Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1184 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 218 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×#3483 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×#3018 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C5×#2205 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C5×#2204 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C5×#2132 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C5×#585 | C22 | 1 | 1 | yes | characteristic |
| 7 | C5×#575 | — | 2 | 3 | no | — |
| 8 | C5×Q82 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | C5×#555 | — | 2 | 3 | no | — |
| 10 | C5×#555 | C22 | 1 | 3 | yes | complemented |
| 11 | C5×#550 | — | 2 | 3 | no | — |
| 12 | C5×#532 | — | 2 | 3 | no | — |
| 13 | C5×#532 | C22 | 1 | 3 | yes | — |
| 14 | C4×C5×#41 | — | 2 | 3 | no | — |
| 15 | C5×#456 | C22 | 1 | 6 | yes | — |
| 16 | C5×#455 | — | 2 | 3 | no | — |
| 17 | C5×#454 | C22 | 1 | 6 | yes | — |
| 18 | C5×#453 | — | 2 | 3 | no | — |
| 19 | C2×C5×#104 | — | 2 | 3 | no | — |
| 20 | C5×#413 | C22 | 1 | 3 | yes | — |
| 21 | C5×#356 | C22 | 1 | 6 | yes | complemented |
| 22 | C5×#355 | C22 | 1 | 6 | yes | complemented |
| 23 | #33567 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 24 | C5×2−1+4 | — | 4 | 1 | no | — |
| 25 | C5×2−1+4 | C23 | 1 | 2 | yes | — |
| 26 | C5×H(5,𝔽2) | — | 2 | 3 | no | — |
| 27 | C5×H(5,𝔽2) | — | 4 | 1 | no | — |
| 28 | C2×C5×#41 | — | 2 | 3 | no | — |
| 29 | C2×C5×#41 | — | 2 | 1 | no | — |
| 30 | C2×C5×#41 | — | 2 | 3 | no | — |
| 31 | C2×C5×#41 | — | 4 | 2 | no | — |
| 32 | C2×C5×#41 | D4 | 1 | 3 | yes | — |
| 33 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 34 | C5×#137 | — | 2 | 6 | no | — |
| 35 | C5×#137 | — | 4 | 3 | no | — |
| 36 | C5×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 37 | C5×AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 38 | C5×#135 | — | 4 | 6 | no | — |
| 39 | C2×C5×M16 | — | 2 | 3 | no | — |
| 40 | C5×C4⋊Q8 | — | 2 | 3 | no | — |
| 41 | C5×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 42 | C5×#127 | — | 2 | 3 | no | — |
| 43 | C5×#127 | D4 | 1 | 3 | yes | — |
| 44 | C5×#124 | — | 2 | 3 | no | — |
| 45 | C5×#124 | — | 2 | 3 | no | — |
| 46 | C5×#124 | D4 | 1 | 3 | yes | — |
| 47 | C5×#124 | C23 | 1 | 3 | yes | — |
| 48 | C5×#121 | — | 2 | 6 | no | — |
| 49 | C5×#121 | — | 2 | 6 | no | — |
| 50 | C5×#121 | — | 2 | 6 | no | — |
| 51 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 52 | C4×C5×Q8 | — | 2 | 3 | no | — |
| 53 | C4×C5×D4 | — | 2 | 3 | no | — |
| 54 | C4×C5×D4 | — | 2 | 6 | no | — |
| 55 | C4×C5×D4 | — | 2 | 6 | no | — |
| 56 | C4×C5×D4 | — | 2 | 3 | no | — |
| 57 | C5×#117 | — | 2 | 3 | no | — |
| 58 | C5×#117 | — | 2 | 6 | no | — |
| 59 | C2×C42×C5 | — | 2 | 3 | no | — |
| 60 | C2×C42×C5 | D4 | 1 | 3 | yes | — |
| 61 | C5×#104 | — | 2 | 6 | no | — |
| 62 | C5×#104 | — | 2 | 6 | no | — |
| 63 | C5×#101 | C23 | 1 | 6 | yes | — |
| 64 | C5×#100 | — | 2 | 3 | no | — |
| 65 | #3483 | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 66 | #3018 | C2×C5 | 1 | 3 | yes | complemented |
| 67 | #2205 | C2×C5 | 1 | 2 | yes | complemented |
| 68 | #2204 | C2×C5 | 1 | 6 | yes | complemented |
| 69 | #2132 | C2×C5 | 1 | 3 | yes | complemented |
| 70 | C5×#41 | — | 2 | 6 | no | — |
| 71 | C5×#41 | — | 2 | 6 | no | — |
| 72 | C5×#41 | — | 4 | 1 | no | — |
| 73 | C5×#41 | — | 4 | 1 | no | — |
| 74 | C5×#41 | — | 4 | 3 | no | — |
| 75 | C5×#41 | — | 4 | 3 | no | — |
| 76 | C5×#41 | — | 4 | 3 | no | — |
| 77 | C5×#41 | — | 4 | 2 | no | — |
| 78 | C5×#41 | — | 4 | 12 | no | — |
| 79 | C5×#41 | — | 4 | 6 | no | — |
| 80 | C5×#41 | — | 4 | 1 | no | — |
| 81 | C5×#41 | — | 8 | 1 | no | — |
| 82 | C5×#41 | — | 8 | 1 | no | — |
| 83 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 84 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 85 | C2×C5×Q8 | — | 2 | 3 | no | — |
| 86 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 87 | C2×C5×Q8 | C2×D4 | 1 | 3 | yes | — |
| 88 | C2×C5×Q8 | C24 | 1 | 1 | yes | characteristic |
| 89 | C2×C5×D4 | — | 2 | 3 | no | — |
| 90 | C2×C5×D4 | — | 2 | 3 | no | — |
| 91 | C2×C5×D4 | — | 2 | 6 | no | — |
| 92 | C2×C5×D4 | — | 2 | 3 | no | — |
| 93 | C2×C5×D4 | — | 2 | 3 | no | — |
| 94 | C2×C5×D4 | — | 4 | 6 | no | — |
| 95 | C2×C5×D4 | — | 4 | 3 | no | — |
| 96 | C2×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 97 | C2×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 98 | C22×C4×C5 | — | 2 | 6 | no | — |
| 99 | C22×C4×C5 | — | 2 | 3 | no | — |
| 100 | C22×C4×C5 | — | 2 | 3 | no | — |
| 101 | C22×C4×C5 | — | 4 | 3 | no | — |
| 102 | C22×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 103 | C5×Q16 | — | 4 | 6 | no | — |
| 104 | C5×SD16 | — | 4 | 6 | no | — |
| 105 | C5×SD16 | — | 4 | 6 | no | — |
| 106 | C5×D8 | — | 4 | 6 | no | — |
| 107 | C5×M16 | — | 2 | 6 | no | — |
| 108 | C5×M16 | — | 4 | 3 | no | — |
| 109 | C2×C5×C8 | — | 4 | 3 | no | — |
| 110 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 111 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 112 | C5×C4⋊C4 | — | 2 | 6 | no | — |
| 113 | C5×C22⋊C4 | — | 2 | 6 | no | — |
| 114 | C5×C22⋊C4 | — | 2 | 6 | no | — |
| 115 | C5×C22⋊C4 | — | 2 | 6 | no | — |
| 116 | C42×C5 | — | 2 | 3 | no | — |
| 117 | C42×C5 | — | 2 | 3 | no | — |
| 118 | C42×C5 | — | 2 | 3 | no | — |
| 119 | C42×C5 | C2×D4 | 1 | 3 | yes | — |
| 120 | C42×C5 | C2×D4 | 1 | 3 | yes | — |
| 121 | #585 | C22×C5 | 1 | 1 | yes | characteristic |
| 122 | #575 | — | 2 | 3 | no | — |
| 123 | Q82 | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 124 | #555 | — | 2 | 3 | no | — |
| 125 | #555 | C22×C5 | 1 | 3 | yes | complemented |
| 126 | #550 | — | 2 | 3 | no | — |
| 127 | #532 | — | 2 | 3 | no | — |
| 128 | #532 | C22×C5 | 1 | 3 | yes | — |
| 129 | C4×#41 | — | 2 | 3 | no | — |
| 130 | #456 | C22×C5 | 1 | 6 | yes | — |
| 131 | #455 | — | 2 | 3 | no | — |
| 132 | #454 | C22×C5 | 1 | 6 | yes | — |
| 133 | #453 | — | 2 | 3 | no | — |
| 134 | C2×#104 | — | 2 | 3 | no | — |
| 135 | #413 | C22×C5 | 1 | 3 | yes | — |
| 136 | #356 | C22×C5 | 1 | 6 | yes | complemented |
| 137 | #355 | C22×C5 | 1 | 6 | yes | complemented |
| 138 | C23×C5 | — | 2 | 3 | no | — |
| 139 | C23×C5 | — | 4 | 3 | no | — |
| 140 | C23×C5 | #120 | 1 | 3 | yes | — |
| 141 | C5×Q8 | — | 2 | 4 | no | — |
| 142 | C5×Q8 | — | 2 | 6 | no | — |
| 143 | C5×Q8 | — | 4 | 1 | no | — |
| 144 | C5×Q8 | — | 4 | 3 | no | — |
| 145 | C5×Q8 | — | 4 | 1 | no | — |
| 146 | C5×Q8 | — | 8 | 1 | no | — |
| 147 | C5×D4 | — | 2 | 6 | no | — |
| 148 | C5×D4 | — | 4 | 3 | no | — |
| 149 | C5×D4 | — | 4 | 3 | no | — |
| 150 | C5×D4 | — | 4 | 12 | no | — |
| 151 | C5×D4 | — | 4 | 6 | no | — |
| 152 | C5×D4 | — | 4 | 6 | no | — |
| 153 | C5×D4 | — | 4 | 2 | no | — |
| 154 | C5×D4 | — | 4 | 1 | no | — |
| 155 | C5×D4 | — | 8 | 3 | no | — |
| 156 | C5×D4 | — | 8 | 3 | no | — |
| 157 | C2×C4×C5 | — | 2 | 3 | no | — |
| 158 | C2×C4×C5 | — | 2 | 3 | no | — |
| 159 | C2×C4×C5 | — | 2 | 3 | no | — |
| 160 | C2×C4×C5 | — | 2 | 3 | no | — |
| 161 | C2×C4×C5 | — | 2 | 3 | no | — |
| 162 | C2×C4×C5 | — | 4 | 6 | no | — |
| 163 | C2×C4×C5 | — | 4 | 12 | no | — |
| 164 | C2×C4×C5 | — | 4 | 6 | no | — |
| 165 | C2×C4×C5 | — | 4 | 3 | no | — |
| 166 | C2×C4×C5 | — | 4 | 3 | no | — |
| 167 | C2×C4×C5 | — | 4 | 3 | no | — |
| 168 | C2×C4×C5 | — | 4 | 2 | no | — |
| 169 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 171 | C5×C8 | — | 4 | 6 | no | — |
| 172 | 2−1+4 | — | 4 | 1 | no | — |
| 173 | 2−1+4 | C23×C5 | 1 | 2 | yes | — |
| 174 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 175 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 176 | C2×#41 | — | 2 | 3 | no | — |
| 177 | C2×#41 | — | 2 | 1 | no | — |
| 178 | C2×#41 | — | 2 | 3 | no | — |
| 179 | C2×#41 | — | 4 | 2 | no | — |
| 180 | C2×#41 | C5×D4 | 1 | 3 | yes | — |
| 181 | C2×#41 | C23×C5 | 1 | 1 | yes | characteristic |
| 182 | #137 | — | 2 | 6 | no | — |
| 183 | #137 | — | 4 | 3 | no | — |
| 184 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 185 | AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 186 | #135 | — | 4 | 6 | no | — |
| 187 | C2×M16 | — | 2 | 3 | no | — |
| 188 | C4⋊Q8 | — | 2 | 3 | no | — |
| 189 | C4⋊Q8 | C23×C5 | 1 | 3 | yes | — |
| 190 | #127 | — | 2 | 3 | no | — |
| 191 | #127 | C5×D4 | 1 | 3 | yes | — |
| 192 | #124 | — | 2 | 3 | no | — |
| 193 | #124 | — | 2 | 3 | no | — |
| 194 | #124 | C5×D4 | 1 | 3 | yes | — |
| 195 | #124 | C23×C5 | 1 | 3 | yes | — |
| 196 | #121 | — | 2 | 6 | no | — |
| 197 | #121 | — | 2 | 6 | no | — |
| 198 | #121 | — | 2 | 6 | no | — |
| 199 | C4×Q8 | — | 2 | 1 | no | — |
| 200 | C4×Q8 | — | 2 | 3 | no | — |
| 201 | C4×D4 | — | 2 | 3 | no | — |
| 202 | C4×D4 | — | 2 | 6 | no | — |
| 203 | C4×D4 | — | 2 | 6 | no | — |
| 204 | C4×D4 | — | 2 | 3 | no | — |
| 205 | #117 | — | 2 | 3 | no | — |
| 206 | #117 | — | 2 | 6 | no | — |
| 207 | C2×C42 | — | 2 | 3 | no | — |
| 208 | C2×C42 | C5×D4 | 1 | 3 | yes | — |
| 209 | #104 | — | 2 | 6 | no | — |
| 210 | #104 | — | 2 | 6 | no | — |
| 211 | #101 | C23×C5 | 1 | 6 | yes | — |
| 212 | #100 | — | 2 | 3 | no | — |
| 213 | C22×C5 | — | 2 | 3 | no | — |
| 214 | C22×C5 | — | 4 | 3 | no | — |
| 215 | C22×C5 | — | 4 | 6 | no | — |
| 216 | C22×C5 | — | 4 | 2 | no | — |
| 217 | C22×C5 | — | 4 | 3 | no | — |
| 218 | C22×C5 | — | 16 | 3 | no | — |
| 219 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 220 | C4×C5 | — | 2 | 6 | no | — |
| 221 | C4×C5 | — | 2 | 3 | no | — |
| 222 | C4×C5 | — | 4 | 3 | no | — |
| 223 | C4×C5 | — | 4 | 3 | no | — |
| 224 | C4×C5 | — | 4 | 2 | no | — |
| 225 | C4×C5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 226 | C4×C5 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 227 | #41 | — | 2 | 6 | no | — |
| 228 | #41 | — | 2 | 6 | no | — |
| 229 | #41 | — | 4 | 1 | no | — |
| 230 | #41 | — | 4 | 1 | no | — |
| 231 | #41 | — | 4 | 3 | no | — |
| 232 | #41 | — | 4 | 3 | no | — |
| 233 | #41 | — | 4 | 3 | no | — |
| 234 | #41 | — | 4 | 2 | no | — |
| 235 | #41 | — | 4 | 12 | no | — |
| 236 | #41 | — | 4 | 6 | no | — |
| 237 | #41 | — | 4 | 1 | no | — |
| 238 | #41 | — | 8 | 1 | no | — |
| 239 | #41 | — | 8 | 1 | no | — |
| 240 | C2×Q8 | — | 2 | 1 | no | — |
| 241 | C2×Q8 | — | 2 | 1 | no | — |
| 242 | C2×Q8 | — | 2 | 3 | no | — |
| 243 | C2×Q8 | — | 4 | 2 | no | — |
| 244 | C2×Q8 | C2×C5×D4 | 1 | 3 | yes | — |
| 245 | C2×Q8 | C24×C5 | 1 | 1 | yes | characteristic |
| 246 | C2×D4 | — | 2 | 3 | no | — |
| 247 | C2×D4 | — | 2 | 3 | no | — |
| 248 | C2×D4 | — | 2 | 6 | no | — |
| 249 | C2×D4 | — | 2 | 3 | no | — |
| 250 | C2×D4 | — | 2 | 3 | no | — |
| 251 | C2×D4 | — | 4 | 6 | no | — |
| 252 | C2×D4 | — | 4 | 3 | no | — |
| 253 | C2×D4 | C2×C5×D4 | 1 | 3 | yes | — |
| 254 | C2×D4 | C2×C5×D4 | 1 | 3 | yes | — |
| 255 | C22×C4 | — | 2 | 6 | no | — |
| 256 | C22×C4 | — | 2 | 3 | no | — |
| 257 | C22×C4 | — | 2 | 3 | no | — |
| 258 | C22×C4 | — | 4 | 3 | no | — |
| 259 | C22×C4 | C2×C5×D4 | 1 | 3 | yes | — |
| 260 | Q16 | — | 4 | 6 | no | — |
| 261 | SD16 | — | 4 | 6 | no | — |
| 262 | SD16 | — | 4 | 6 | no | — |
| 263 | D8 | — | 4 | 6 | no | — |
| 264 | M16 | — | 2 | 6 | no | — |
| 265 | M16 | — | 4 | 3 | no | — |
| 266 | C2×C8 | — | 4 | 3 | no | — |
| 267 | C4⋊C4 | — | 2 | 3 | no | — |
| 268 | C4⋊C4 | — | 2 | 3 | no | — |
| 269 | C4⋊C4 | — | 2 | 6 | no | — |
| 270 | C22⋊C4 | — | 2 | 6 | no | — |
| 271 | C22⋊C4 | — | 2 | 6 | no | — |
| 272 | C22⋊C4 | — | 2 | 6 | no | — |
| 273 | C42 | — | 2 | 3 | no | — |
| 274 | C42 | — | 2 | 3 | no | — |
| 275 | C42 | — | 2 | 3 | no | — |
| 276 | C42 | C2×C5×D4 | 1 | 3 | yes | — |
| 277 | C42 | C2×C5×D4 | 1 | 3 | yes | — |
| 278 | C2×C5 | — | 2 | 1 | no | — |
| 279 | C2×C5 | — | 4 | 3 | no | — |
| 280 | C2×C5 | — | 8 | 3 | no | — |
| 281 | C2×C5 | — | 8 | 2 | no | — |
| 282 | C2×C5 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 283 | C23 | — | 2 | 3 | no | — |
| 284 | C23 | — | 4 | 3 | no | — |
| 285 | C23 | C5×#120 | 1 | 3 | yes | — |
| 286 | Q8 | — | 2 | 4 | no | — |
| 287 | Q8 | — | 2 | 6 | no | — |
| 288 | Q8 | — | 4 | 1 | no | — |
| 289 | Q8 | — | 4 | 3 | no | — |
| 290 | Q8 | — | 4 | 1 | no | — |
| 291 | Q8 | — | 8 | 1 | no | — |
| 292 | D4 | — | 2 | 6 | no | — |
| 293 | D4 | — | 4 | 3 | no | — |
| 294 | D4 | — | 4 | 3 | no | — |
| 295 | D4 | — | 4 | 12 | no | — |
| 296 | D4 | — | 4 | 6 | no | — |
| 297 | D4 | — | 4 | 6 | no | — |
| 298 | D4 | — | 4 | 2 | no | — |
| 299 | D4 | — | 4 | 1 | no | — |
| 300 | D4 | — | 8 | 3 | no | — |
| 301 | D4 | — | 8 | 3 | no | — |
| 302 | C2×C4 | — | 2 | 3 | no | — |
| 303 | C2×C4 | — | 2 | 3 | no | — |
| 304 | C2×C4 | — | 2 | 3 | no | — |
| 305 | C2×C4 | — | 2 | 3 | no | — |
| 306 | C2×C4 | — | 2 | 3 | no | — |
| 307 | C2×C4 | — | 4 | 6 | no | — |
| 308 | C2×C4 | — | 4 | 12 | no | — |
| 309 | C2×C4 | — | 4 | 6 | no | — |
| 310 | C2×C4 | — | 4 | 3 | no | — |
| 311 | C2×C4 | — | 4 | 3 | no | — |
| 312 | C2×C4 | — | 4 | 3 | no | — |
| 313 | C2×C4 | — | 4 | 2 | no | — |
| 314 | C2×C4 | C5×#120 | 1 | 1 | yes | characteristic |
| 315 | C2×C4 | C22×C5×D4 | 1 | 3 | yes | — |
| 316 | C8 | — | 4 | 6 | no | — |
| 317 | C5 | #33567 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 318 | C22 | — | 2 | 3 | no | — |
| 319 | C22 | — | 4 | 3 | no | — |
| 320 | C22 | — | 4 | 6 | no | — |
| 321 | C22 | — | 4 | 2 | no | — |
| 322 | C22 | — | 4 | 3 | no | — |
| 323 | C22 | — | 16 | 3 | no | — |
| 324 | C22 | C2×C5×#120 | 1 | 1 | yes | characteristic |
| 325 | C4 | — | 2 | 6 | no | — |
| 326 | C4 | — | 2 | 3 | no | — |
| 327 | C4 | — | 4 | 3 | no | — |
| 328 | C4 | — | 4 | 3 | no | — |
| 329 | C4 | — | 4 | 2 | no | — |
| 330 | C4 | C5×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 331 | C4 | C5×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 332 | C2 | — | 2 | 1 | no | — |
| 333 | C2 | — | 4 | 3 | no | — |
| 334 | C2 | — | 8 | 3 | no | — |
| 335 | C2 | — | 8 | 2 | no | — |
| 336 | C2 | C2×C5×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C5 |
| socle | C2×C5 | C2×B(4,𝔽2) |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3483 | C2 | semidirect |
| 2. C5×#3018 | C2 | semidirect |
| 3. C5×#2205 | C2 | semidirect |
| 4. C5×#2204 | C2 | semidirect |
| 5. C5×#2132 | C2 | semidirect |
| 8. C5×Q82 | C22 | semidirect |
| 10. C5×#555 | C22 | semidirect |
| 21. C5×#356 | C22 | semidirect |
| 22. C5×#355 | C22 | semidirect |
| 23. #33567 | C5 | direct (N × H) |
| 65. #3483 | C2×C5 | semidirect |
| 66. #3018 | C2×C5 | semidirect |
| 67. #2205 | C2×C5 | semidirect |
| 68. #2204 | C2×C5 | semidirect |
| 69. #2132 | C2×C5 | semidirect |
| 123. Q82 | C22×C5 | semidirect |
| 125. #555 | C22×C5 | semidirect |
| 136. #356 | C22×C5 | semidirect |
| 137. #355 | C22×C5 | semidirect |
| 317. C5 | #33567 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3483 | 2 |
| C5×#3018 | 2 |
| C5×#2205 | 2 |
| C5×#2204 | 2 |
| C5×#2132 | 2 |
| #33567 | 5 |