 | no | — |
| 291 | #135 | — | 3 | 1 | no | — |
| 292 | #135 | — | 6 | 1 | no | — |
| 293 | #135 | — | 6 | 1 | no | — |
| 294 | #135 | — | 6 | 1 | no | — |
| 295 | C2×Q16 | — | 3 | 1 | no | — |
| 296 | C2×Q16 | — | 3 | 1 | no | — |
| 297 | C2×Q16 | — | 6 | 1 | no | — |
| 298 | C2×SD16 | — | 3 | 1 | no | — |
| 299 | C2×SD16 | — | 3 | 1 | no | — |
| 300 | C2×SD16 | — | 6 | 1 | no | — |
| 301 | C2×SD16 | — | 6 | 1 | no | — |
| 302 | #131 | — | 3 | 1 | no | — |
| 303 | #131 | — | 3 | 1 | no | — |
| 304 | #131 | — | 3 | 1 | no | — |
| 305 | #131 | C2×C5×D3 | 1 | 1 | yes | characteristic, complemented |
| 306 | C4⋊Q8 | — | 3 | 1 | no | — |
| 307 | #124 | — | 3 | 1 | no | — |
| 308 | #108 | — | 3 | 1 | no | — |
| 309 | #108 | — | 3 | 1 | no | — |
| 310 | #104 | — | 3 | 1 | no | — |
| 311 | #104 | — | 3 | 1 | no | — |
| 312 | #104 | — | 3 | 1 | no | — |
| 313 | #104 | — | 3 | 1 | no | — |
| 314 | #101 | — | 3 | 1 | no | — |
| 315 | #101 | — | 3 | 1 | no | — |
| 316 | #101 | — | 3 | 1 | no | — |
| 317 | #100 | — | 3 | 1 | no | — |
| 318 | #97 | — | 3 | 1 | no | — |
| 319 | C2×C3×C5 | — | 4 | 1 | no | — |
| 320 | C2×C3×C5 | — | 16 | 1 | no | — |
| 321 | C2×C3×C5 | — | 16 | 1 | no | — |
| 322 | C5×D3 | — | 8 | 1 | no | — |
| 323 | C5×D3 | — | 16 | 1 | no | — |
| 324 | C22×D3 | — | 8 | 1 | no | — |
| 325 | C3×D4 | — | 4 | 1 | no | — |
| 326 | C3×D4 | — | 4 | 1 | no | — |
| 327 | #67 | — | 8 | 1 | no | — |
| 328 | #67 | — | 8 | 1 | no | — |
| 329 | C2×Dic3 | — | 8 | 1 | no | — |
| 330 | D12 | — | 4 | 1 | no | — |
| 331 | C4×D3 | — | 4 | 1 | no | — |
| 332 | Dic6 | — | 4 | 1 | no | — |
| 333 | SL(2,𝔽3) | C2×C5×D4 | 1 | 1 | yes | characteristic |
| 334 | C3×C8 | — | 4 | 1 | no | — |
| 335 | C3⋊C8 | — | 4 | 1 | no | — |
| 336 | C22×C5 | — | 2 | 1 | no | — |
| 337 | C22×C5 | — | 2 | 1 | no | — |
| 338 | C22×C5 | — | 3 | 1 | no | — |
| 339 | C22×C5 | — | 6 | 1 | no | — |
| 340 | C22×C5 | — | 12 | 1 | no | — |
| 341 | C22×C5 | — | 24 | 1 | no | — |
| 342 | C22×C5 | — | 48 | 1 | no | — |
| 343 | C4×C5 | — | 3 | 1 | no | — |
| 344 | C4×C5 | — | 6 | 1 | no | — |
| 345 | C4×C5 | — | 6 | 1 | no | — |
| 346 | C4×C5 | — | 6 | 1 | no | — |
| 347 | C4×C5 | — | 12 | 1 | no | — |
| 348 | C4×C5 | — | 12 | 1 | no | — |
| 349 | C4×C5 | C22×S4 | 1 | 1 | yes | characteristic |
| 350 | #41 | — | 3 | 1 | no | — |
| 351 | #41 | — | 3 | 1 | no | — |
| 352 | #41 | — | 3 | 1 | no | — |
| 353 | #41 | — | 6 | 1 | no | — |
| 354 | #41 | — | 6 | 1 | no | — |
| 355 | #41 | — | 6 | 1 | no | — |
| 356 | #41 | — | 6 | 1 | no | — |
| 357 | #41 | — | 6 | 1 | no | — |
| 358 | #41 | — | 6 | 1 | no | — |
| 359 | #41 | — | 12 | 1 | no | — |
| 360 | #41 | C22×C5×D3 | 1 | 1 | yes | characteristic |
| 361 | C2×Q8 | — | 2 | 1 | no | — |
| 362 | C2×Q8 | — | 2 | 1 | no | — |
| 363 | C2×Q8 | — | 3 | 1 | no | — |
| 364 | C2×Q8 | — | 3 | 1 | no | — |
| 365 | C2×Q8 | — | 3 | 1 | no | — |
| 366 | C2×Q8 | — | 6 | 1 | no | — |
| 367 | C2×Q8 | — | 6 | 1 | no | — |
| 368 | C2×D4 | — | 3 | 1 | no | — |
| 369 | C2×D4 | — | 6 | 1 | no | — |
| 370 | C2×D4 | — | 6 | 1 | no | — |
| 371 | C2×D4 | — | 12 | 1 | no | — |
| 372 | Q16 | — | 3 | 1 | no | — |
| 373 | Q16 | — | 3 | 1 | no | — |
| 374 | Q16 | — | 6 | 1 | no | — |
| 375 | Q16 | — | 6 | 1 | no | — |
| 376 | Q16 | — | 6 | 1 | no | — |
| 377 | Q16 | — | 6 | 1 | no | — |
| 378 | Q16 | — | 6 | 1 | no | — |
| 379 | Q16 | — | 6 | 1 | no | — |
| 380 | Q16 | — | 6 | 1 | no | — |
| 381 | SD16 | — | 3 | 1 | no | — |
| 382 | SD16 | — | 3 | 1 | no | — |
| 383 | SD16 | — | 3 | 1 | no | — |
| 384 | SD16 | — | 3 | 1 | no | — |
| 385 | SD16 | — | 6 | 1 | no | — |
| 386 | SD16 | — | 6 | 1 | no | — |
| 387 | SD16 | — | 6 | 1 | no | — |
| 388 | SD16 | — | 6 | 1 | no | — |
| 389 | SD16 | — | 6 | 1 | no | — |
| 390 | SD16 | — | 6 | 1 | no | — |
| 391 | SD16 | — | 6 | 1 | no | — |
| 392 | SD16 | — | 6 | 1 | no | — |
| 393 | SD16 | — | 6 | 1 | no | — |
| 394 | SD16 | — | 6 | 1 | no | — |
| 395 | D8 | — | 3 | 1 | no | — |
| 396 | D8 | — | 6 | 1 | no | — |
| 397 | D8 | — | 6 | 1 | no | — |
| 398 | D8 | C5×S4 | 1 | 1 | yes | characteristic |
| 399 | M16 | — | 3 | 1 | no | — |
| 400 | M16 | — | 3 | 1 | no | — |
| 401 | M16 | — | 3 | 1 | no | — |
| 402 | M16 | — | 3 | 1 | no | — |
| 403 | M16 | — | 6 | 1 | no | — |
| 404 | M16 | — | 6 | 1 | no | — |
| 405 | M16 | — | 6 | 1 | no | — |
| 406 | C2×C8 | — | 3 | 1 | no | — |
| 407 | C2×C8 | — | 3 | 1 | no | — |
| 408 | C2×C8 | — | 6 | 1 | no | — |
| 409 | C2×C8 | — | 6 | 1 | no | — |
| 410 | C2×C8 | — | 6 | 1 | no | — |
| 411 | C4⋊C4 | — | 12 | 1 | no | — |
| 412 | C22⋊C4 | — | 12 | 1 | no | — |
| 413 | C42 | — | 3 | 1 | no | — |
| 414 | C3×C5 | — | 4 | 1 | no | Hall |
| 415 | C22×C3 | — | 8 | 1 | no | — |
| 416 | C22×C3 | — | 8 | 1 | no | — |
| 417 | C2×D3 | — | 4 | 1 | no | — |
| 418 | C2×D3 | — | 8 | 1 | no | — |
| 419 | C2×D3 | — | 16 | 2 | no | — |
| 420 | C3×C4 | — | 4 | 1 | no | — |
| 421 | Dic3 | — | 4 | 1 | no | — |
| 422 | Dic3 | — | 8 | 1 | no | — |
| 423 | C2×C5 | — | 4 | 1 | no | — |
| 424 | C2×C5 | — | 4 | 1 | no | — |
| 425 | C2×C5 | — | 6 | 1 | no | — |
| 426 | C2×C5 | — | 12 | 1 | no | — |
| 427 | C2×C5 | — | 24 | 1 | no | — |
| 428 | C2×C5 | D4×S4 | 1 | 1 | yes | characteristic |
| 429 | C23 | — | 6 | 1 | no | — |
| 430 | C23 | — | 12 | 1 | no | — |
| 431 | Q8 | — | 3 | 1 | no | — |
| 432 | Q8 | — | 3 | 1 | no | — |
| 433 | Q8 | — | 3 | 1 | no | — |
| 434 | Q8 | — | 6 | 1 | no | — |
| 435 | Q8 | — | 6 | 1 | no | — |
| 436 | Q8 | — | 6 | 1 | no | — |
| 437 | Q8 | — | 6 | 1 | no | — |
| 438 | Q8 | — | 12 | 1 | no | — |
| 439 | Q8 | C5×D3×D4 | 1 | 1 | yes | characteristic |
| 440 | D4 | — | 3 | 1 | no | — |
| 441 | D4 | — | 3 | 1 | no | — |
| 442 | D4 | — | 6 | 1 | no | — |
| 443 | D4 | — | 6 | 1 | no | — |
| 444 | D4 | — | 6 | 1 | no | — |
| 445 | D4 | — | 6 | 1 | no | — |
| 446 | D4 | — | 6 | 1 | no | — |
| 447 | D4 | — | 12 | 1 | no | — |
| 448 | D4 | — | 12 | 1 | no | — |
| 449 | D4 | — | 12 | 1 | no | — |
| 450 | D4 | C2×C5×S4 | 1 | 1 | yes | characteristic |
| 451 | D4 | C2×C5×S4 | 1 | 1 | yes | characteristic |
| 452 | C2×C4 | — | 3 | 1 | no | — |
| 453 | C2×C4 | — | 6 | 1 | no | — |
| 454 | C2×C4 | — | 6 | 1 | no | — |
| 455 | C2×C4 | — | 6 | 1 | no | — |
| 456 | C2×C4 | — | 6 | 1 | no | — |
| 457 | C2×C4 | — | 6 | 1 | no | — |
| 458 | C2×C4 | — | 6 | 1 | no | — |
| 459 | C2×C4 | — | 6 | 1 | no | — |
| 460 | C2×C4 | — | 12 | 1 | no | — |
| 461 | C2×C4 | — | 12 | 1 | no | — |
| 462 | C2×C4 | — | 12 | 1 | no | — |
| 463 | C8 | — | 3 | 1 | no | — |
| 464 | C8 | — | 3 | 1 | no | — |
| 465 | C8 | — | 3 | 1 | no | — |
| 466 | C8 | — | 6 | 1 | no | — |
| 467 | C8 | — | 6 | 1 | no | — |
| 468 | C8 | — | 6 | 1 | no | — |
| 469 | C8 | C2×C5×S4 | 1 | 1 | yes | characteristic |
| 470 | C2×C3 | — | 4 | 1 | no | — |
| 471 | C2×C3 | — | 16 | 1 | no | — |
| 472 | C2×C3 | — | 16 | 1 | no | — |
| 473 | D3 | — | 8 | 1 | no | — |
| 474 | D3 | — | 16 | 1 | no | — |
| 475 | C5 | #85474 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 476 | C22 | — | 2 | 1 | no | — |
| 477 | C22 | — | 2 | 1 | no | — |
| 478 | C22 | — | 3 | 1 | no | — |
| 479 | C22 | — | 6 | 1 | no | — |
| 480 | C22 | — | 12 | 1 | no | — |
| 481 | C22 | — | 24 | 1 | no | — |
| 482 | C22 | — | 48 | 1 | no | — |
| 483 | C4 | — | 3 | 1 | no | — |
| 484 | C4 | — | 6 | 1 | no | — |
| 485 | C4 | — | 6 | 1 | no | — |
| 486 | C4 | — | 6 | 1 | no | — |
| 487 | C4 | — | 12 | 1 | no | — |
| 488 | C4 | — | 12 | 1 | no | — |
| 489 | C4 | C22×C5×S4 | 1 | 1 | yes | characteristic |
| 490 | C3 | — | 4 | 1 | no | Sylow |
| 491 | C2 | — | 4 | 1 | no | — |
| 492 | C2 | — | 4 | 1 | no | — |
| 493 | C2 | — | 6 | 1 | no | — |
| 494 | C2 | — | 12 | 1 | no | — |
| 495 | C2 | — | 24 | 1 | no | — |
| 496 | C2 | C5×D4×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | D4×S4 |
| commutator, cosocle | #41⋊C3 | C23×C5 |
| Frattini | C4 | C22×C5×S4 |
| Fitting | C5×#578 | D3 |
| hypercenter | C5×D8 | S4 |
| hypocenter | SL(2,𝔽3) | C2×C5×D4 |
| LCS | G ▷ #41⋊C3 ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#5927 | C2 | semidirect |
| 2. C5×#5926 | C2 | semidirect |
| 3. C5×#578⋊C3 | C2 | semidirect |
| 4. C5×#5431 | C2 | semidirect |
| 5. C5×#5430 | C2 | semidirect |
| 6. C5×#5406 | C2 | semidirect |
| 7. C5×#5405 | C2 | semidirect |
| 10. C5×2−1+4⋊C3 | C22 | semidirect |
| 13. C5×#984 | C22 | semidirect |
| 19. C5×#131⋊C3 | C22 | semidirect |
| 20. C5×GU(2,𝔽3) | C22 | semidirect |
| 21. #85474 | C5 | direct (N × H) |
| 23. C5×#578 | D3 | semidirect |
| 51. #5927 | C2×C5 | semidirect |
| 52. #5926 | C2×C5 | semidirect |
| 53. #578⋊C3 | C2×C5 | semidirect |
| 54. #5431 | C2×C5 | semidirect |
| 55. #5430 | C2×C5 | semidirect |
| 56. #5406 | C2×C5 | semidirect |
| 57. #5405 | C2×C5 | semidirect |
| 60. C5×2−1+4 | C2×D3 | semidirect |
| 91. C5×#131 | C2×D3 | semidirect |
| 119. 2−1+4⋊C3 | C22×C5 | semidirect |
| 122. #984 | C22×C5 | semidirect |
| 128. #131⋊C3 | C22×C5 | semidirect |
| 129. GU(2,𝔽3) | C22×C5 | semidirect |
| 195. #578 | C5×D3 | semidirect |
| 274. 2−1+4 | C2×C5×D3 | semidirect |
| 305. #131 | C2×C5×D3 | semidirect |
| 475. C5 | #85474 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5927 | 2 |
| C5×#5926 | 2 |
| C5×#578⋊C3 | 2 |
| C5×#5431 | 2 |
| C5×#5430 | 2 |
| C5×#5406 | 2 |
| C5×#5405 | 2 |
| C5×#3289 | 3 |
| C5×#911 | 4 |
| #85474 | 5 |