Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
936 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 108 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×#575 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10604856 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | D5⋊#360 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10604761 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D5⋊#349 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×D5×#41 | — | 2 | 1 | no | — |
| 7 | C5×#575 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | #66156 | — | 2 | 1 | no | — |
| 9 | #66111 | — | 2 | 2 | no | — |
| 10 | D5×#137 | — | 2 | 2 | no | — |
| 11 | #66107 | — | 2 | 2 | no | — |
| 12 | D5×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 13 | #66102 | — | 2 | 1 | no | — |
| 14 | #66102 | C4 | 1 | 2 | yes | complemented |
| 15 | D5×#135 | — | 2 | 1 | no | — |
| 16 | D5×#135 | C22 | 1 | 2 | yes | — |
| 17 | #66082 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×D5×M16 | C22 | 1 | 1 | yes | characteristic |
| 19 | #65765 | — | 2 | 1 | no | — |
| 20 | C2×#3994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#3993 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | D5⋊M32 | C22 | 1 | 2 | yes | complemented |
| 23 | #64912 | — | 2 | 1 | no | — |
| 24 | #64908 | — | 2 | 2 | no | — |
| 25 | #64907 | — | 2 | 2 | no | — |
| 26 | #64904 | — | 2 | 2 | no | — |
| 27 | #64903 | — | 2 | 2 | no | — |
| 28 | #64893 | — | 2 | 1 | no | — |
| 29 | #64891 | — | 2 | 1 | no | — |
| 30 | #12739 | — | 5 | 1 | no | maximal, Sylow |
| 31 | C2×C5×#41 | — | 2 | 1 | no | — |
| 32 | D5×#41 | — | 2 | 2 | no | — |
| 33 | D5×#41 | — | 2 | 2 | no | — |
| 34 | D5×#41 | — | 2 | 2 | no | — |
| 35 | D5×#41 | — | 2 | 2 | no | — |
| 36 | D5×#41 | — | 4 | 1 | no | — |
| 37 | D5×#41 | — | 4 | 1 | no | — |
| 38 | D5×#41 | — | 4 | 1 | no | — |
| 39 | D5×#41 | — | 4 | 1 | no | — |
| 40 | C2×#713 | — | 2 | 1 | no | — |
| 41 | C2×Q8×D5 | — | 2 | 1 | no | — |
| 42 | C2×#711 | — | 2 | 1 | no | — |
| 43 | C2×#711 | — | 4 | 1 | no | — |
| 44 | C2×D4×D5 | — | 2 | 1 | no | — |
| 45 | C2×D4×D5 | — | 4 | 1 | no | — |
| 46 | C2×#709 | — | 2 | 1 | no | — |
| 47 | C2×#709 | — | 4 | 1 | no | — |
| 48 | C22×C4×D5 | — | 4 | 1 | no | — |
| 49 | C22×C4×D5 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×C22⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 51 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 52 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 53 | C5×#137 | — | 2 | 2 | no | — |
| 54 | C5×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 55 | C5×#135 | — | 2 | 1 | no | — |
| 56 | C5×#135 | C2×C4 | 1 | 2 | yes | — |
| 57 | C2×C5×M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | #4097 | — | 2 | 2 | no | — |
| 59 | #4096 | — | 2 | 2 | no | — |
| 60 | #4096 | — | 2 | 2 | no | — |
| 61 | #4095 | — | 2 | 2 | no | — |
| 62 | #4088 | — | 2 | 2 | no | — |
| 63 | #4078 | — | 2 | 2 | no | — |
| 64 | C2×#681 | D4 | 1 | 1 | yes | characteristic |
| 65 | #4065 | — | 2 | 1 | no | — |
| 66 | #4065 | D4 | 1 | 2 | yes | — |
| 67 | #4064 | — | 2 | 2 | no | — |
| 68 | #4064 | — | 2 | 2 | no | — |
| 69 | D5×Q16 | — | 2 | 1 | no | — |
| 70 | D5×Q16 | D4 | 1 | 2 | yes | — |
| 71 | #4062 | — | 2 | 2 | no | — |
| 72 | #4062 | — | 2 | 2 | no | — |
| 73 | #4061 | — | 2 | 2 | no | — |
| 74 | #4061 | — | 2 | 2 | no | — |
| 75 | #4060 | — | 2 | 2 | no | — |
| 76 | #4060 | — | 2 | 2 | no | — |
| 77 | D5×SD16 | — | 2 | 2 | no | — |
| 78 | D5×SD16 | — | 2 | 2 | no | — |
| 79 | #4058 | — | 2 | 1 | no | — |
| 80 | #4058 | D4 | 1 | 2 | yes | — |
| 81 | #4057 | — | 2 | 2 | no | — |
| 82 | #4057 | — | 2 | 2 | no | — |
| 83 | D5×D8 | — | 2 | 1 | no | — |
| 84 | D5×D8 | D4 | 1 | 2 | yes | — |
| 85 | #4055 | — | 2 | 2 | no | — |
| 86 | #4054 | — | 2 | 2 | no | — |
| 87 | D5×M16 | — | 2 | 2 | no | — |
| 88 | D5×M16 | — | 2 | 2 | no | — |
| 89 | #4050 | — | 2 | 1 | no | — |
| 90 | #4050 | C2×C4 | 1 | 2 | yes | — |
| 91 | C2×#676 | C2×C4 | 1 | 1 | yes | characteristic |
| 92 | C2×#676 | D4 | 1 | 1 | yes | characteristic |
| 93 | C2×C8×D5 | D4 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 95 | (C2×AGL(1,𝔽5))⋊C4 | — | 4 | 1 | no | — |
| 96 | #3998 | — | 2 | 2 | no | — |
| 97 | #3994 | — | 2 | 2 | no | — |
| 98 | #3993 | — | 2 | 2 | no | — |
| 99 | #3990 | — | 2 | 2 | no | — |
| 100 | D5⋊C16 | — | 2 | 2 | no | — |
| 101 | C2×#575 | — | 5 | 1 | no | — |
| 102 | C2×#360 | — | 5 | 2 | no | — |
| 103 | #2139 | — | 5 | 2 | no | — |
| 104 | C2×#349 | — | 5 | 1 | no | — |
| 105 | #1809 | — | 5 | 1 | no | — |
| 106 | C23×D5 | — | 4 | 1 | no | — |
| 107 | C23×D5 | D8 | 1 | 1 | yes | characteristic |
| 108 | C22×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 109 | C22×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 110 | C5×#41 | — | 2 | 2 | no | — |
| 111 | C5×#41 | — | 2 | 2 | no | — |
| 112 | C5×#41 | — | 4 | 1 | no | — |
| 113 | C5×#41 | — | 4 | 1 | no | — |
| 114 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 115 | C2×C5×D4 | — | 2 | 1 | no | — |
| 116 | C2×C5×D4 | — | 4 | 1 | no | — |
| 117 | C22×C4×C5 | — | 4 | 1 | no | — |
| 118 | C22×C4×C5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 119 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 120 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 121 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 122 | C22×Dic5 | — | 4 | 1 | no | — |
| 123 | C22×Dic5 | SD16 | 1 | 1 | yes | characteristic |
| 124 | #713 | — | 2 | 2 | no | — |
| 125 | #713 | — | 2 | 2 | no | — |
| 126 | #713 | — | 4 | 1 | no | — |
| 127 | #713 | — | 4 | 1 | no | — |
| 128 | Q8×D5 | — | 2 | 2 | no | — |
| 129 | Q8×D5 | — | 2 | 2 | no | — |
| 130 | Q8×D5 | — | 4 | 1 | no | — |
| 131 | Q8×D5 | — | 4 | 1 | no | — |
| 132 | #711 | — | 2 | 2 | no | — |
| 133 | #711 | — | 2 | 2 | no | — |
| 134 | #711 | — | 4 | 1 | no | — |
| 135 | #711 | — | 4 | 1 | no | — |
| 136 | #711 | — | 4 | 2 | no | — |
| 137 | #711 | — | 4 | 2 | no | — |
| 138 | #711 | — | 4 | 2 | no | — |
| 139 | #711 | — | 4 | 2 | no | — |
| 140 | D4×D5 | — | 2 | 2 | no | — |
| 141 | D4×D5 | — | 2 | 2 | no | — |
| 142 | D4×D5 | — | 4 | 1 | no | — |
| 143 | D4×D5 | — | 4 | 1 | no | — |
| 144 | D4×D5 | — | 4 | 2 | no | — |
| 145 | D4×D5 | — | 4 | 2 | no | — |
| 146 | D4×D5 | — | 4 | 2 | no | — |
| 147 | D4×D5 | — | 4 | 2 | no | — |
| 148 | #709 | — | 2 | 2 | no | — |
| 149 | #709 | — | 2 | 2 | no | — |
| 150 | #709 | — | 4 | 2 | no | — |
| 151 | #709 | — | 4 | 2 | no | — |
| 152 | #709 | — | 4 | 2 | no | — |
| 153 | #709 | — | 4 | 1 | no | — |
| 154 | #709 | — | 4 | 1 | no | — |
| 155 | #709 | — | 4 | 2 | no | — |
| 156 | C2×D20 | — | 2 | 1 | no | — |
| 157 | C2×D20 | — | 4 | 1 | no | — |
| 158 | C2×C4×D5 | — | 2 | 1 | no | — |
| 159 | C2×C4×D5 | — | 2 | 1 | no | — |
| 160 | C2×C4×D5 | — | 2 | 1 | no | — |
| 161 | C2×C4×D5 | — | 2 | 1 | no | — |
| 162 | C2×C4×D5 | — | 4 | 2 | no | — |
| 163 | C2×C4×D5 | — | 4 | 2 | no | — |
| 164 | C2×C4×D5 | — | 4 | 2 | no | — |
| 165 | C2×C4×D5 | — | 4 | 1 | no | — |
| 166 | C2×C4×D5 | — | 4 | 1 | no | — |
| 167 | C2×C4×D5 | — | 4 | 1 | no | — |
| 168 | C2×C4×D5 | — | 4 | 2 | no | — |
| 169 | C2×C4×D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×D5 | D8 | 1 | 1 | yes | characteristic |
| 171 | C2×C4×D5 | SD16 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×Dic10 | — | 2 | 1 | no | — |
| 174 | C2×Dic10 | — | 4 | 1 | no | — |
| 175 | C22⋊AGL(1,𝔽5) | — | 8 | 2 | no | — |
| 176 | C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 177 | C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 178 | C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 179 | C4⋊AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 180 | C5×Q16 | — | 2 | 1 | no | — |
| 181 | C5×Q16 | C22⋊C4 | 1 | 2 | yes | complemented |
| 182 | C5×SD16 | — | 2 | 2 | no | — |
| 183 | C5×SD16 | — | 2 | 2 | no | — |
| 184 | C5×D8 | — | 2 | 1 | no | — |
| 185 | C5×D8 | C22⋊C4 | 1 | 2 | yes | complemented |
| 186 | C5×M16 | — | 2 | 2 | no | — |
| 187 | C2×C5×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 188 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 189 | #689 | — | 2 | 2 | no | — |
| 190 | #689 | — | 2 | 2 | no | — |
| 191 | #688 | — | 2 | 2 | no | — |
| 192 | #688 | — | 2 | 2 | no | — |
| 193 | #687 | — | 2 | 2 | no | — |
| 194 | #687 | — | 2 | 2 | no | — |
| 195 | #686 | — | 2 | 2 | no | — |
| 196 | #686 | — | 2 | 2 | no | — |
| 197 | #681 | — | 2 | 2 | no | — |
| 198 | C2×#168 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 199 | C2×#168 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | Dic20 | — | 2 | 1 | no | — |
| 201 | Dic20 | C22⋊C4 | 1 | 2 | yes | complemented |
| 202 | D40 | — | 2 | 1 | no | — |
| 203 | D40 | C22⋊C4 | 1 | 2 | yes | complemented |
| 204 | #677 | — | 2 | 2 | no | — |
| 205 | #677 | — | 2 | 2 | no | — |
| 206 | #676 | — | 2 | 2 | no | — |
| 207 | #676 | — | 2 | 2 | no | — |
| 208 | C8×D5 | — | 2 | 1 | no | — |
| 209 | C8×D5 | — | 2 | 1 | no | — |
| 210 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 211 | C8×D5 | C2×D4 | 1 | 2 | yes | — |
| 212 | #674 | — | 4 | 2 | no | — |
| 213 | C22×#41 | — | 10 | 1 | no | — |
| 214 | #575 | — | 5 | 2 | no | — |
| 215 | #575 | — | 5 | 1 | no | — |
| 216 | #575 | — | 10 | 1 | no | — |
| 217 | #575 | — | 10 | 1 | no | — |
| 218 | #575 | — | 10 | 2 | no | — |
| 219 | #575 | — | 10 | 2 | no | — |
| 220 | #575 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 221 | C2×#137 | — | 10 | 2 | no | — |
| 222 | C2×AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 223 | C2×#135 | — | 5 | 2 | no | — |
| 224 | C2×#135 | — | 10 | 1 | no | — |
| 225 | C22×M16 | — | 5 | 1 | no | — |
| 226 | C2×M32 | — | 5 | 2 | no | — |
| 227 | C2×#107 | — | 5 | 1 | no | — |
| 228 | C2×#106 | — | 5 | 1 | no | — |
| 229 | #380 | — | 10 | 1 | no | — |
| 230 | #360 | — | 10 | 2 | no | — |
| 231 | #360 | — | 10 | 2 | no | — |
| 232 | #358 | — | 10 | 2 | no | — |
| 233 | #357 | — | 10 | 2 | no | — |
| 234 | #349 | — | 10 | 1 | no | — |
| 235 | #349 | — | 10 | 1 | no | — |
| 236 | #340 | — | 10 | 1 | no | — |
| 237 | C23×C5 | — | 4 | 1 | no | — |
| 238 | C23×C5 | #102 | 1 | 1 | yes | characteristic |
| 239 | C22×D5 | — | 2 | 1 | no | — |
| 240 | C22×D5 | — | 2 | 1 | no | — |
| 241 | C22×D5 | — | 4 | 1 | no | — |
| 242 | C22×D5 | — | 4 | 1 | no | — |
| 243 | C22×D5 | — | 4 | 2 | no | — |
| 244 | C22×D5 | — | 4 | 1 | no | — |
| 245 | C22×D5 | — | 4 | 2 | no | — |
| 246 | C22×D5 | — | 8 | 2 | no | — |
| 247 | C22×D5 | — | 8 | 2 | no | — |
| 248 | C22×D5 | #102 | 1 | 1 | yes | characteristic |
| 249 | C22×D5 | C2×D8 | 1 | 1 | yes | characteristic |
| 250 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 251 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 252 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 253 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 254 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 255 | C2×AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 256 | C5×Q8 | — | 2 | 2 | no | — |
| 257 | C5×Q8 | — | 4 | 1 | no | — |
| 258 | C5×D4 | — | 2 | 2 | no | — |
| 259 | C5×D4 | — | 4 | 1 | no | — |
| 260 | C5×D4 | — | 4 | 2 | no | — |
| 261 | C5×D4 | — | 4 | 2 | no | — |
| 262 | C2×C4×C5 | — | 2 | 1 | no | — |
| 263 | C2×C4×C5 | — | 2 | 1 | no | — |
| 264 | C2×C4×C5 | — | 4 | 2 | no | — |
| 265 | C2×C4×C5 | — | 4 | 1 | no | — |
| 266 | C2×C4×C5 | — | 4 | 2 | no | — |
| 267 | C2×C4×C5 | #102 | 1 | 1 | yes | characteristic |
| 268 | C2×C4×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 269 | C22⋊D5 | — | 4 | 2 | no | — |
| 270 | C22⋊D5 | — | 4 | 2 | no | — |
| 271 | C22⋊D5 | — | 4 | 2 | no | — |
| 272 | C22⋊D5 | — | 4 | 2 | no | — |
| 273 | C22⋊D5 | — | 4 | 2 | no | — |
| 274 | C22⋊D5 | — | 4 | 2 | no | — |
| 275 | C2×Dic5 | — | 2 | 1 | no | — |
| 276 | C2×Dic5 | — | 2 | 1 | no | — |
| 277 | C2×Dic5 | — | 4 | 2 | no | — |
| 278 | C2×Dic5 | — | 4 | 1 | no | — |
| 279 | C2×Dic5 | — | 4 | 2 | no | — |
| 280 | C2×Dic5 | #102 | 1 | 1 | yes | characteristic |
| 281 | C2×Dic5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 282 | D20 | — | 2 | 2 | no | — |
| 283 | D20 | — | 4 | 1 | no | — |
| 284 | D20 | — | 4 | 2 | no | — |
| 285 | D20 | — | 4 | 2 | no | — |
| 286 | C4×D5 | — | 2 | 1 | no | — |
| 287 | C4×D5 | — | 2 | 1 | no | — |
| 288 | C4×D5 | — | 2 | 1 | no | — |
| 289 | C4×D5 | — | 2 | 1 | no | — |
| 290 | C4×D5 | — | 2 | 1 | no | — |
| 291 | C4×D5 | — | 2 | 1 | no | — |
| 292 | C4×D5 | — | 4 | 2 | no | — |
| 293 | C4×D5 | — | 4 | 2 | no | — |
| 294 | C4×D5 | — | 4 | 2 | no | — |
| 295 | C4×D5 | — | 4 | 2 | no | — |
| 296 | C4×D5 | — | 4 | 2 | no | — |
| 297 | C4×D5 | — | 4 | 2 | no | — |
| 298 | C4×D5 | #120 | 1 | 1 | yes | characteristic |
| 299 | C4×D5 | #120 | 1 | 1 | yes | characteristic |
| 300 | C4×D5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 301 | C4×D5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 302 | Dic10 | — | 2 | 2 | no | — |
| 303 | Dic10 | — | 4 | 2 | no | — |
| 304 | Dic10 | — | 4 | 1 | no | — |
| 305 | Dic10 | — | 4 | 2 | no | — |
| 306 | C5×C8 | — | 2 | 1 | no | — |
| 307 | C5×C8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 308 | #168 | — | 2 | 1 | no | — |
| 309 | #168 | #120 | 1 | 2 | yes | — |
| 310 | C2×#41 | — | 2 | 1 | no | — |
| 311 | C2×#41 | — | 10 | 2 | no | — |
| 312 | C2×#41 | — | 10 | 2 | no | — |
| 313 | C2×#41 | — | 10 | 1 | no | — |
| 314 | C2×#41 | — | 10 | 1 | no | — |
| 315 | C2×#41 | — | 10 | 2 | no | — |
| 316 | C2×#41 | — | 10 | 2 | no | — |
| 317 | C2×#41 | — | 10 | 1 | no | — |
| 318 | C2×#41 | — | 20 | 1 | no | — |
| 319 | C2×#41 | — | 20 | 1 | no | — |
| 320 | C2×#41 | — | 20 | 1 | no | — |
| 321 | C2×#41 | — | 20 | 1 | no | — |
| 322 | C2×#41 | — | 20 | 1 | no | — |
| 323 | C2×#41 | — | 20 | 1 | no | — |
| 324 | C22×Q8 | — | 10 | 1 | no | — |
| 325 | C22×D4 | — | 10 | 1 | no | — |
| 326 | C22×D4 | — | 20 | 1 | no | — |
| 327 | C23×C4 | — | 5 | 1 | no | — |
| 328 | C23×C4 | — | 20 | 1 | no | — |
| 329 | #137 | — | 2 | 2 | no | — |
| 330 | #137 | — | 10 | 2 | no | — |
| 331 | #137 | — | 10 | 2 | no | — |
| 332 | #137 | — | 10 | 2 | no | — |
| 333 | #137 | — | 10 | 2 | no | — |
| 334 | #137 | — | 10 | 2 | no | — |
| 335 | #137 | — | 10 | 2 | no | — |
| 336 | #137 | — | 10 | 2 | no | — |
| 337 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 338 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 339 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 340 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 341 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 342 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 343 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 344 | AGL(1,ℤ/8) | — | 10 | 2 | no | — |
| 345 | #135 | — | 2 | 1 | no | — |
| 346 | #135 | — | 5 | 2 | no | — |
| 347 | #135 | — | 5 | 2 | no | — |
| 348 | #135 | — | 5 | 2 | no | — |
| 349 | #135 | — | 10 | 2 | no | — |
| 350 | #135 | — | 10 | 2 | no | — |
| 351 | #135 | — | 10 | 2 | no | — |
| 352 | #135 | — | 10 | 1 | no | — |
| 353 | #135 | — | 10 | 2 | no | — |
| 354 | #135 | — | 10 | 1 | no | — |
| 355 | #135 | — | 10 | 1 | no | — |
| 356 | #135 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 357 | C2×Q16 | — | 5 | 2 | no | — |
| 358 | C2×Q16 | — | 10 | 1 | no | — |
| 359 | C2×SD16 | — | 10 | 2 | no | — |
| 360 | C2×SD16 | — | 10 | 2 | no | — |
| 361 | C2×D8 | — | 5 | 2 | no | — |
| 362 | C2×D8 | — | 10 | 1 | no | — |
| 363 | C2×M16 | — | 5 | 1 | no | — |
| 364 | C2×M16 | — | 5 | 1 | no | — |
| 365 | C2×M16 | — | 5 | 1 | no | — |
| 366 | C2×M16 | — | 10 | 2 | no | — |
| 367 | C2×M16 | — | 10 | 2 | no | — |
| 368 | C2×M16 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 369 | C22×C8 | — | 5 | 1 | no | — |
| 370 | C22×C8 | — | 5 | 1 | no | — |
| 371 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 372 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 373 | C2×C22⋊C4 | — | 20 | 1 | no | — |
| 374 | M32 | — | 10 | 2 | no | — |
| 375 | M32 | — | 10 | 2 | no | — |
| 376 | C2×C16 | — | 10 | 2 | no | — |
| 377 | #107 | — | 10 | 2 | no | — |
| 378 | #106 | — | 10 | 2 | no | — |
| 379 | #95 | — | 20 | 1 | no | — |
| 380 | C22×C5 | — | 2 | 1 | no | — |
| 381 | C22×C5 | — | 4 | 1 | no | — |
| 382 | C22×C5 | — | 4 | 2 | no | — |
| 383 | C22×C5 | — | 8 | 2 | no | — |
| 384 | C22×C5 | C2×#102 | 1 | 1 | yes | characteristic |
| 385 | C2×D5 | — | 2 | 1 | no | — |
| 386 | C2×D5 | — | 2 | 1 | no | — |
| 387 | C2×D5 | — | 2 | 1 | no | — |
| 388 | C2×D5 | — | 4 | 1 | no | — |
| 389 | C2×D5 | — | 4 | 1 | no | — |
| 390 | C2×D5 | — | 4 | 1 | no | — |
| 391 | C2×D5 | — | 4 | 2 | no | — |
| 392 | C2×D5 | — | 8 | 1 | no | — |
| 393 | C2×D5 | — | 8 | 4 | no | — |
| 394 | C2×D5 | — | 8 | 2 | no | — |
| 395 | C2×D5 | — | 8 | 2 | no | — |
| 396 | C2×D5 | — | 8 | 2 | no | — |
| 397 | C2×D5 | #447 | 1 | 1 | yes | characteristic |
| 398 | C2×D5 | #447 | 1 | 1 | yes | characteristic |
| 399 | AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 400 | AGL(1,𝔽5) | — | 16 | 1 | no | — |
| 401 | C4×C5 | — | 2 | 1 | no | — |
| 402 | C4×C5 | — | 4 | 2 | no | — |
| 403 | C4×C5 | #379 | 1 | 1 | yes | characteristic |
| 404 | C4×C5 | #418 | 1 | 1 | yes | characteristic |
| 405 | Dic5 | — | 2 | 1 | no | — |
| 406 | Dic5 | — | 4 | 2 | no | — |
| 407 | Dic5 | #450 | 1 | 1 | yes | characteristic |
| 408 | Dic5 | #450 | 1 | 1 | yes | characteristic |
| 409 | C24 | — | 5 | 1 | no | — |
| 410 | C24 | — | 20 | 1 | no | — |
| 411 | #41 | — | 2 | 2 | no | — |
| 412 | #41 | — | 2 | 2 | no | — |
| 413 | #41 | — | 4 | 1 | no | — |
| 414 | #41 | — | 4 | 1 | no | — |
| 415 | #41 | — | 10 | 2 | no | — |
| 416 | #41 | — | 10 | 2 | no | — |
| 417 | #41 | — | 10 | 2 | no | — |
| 418 | #41 | — | 10 | 2 | no | — |
| 419 | #41 | — | 10 | 2 | no | — |
| 420 | #41 | — | 10 | 2 | no | — |
| 421 | #41 | — | 20 | 1 | no | — |
| 422 | #41 | — | 20 | 2 | no | — |
| 423 | #41 | — | 20 | 2 | no | — |
| 424 | #41 | — | 20 | 2 | no | — |
| 425 | #41 | — | 20 | 2 | no | — |
| 426 | #41 | — | 20 | 2 | no | — |
| 427 | #41 | — | 20 | 2 | no | — |
| 428 | #41 | — | 20 | 1 | no | — |
| 429 | #41 | — | 20 | 1 | no | — |
| 430 | #41 | — | 20 | 2 | no | — |
| 431 | #41 | — | 20 | 2 | no | — |
| 432 | #41 | — | 20 | 1 | no | — |
| 433 | #41 | — | 20 | 1 | no | — |
| 434 | #41 | — | 20 | 1 | no | — |
| 435 | C2×Q8 | — | 2 | 1 | no | — |
| 436 | C2×Q8 | — | 10 | 1 | no | — |
| 437 | C2×Q8 | — | 10 | 2 | no | — |
| 438 | C2×Q8 | — | 10 | 2 | no | — |
| 439 | C2×Q8 | — | 20 | 1 | no | — |
| 440 | C2×Q8 | — | 20 | 1 | no | — |
| 441 | C2×Q8 | — | 20 | 1 | no | — |
| 442 | C2×D4 | — | 2 | 1 | no | — |
| 443 | C2×D4 | — | 4 | 1 | no | — |
| 444 | C2×D4 | — | 10 | 1 | no | — |
| 445 | C2×D4 | — | 10 | 2 | no | — |
| 446 | C2×D4 | — | 10 | 2 | no | — |
| 447 | C2×D4 | — | 20 | 1 | no | — |
| 448 | C2×D4 | — | 20 | 1 | no | — |
| 449 | C2×D4 | — | 20 | 1 | no | — |
| 450 | C2×D4 | — | 20 | 1 | no | — |
| 451 | C2×D4 | — | 20 | 2 | no | — |
| 452 | C2×D4 | — | 20 | 2 | no | — |
| 453 | C2×D4 | — | 20 | 2 | no | — |
| 454 | C2×D4 | — | 20 | 2 | no | — |
| 455 | C2×D4 | — | 20 | 1 | no | — |
| 456 | C2×D4 | — | 20 | 1 | no | — |
| 457 | C22×C4 | — | 4 | 1 | no | — |
| 458 | C22×C4 | — | 5 | 1 | no | — |
| 459 | C22×C4 | — | 5 | 1 | no | — |
| 460 | C22×C4 | — | 5 | 1 | no | — |
| 461 | C22×C4 | — | 5 | 1 | no | — |
| 462 | C22×C4 | — | 5 | 1 | no | — |
| 463 | C22×C4 | — | 10 | 1 | no | — |
| 464 | C22×C4 | — | 10 | 1 | no | — |
| 465 | C22×C4 | — | 10 | 1 | no | — |
| 466 | C22×C4 | — | 10 | 1 | no | — |
| 467 | C22×C4 | — | 20 | 1 | no | — |
| 468 | C22×C4 | — | 20 | 2 | no | — |
| 469 | C22×C4 | — | 20 | 2 | no | — |
| 470 | C22×C4 | — | 20 | 2 | no | — |
| 471 | C22×C4 | — | 20 | 1 | no | — |
| 472 | C22×C4 | — | 20 | 2 | no | — |
| 473 | C22×C4 | — | 20 | 1 | no | — |
| 474 | C22×C4 | — | 20 | 1 | no | — |
| 475 | C22×C4 | — | 20 | 1 | no | — |
| 476 | C22×C4 | — | 20 | 1 | no | — |
| 477 | C22×C4 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 478 | Q16 | — | 2 | 1 | no | — |
| 479 | Q16 | — | 5 | 2 | no | — |
| 480 | Q16 | — | 10 | 1 | no | — |
| 481 | Q16 | — | 10 | 2 | no | — |
| 482 | Q16 | — | 10 | 2 | no | — |
| 483 | Q16 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 484 | SD16 | — | 2 | 2 | no | — |
| 485 | SD16 | — | 2 | 2 | no | — |
| 486 | SD16 | — | 10 | 2 | no | — |
| 487 | SD16 | — | 10 | 2 | no | — |
| 488 | SD16 | — | 10 | 2 | no | — |
| 489 | SD16 | — | 10 | 2 | no | — |
| 490 | SD16 | — | 10 | 2 | no | — |
| 491 | SD16 | — | 10 | 2 | no | — |
| 492 | D8 | — | 2 | 1 | no | — |
| 493 | D8 | — | 5 | 2 | no | — |
| 494 | D8 | — | 10 | 1 | no | — |
| 495 | D8 | — | 10 | 2 | no | — |
| 496 | D8 | — | 10 | 2 | no | — |
| 497 | D8 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 498 | M16 | — | 2 | 2 | no | — |
| 499 | M16 | — | 10 | 2 | no | — |
| 500 | M16 | — | 10 | 2 | no | — |
| 501 | M16 | — | 10 | 2 | no | — |
| 502 | C2×C8 | — | 5 | 1 | no | — |
| 503 | C2×C8 | — | 5 | 2 | no | — |
| 504 | C2×C8 | — | 5 | 2 | no | — |
| 505 | C2×C8 | — | 5 | 1 | no | — |
| 506 | C2×C8 | — | 10 | 1 | no | — |
| 507 | C2×C8 | — | 10 | 1 | no | — |
| 508 | C2×C8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 509 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 510 | C4⋊C4 | — | 20 | 1 | no | — |
| 511 | C4⋊C4 | — | 20 | 1 | no | — |
| 512 | C4⋊C4 | — | 20 | 1 | no | — |
| 513 | C4⋊C4 | — | 20 | 1 | no | — |
| 514 | C22⋊C4 | — | 40 | 2 | no | — |
| 515 | C16 | — | 20 | 2 | no | — |
| 516 | C2×C5 | — | 2 | 1 | no | — |
| 517 | C2×C5 | — | 4 | 1 | no | — |
| 518 | C2×C5 | — | 8 | 2 | no | — |
| 519 | C2×C5 | #1786 | 1 | 1 | yes | characteristic |
| 520 | D5 | — | 2 | 1 | no | — |
| 521 | D5 | — | 4 | 1 | no | — |
| 522 | D5 | — | 8 | 2 | no | — |
| 523 | D5 | #2190 | 1 | 1 | yes | characteristic |
| 524 | D5 | #2191 | 1 | 1 | yes | characteristic |
| 525 | C23 | — | 4 | 1 | no | — |
| 526 | C23 | — | 5 | 1 | no | — |
| 527 | C23 | — | 5 | 1 | no | — |
| 528 | C23 | — | 10 | 1 | no | — |
| 529 | C23 | — | 10 | 1 | no | — |
| 530 | C23 | — | 20 | 1 | no | — |
| 531 | C23 | — | 20 | 2 | no | — |
| 532 | C23 | — | 20 | 1 | no | — |
| 533 | C23 | — | 20 | 1 | no | — |
| 534 | C23 | — | 20 | 2 | no | — |
| 535 | C23 | — | 40 | 2 | no | — |
| 536 | C23 | — | 40 | 2 | no | — |
| 537 | C23 | #4007 | 1 | 1 | yes | characteristic |
| 538 | Q8 | — | 2 | 2 | no | — |
| 539 | Q8 | — | 4 | 1 | no | — |
| 540 | Q8 | — | 10 | 2 | no | — |
| 541 | Q8 | — | 20 | 1 | no | — |
| 542 | Q8 | — | 20 | 2 | no | — |
| 543 | Q8 | — | 20 | 2 | no | — |
| 544 | D4 | — | 2 | 2 | no | — |
| 545 | D4 | — | 4 | 1 | no | — |
| 546 | D4 | — | 4 | 2 | no | — |
| 547 | D4 | — | 4 | 2 | no | — |
| 548 | D4 | — | 10 | 2 | no | — |
| 549 | D4 | — | 20 | 1 | no | — |
| 550 | D4 | — | 20 | 2 | no | — |
| 551 | D4 | — | 20 | 2 | no | — |
| 552 | D4 | — | 20 | 2 | no | — |
| 553 | D4 | — | 20 | 2 | no | — |
| 554 | D4 | — | 20 | 2 | no | — |
| 555 | D4 | — | 20 | 2 | no | — |
| 556 | D4 | — | 20 | 2 | no | — |
| 557 | D4 | — | 20 | 2 | no | — |
| 558 | C2×C4 | — | 2 | 1 | no | — |
| 559 | C2×C4 | — | 2 | 1 | no | — |
| 560 | C2×C4 | — | 4 | 2 | no | — |
| 561 | C2×C4 | — | 4 | 1 | no | — |
| 562 | C2×C4 | — | 4 | 2 | no | — |
| 563 | C2×C4 | — | 5 | 1 | no | — |
| 564 | C2×C4 | — | 5 | 1 | no | — |
| 565 | C2×C4 | — | 5 | 1 | no | — |
| 566 | C2×C4 | — | 5 | 1 | no | — |
| 567 | C2×C4 | — | 5 | 1 | no | — |
| 568 | C2×C4 | — | 5 | 1 | no | — |
| 569 | C2×C4 | — | 10 | 1 | no | — |
| 570 | C2×C4 | — | 10 | 1 | no | — |
| 571 | C2×C4 | — | 10 | 1 | no | — |
| 572 | C2×C4 | — | 10 | 1 | no | — |
| 573 | C2×C4 | — | 10 | 1 | no | — |
| 574 | C2×C4 | — | 10 | 1 | no | — |
| 575 | C2×C4 | — | 10 | 1 | no | — |
| 576 | C2×C4 | — | 10 | 1 | no | — |
| 577 | C2×C4 | — | 20 | 2 | no | — |
| 578 | C2×C4 | — | 20 | 2 | no | — |
| 579 | C2×C4 | — | 20 | 2 | no | — |
| 580 | C2×C4 | — | 20 | 2 | no | — |
| 581 | C2×C4 | — | 20 | 2 | no | — |
| 582 | C2×C4 | — | 20 | 2 | no | — |
| 583 | C2×C4 | — | 20 | 2 | no | — |
| 584 | C2×C4 | — | 20 | 1 | no | — |
| 585 | C2×C4 | — | 20 | 2 | no | — |
| 586 | C2×C4 | — | 40 | 1 | no | — |
| 587 | C2×C4 | — | 40 | 1 | no | — |
| 588 | C2×C4 | — | 40 | 1 | no | — |
| 589 | C2×C4 | — | 40 | 1 | no | — |
| 590 | C2×C4 | — | 40 | 1 | no | — |
| 591 | C2×C4 | — | 40 | 1 | no | — |
| 592 | C2×C4 | #4007 | 1 | 1 | yes | characteristic |
| 593 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 594 | C8 | — | 2 | 1 | no | — |
| 595 | C8 | — | 5 | 2 | no | — |
| 596 | C8 | — | 10 | 1 | no | — |
| 597 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 598 | C5 | #12739 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 599 | C22 | — | 2 | 1 | no | — |
| 600 | C22 | — | 4 | 1 | no | — |
| 601 | C22 | — | 4 | 2 | no | — |
| 602 | C22 | — | 5 | 1 | no | — |
| 603 | C22 | — | 5 | 1 | no | — |
| 604 | C22 | — | 8 | 2 | no | — |
| 605 | C22 | — | 10 | 1 | no | — |
| 606 | C22 | — | 10 | 1 | no | — |
| 607 | C22 | — | 10 | 1 | no | — |
| 608 | C22 | — | 20 | 1 | no | — |
| 609 | C22 | — | 20 | 1 | no | — |
| 610 | C22 | — | 20 | 1 | no | — |
| 611 | C22 | — | 20 | 2 | no | — |
| 612 | C22 | — | 40 | 1 | no | — |
| 613 | C22 | — | 40 | 2 | no | — |
| 614 | C22 | — | 40 | 2 | no | — |
| 615 | C22 | — | 40 | 2 | no | — |
| 616 | C22 | — | 40 | 4 | no | — |
| 617 | C22 | C2×#4007 | 1 | 1 | yes | characteristic |
| 618 | C4 | — | 2 | 1 | no | — |
| 619 | C4 | — | 4 | 2 | no | — |
| 620 | C4 | — | 5 | 1 | no | — |
| 621 | C4 | — | 5 | 1 | no | — |
| 622 | C4 | — | 10 | 1 | no | — |
| 623 | C4 | — | 20 | 2 | no | — |
| 624 | C4 | — | 80 | 1 | no | — |
| 625 | C4 | — | 80 | 1 | no | — |
| 626 | C4 | #65767 | 1 | 1 | yes | characteristic |
| 627 | C4 | #65800 | 1 | 1 | yes | characteristic |
| 628 | C2 | — | 2 | 1 | no | — |
| 629 | C2 | — | 4 | 1 | no | — |
| 630 | C2 | — | 5 | 1 | no | — |
| 631 | C2 | — | 5 | 1 | no | — |
| 632 | C2 | — | 8 | 2 | no | — |
| 633 | C2 | — | 10 | 1 | no | — |
| 634 | C2 | — | 20 | 1 | no | — |
| 635 | C2 | — | 40 | 2 | no | — |
| 636 | C2 | #10604928 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10604856 | C2 | semidirect |
| 3. D5⋊#360 | C2 | semidirect |
| 4. #10604761 | C2 | semidirect |
| 5. D5⋊#349 | C2 | semidirect |
| 7. C5×#575 | C4 | semidirect |
| 14. #66102 | C4 | semidirect |
| 17. #66082 | C4 | semidirect |
| 20. C2×#3994 | C22 | semidirect |
| 21. C2×#3993 | C22 | semidirect |
| 22. D5⋊M32 | C22 | semidirect |
| 181. C5×Q16 | C22⋊C4 | semidirect |
| 185. C5×D8 | C22⋊C4 | semidirect |
| 201. Dic20 | C22⋊C4 | semidirect |
| 203. D40 | C22⋊C4 | semidirect |
| 220. #575 | AGL(1,𝔽5) | semidirect |
| 483. Q16 | C22⋊AGL(1,𝔽5) | semidirect |
| 497. D8 | C22⋊AGL(1,𝔽5) | semidirect |
| 598. C5 | #12739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#575 | 2 |
| #10604856 | 2 |
| D5⋊#360 | 2 |
| #10604761 | 2 |
| D5⋊#349 | 2 |
| #12739 | 5 |