Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
518 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 91 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×#408 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | D5×#349 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C5×#1321 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10598181 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10598022 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×D5×#41 | C4 | 1 | 1 | yes | characteristic |
| 7 | C2×D5×M16 | C22 | 1 | 1 | yes | characteristic |
| 8 | C22×C8×D5 | C4 | 1 | 1 | yes | characteristic |
| 9 | C5×#408 | C22 | 1 | 1 | yes | characteristic |
| 10 | #65523 | C4 | 1 | 1 | yes | characteristic |
| 11 | #65418 | C22 | 1 | 1 | yes | characteristic |
| 12 | #65399 | C4 | 1 | 1 | yes | characteristic |
| 13 | D5×M32 | — | 2 | 2 | no | — |
| 14 | #65016 | — | 2 | 2 | no | — |
| 15 | D5×C22⋊C8 | — | 2 | 2 | no | — |
| 16 | C5×#349 | C22 | 1 | 2 | yes | complemented |
| 17 | #64773 | C22 | 1 | 2 | yes | complemented |
| 18 | #64734 | — | 2 | 2 | no | — |
| 19 | C2×#1321 | — | 5 | 1 | no | maximal, Sylow |
| 20 | C2×C5×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 21 | D5×#41 | — | 4 | 1 | no | — |
| 22 | D5×#41 | — | 4 | 1 | no | — |
| 23 | D5×#41 | — | 4 | 1 | no | — |
| 24 | D5×#41 | — | 4 | 1 | no | — |
| 25 | C2×#713 | C8 | 1 | 1 | yes | characteristic |
| 26 | C2×Q8×D5 | C8 | 1 | 1 | yes | characteristic |
| 27 | C2×#711 | — | 2 | 1 | no | — |
| 28 | C2×#711 | C8 | 1 | 1 | yes | characteristic |
| 29 | C2×D4×D5 | — | 2 | 1 | no | — |
| 30 | C2×D4×D5 | C8 | 1 | 1 | yes | characteristic |
| 31 | C2×#709 | — | 2 | 1 | no | — |
| 32 | C2×#709 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C22×C4×D5 | — | 2 | 1 | no | — |
| 34 | C22×C4×D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 36 | C22×C5×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×#681 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C22×#168 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | D5×M16 | — | 4 | 1 | no | — |
| 40 | D5×M16 | — | 4 | 1 | no | — |
| 41 | C2×#676 | D4 | 1 | 2 | yes | — |
| 42 | C2×C8×D5 | — | 2 | 1 | no | — |
| 43 | C2×C8×D5 | — | 2 | 1 | no | — |
| 44 | C2×C8×D5 | — | 4 | 1 | no | — |
| 45 | C2×C8×D5 | — | 4 | 1 | no | — |
| 46 | C2×C8×D5 | D4 | 1 | 2 | yes | — |
| 47 | C5×M32 | — | 2 | 2 | no | — |
| 48 | C5×C22⋊C8 | — | 2 | 2 | no | — |
| 49 | C22⋊#168 | — | 2 | 2 | no | — |
| 50 | #3952 | — | 2 | 2 | no | — |
| 51 | #3952 | — | 2 | 2 | no | — |
| 52 | #3944 | — | 2 | 2 | no | — |
| 53 | #3930 | — | 4 | 2 | no | — |
| 54 | D5×C16 | — | 4 | 2 | no | — |
| 55 | C2×#408 | — | 5 | 1 | no | — |
| 56 | C2×#349 | — | 5 | 2 | no | — |
| 57 | #1321 | — | 5 | 1 | no | — |
| 58 | #1321 | — | 5 | 2 | no | — |
| 59 | #1321 | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 60 | C23×D5 | — | 2 | 1 | no | — |
| 61 | C23×D5 | M16 | 1 | 1 | yes | characteristic |
| 62 | C5×#41 | — | 4 | 1 | no | — |
| 63 | C5×#41 | — | 4 | 1 | no | — |
| 64 | C2×C5×Q8 | C2×C8 | 1 | 1 | yes | characteristic |
| 65 | C2×C5×D4 | — | 2 | 1 | no | — |
| 66 | C2×C5×D4 | C2×C8 | 1 | 1 | yes | characteristic |
| 67 | C22×C4×C5 | — | 2 | 1 | no | — |
| 68 | C22×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 69 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 70 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 71 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 72 | C22×Dic5 | — | 2 | 1 | no | — |
| 73 | C22×Dic5 | M16 | 1 | 1 | yes | characteristic |
| 74 | #713 | — | 4 | 1 | no | — |
| 75 | #713 | — | 4 | 1 | no | — |
| 76 | Q8×D5 | — | 4 | 1 | no | — |
| 77 | Q8×D5 | — | 4 | 1 | no | — |
| 78 | #711 | — | 4 | 1 | no | — |
| 79 | #711 | — | 4 | 1 | no | — |
| 80 | #711 | — | 4 | 2 | no | — |
| 81 | #711 | — | 4 | 2 | no | — |
| 82 | D4×D5 | — | 4 | 1 | no | — |
| 83 | D4×D5 | — | 4 | 1 | no | — |
| 84 | D4×D5 | — | 4 | 2 | no | — |
| 85 | D4×D5 | — | 4 | 2 | no | — |
| 86 | #709 | — | 4 | 2 | no | — |
| 87 | #709 | — | 4 | 2 | no | — |
| 88 | #709 | — | 4 | 1 | no | — |
| 89 | #709 | — | 4 | 1 | no | — |
| 90 | C2×D20 | — | 2 | 1 | no | — |
| 91 | C2×D20 | C2×C8 | 1 | 1 | yes | characteristic |
| 92 | C2×C4×D5 | — | 2 | 1 | no | — |
| 93 | C2×C4×D5 | — | 2 | 1 | no | — |
| 94 | C2×C4×D5 | — | 2 | 1 | no | — |
| 95 | C2×C4×D5 | — | 2 | 1 | no | — |
| 96 | C2×C4×D5 | — | 2 | 1 | no | — |
| 97 | C2×C4×D5 | — | 2 | 1 | no | — |
| 98 | C2×C4×D5 | — | 2 | 1 | no | — |
| 99 | C2×C4×D5 | — | 4 | 1 | no | — |
| 100 | C2×C4×D5 | — | 4 | 1 | no | — |
| 101 | C2×C4×D5 | — | 4 | 1 | no | — |
| 102 | C2×C4×D5 | — | 4 | 1 | no | — |
| 103 | C2×C4×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×D5 | C2×C8 | 1 | 1 | yes | characteristic |
| 106 | C2×C4×D5 | C2×C8 | 1 | 1 | yes | characteristic |
| 107 | C2×Dic10 | — | 2 | 1 | no | — |
| 108 | C2×Dic10 | C2×C8 | 1 | 1 | yes | characteristic |
| 109 | C5×M16 | — | 4 | 1 | no | — |
| 110 | C2×C5×C8 | — | 2 | 1 | no | — |
| 111 | C2×C5×C8 | — | 4 | 1 | no | — |
| 112 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 113 | #681 | — | 4 | 1 | no | — |
| 114 | C2×#168 | — | 2 | 1 | no | — |
| 115 | C2×#168 | — | 4 | 1 | no | — |
| 116 | C2×#168 | C22⋊C4 | 1 | 2 | yes | — |
| 117 | #676 | — | 4 | 2 | no | — |
| 118 | C8×D5 | — | 2 | 2 | no | — |
| 119 | C8×D5 | — | 2 | 2 | no | — |
| 120 | C8×D5 | — | 4 | 2 | no | — |
| 121 | C8×D5 | — | 4 | 1 | no | — |
| 122 | C8×D5 | — | 4 | 1 | no | — |
| 123 | C5×C16 | — | 4 | 2 | no | — |
| 124 | #672 | — | 4 | 2 | no | — |
| 125 | C22×#41 | — | 5 | 1 | no | — |
| 126 | C22×M16 | — | 5 | 1 | no | — |
| 127 | C23×C8 | — | 5 | 1 | no | — |
| 128 | C2×M32 | — | 10 | 2 | no | — |
| 129 | #408 | — | 5 | 1 | no | — |
| 130 | #408 | — | 5 | 1 | no | — |
| 131 | #408 | — | 5 | 1 | no | — |
| 132 | #408 | — | 10 | 2 | no | — |
| 133 | #408 | C2×D5 | 1 | 1 | yes | characteristic |
| 134 | C2×C22⋊C8 | — | 10 | 2 | no | — |
| 135 | #349 | — | 5 | 2 | no | — |
| 136 | #349 | — | 10 | 2 | no | — |
| 137 | #349 | C2×D5 | 1 | 2 | yes | complemented |
| 138 | C23×C5 | — | 2 | 1 | no | — |
| 139 | C23×C5 | C2×M16 | 1 | 1 | yes | characteristic |
| 140 | C22×D5 | — | 2 | 1 | no | — |
| 141 | C22×D5 | — | 2 | 1 | no | — |
| 142 | C22×D5 | — | 2 | 1 | no | — |
| 143 | C22×D5 | — | 4 | 2 | no | — |
| 144 | C22×D5 | — | 4 | 4 | no | — |
| 145 | C22×D5 | — | 4 | 1 | no | — |
| 146 | C22×D5 | — | 4 | 1 | no | — |
| 147 | C22×D5 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 148 | C22×D5 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 149 | C5×Q8 | — | 4 | 1 | no | — |
| 150 | C5×D4 | — | 4 | 1 | no | — |
| 151 | C5×D4 | — | 4 | 2 | no | — |
| 152 | C2×C4×C5 | — | 2 | 1 | no | — |
| 153 | C2×C4×C5 | — | 2 | 1 | no | — |
| 154 | C2×C4×C5 | — | 2 | 1 | no | — |
| 155 | C2×C4×C5 | — | 4 | 1 | no | — |
| 156 | C2×C4×C5 | — | 4 | 1 | no | — |
| 157 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 158 | C2×C4×C5 | C22×C8 | 1 | 1 | yes | characteristic |
| 159 | C22⋊D5 | — | 4 | 2 | no | — |
| 160 | C22⋊D5 | — | 4 | 2 | no | — |
| 161 | C22⋊D5 | — | 4 | 2 | no | — |
| 162 | C2×Dic5 | — | 2 | 1 | no | — |
| 163 | C2×Dic5 | — | 2 | 1 | no | — |
| 164 | C2×Dic5 | — | 2 | 1 | no | — |
| 165 | C2×Dic5 | — | 4 | 1 | no | — |
| 166 | C2×Dic5 | — | 4 | 1 | no | — |
| 167 | C2×Dic5 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 168 | C2×Dic5 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 169 | D20 | — | 4 | 1 | no | — |
| 170 | D20 | — | 4 | 2 | no | — |
| 171 | C4×D5 | — | 2 | 1 | no | — |
| 172 | C4×D5 | — | 2 | 1 | no | — |
| 173 | C4×D5 | — | 2 | 1 | no | — |
| 174 | C4×D5 | — | 2 | 1 | no | — |
| 175 | C4×D5 | — | 2 | 1 | no | — |
| 176 | C4×D5 | — | 2 | 1 | no | — |
| 177 | C4×D5 | — | 4 | 1 | no | — |
| 178 | C4×D5 | — | 4 | 1 | no | — |
| 179 | C4×D5 | — | 4 | 1 | no | — |
| 180 | C4×D5 | — | 4 | 1 | no | — |
| 181 | C4×D5 | — | 4 | 1 | no | — |
| 182 | C4×D5 | — | 4 | 1 | no | — |
| 183 | C4×D5 | #99 | 1 | 1 | yes | characteristic |
| 184 | C4×D5 | #99 | 1 | 1 | yes | characteristic |
| 185 | C4×D5 | #100 | 1 | 1 | yes | characteristic |
| 186 | C4×D5 | #100 | 1 | 1 | yes | characteristic |
| 187 | Dic10 | — | 4 | 2 | no | — |
| 188 | Dic10 | — | 4 | 1 | no | — |
| 189 | C5×C8 | — | 2 | 2 | no | — |
| 190 | C5×C8 | — | 4 | 1 | no | — |
| 191 | #168 | — | 2 | 2 | no | — |
| 192 | #168 | — | 4 | 1 | no | — |
| 193 | C2×#41 | — | 5 | 1 | no | — |
| 194 | C2×#41 | — | 5 | 1 | no | — |
| 195 | C2×#41 | — | 5 | 1 | no | — |
| 196 | C2×#41 | — | 10 | 1 | no | — |
| 197 | C2×#41 | — | 10 | 1 | no | — |
| 198 | C2×#41 | — | 20 | 1 | no | — |
| 199 | C2×#41 | — | 20 | 1 | no | — |
| 200 | C2×#41 | — | 20 | 1 | no | — |
| 201 | C2×#41 | — | 20 | 1 | no | — |
| 202 | C2×#41 | C4×D5 | 1 | 1 | yes | characteristic |
| 203 | C22×Q8 | — | 5 | 1 | no | — |
| 204 | C22×D4 | — | 5 | 1 | no | — |
| 205 | C22×D4 | — | 10 | 1 | no | — |
| 206 | C23×C4 | — | 5 | 1 | no | — |
| 207 | C23×C4 | — | 10 | 1 | no | — |
| 208 | C2×M16 | — | 5 | 1 | no | — |
| 209 | C2×M16 | — | 5 | 2 | no | — |
| 210 | C2×M16 | — | 20 | 1 | no | — |
| 211 | C2×M16 | — | 20 | 1 | no | — |
| 212 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 213 | C22×C8 | — | 5 | 2 | no | — |
| 214 | C22×C8 | — | 5 | 1 | no | — |
| 215 | C22×C8 | — | 10 | 1 | no | — |
| 216 | C22×C8 | — | 10 | 1 | no | — |
| 217 | C22×C8 | — | 20 | 1 | no | — |
| 218 | C22×C8 | — | 20 | 1 | no | — |
| 219 | C22×C8 | C4×D5 | 1 | 1 | yes | characteristic |
| 220 | M32 | — | 2 | 2 | no | — |
| 221 | M32 | — | 10 | 2 | no | — |
| 222 | M32 | — | 20 | 2 | no | — |
| 223 | C2×C16 | — | 20 | 2 | no | — |
| 224 | C22⋊C8 | — | 2 | 2 | no | — |
| 225 | C22⋊C8 | — | 10 | 2 | no | — |
| 226 | C22⋊C8 | — | 10 | 2 | no | — |
| 227 | C22⋊C8 | — | 10 | 2 | no | — |
| 228 | C22×C5 | — | 2 | 1 | no | — |
| 229 | C22×C5 | — | 4 | 1 | no | — |
| 230 | C22×C5 | — | 4 | 2 | no | — |
| 231 | C22×C5 | — | 4 | 1 | no | — |
| 232 | C22×C5 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 233 | C2×D5 | — | 2 | 2 | no | — |
| 234 | C2×D5 | — | 2 | 1 | no | — |
| 235 | C2×D5 | — | 4 | 2 | no | — |
| 236 | C2×D5 | — | 4 | 2 | no | — |
| 237 | C2×D5 | — | 4 | 1 | no | — |
| 238 | C2×D5 | — | 4 | 2 | no | — |
| 239 | C2×D5 | — | 4 | 1 | no | — |
| 240 | C2×D5 | — | 8 | 2 | no | — |
| 241 | C2×D5 | — | 8 | 2 | no | — |
| 242 | C2×D5 | #323 | 1 | 1 | yes | characteristic |
| 243 | C2×D5 | #323 | 1 | 1 | yes | characteristic |
| 244 | C4×C5 | — | 2 | 1 | no | — |
| 245 | C4×C5 | — | 4 | 1 | no | — |
| 246 | C4×C5 | C2×#99 | 1 | 1 | yes | characteristic |
| 247 | C4×C5 | C2×#100 | 1 | 1 | yes | characteristic |
| 248 | Dic5 | — | 2 | 1 | no | — |
| 249 | Dic5 | — | 4 | 1 | no | — |
| 250 | Dic5 | #323 | 1 | 1 | yes | characteristic |
| 251 | Dic5 | #323 | 1 | 1 | yes | characteristic |
| 252 | C24 | — | 5 | 1 | no | — |
| 253 | C24 | — | 10 | 1 | no | — |
| 254 | #41 | — | 4 | 1 | no | — |
| 255 | #41 | — | 4 | 1 | no | — |
| 256 | #41 | — | 20 | 1 | no | — |
| 257 | #41 | — | 20 | 1 | no | — |
| 258 | #41 | — | 20 | 2 | no | — |
| 259 | #41 | — | 20 | 2 | no | — |
| 260 | #41 | — | 20 | 2 | no | — |
| 261 | #41 | — | 20 | 2 | no | — |
| 262 | #41 | — | 20 | 1 | no | — |
| 263 | #41 | — | 20 | 1 | no | — |
| 264 | #41 | — | 20 | 1 | no | — |
| 265 | #41 | — | 20 | 1 | no | — |
| 266 | C2×Q8 | — | 5 | 1 | no | — |
| 267 | C2×Q8 | — | 10 | 1 | no | — |
| 268 | C2×Q8 | — | 20 | 1 | no | — |
| 269 | C2×Q8 | — | 20 | 1 | no | — |
| 270 | C2×Q8 | C8×D5 | 1 | 1 | yes | characteristic |
| 271 | C2×D4 | — | 2 | 1 | no | — |
| 272 | C2×D4 | — | 5 | 1 | no | — |
| 273 | C2×D4 | — | 10 | 1 | no | — |
| 274 | C2×D4 | — | 10 | 1 | no | — |
| 275 | C2×D4 | — | 10 | 1 | no | — |
| 276 | C2×D4 | — | 10 | 1 | no | — |
| 277 | C2×D4 | — | 20 | 1 | no | — |
| 278 | C2×D4 | — | 20 | 1 | no | — |
| 279 | C2×D4 | — | 20 | 2 | no | — |
| 280 | C2×D4 | — | 20 | 2 | no | — |
| 281 | C2×D4 | C8×D5 | 1 | 1 | yes | characteristic |
| 282 | C22×C4 | — | 2 | 1 | no | — |
| 283 | C22×C4 | — | 5 | 1 | no | — |
| 284 | C22×C4 | — | 5 | 1 | no | — |
| 285 | C22×C4 | — | 5 | 1 | no | — |
| 286 | C22×C4 | — | 5 | 1 | no | — |
| 287 | C22×C4 | — | 5 | 1 | no | — |
| 288 | C22×C4 | — | 10 | 1 | no | — |
| 289 | C22×C4 | — | 10 | 1 | no | — |
| 290 | C22×C4 | — | 10 | 1 | no | — |
| 291 | C22×C4 | — | 10 | 1 | no | — |
| 292 | C22×C4 | — | 10 | 1 | no | — |
| 293 | C22×C4 | — | 10 | 1 | no | — |
| 294 | C22×C4 | — | 10 | 1 | no | — |
| 295 | C22×C4 | — | 10 | 1 | no | — |
| 296 | C22×C4 | — | 20 | 1 | no | — |
| 297 | C22×C4 | — | 20 | 1 | no | — |
| 298 | C22×C4 | — | 20 | 1 | no | — |
| 299 | C22×C4 | — | 20 | 1 | no | — |
| 300 | C22×C4 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 301 | M16 | — | 4 | 1 | no | — |
| 302 | M16 | — | 20 | 2 | no | — |
| 303 | M16 | — | 20 | 1 | no | — |
| 304 | C2×C8 | — | 2 | 1 | no | — |
| 305 | C2×C8 | — | 4 | 1 | no | — |
| 306 | C2×C8 | — | 5 | 2 | no | — |
| 307 | C2×C8 | — | 10 | 2 | no | — |
| 308 | C2×C8 | — | 10 | 2 | no | — |
| 309 | C2×C8 | — | 10 | 1 | no | — |
| 310 | C2×C8 | — | 20 | 1 | no | — |
| 311 | C2×C8 | — | 20 | 1 | no | — |
| 312 | C2×C8 | — | 20 | 2 | no | — |
| 313 | C2×C8 | — | 20 | 1 | no | — |
| 314 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 315 | C16 | — | 4 | 2 | no | — |
| 316 | C16 | — | 20 | 2 | no | — |
| 317 | C2×C5 | — | 2 | 1 | no | — |
| 318 | C2×C5 | — | 4 | 1 | no | — |
| 319 | C2×C5 | — | 8 | 1 | no | — |
| 320 | C2×C5 | C2×#323 | 1 | 1 | yes | characteristic |
| 321 | D5 | — | 2 | 1 | no | — |
| 322 | D5 | — | 4 | 1 | no | — |
| 323 | D5 | — | 8 | 1 | no | — |
| 324 | D5 | #1321 | 1 | 2 | yes | direct product factor |
| 325 | C23 | — | 2 | 1 | no | — |
| 326 | C23 | — | 5 | 1 | no | — |
| 327 | C23 | — | 5 | 1 | no | — |
| 328 | C23 | — | 10 | 1 | no | — |
| 329 | C23 | — | 10 | 1 | no | — |
| 330 | C23 | — | 10 | 1 | no | — |
| 331 | C23 | — | 20 | 1 | no | — |
| 332 | C23 | — | 20 | 1 | no | — |
| 333 | C23 | — | 20 | 2 | no | — |
| 334 | C23 | — | 20 | 4 | no | — |
| 335 | C23 | D5×M16 | 1 | 1 | yes | characteristic |
| 336 | Q8 | — | 4 | 1 | no | — |
| 337 | Q8 | — | 20 | 1 | no | — |
| 338 | Q8 | — | 20 | 2 | no | — |
| 339 | D4 | — | 4 | 1 | no | — |
| 340 | D4 | — | 4 | 2 | no | — |
| 341 | D4 | — | 20 | 1 | no | — |
| 342 | D4 | — | 20 | 2 | no | — |
| 343 | D4 | — | 20 | 2 | no | — |
| 344 | D4 | — | 20 | 2 | no | — |
| 345 | D4 | — | 20 | 2 | no | — |
| 346 | C2×C4 | — | 2 | 1 | no | — |
| 347 | C2×C4 | — | 2 | 1 | no | — |
| 348 | C2×C4 | — | 2 | 1 | no | — |
| 349 | C2×C4 | — | 4 | 1 | no | — |
| 350 | C2×C4 | — | 4 | 1 | no | — |
| 351 | C2×C4 | — | 5 | 1 | no | — |
| 352 | C2×C4 | — | 5 | 1 | no | — |
| 353 | C2×C4 | — | 5 | 1 | no | — |
| 354 | C2×C4 | — | 5 | 1 | no | — |
| 355 | C2×C4 | — | 5 | 1 | no | — |
| 356 | C2×C4 | — | 5 | 1 | no | — |
| 357 | C2×C4 | — | 10 | 1 | no | — |
| 358 | C2×C4 | — | 10 | 1 | no | — |
| 359 | C2×C4 | — | 10 | 1 | no | — |
| 360 | C2×C4 | — | 10 | 1 | no | — |
| 361 | C2×C4 | — | 10 | 1 | no | — |
| 362 | C2×C4 | — | 10 | 1 | no | — |
| 363 | C2×C4 | — | 10 | 1 | no | — |
| 364 | C2×C4 | — | 10 | 1 | no | — |
| 365 | C2×C4 | — | 10 | 1 | no | — |
| 366 | C2×C4 | — | 20 | 1 | no | — |
| 367 | C2×C4 | — | 20 | 1 | no | — |
| 368 | C2×C4 | — | 20 | 1 | no | — |
| 369 | C2×C4 | — | 20 | 1 | no | — |
| 370 | C2×C4 | — | 20 | 1 | no | — |
| 371 | C2×C4 | — | 20 | 1 | no | — |
| 372 | C2×C4 | — | 20 | 1 | no | — |
| 373 | C2×C4 | — | 20 | 1 | no | — |
| 374 | C2×C4 | D5×C22⋊C4 | 1 | 1 | yes | characteristic |
| 375 | C2×C4 | C2×C8×D5 | 1 | 1 | yes | characteristic |
| 376 | C8 | — | 2 | 2 | no | — |
| 377 | C8 | — | 4 | 1 | no | — |
| 378 | C8 | — | 10 | 2 | no | — |
| 379 | C8 | — | 20 | 1 | no | — |
| 380 | C5 | C2×#1321 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 381 | C22 | — | 2 | 1 | no | — |
| 382 | C22 | — | 4 | 1 | no | — |
| 383 | C22 | — | 4 | 2 | no | — |
| 384 | C22 | — | 4 | 1 | no | — |
| 385 | C22 | — | 5 | 1 | no | — |
| 386 | C22 | — | 5 | 1 | no | — |
| 387 | C22 | — | 10 | 2 | no | — |
| 388 | C22 | — | 10 | 1 | no | — |
| 389 | C22 | — | 20 | 1 | no | — |
| 390 | C22 | — | 20 | 2 | no | — |
| 391 | C22 | — | 20 | 2 | no | — |
| 392 | C22 | — | 20 | 2 | no | — |
| 393 | C22 | — | 20 | 1 | no | — |
| 394 | C22 | — | 40 | 2 | no | — |
| 395 | C22 | — | 40 | 2 | no | — |
| 396 | C22 | D5×C22⋊C8 | 1 | 1 | yes | characteristic |
| 397 | C4 | — | 2 | 1 | no | — |
| 398 | C4 | — | 4 | 1 | no | — |
| 399 | C4 | — | 5 | 1 | no | — |
| 400 | C4 | — | 5 | 1 | no | — |
| 401 | C4 | — | 10 | 1 | no | — |
| 402 | C4 | — | 20 | 1 | no | — |
| 403 | C4 | D5×#99 | 1 | 1 | yes | characteristic |
| 404 | C4 | D5×#100 | 1 | 1 | yes | characteristic |
| 405 | C2 | — | 2 | 1 | no | — |
| 406 | C2 | — | 4 | 1 | no | — |
| 407 | C2 | — | 5 | 2 | no | — |
| 408 | C2 | — | 8 | 1 | no | — |
| 409 | C2 | — | 10 | 1 | no | — |
| 410 | C2 | — | 20 | 1 | no | — |
| 411 | C2 | — | 40 | 1 | no | — |
| 412 | C2 | D5×#323 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. D5×#349 | C2 | semidirect |
| 3. C5×#1321 | C2 | semidirect |
| 4. #10598181 | C2 | semidirect |
| 5. #10598022 | C2 | semidirect |
| 16. C5×#349 | C22 | semidirect |
| 17. #64773 | C22 | semidirect |
| 59. #1321 | D5 | direct (N × H) |
| 137. #349 | C2×D5 | semidirect |
| 324. D5 | #1321 | direct (N × H) |
| 380. C5 | C2×#1321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#408 | 2 |
| D5×#349 | 2 |
| C5×#1321 | 2 |
| #10598181 | 2 |
| #10598022 | 2 |
| C2×#1321 | 5 |