← #41×D5⋊AGL(1,𝔽5) #72220988
Order 3200.
3766 conjugacy classes of subgroups.
The subgroup lattice has 630 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D52×#41 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #41×#1044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #41×#1043 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13107575 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | Q8×D5⋊AGL(1,𝔽5) | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13107568 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | D4×D5⋊AGL(1,𝔽5) | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #13107561 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | D5⋊#4130 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #13107559 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×C4×D5⋊AGL(1,𝔽5) | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C22×D5⋊AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 13 | #41×C5⋊D5 | C22 | 1 | 1 | yes | characteristic |
| 14 | C5×D5×#41 | C4 | 1 | 2 | yes | complemented |
| 15 | #11717484 | C22 | 1 | 1 | yes | characteristic |
| 16 | D5×#713 | C4 | 1 | 2 | yes | complemented |
| 17 | Q8×D52 | C22 | 1 | 1 | yes | characteristic |
| 18 | #11717477 | C22 | 1 | 3 | yes | — |
| 19 | D5×#711 | C4 | 1 | 6 | yes | complemented |
| 20 | D4×D52 | C22 | 1 | 3 | yes | — |
| 21 | #11717471 | C22 | 1 | 3 | yes | — |
| 22 | D5×#709 | C4 | 1 | 6 | yes | complemented |
| 23 | C2×C4×D52 | C22 | 1 | 3 | yes | — |
| 24 | Q8×#1044 | C22 | 1 | 2 | yes | complemented |
| 25 | D4×#1044 | C22 | 1 | 6 | yes | complemented |
| 26 | #11717451 | C22 | 1 | 3 | yes | complemented |
| 27 | C2×C4×#1044 | C22 | 1 | 3 | yes | complemented |
| 28 | Q8×#1043 | C22 | 1 | 2 | yes | complemented |
| 29 | D4×#1043 | C22 | 1 | 6 | yes | complemented |
| 30 | #11717438 | C22 | 1 | 3 | yes | complemented |
| 31 | C2×C4×#1043 | C22 | 1 | 3 | yes | complemented |
| 32 | #11717377 | C22 | 1 | 12 | yes | complemented |
| 33 | D5⋊(C22⋊AGL(1,𝔽5)) | C22 | 1 | 6 | yes | — |
| 34 | #11717375 | C22 | 1 | 12 | yes | complemented |
| 35 | #11717367 | C22 | 1 | 6 | yes | complemented |
| 36 | C2×#87830 | C22 | 1 | 6 | yes | complemented |
| 37 | #11717365 | C22 | 1 | 6 | yes | complemented |
| 38 | D5⋊(C4⋊AGL(1,𝔽5)) | C22 | 1 | 6 | yes | — |
| 39 | #11717363 | C22 | 1 | 6 | yes | complemented |
| 40 | C4×D5⋊AGL(1,𝔽5) | C22 | 1 | 1 | yes | characteristic |
| 41 | C4×D5⋊AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 42 | C4×D5⋊AGL(1,𝔽5) | C22 | 1 | 6 | yes | — |
| 43 | C4×D5⋊AGL(1,𝔽5) | C22 | 1 | 3 | yes | complemented |
| 44 | C4×D5⋊AGL(1,𝔽5) | C22 | 1 | 3 | yes | complemented |
| 45 | C4×D5⋊AGL(1,𝔽5) | C22 | 1 | 6 | yes | complemented |
| 46 | #11717356 | C22 | 1 | 6 | yes | complemented |
| 47 | #11717355 | C22 | 1 | 6 | yes | complemented |
| 48 | #11717354 | C22 | 1 | 6 | yes | complemented |
| 49 | #11717353 | C22 | 1 | 6 | yes | complemented |
| 50 | C2×#41×AGL(1,𝔽5) | — | 5 | 2 | no | maximal |
| 51 | C22×D52 | C23 | 1 | 3 | yes | — |
| 52 | C22×#1044 | C23 | 1 | 6 | yes | — |
| 53 | C22×#1043 | C23 | 1 | 6 | yes | — |
| 54 | C2×D5⋊AGL(1,𝔽5) | — | 2 | 24 | no | — |
| 55 | C2×D5⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 56 | C2×D5⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 57 | C2×D5⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 58 | C2×D5⋊AGL(1,𝔽5) | C23 | 1 | 2 | yes | — |
| 59 | C52×#41 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 60 | #87904 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 61 | Q8×C5⋊D5 | C23 | 1 | 1 | yes | characteristic |
| 62 | #87902 | C2×C4 | 1 | 3 | yes | complemented |
| 63 | D4×C5⋊D5 | C23 | 1 | 3 | yes | — |
| 64 | #87900 | C2×C4 | 1 | 3 | yes | complemented |
| 65 | C2×C4×C5⋊D5 | C23 | 1 | 3 | yes | — |
| 66 | C5×#713 | C2×C4 | 1 | 2 | yes | complemented |
| 67 | C5×Q8×D5 | C2×C4 | 1 | 2 | yes | complemented |
| 68 | C5×#711 | C2×C4 | 1 | 6 | yes | complemented |
| 69 | C5×D4×D5 | C2×C4 | 1 | 6 | yes | complemented |
| 70 | C5×#709 | C2×C4 | 1 | 6 | yes | complemented |
| 71 | C2×C4×C5×D5 | C2×C4 | 1 | 6 | yes | complemented |
| 72 | #87886 | C23 | 1 | 6 | yes | — |
| 73 | D5×C22⋊D5 | C2×C4 | 1 | 12 | yes | complemented |
| 74 | C2×#6036 | C23 | 1 | 3 | yes | — |
| 75 | #87880 | C2×C4 | 1 | 6 | yes | complemented |
| 76 | #87879 | C2×C4 | 1 | 12 | yes | complemented |
| 77 | C2×D5×Dic5 | C2×C4 | 1 | 6 | yes | complemented |
| 78 | #87877 | C23 | 1 | 3 | yes | — |
| 79 | D5×D20 | C2×C4 | 1 | 6 | yes | complemented |
| 80 | C4×D52 | C2×C4 | 1 | 6 | yes | complemented |
| 81 | C4×D52 | C2×C4 | 1 | 6 | yes | complemented |
| 82 | C4×D52 | C23 | 1 | 1 | yes | characteristic |
| 83 | C4×D52 | C23 | 1 | 3 | yes | — |
| 84 | C4×D52 | C23 | 1 | 3 | yes | — |
| 85 | C4×D52 | C23 | 1 | 3 | yes | — |
| 86 | #87874 | C2×C4 | 1 | 6 | yes | complemented |
| 87 | #87873 | C2×C4 | 1 | 6 | yes | complemented |
| 88 | #87872 | C23 | 1 | 3 | yes | — |
| 89 | #87871 | C2×C4 | 1 | 6 | yes | complemented |
| 90 | #87870 | C2×C4 | 1 | 6 | yes | complemented |
| 91 | D5×Dic10 | C2×C4 | 1 | 6 | yes | complemented |
| 92 | C22⋊#1044 | C23 | 1 | 6 | yes | — |
| 93 | C4⋊#1044 | C23 | 1 | 6 | yes | — |
| 94 | C4×#1044 | C23 | 1 | 1 | yes | characteristic |
| 95 | C4×#1044 | C23 | 1 | 3 | yes | — |
| 96 | C4×#1044 | C23 | 1 | 6 | yes | — |
| 97 | C22⋊#1043 | C23 | 1 | 6 | yes | — |
| 98 | C4⋊#1043 | C23 | 1 | 6 | yes | — |
| 99 | C4×#1043 | C23 | 1 | 1 | yes | characteristic |
| 100 | C4×#1043 | C23 | 1 | 3 | yes | — |
| 101 | C4×#1043 | C23 | 1 | 6 | yes | — |
| 102 | #87832 | C23 | 1 | 12 | yes | — |
| 103 | #87831 | C23 | 1 | 12 | yes | — |
| 104 | #87830 | C23 | 1 | 6 | yes | — |
| 105 | #87830 | C23 | 1 | 6 | yes | — |
| 106 | #87830 | C23 | 1 | 6 | yes | — |
| 107 | #87830 | C23 | 1 | 2 | yes | — |
| 108 | C2×D5×#41 | — | 5 | 2 | no | — |
| 109 | #41×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 110 | #41×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 111 | #41×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 112 | #41×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 113 | #41×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 114 | #41×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 115 | #41×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 116 | C2×Q8×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 117 | C2×D4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 118 | C2×#4130 | — | 5 | 6 | no | — |
| 119 | C22×C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 120 | C22×C5⋊D5 | C24 | 1 | 3 | yes | — |
| 121 | C22×C5×D5 | C22×C4 | 1 | 6 | yes | — |
| 122 | C2×D52 | — | 2 | 12 | no | — |
| 123 | C2×D52 | C22×C4 | 1 | 6 | yes | — |
| 124 | C2×D52 | C24 | 1 | 3 | yes | — |
| 125 | C2×D52 | C24 | 1 | 1 | yes | characteristic |
| 126 | C2×#1044 | — | 2 | 12 | no | — |
| 127 | C2×#1044 | C24 | 1 | 6 | yes | — |
| 128 | C2×#1044 | C24 | 1 | 2 | yes | — |
| 129 | C2×#1043 | — | 2 | 12 | no | — |
| 130 | C2×#1043 | C24 | 1 | 6 | yes | — |
| 131 | C2×#1043 | C24 | 1 | 2 | yes | — |
| 132 | D5⋊AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 133 | D5⋊AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 134 | D5⋊AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 135 | D5⋊AGL(1,𝔽5) | #41 | 1 | 8 | yes | direct product factor |
| 136 | C52×Q8 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 137 | C52×D4 | C22×C4 | 1 | 3 | yes | complemented |
| 138 | C2×C4×C52 | C22×C4 | 1 | 3 | yes | complemented |
| 139 | C22⋊(C5⋊D5) | C22×C4 | 1 | 6 | yes | complemented |
| 140 | C2×#1039 | C22×C4 | 1 | 3 | yes | complemented |
| 141 | C4⋊(C5⋊D5) | C22×C4 | 1 | 3 | yes | complemented |
| 142 | C4×C5⋊D5 | C22×C4 | 1 | 3 | yes | complemented |
| 143 | C4×C5⋊D5 | C22×C4 | 1 | 3 | yes | complemented |
| 144 | C4×C5⋊D5 | C24 | 1 | 1 | yes | characteristic |
| 145 | C4×C5⋊D5 | C24 | 1 | 3 | yes | — |
| 146 | #6045 | C22×C4 | 1 | 3 | yes | complemented |
| 147 | C5×C22⋊D5 | C22×C4 | 1 | 12 | yes | complemented |
| 148 | C2×C5×Dic5 | C22×C4 | 1 | 6 | yes | complemented |
| 149 | C5×D20 | C22×C4 | 1 | 6 | yes | complemented |
| 150 | C4×C5×D5 | C22×C4 | 1 | 6 | yes | — |
| 151 | C4×C5×D5 | C22×C4 | 1 | 2 | yes | — |
| 152 | C4×C5×D5 | C22×C4 | 1 | 6 | yes | complemented |
| 153 | C4×C5×D5 | C22×C4 | 1 | 6 | yes | complemented |
| 154 | C5×Dic10 | C22×C4 | 1 | 6 | yes | complemented |
| 155 | #6039 | C22×C4 | 1 | 6 | yes | complemented |
| 156 | #6038 | C22×C4 | 1 | 12 | yes | complemented |
| 157 | #6037 | C22×C4 | 1 | 6 | yes | complemented |
| 158 | #6036 | C22×C4 | 1 | 6 | yes | complemented |
| 159 | #6036 | C24 | 1 | 1 | yes | characteristic |
| 160 | #6036 | C24 | 1 | 3 | yes | — |
| 161 | D5×Dic5 | C22×C4 | 1 | 6 | yes | — |
| 162 | D5×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 163 | D5×Dic5 | C22×C4 | 1 | 6 | yes | complemented |
| 164 | D5×Dic5 | C22×C4 | 1 | 6 | yes | complemented |
| 165 | C23×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 166 | C2×C5×#41 | — | 5 | 2 | no | — |
| 167 | D5×#41 | — | 5 | 2 | no | — |
| 168 | D5×#41 | — | 5 | 2 | no | — |
| 169 | D5×#41 | — | 5 | 2 | no | — |
| 170 | D5×#41 | — | 5 | 6 | no | — |
| 171 | D5×#41 | — | 5 | 6 | no | — |
| 172 | D5×#41 | — | 5 | 6 | no | — |
| 173 | D5×#41 | — | 5 | 6 | no | — |
| 174 | D5×#41 | — | 10 | 2 | no | — |
| 175 | D5×#41 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 176 | C2×#713 | — | 5 | 2 | no | — |
| 177 | C2×Q8×D5 | — | 5 | 2 | no | — |
| 178 | C2×#711 | — | 5 | 6 | no | — |
| 179 | C2×D4×D5 | — | 5 | 6 | no | — |
| 180 | C2×#709 | — | 5 | 6 | no | — |
| 181 | C22×C4×D5 | — | 5 | 6 | no | — |
| 182 | C2×C22⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 183 | Q8×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 184 | Q8×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 185 | Q8×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 186 | Q8×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 187 | Q8×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 188 | D4×AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 189 | D4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 190 | D4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 191 | D4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 192 | D4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 193 | D4×AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 194 | D4×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 195 | #4130 | — | 5 | 6 | no | — |
| 196 | #4130 | — | 5 | 6 | no | — |
| 197 | #4130 | — | 5 | 12 | no | — |
| 198 | #4130 | — | 5 | 12 | no | — |
| 199 | #4130 | — | 5 | 12 | no | — |
| 200 | #4130 | — | 10 | 6 | no | — |
| 201 | C2×C4⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 202 | C2×C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 203 | C2×C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 204 | C2×C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 205 | C2×C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 206 | C2×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 207 | C2×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 208 | C2×C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 209 | C2×C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 210 | C2×C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 211 | C2×C4×AGL(1,𝔽5) | — | 10 | 6 | no | — |
| 212 | C2×C4×#41 | — | 25 | 1 | no | Sylow |
| 213 | C22×C52 | C23×C4 | 1 | 3 | yes | — |
| 214 | C2×C5⋊D5 | — | 2 | 6 | no | — |
| 215 | C2×C5⋊D5 | C23×C4 | 1 | 3 | yes | — |
| 216 | C2×C5⋊D5 | C25 | 1 | 1 | yes | characteristic |
| 217 | C2×C5×D5 | — | 2 | 12 | no | — |
| 218 | C2×C5×D5 | C23×C4 | 1 | 6 | yes | — |
| 219 | C2×C5×D5 | C23×C4 | 1 | 2 | yes | — |
| 220 | D52 | — | 2 | 12 | no | — |
| 221 | D52 | — | 2 | 6 | no | — |
| 222 | D52 | C2×#41 | 1 | 4 | yes | — |
| 223 | #1044 | — | 2 | 6 | no | — |
| 224 | #1044 | C2×#41 | 1 | 4 | yes | complemented |
| 225 | #1043 | — | 2 | 6 | no | — |
| 226 | #1043 | C2×#41 | 1 | 4 | yes | complemented |
| 227 | C4×C52 | C23×C4 | 1 | 3 | yes | — |
| 228 | C4×C52 | C23×C4 | 1 | 1 | yes | characteristic |
| 229 | #1039 | C23×C4 | 1 | 1 | yes | characteristic |
| 230 | #1039 | C23×C4 | 1 | 3 | yes | — |
| 231 | C5×Dic5 | C23×C4 | 1 | 2 | yes | — |
| 232 | C5×Dic5 | C23×C4 | 1 | 6 | yes | — |
| 233 | C23×D5 | — | 5 | 6 | no | — |
| 234 | C22×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 235 | C22×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 236 | C22×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 237 | C22×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 238 | C22×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 239 | C22×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 240 | C22×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 241 | C22×AGL(1,𝔽5) | — | 10 | 48 | no | — |
| 242 | C5×#41 | — | 2 | 2 | no | — |
| 243 | C5×#41 | — | 5 | 2 | no | — |
| 244 | C5×#41 | — | 5 | 6 | no | — |
| 245 | C5×#41 | — | 5 | 6 | no | — |
| 246 | C5×#41 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 247 | C2×C5×Q8 | — | 5 | 2 | no | — |
| 248 | C2×C5×D4 | — | 5 | 6 | no | — |
| 249 | C22×C4×C5 | — | 5 | 6 | no | — |
| 250 | C2×C22⋊D5 | — | 5 | 12 | no | — |
| 251 | C22×Dic5 | — | 5 | 6 | no | — |
| 252 | #713 | — | 5 | 2 | no | — |
| 253 | #713 | — | 5 | 6 | no | — |
| 254 | #713 | — | 5 | 6 | no | — |
| 255 | #713 | — | 10 | 2 | no | — |
| 256 | #713 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 257 | Q8×D5 | — | 5 | 2 | no | — |
| 258 | Q8×D5 | — | 5 | 6 | no | — |
| 259 | Q8×D5 | — | 5 | 6 | no | — |
| 260 | Q8×D5 | — | 10 | 2 | no | — |
| 261 | Q8×D5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 262 | #711 | — | 5 | 6 | no | — |
| 263 | #711 | — | 5 | 12 | no | — |
| 264 | #711 | — | 5 | 12 | no | — |
| 265 | #711 | — | 5 | 6 | no | — |
| 266 | #711 | — | 5 | 6 | no | — |
| 267 | #711 | — | 10 | 6 | no | — |
| 268 | #711 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 269 | D4×D5 | — | 5 | 12 | no | — |
| 270 | D4×D5 | — | 5 | 6 | no | — |
| 271 | D4×D5 | — | 5 | 12 | no | — |
| 272 | D4×D5 | — | 5 | 6 | no | — |
| 273 | D4×D5 | — | 5 | 6 | no | — |
| 274 | D4×D5 | — | 10 | 6 | no | — |
| 275 | D4×D5 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 276 | #709 | — | 5 | 6 | no | — |
| 277 | #709 | — | 5 | 12 | no | — |
| 278 | #709 | — | 5 | 6 | no | — |
| 279 | #709 | — | 5 | 12 | no | — |
| 280 | #709 | — | 5 | 6 | no | — |
| 281 | #709 | — | 10 | 6 | no | — |
| 282 | #709 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 283 | C2×D20 | — | 5 | 6 | no | — |
| 284 | C2×C4×D5 | — | 5 | 6 | no | — |
| 285 | C2×C4×D5 | — | 5 | 6 | no | — |
| 286 | C2×C4×D5 | — | 5 | 6 | no | — |
| 287 | C2×C4×D5 | — | 5 | 2 | no | — |
| 288 | C2×C4×D5 | — | 5 | 6 | no | — |
| 289 | C2×C4×D5 | — | 5 | 6 | no | — |
| 290 | C2×C4×D5 | — | 5 | 6 | no | — |
| 291 | C2×C4×D5 | — | 5 | 6 | no | — |
| 292 | C2×C4×D5 | — | 5 | 6 | no | — |
| 293 | C2×C4×D5 | — | 5 | 6 | no | — |
| 294 | C2×C4×D5 | — | 5 | 6 | no | — |
| 295 | C2×C4×D5 | — | 10 | 6 | no | — |
| 296 | C2×C4×D5 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 297 | C2×Dic10 | — | 5 | 6 | no | — |
| 298 | C22⋊AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 299 | C22⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 300 | C22⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 301 | C22⋊AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 302 | C4⋊AGL(1,𝔽5) | — | 5 | 24 | no | — |
| 303 | C4⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 304 | C4⋊AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 305 | C4⋊AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 306 | C4×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 307 | C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 308 | C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 309 | C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 310 | C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 311 | C4×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 312 | C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 313 | C4×AGL(1,𝔽5) | — | 5 | 6 | no | — |
| 314 | C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 315 | C4×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 316 | C4×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 317 | C4×AGL(1,𝔽5) | — | 10 | 6 | no | — |
| 318 | C4×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 319 | C22×#41 | — | 25 | 1 | no | — |
| 320 | C4×#41 | — | 25 | 3 | no | — |
| 321 | C4×#41 | — | 25 | 1 | no | — |
| 322 | C4×#41 | — | 25 | 2 | no | — |
| 323 | C4×#41 | — | 25 | 6 | no | — |
| 324 | C4×#41 | — | 25 | 3 | no | — |
| 325 | C4×#41 | — | 25 | 1 | no | — |
| 326 | C2×C4×Q8 | — | 25 | 2 | no | — |
| 327 | C2×C4×D4 | — | 25 | 6 | no | — |
| 328 | C2×#117 | — | 25 | 3 | no | — |
| 329 | C22×C42 | — | 25 | 3 | no | — |
| 330 | C2×C52 | — | 2 | 3 | no | — |
| 331 | C2×C52 | C24×C4 | 1 | 1 | yes | characteristic |
| 332 | C5⋊D5 | — | 2 | 3 | no | — |
| 333 | C5⋊D5 | C22×#41 | 1 | 2 | yes | — |
| 334 | C5×D5 | — | 2 | 6 | no | — |
| 335 | C5×D5 | C4×#41 | 1 | 4 | yes | complemented |
| 336 | C23×C5 | — | 5 | 6 | no | — |
| 337 | C22×D5 | — | 5 | 2 | no | — |
| 338 | C22×D5 | — | 5 | 6 | no | — |
| 339 | C22×D5 | — | 5 | 6 | no | — |
| 340 | C22×D5 | — | 5 | 6 | no | — |
| 341 | C22×D5 | — | 5 | 6 | no | — |
| 342 | C22×D5 | — | 10 | 6 | no | — |
| 343 | C22×D5 | — | 10 | 24 | no | — |
| 344 | C22×D5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 345 | C2×AGL(1,𝔽5) | — | 5 | 16 | no | — |
| 346 | C2×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 347 | C2×AGL(1,𝔽5) | — | 5 | 4 | no | — |
| 348 | C2×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 349 | C2×AGL(1,𝔽5) | — | 5 | 12 | no | — |
| 350 | C2×AGL(1,𝔽5) | — | 10 | 4 | no | — |
| 351 | C2×AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 352 | C2×AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 353 | C2×AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 354 | C2×AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 355 | C2×AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 356 | C2×AGL(1,𝔽5) | — | 10 | 24 | no | — |
| 357 | C2×AGL(1,𝔽5) | — | 20 | 24 | no | — |
| 358 | C5×Q8 | — | 2 | 2 | no | — |
| 359 | C5×Q8 | — | 5 | 6 | no | — |
| 360 | C5×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 361 | C5×D4 | — | 2 | 6 | no | — |
| 362 | C5×D4 | — | 5 | 12 | no | — |
| 363 | C5×D4 | — | 5 | 6 | no | — |
| 364 | C5×D4 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 365 | C2×C4×C5 | — | 2 | 6 | no | — |
| 366 | C2×C4×C5 | — | 5 | 6 | no | — |
| 367 | C2×C4×C5 | — | 5 | 6 | no | — |
| 368 | C2×C4×C5 | — | 5 | 2 | no | — |
| 369 | C2×C4×C5 | — | 5 | 6 | no | — |
| 370 | C2×C4×C5 | — | 5 | 6 | no | — |
| 371 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 372 | C22⋊D5 | — | 5 | 12 | no | — |
| 373 | C22⋊D5 | — | 5 | 12 | no | — |
| 374 | C22⋊D5 | — | 5 | 12 | no | — |
| 375 | C22⋊D5 | — | 10 | 12 | no | — |
| 376 | C22⋊D5 | C22×AGL(1,𝔽5) | 1 | 12 | yes | complemented |
| 377 | C2×Dic5 | — | 5 | 6 | no | — |
| 378 | C2×Dic5 | — | 5 | 6 | no | — |
| 379 | C2×Dic5 | — | 5 | 2 | no | — |
| 380 | C2×Dic5 | — | 5 | 6 | no | — |
| 381 | C2×Dic5 | — | 5 | 6 | no | — |
| 382 | C2×Dic5 | — | 10 | 6 | no | — |
| 383 | C2×Dic5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 384 | D20 | — | 5 | 12 | no | — |
| 385 | D20 | — | 5 | 6 | no | — |
| 386 | D20 | — | 10 | 6 | no | — |
| 387 | D20 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 388 | C4×D5 | — | 5 | 2 | no | — |
| 389 | C4×D5 | — | 5 | 6 | no | — |
| 390 | C4×D5 | — | 5 | 6 | no | — |
| 391 | C4×D5 | — | 5 | 6 | no | — |
| 392 | C4×D5 | — | 5 | 6 | no | — |
| 393 | C4×D5 | — | 5 | 6 | no | — |
| 394 | C4×D5 | — | 5 | 2 | no | — |
| 395 | C4×D5 | — | 5 | 6 | no | — |
| 396 | C4×D5 | — | 5 | 6 | no | — |
| 397 | C4×D5 | — | 5 | 6 | no | — |
| 398 | C4×D5 | — | 5 | 2 | no | — |
| 399 | C4×D5 | — | 5 | 6 | no | — |
| 400 | C4×D5 | — | 10 | 6 | no | — |
| 401 | C4×D5 | — | 10 | 6 | no | — |
| 402 | C4×D5 | — | 10 | 2 | no | — |
| 403 | C4×D5 | — | 10 | 6 | no | — |
| 404 | C4×D5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 405 | C4×D5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 406 | C4×D5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 407 | C4×D5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 408 | Dic10 | — | 5 | 6 | no | — |
| 409 | Dic10 | — | 5 | 12 | no | — |
| 410 | Dic10 | — | 10 | 6 | no | — |
| 411 | Dic10 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 412 | C2×#41 | — | 5 | 2 | no | — |
| 413 | C2×#41 | — | 25 | 6 | no | — |
| 414 | C2×#41 | — | 25 | 6 | no | — |
| 415 | C2×#41 | — | 25 | 2 | no | — |
| 416 | C2×#41 | — | 25 | 1 | no | — |
| 417 | C2×#41 | — | 25 | 3 | no | — |
| 418 | C2×#41 | — | 25 | 3 | no | — |
| 419 | C2×#41 | — | 25 | 1 | no | — |
| 420 | C22×Q8 | — | 25 | 1 | no | — |
| 421 | C22×D4 | — | 25 | 3 | no | — |
| 422 | C23×C4 | — | 25 | 3 | no | — |
| 423 | C23×C4 | — | 25 | 6 | no | — |
| 424 | C4×Q8 | — | 25 | 2 | no | — |
| 425 | C4×Q8 | — | 25 | 6 | no | — |
| 426 | C4×Q8 | — | 25 | 6 | no | — |
| 427 | C4×Q8 | — | 25 | 2 | no | — |
| 428 | C4×D4 | — | 25 | 6 | no | — |
| 429 | C4×D4 | — | 25 | 12 | no | — |
| 430 | C4×D4 | — | 25 | 6 | no | — |
| 431 | C4×D4 | — | 25 | 12 | no | — |
| 432 | C4×D4 | — | 25 | 6 | no | — |
| 433 | C4×D4 | — | 25 | 6 | no | — |
| 434 | #117 | — | 25 | 3 | no | — |
| 435 | #117 | — | 25 | 6 | no | — |
| 436 | #117 | — | 25 | 6 | no | — |
| 437 | #117 | — | 25 | 6 | no | — |
| 438 | #117 | — | 25 | 3 | no | — |
| 439 | C2×C4⋊C4 | — | 25 | 6 | no | — |
| 440 | C2×C22⋊C4 | — | 25 | 6 | no | — |
| 441 | C2×C42 | — | 25 | 3 | no | — |
| 442 | C2×C42 | — | 25 | 6 | no | — |
| 443 | C2×C42 | — | 25 | 3 | no | — |
| 444 | C2×C42 | — | 25 | 6 | no | — |
| 445 | C2×C42 | — | 25 | 3 | no | — |
| 446 | C2×C42 | — | 25 | 6 | no | — |
| 447 | C2×C42 | — | 25 | 3 | no | — |
| 448 | C2×C42 | — | 25 | 3 | no | — |
| 449 | C2×C42 | — | 25 | 1 | no | — |
| 450 | C52 | C2×C4×#41 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 451 | C22×C5 | — | 2 | 6 | no | — |
| 452 | C22×C5 | — | 5 | 2 | no | — |
| 453 | C22×C5 | — | 5 | 6 | no | — |
| 454 | C22×C5 | — | 10 | 12 | no | — |
| 455 | C22×C5 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 456 | C2×D5 | — | 2 | 12 | no | — |
| 457 | C2×D5 | — | 5 | 2 | no | — |
| 458 | C2×D5 | — | 5 | 8 | no | — |
| 459 | C2×D5 | — | 5 | 6 | no | — |
| 460 | C2×D5 | — | 10 | 2 | no | — |
| 461 | C2×D5 | — | 10 | 6 | no | — |
| 462 | C2×D5 | — | 10 | 12 | no | — |
| 463 | C2×D5 | — | 10 | 12 | no | — |
| 464 | C2×D5 | — | 10 | 12 | no | — |
| 465 | C2×D5 | — | 10 | 12 | no | — |
| 466 | C2×D5 | — | 20 | 12 | no | — |
| 467 | C2×D5 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 468 | C2×D5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 469 | AGL(1,𝔽5) | — | 5 | 8 | no | — |
| 470 | AGL(1,𝔽5) | — | 5 | 8 | no | — |
| 471 | AGL(1,𝔽5) | — | 10 | 8 | no | — |
| 472 | AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 473 | AGL(1,𝔽5) | — | 10 | 12 | no | — |
| 474 | AGL(1,𝔽5) | — | 20 | 12 | no | — |
| 475 | C4×C5 | — | 2 | 6 | no | — |
| 476 | C4×C5 | — | 2 | 2 | no | — |
| 477 | C4×C5 | — | 5 | 6 | no | — |
| 478 | C4×C5 | — | 5 | 2 | no | — |
| 479 | C4×C5 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 480 | C4×C5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 481 | Dic5 | — | 5 | 6 | no | — |
| 482 | Dic5 | — | 5 | 2 | no | — |
| 483 | Dic5 | — | 10 | 6 | no | — |
| 484 | Dic5 | — | 10 | 2 | no | — |
| 485 | Dic5 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 486 | Dic5 | C23×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 487 | C24 | — | 25 | 3 | no | — |
| 488 | #41 | — | 5 | 2 | no | — |
| 489 | #41 | — | 5 | 6 | no | — |
| 490 | #41 | — | 5 | 6 | no | — |
| 491 | #41 | — | 25 | 6 | no | — |
| 492 | #41 | — | 25 | 12 | no | — |
| 493 | #41 | — | 25 | 6 | no | — |
| 494 | #41 | — | 25 | 6 | no | — |
| 495 | #41 | — | 25 | 6 | no | — |
| 496 | #41 | — | 25 | 6 | no | — |
| 497 | #41 | — | 25 | 1 | no | — |
| 498 | #41 | — | 25 | 3 | no | — |
| 499 | #41 | — | 25 | 3 | no | — |
| 500 | #41 | D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 501 | C2×Q8 | — | 5 | 2 | no | — |
| 502 | C2×Q8 | — | 25 | 6 | no | — |
| 503 | C2×Q8 | — | 25 | 3 | no | — |
| 504 | C2×Q8 | — | 25 | 1 | no | — |
| 505 | C2×D4 | — | 5 | 6 | no | — |
| 506 | C2×D4 | — | 25 | 6 | no | — |
| 507 | C2×D4 | — | 25 | 6 | no | — |
| 508 | C2×D4 | — | 25 | 3 | no | — |
| 509 | C2×D4 | — | 25 | 12 | no | — |
| 510 | C2×D4 | — | 25 | 3 | no | — |
| 511 | C22×C4 | — | 5 | 6 | no | — |
| 512 | C22×C4 | — | 25 | 1 | no | — |
| 513 | C22×C4 | — | 25 | 3 | no | — |
| 514 | C22×C4 | — | 25 | 3 | no | — |
| 515 | C22×C4 | — | 25 | 3 | no | — |
| 516 | C22×C4 | — | 25 | 3 | no | — |
| 517 | C22×C4 | — | 25 | 6 | no | — |
| 518 | C22×C4 | — | 25 | 6 | no | — |
| 519 | C22×C4 | — | 25 | 6 | no | — |
| 520 | C22×C4 | — | 25 | 2 | no | — |
| 521 | C22×C4 | — | 25 | 3 | no | — |
| 522 | C22×C4 | — | 25 | 6 | no | — |
| 523 | C22×C4 | — | 25 | 6 | no | — |
| 524 | C22×C4 | — | 25 | 6 | no | — |
| 525 | C22×C4 | — | 25 | 6 | no | — |
| 526 | C22×C4 | — | 25 | 6 | no | — |
| 527 | C22×C4 | — | 50 | 24 | no | — |
| 528 | C4⋊C4 | — | 25 | 12 | no | — |
| 529 | C4⋊C4 | — | 25 | 6 | no | — |
| 530 | C4⋊C4 | — | 25 | 6 | no | — |
| 531 | C22⋊C4 | — | 25 | 6 | no | — |
| 532 | C22⋊C4 | — | 25 | 12 | no | — |
| 533 | C22⋊C4 | — | 25 | 6 | no | — |
| 534 | C42 | — | 25 | 2 | no | — |
| 535 | C42 | — | 25 | 1 | no | — |
| 536 | C42 | — | 25 | 1 | no | — |
| 537 | C42 | — | 25 | 6 | no | — |
| 538 | C42 | — | 25 | 3 | no | — |
| 539 | C42 | — | 25 | 3 | no | — |
| 540 | C42 | — | 25 | 6 | no | — |
| 541 | C42 | — | 25 | 6 | no | — |
| 542 | C42 | — | 25 | 6 | no | — |
| 543 | C42 | — | 25 | 6 | no | — |
| 544 | C2×C5 | — | 2 | 6 | no | — |
| 545 | C2×C5 | — | 2 | 2 | no | — |
| 546 | C2×C5 | — | 4 | 6 | no | — |
| 547 | C2×C5 | — | 5 | 4 | no | — |
| 548 | C2×C5 | — | 10 | 6 | no | — |
| 549 | C2×C5 | C24×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 550 | D5 | — | 2 | 6 | no | — |
| 551 | D5 | — | 5 | 4 | no | — |
| 552 | D5 | — | 10 | 4 | no | — |
| 553 | D5 | — | 10 | 6 | no | — |
| 554 | D5 | — | 20 | 6 | no | — |
| 555 | D5 | #41×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 556 | C23 | — | 5 | 6 | no | — |
| 557 | C23 | — | 25 | 1 | no | — |
| 558 | C23 | — | 25 | 3 | no | — |
| 559 | C23 | — | 25 | 6 | no | — |
| 560 | C23 | — | 25 | 3 | no | — |
| 561 | C23 | — | 50 | 12 | no | — |
| 562 | Q8 | — | 5 | 6 | no | — |
| 563 | Q8 | — | 25 | 6 | no | — |
| 564 | Q8 | — | 25 | 3 | no | — |
| 565 | Q8 | C2×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 566 | D4 | — | 5 | 12 | no | — |
| 567 | D4 | — | 5 | 6 | no | — |
| 568 | D4 | — | 25 | 12 | no | — |
| 569 | D4 | — | 25 | 6 | no | — |
| 570 | D4 | — | 25 | 6 | no | — |
| 571 | D4 | — | 25 | 3 | no | — |
| 572 | D4 | C2×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 573 | C2×C4 | — | 5 | 6 | no | — |
| 574 | C2×C4 | — | 5 | 6 | no | — |
| 575 | C2×C4 | — | 5 | 6 | no | — |
| 576 | C2×C4 | — | 5 | 2 | no | — |
| 577 | C2×C4 | — | 5 | 6 | no | — |
| 578 | C2×C4 | — | 25 | 1 | no | — |
| 579 | C2×C4 | — | 25 | 3 | no | — |
| 580 | C2×C4 | — | 25 | 6 | no | — |
| 581 | C2×C4 | — | 25 | 2 | no | — |
| 582 | C2×C4 | — | 25 | 6 | no | — |
| 583 | C2×C4 | — | 25 | 6 | no | — |
| 584 | C2×C4 | — | 25 | 6 | no | — |
| 585 | C2×C4 | — | 25 | 2 | no | — |
| 586 | C2×C4 | — | 25 | 2 | no | — |
| 587 | C2×C4 | — | 25 | 8 | no | — |
| 588 | C2×C4 | — | 25 | 3 | no | — |
| 589 | C2×C4 | — | 25 | 3 | no | — |
| 590 | C2×C4 | — | 25 | 3 | no | — |
| 591 | C2×C4 | — | 25 | 1 | no | — |
| 592 | C2×C4 | — | 25 | 3 | no | — |
| 593 | C2×C4 | — | 25 | 6 | no | — |
| 594 | C2×C4 | — | 25 | 6 | no | — |
| 595 | C2×C4 | — | 50 | 12 | no | — |
| 596 | C2×C4 | — | 50 | 12 | no | — |
| 597 | C2×C4 | — | 50 | 12 | no | — |
| 598 | C2×C4 | — | 50 | 12 | no | — |
| 599 | C2×C4 | — | 50 | 12 | no | — |
| 600 | C2×C4 | C2×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | complemented |
| 601 | C5 | — | 2 | 2 | no | — |
| 602 | C5 | C2×#41×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 603 | C22 | — | 5 | 2 | no | — |
| 604 | C22 | — | 5 | 6 | no | — |
| 605 | C22 | — | 10 | 12 | no | — |
| 606 | C22 | — | 25 | 4 | no | — |
| 607 | C22 | — | 25 | 1 | no | — |
| 608 | C22 | — | 25 | 3 | no | — |
| 609 | C22 | — | 50 | 6 | no | — |
| 610 | C22 | — | 50 | 12 | no | — |
| 611 | C22 | — | 50 | 6 | no | — |
| 612 | C22 | C22×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 613 | C4 | — | 5 | 2 | no | — |
| 614 | C4 | — | 5 | 6 | no | — |
| 615 | C4 | — | 25 | 4 | no | — |
| 616 | C4 | — | 25 | 4 | no | — |
| 617 | C4 | — | 25 | 1 | no | — |
| 618 | C4 | — | 25 | 3 | no | — |
| 619 | C4 | — | 50 | 6 | no | — |
| 620 | C4 | — | 50 | 6 | no | — |
| 621 | C4 | C22×D5⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 622 | C4 | C22×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 623 | C2 | — | 2 | 3 | no | — |
| 624 | C2 | — | 5 | 4 | no | — |
| 625 | C2 | — | 10 | 6 | no | — |
| 626 | C2 | — | 25 | 2 | no | — |
| 627 | C2 | — | 50 | 3 | no | — |
| 628 | C2 | C23×D5⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 2. #41×#1044 | C2 | semidirect |
| 3. #41×#1043 | C2 | semidirect |
| 4. #13107575 | C2 | semidirect |
| 5. Q8×D5⋊AGL(1,𝔽5) | C2 | semidirect |
| 6. #13107568 | C2 | semidirect |
| 7. D4×D5⋊AGL(1,𝔽5) | C2 | semidirect |
| 8. #13107561 | C2 | semidirect |
| 9. D5⋊#4130 | C2 | semidirect |
| 10. #13107559 | C2 | semidirect |
| 11. C2×C4×D5⋊AGL(1,𝔽5) | C2 | semidirect |
| 14. C5×D5×#41 | C4 | semidirect |
| 16. D5×#713 | C4 | semidirect |
| 19. D5×#711 | C4 | semidirect |
| 22. D5×#709 | C4 | semidirect |
| 24. Q8×#1044 | C22 | semidirect |
| 25. D4×#1044 | C22 | semidirect |
| 26. #11717451 | C22 | semidirect |
| 27. C2×C4×#1044 | C22 | semidirect |
| 28. Q8×#1043 | C22 | semidirect |
| 29. D4×#1043 | C22 | semidirect |
| 30. #11717438 | C22 | semidirect |
| 31. C2×C4×#1043 | C22 | semidirect |
| 32. #11717377 | C22 | semidirect |
| 34. #11717375 | C22 | semidirect |
| 35. #11717367 | C22 | semidirect |
| 36. C2×#87830 | C22 | semidirect |
| 37. #11717365 | C22 | semidirect |
| 39. #11717363 | C22 | semidirect |
| 43. C4×D5⋊AGL(1,𝔽5) | C22 | semidirect |
| 44. C4×D5⋊AGL(1,𝔽5) | C22 | semidirect |
| 45. C4×D5⋊AGL(1,𝔽5) | C22 | semidirect |
| 46. #11717356 | C22 | semidirect |
| 47. #11717355 | C22 | semidirect |
| 48. #11717354 | C22 | semidirect |
| 49. #11717353 | C22 | semidirect |
| 59. C52×#41 | C2×C4 | semidirect |
| 60. #87904 | C2×C4 | semidirect |
| 62. #87902 | C2×C4 | semidirect |
| 64. #87900 | C2×C4 | semidirect |
| 66. C5×#713 | C2×C4 | semidirect |
| 67. C5×Q8×D5 | C2×C4 | semidirect |
| 68. C5×#711 | C2×C4 | semidirect |
| 69. C5×D4×D5 | C2×C4 | semidirect |
| 70. C5×#709 | C2×C4 | semidirect |
| 71. C2×C4×C5×D5 | C2×C4 | semidirect |
| 73. D5×C22⋊D5 | C2×C4 | semidirect |
| 75. #87880 | C2×C4 | semidirect |
| 76. #87879 | C2×C4 | semidirect |
| 77. C2×D5×Dic5 | C2×C4 | semidirect |
| 79. D5×D20 | C2×C4 | semidirect |
| 80. C4×D52 | C2×C4 | semidirect |
| 81. C4×D52 | C2×C4 | semidirect |
| 86. #87874 | C2×C4 | semidirect |
| 87. #87873 | C2×C4 | semidirect |
| 89. #87871 | C2×C4 | semidirect |
| 90. #87870 | C2×C4 | semidirect |
| 91. D5×Dic10 | C2×C4 | semidirect |
| 135. D5⋊AGL(1,𝔽5) | #41 | direct (N × H) |
| 136. C52×Q8 | C22×C4 | semidirect |
| 137. C52×D4 | C22×C4 | semidirect |
| 138. C2×C4×C52 | C22×C4 | semidirect |
| 139. C22⋊(C5⋊D5) | C22×C4 | semidirect |
| 140. C2×#1039 | C22×C4 | semidirect |
| 141. C4⋊(C5⋊D5) | C22×C4 | semidirect |
| 142. C4×C5⋊D5 | C22×C4 | semidirect |
| 143. C4×C5⋊D5 | C22×C4 | semidirect |
| 146. #6045 | C22×C4 | semidirect |
| 147. C5×C22⋊D5 | C22×C4 | semidirect |
| 148. C2×C5×Dic5 | C22×C4 | semidirect |
| 149. C5×D20 | C22×C4 | semidirect |
| 152. C4×C5×D5 | C22×C4 | semidirect |
| 153. C4×C5×D5 | C22×C4 | semidirect |
| 154. C5×Dic10 | C22×C4 | semidirect |
| 155. #6039 | C22×C4 | semidirect |
| 156. #6038 | C22×C4 | semidirect |
| 157. #6037 | C22×C4 | semidirect |
| 158. #6036 | C22×C4 | semidirect |
| 163. D5×Dic5 | C22×C4 | semidirect |
| 164. D5×Dic5 | C22×C4 | semidirect |
| 175. D5×#41 | AGL(1,𝔽5) | semidirect |
| 224. #1044 | C2×#41 | semidirect |
| 226. #1043 | C2×#41 | semidirect |
| 246. C5×#41 | C2×AGL(1,𝔽5) | semidirect |
| 256. #713 | C2×AGL(1,𝔽5) | semidirect |
| 261. Q8×D5 | C2×AGL(1,𝔽5) | semidirect |
| 268. #711 | C2×AGL(1,𝔽5) | semidirect |
| 275. D4×D5 | C2×AGL(1,𝔽5) | semidirect |
| 282. #709 | C2×AGL(1,𝔽5) | semidirect |
| 296. C2×C4×D5 | C2×AGL(1,𝔽5) | semidirect |
| 335. C5×D5 | C4×#41 | semidirect |
| 360. C5×Q8 | C22×AGL(1,𝔽5) | semidirect |
| 364. C5×D4 | C22×AGL(1,𝔽5) | semidirect |
| 371. C2×C4×C5 | C22×AGL(1,𝔽5) | semidirect |
| 376. C22⋊D5 | C22×AGL(1,𝔽5) | semidirect |
| 383. C2×Dic5 | C22×AGL(1,𝔽5) | semidirect |
| 387. D20 | C22×AGL(1,𝔽5) | semidirect |
| 406. C4×D5 | C22×AGL(1,𝔽5) | semidirect |
| 407. C4×D5 | C22×AGL(1,𝔽5) | semidirect |
| 411. Dic10 | C22×AGL(1,𝔽5) | semidirect |
| 450. C52 | C2×C4×#41 | semidirect |
| 500. #41 | D5⋊AGL(1,𝔽5) | direct (N × H) |
| 555. D5 | #41×AGL(1,𝔽5) | semidirect |
| 565. Q8 | C2×D5⋊AGL(1,𝔽5) | semidirect |
| 572. D4 | C2×D5⋊AGL(1,𝔽5) | semidirect |
| 600. C2×C4 | C2×D5⋊AGL(1,𝔽5) | semidirect |
| 602. C5 | C2×#41×AGL(1,𝔽5) | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta