← C22×AGL(1,𝔽5)×H(5,𝔽2) #72242755
Order 2560.
125924 conjugacy classes of subgroups.
The subgroup lattice has 532 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×AGL(1,𝔽5)×H(5,𝔽2) | C2 | 1 | 96 | yes | maximal, direct product factor |
| 2 | C22×#66266 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | C22×#66258 | C2 | 1 | 9 | yes | maximal, complemented |
| 4 | C22×#41×AGL(1,𝔽5) | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C23×D4×AGL(1,𝔽5) | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | C22×D5×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C25×AGL(1,𝔽5) | C22 | 1 | 6 | yes | complemented |
| 8 | C22×C5×H(5,𝔽2) | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×D5×H(5,𝔽2) | C4 | 1 | 48 | yes | complemented |
| 10 | C2×D5×H(5,𝔽2) | C22 | 1 | 48 | yes | — |
| 11 | C22×#4149 | C4 | 1 | 6 | yes | complemented |
| 12 | C22×D5×#41 | C22 | 1 | 6 | yes | — |
| 13 | C22×#4144 | C4 | 1 | 9 | yes | complemented |
| 14 | C23×D4×D5 | C22 | 1 | 9 | yes | — |
| 15 | C23×C22⋊AGL(1,𝔽5) | C22 | 1 | 18 | yes | complemented |
| 16 | AGL(1,𝔽5)×H(5,𝔽2) | C22 | 1 | 1024 | yes | direct product factor |
| 17 | C2×#66266 | C22 | 1 | 288 | yes | complemented |
| 18 | C2×#41×AGL(1,𝔽5) | C22 | 1 | 288 | yes | complemented |
| 19 | C22×Q8×AGL(1,𝔽5) | C22 | 1 | 2 | yes | complemented |
| 20 | C22×Q8×AGL(1,𝔽5) | C22 | 1 | 6 | yes | complemented |
| 21 | C2×#66258 | C22 | 1 | 432 | yes | complemented |
| 22 | C22×D4×AGL(1,𝔽5) | C22 | 1 | 18 | yes | complemented |
| 23 | C22×D4×AGL(1,𝔽5) | C22 | 1 | 36 | yes | complemented |
| 24 | C22×D4×AGL(1,𝔽5) | C22 | 1 | 18 | yes | complemented |
| 25 | C22×D4×AGL(1,𝔽5) | C22 | 1 | 432 | yes | complemented |
| 26 | C22×#4130 | C22 | 1 | 18 | yes | complemented |
| 27 | C23×C4⋊AGL(1,𝔽5) | C22 | 1 | 9 | yes | complemented |
| 28 | C23×C4×AGL(1,𝔽5) | C22 | 1 | 9 | yes | complemented |
| 29 | C22×C4×H(5,𝔽2) | — | 5 | 1 | no | maximal, Sylow |
| 30 | C25×D5 | C23 | 1 | 6 | yes | — |
| 31 | C24×AGL(1,𝔽5) | — | 4 | 48 | no | — |
| 32 | C24×AGL(1,𝔽5) | C23 | 1 | 9 | yes | — |
| 33 | C24×AGL(1,𝔽5) | C23 | 1 | 9 | yes | — |
| 34 | C24×AGL(1,𝔽5) | C23 | 1 | 18 | yes | — |
| 35 | C24×AGL(1,𝔽5) | C23 | 1 | 144 | yes | complemented |
| 36 | C2×C5×H(5,𝔽2) | C2×C4 | 1 | 48 | yes | complemented |
| 37 | C22×C5×#41 | C2×C4 | 1 | 6 | yes | complemented |
| 38 | C23×C5×D4 | C2×C4 | 1 | 9 | yes | complemented |
| 39 | C23×C22⋊D5 | C2×C4 | 1 | 18 | yes | complemented |
| 40 | D5×H(5,𝔽2) | C2×C4 | 1 | 768 | yes | complemented |
| 41 | D5×H(5,𝔽2) | C23 | 1 | 256 | yes | — |
| 42 | C2×#4149 | C2×C4 | 1 | 288 | yes | complemented |
| 43 | C2×D5×#41 | C2×C4 | 1 | 144 | yes | complemented |
| 44 | C2×D5×#41 | C23 | 1 | 144 | yes | — |
| 45 | C22×#713 | C2×C4 | 1 | 6 | yes | complemented |
| 46 | C22×Q8×D5 | C23 | 1 | 2 | yes | — |
| 47 | C2×#4144 | C2×C4 | 1 | 432 | yes | complemented |
| 48 | C22×#711 | C2×C4 | 1 | 18 | yes | complemented |
| 49 | C22×D4×D5 | C2×C4 | 1 | 36 | yes | complemented |
| 50 | C22×D4×D5 | C2×C4 | 1 | 216 | yes | complemented |
| 51 | C22×D4×D5 | C23 | 1 | 18 | yes | — |
| 52 | C22×D4×D5 | C23 | 1 | 216 | yes | — |
| 53 | C22×#709 | C2×C4 | 1 | 18 | yes | complemented |
| 54 | C23×D20 | C2×C4 | 1 | 9 | yes | complemented |
| 55 | C23×C4×D5 | C23 | 1 | 9 | yes | — |
| 56 | C22×C22⋊AGL(1,𝔽5) | C23 | 1 | 36 | yes | — |
| 57 | C22×C22⋊AGL(1,𝔽5) | C23 | 1 | 432 | yes | complemented |
| 58 | #66266 | C23 | 1 | 1536 | yes | complemented |
| 59 | #41×AGL(1,𝔽5) | C23 | 1 | 1536 | yes | complemented |
| 60 | C2×Q8×AGL(1,𝔽5) | C23 | 1 | 48 | yes | complemented |
| 61 | C2×Q8×AGL(1,𝔽5) | C23 | 1 | 144 | yes | complemented |
| 62 | #66258 | C23 | 1 | 2304 | yes | complemented |
| 63 | C2×D4×AGL(1,𝔽5) | C23 | 1 | 432 | yes | complemented |
| 64 | C2×D4×AGL(1,𝔽5) | C23 | 1 | 864 | yes | complemented |
| 65 | C2×D4×AGL(1,𝔽5) | C23 | 1 | 432 | yes | complemented |
| 66 | C2×D4×AGL(1,𝔽5) | C23 | 1 | 2304 | yes | complemented |
| 67 | C2×#4130 | C23 | 1 | 432 | yes | complemented |
| 68 | C22×C4⋊AGL(1,𝔽5) | C23 | 1 | 18 | yes | — |
| 69 | C22×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 70 | C22×C4⋊AGL(1,𝔽5) | C23 | 1 | 216 | yes | complemented |
| 71 | C22×C4×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 72 | C22×C4×AGL(1,𝔽5) | C23 | 1 | 18 | yes | — |
| 73 | C22×C4×AGL(1,𝔽5) | C23 | 1 | 216 | yes | complemented |
| 74 | C23×H(5,𝔽2) | — | 5 | 1 | no | — |
| 75 | C2×C4×H(5,𝔽2) | — | 5 | 96 | no | — |
| 76 | C22×#520 | — | 5 | 6 | no | — |
| 77 | C22×#518 | — | 5 | 9 | no | — |
| 78 | C22×C4×#41 | — | 5 | 6 | no | — |
| 79 | C23×C4×D4 | — | 5 | 9 | no | — |
| 80 | C25×C5 | C22×C4 | 1 | 6 | yes | complemented |
| 81 | C24×D5 | — | 4 | 24 | no | — |
| 82 | C24×D5 | — | 4 | 24 | no | — |
| 83 | C24×D5 | C22×C4 | 1 | 72 | yes | complemented |
| 84 | C24×D5 | C22×C4 | 1 | 18 | yes | complemented |
| 85 | C24×D5 | C24 | 1 | 9 | yes | — |
| 86 | C24×D5 | C24 | 1 | 72 | yes | — |
| 87 | C23×AGL(1,𝔽5) | — | 2 | 72 | no | — |
| 88 | C23×AGL(1,𝔽5) | — | 4 | 576 | no | — |
| 89 | C23×AGL(1,𝔽5) | — | 4 | 72 | no | — |
| 90 | C23×AGL(1,𝔽5) | — | 4 | 36 | no | — |
| 91 | C23×AGL(1,𝔽5) | C24 | 1 | 6 | yes | — |
| 92 | C23×AGL(1,𝔽5) | C24 | 1 | 9 | yes | — |
| 93 | C23×AGL(1,𝔽5) | C24 | 1 | 108 | yes | — |
| 94 | C23×AGL(1,𝔽5) | C24 | 1 | 108 | yes | — |
| 95 | C23×AGL(1,𝔽5) | C24 | 1 | 216 | yes | — |
| 96 | C23×AGL(1,𝔽5) | C24 | 1 | 1 | yes | characteristic |
| 97 | C23×AGL(1,𝔽5) | C24 | 1 | 384 | yes | complemented |
| 98 | C5×H(5,𝔽2) | C22×C4 | 1 | 256 | yes | complemented |
| 99 | C2×C5×#41 | C22×C4 | 1 | 144 | yes | complemented |
| 100 | C22×C5×Q8 | C22×C4 | 1 | 2 | yes | complemented |
| 101 | C22×C5×D4 | C22×C4 | 1 | 18 | yes | complemented |
| 102 | C22×C5×D4 | C22×C4 | 1 | 216 | yes | complemented |
| 103 | C23×C4×C5 | C22×C4 | 1 | 9 | yes | complemented |
| 104 | C22×C22⋊D5 | C22×C4 | 1 | 36 | yes | complemented |
| 105 | C22×C22⋊D5 | C22×C4 | 1 | 432 | yes | complemented |
| 106 | C23×Dic5 | C22×C4 | 1 | 9 | yes | complemented |
| 107 | #4149 | C22×C4 | 1 | 1536 | yes | complemented |
| 108 | D5×#41 | C22×C4 | 1 | 1152 | yes | complemented |
| 109 | D5×#41 | C24 | 1 | 384 | yes | — |
| 110 | C2×#713 | C22×C4 | 1 | 144 | yes | complemented |
| 111 | C2×Q8×D5 | C22×C4 | 1 | 24 | yes | complemented |
| 112 | C2×Q8×D5 | C24 | 1 | 24 | yes | — |
| 113 | #4144 | C22×C4 | 1 | 2304 | yes | complemented |
| 114 | C2×#711 | C22×C4 | 1 | 432 | yes | complemented |
| 115 | C2×D4×D5 | C22×C4 | 1 | 216 | yes | complemented |
| 116 | C2×D4×D5 | C22×C4 | 1 | 864 | yes | complemented |
| 117 | C2×D4×D5 | C22×C4 | 1 | 1728 | yes | complemented |
| 118 | C2×D4×D5 | C24 | 1 | 216 | yes | — |
| 119 | C2×D4×D5 | C24 | 1 | 576 | yes | — |
| 120 | C2×#709 | C22×C4 | 1 | 432 | yes | complemented |
| 121 | C22×D20 | C22×C4 | 1 | 18 | yes | complemented |
| 122 | C22×D20 | C22×C4 | 1 | 216 | yes | complemented |
| 123 | C22×C4×D5 | C22×C4 | 1 | 108 | yes | complemented |
| 124 | C22×C4×D5 | C22×C4 | 1 | 18 | yes | complemented |
| 125 | C22×C4×D5 | C24 | 1 | 6 | yes | — |
| 126 | C22×C4×D5 | C24 | 1 | 108 | yes | — |
| 127 | C22×Dic10 | C22×C4 | 1 | 6 | yes | complemented |
| 128 | C2×C22⋊AGL(1,𝔽5) | C24 | 1 | 432 | yes | — |
| 129 | C2×C22⋊AGL(1,𝔽5) | C24 | 1 | 1152 | yes | complemented |
| 130 | Q8×AGL(1,𝔽5) | C24 | 1 | 128 | yes | complemented |
| 131 | Q8×AGL(1,𝔽5) | C24 | 1 | 384 | yes | complemented |
| 132 | D4×AGL(1,𝔽5) | C24 | 1 | 1152 | yes | complemented |
| 133 | D4×AGL(1,𝔽5) | C24 | 1 | 2304 | yes | complemented |
| 134 | D4×AGL(1,𝔽5) | C24 | 1 | 1152 | yes | complemented |
| 135 | #4130 | C24 | 1 | 1152 | yes | complemented |
| 136 | C2×C4⋊AGL(1,𝔽5) | C24 | 1 | 216 | yes | — |
| 137 | C2×C4⋊AGL(1,𝔽5) | C24 | 1 | 72 | yes | — |
| 138 | C2×C4⋊AGL(1,𝔽5) | C24 | 1 | 576 | yes | complemented |
| 139 | C2×C4×AGL(1,𝔽5) | C24 | 1 | 72 | yes | — |
| 140 | C2×C4×AGL(1,𝔽5) | C24 | 1 | 216 | yes | — |
| 141 | C2×C4×AGL(1,𝔽5) | C24 | 1 | 576 | yes | complemented |
| 142 | C22×H(5,𝔽2) | — | 5 | 48 | no | — |
| 143 | C22×H(5,𝔽2) | — | 5 | 48 | no | — |
| 144 | C22×H(5,𝔽2) | — | 5 | 6 | no | — |
| 145 | C22×H(5,𝔽2) | — | 5 | 9 | no | — |
| 146 | C22×H(5,𝔽2) | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 147 | C23×#41 | — | 5 | 6 | no | — |
| 148 | C24×D4 | — | 5 | 9 | no | — |
| 149 | C25×C4 | — | 5 | 6 | no | — |
| 150 | C4×H(5,𝔽2) | — | 5 | 1024 | no | — |
| 151 | C2×#520 | — | 5 | 288 | no | — |
| 152 | C2×#518 | — | 5 | 432 | no | — |
| 153 | C2×C4×#41 | — | 5 | 288 | no | — |
| 154 | C22×C4×Q8 | — | 5 | 2 | no | — |
| 155 | C22×C4×Q8 | — | 5 | 6 | no | — |
| 156 | C22×C4×D4 | — | 5 | 18 | no | — |
| 157 | C22×C4×D4 | — | 5 | 36 | no | — |
| 158 | C22×C4×D4 | — | 5 | 432 | no | — |
| 159 | C22×C4×D4 | — | 5 | 18 | no | — |
| 160 | C22×#117 | — | 5 | 18 | no | — |
| 161 | C23×C4⋊C4 | — | 5 | 9 | no | — |
| 162 | C23×C22⋊C4 | — | 5 | 18 | no | — |
| 163 | C23×C42 | — | 5 | 9 | no | — |
| 164 | C24×C5 | — | 4 | 24 | no | — |
| 165 | C24×C5 | C23×C4 | 1 | 9 | yes | — |
| 166 | C24×C5 | C23×C4 | 1 | 72 | yes | complemented |
| 167 | C23×D5 | — | 2 | 36 | no | — |
| 168 | C23×D5 | — | 2 | 36 | no | — |
| 169 | C23×D5 | — | 4 | 144 | no | — |
| 170 | C23×D5 | — | 4 | 288 | no | — |
| 171 | C23×D5 | — | 4 | 144 | no | — |
| 172 | C23×D5 | — | 4 | 72 | no | — |
| 173 | C23×D5 | C23×C4 | 1 | 9 | yes | — |
| 174 | C23×D5 | C23×C4 | 1 | 54 | yes | — |
| 175 | C23×D5 | C23×C4 | 1 | 288 | yes | complemented |
| 176 | C23×D5 | C23×C4 | 1 | 216 | yes | complemented |
| 177 | C23×D5 | C25 | 1 | 54 | yes | — |
| 178 | C23×D5 | C25 | 1 | 96 | yes | — |
| 179 | C23×D5 | C25 | 1 | 1 | yes | characteristic |
| 180 | C22×AGL(1,𝔽5) | — | 2 | 36 | no | — |
| 181 | C22×AGL(1,𝔽5) | — | 2 | 24 | no | — |
| 182 | C22×AGL(1,𝔽5) | — | 2 | 432 | no | — |
| 183 | C22×AGL(1,𝔽5) | — | 4 | 768 | no | — |
| 184 | C22×AGL(1,𝔽5) | — | 4 | 432 | no | — |
| 185 | C22×AGL(1,𝔽5) | — | 4 | 216 | no | — |
| 186 | C22×AGL(1,𝔽5) | H(5,𝔽2) | 1 | 8 | yes | direct product factor |
| 187 | C22×AGL(1,𝔽5) | C25 | 1 | 36 | yes | — |
| 188 | C22×AGL(1,𝔽5) | C25 | 1 | 54 | yes | — |
| 189 | C22×AGL(1,𝔽5) | C25 | 1 | 144 | yes | — |
| 190 | C22×AGL(1,𝔽5) | C25 | 1 | 144 | yes | — |
| 191 | C22×AGL(1,𝔽5) | C25 | 1 | 288 | yes | — |
| 192 | C22×AGL(1,𝔽5) | C25 | 1 | 6 | yes | — |
| 193 | C5×#41 | C23×C4 | 1 | 384 | yes | complemented |
| 194 | C2×C5×Q8 | C23×C4 | 1 | 24 | yes | complemented |
| 195 | C2×C5×D4 | C23×C4 | 1 | 216 | yes | complemented |
| 196 | C2×C5×D4 | C23×C4 | 1 | 576 | yes | complemented |
| 197 | C22×C4×C5 | C23×C4 | 1 | 6 | yes | — |
| 198 | C22×C4×C5 | C23×C4 | 1 | 108 | yes | complemented |
| 199 | C2×C22⋊D5 | C23×C4 | 1 | 432 | yes | complemented |
| 200 | C2×C22⋊D5 | C23×C4 | 1 | 1152 | yes | complemented |
| 201 | C22×Dic5 | C23×C4 | 1 | 6 | yes | — |
| 202 | C22×Dic5 | C23×C4 | 1 | 108 | yes | complemented |
| 203 | #713 | C23×C4 | 1 | 384 | yes | complemented |
| 204 | Q8×D5 | C23×C4 | 1 | 96 | yes | complemented |
| 205 | Q8×D5 | C25 | 1 | 32 | yes | — |
| 206 | #711 | C23×C4 | 1 | 1152 | yes | complemented |
| 207 | D4×D5 | C23×C4 | 1 | 864 | yes | complemented |
| 208 | D4×D5 | C23×C4 | 1 | 2304 | yes | complemented |
| 209 | D4×D5 | C25 | 1 | 288 | yes | — |
| 210 | #709 | C23×C4 | 1 | 1152 | yes | complemented |
| 211 | C2×D20 | C23×C4 | 1 | 216 | yes | complemented |
| 212 | C2×D20 | C23×C4 | 1 | 576 | yes | complemented |
| 213 | C2×C4×D5 | C23×C4 | 1 | 36 | yes | — |
| 214 | C2×C4×D5 | C23×C4 | 1 | 432 | yes | complemented |
| 215 | C2×C4×D5 | C23×C4 | 1 | 216 | yes | complemented |
| 216 | C2×C4×D5 | C25 | 1 | 36 | yes | — |
| 217 | C2×C4×D5 | C25 | 1 | 144 | yes | — |
| 218 | C2×Dic10 | C23×C4 | 1 | 72 | yes | complemented |
| 219 | C22⋊AGL(1,𝔽5) | C25 | 1 | 576 | yes | — |
| 220 | C4⋊AGL(1,𝔽5) | C25 | 1 | 288 | yes | — |
| 221 | C4⋊AGL(1,𝔽5) | C25 | 1 | 96 | yes | — |
| 222 | C4×AGL(1,𝔽5) | C25 | 1 | 96 | yes | — |
| 223 | C4×AGL(1,𝔽5) | C25 | 1 | 288 | yes | — |
| 224 | C26 | — | 5 | 6 | no | — |
| 225 | C2×H(5,𝔽2) | — | 5 | 256 | no | — |
| 226 | C2×H(5,𝔽2) | — | 5 | 768 | no | — |
| 227 | C2×H(5,𝔽2) | — | 5 | 288 | no | — |
| 228 | C2×H(5,𝔽2) | — | 5 | 432 | no | — |
| 229 | C2×H(5,𝔽2) | C2×AGL(1,𝔽5) | 1 | 48 | yes | direct product factor |
| 230 | C22×#41 | — | 5 | 144 | no | — |
| 231 | C22×#41 | — | 5 | 144 | no | — |
| 232 | C22×#41 | — | 5 | 6 | no | — |
| 233 | C22×#41 | — | 5 | 18 | no | — |
| 234 | C22×#41 | — | 5 | 18 | no | — |
| 235 | C22×#41 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 236 | C23×Q8 | — | 5 | 2 | no | — |
| 237 | C23×D4 | — | 5 | 18 | no | — |
| 238 | C23×D4 | — | 5 | 18 | no | — |
| 239 | C23×D4 | — | 5 | 216 | no | — |
| 240 | C23×D4 | — | 5 | 36 | no | — |
| 241 | C23×D4 | — | 5 | 216 | no | — |
| 242 | C23×D4 | — | 5 | 9 | no | — |
| 243 | C23×D4 | C2×AGL(1,𝔽5) | 1 | 9 | yes | complemented |
| 244 | C24×C4 | — | 5 | 9 | no | — |
| 245 | C24×C4 | — | 5 | 9 | no | — |
| 246 | C24×C4 | — | 5 | 18 | no | — |
| 247 | C24×C4 | — | 5 | 144 | no | — |
| 248 | C24×C4 | — | 5 | 9 | no | — |
| 249 | C24×C4 | — | 20 | 48 | no | — |
| 250 | #520 | — | 5 | 1536 | no | — |
| 251 | #518 | — | 5 | 2304 | no | — |
| 252 | C4×#41 | — | 5 | 1536 | no | — |
| 253 | C2×C4×Q8 | — | 5 | 48 | no | — |
| 254 | C2×C4×Q8 | — | 5 | 144 | no | — |
| 255 | C2×C4×D4 | — | 5 | 432 | no | — |
| 256 | C2×C4×D4 | — | 5 | 864 | no | — |
| 257 | C2×C4×D4 | — | 5 | 2304 | no | — |
| 258 | C2×C4×D4 | — | 5 | 432 | no | — |
| 259 | C2×#117 | — | 5 | 432 | no | — |
| 260 | C22×C4⋊C4 | — | 5 | 18 | no | — |
| 261 | C22×C4⋊C4 | — | 5 | 216 | no | — |
| 262 | C22×C4⋊C4 | — | 5 | 6 | no | — |
| 263 | C22×C22⋊C4 | — | 5 | 36 | no | — |
| 264 | C22×C22⋊C4 | — | 5 | 432 | no | — |
| 265 | C22×C42 | — | 5 | 6 | no | — |
| 266 | C22×C42 | — | 5 | 18 | no | — |
| 267 | C22×C42 | — | 5 | 216 | no | — |
| 268 | C23×C5 | — | 2 | 36 | no | — |
| 269 | C23×C5 | — | 4 | 144 | no | — |
| 270 | C23×C5 | C24×C4 | 1 | 54 | yes | — |
| 271 | C23×C5 | C24×C4 | 1 | 1 | yes | characteristic |
| 272 | C23×C5 | C24×C4 | 1 | 96 | yes | complemented |
| 273 | C22×D5 | — | 2 | 36 | no | — |
| 274 | C22×D5 | — | 2 | 108 | no | — |
| 275 | C22×D5 | — | 2 | 108 | no | — |
| 276 | C22×D5 | — | 2 | 216 | no | — |
| 277 | C22×D5 | — | 4 | 96 | no | — |
| 278 | C22×D5 | — | 4 | 576 | no | — |
| 279 | C22×D5 | — | 4 | 96 | no | — |
| 280 | C22×D5 | — | 4 | 432 | no | — |
| 281 | C22×D5 | C24×C4 | 1 | 54 | yes | — |
| 282 | C22×D5 | C24×C4 | 1 | 108 | yes | — |
| 283 | C22×D5 | C24×C4 | 1 | 3 | yes | — |
| 284 | C22×D5 | C24×C4 | 1 | 288 | yes | complemented |
| 285 | C22×D5 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 286 | C22×D5 | #585 | 1 | 4 | yes | — |
| 287 | C22×D5 | C26 | 1 | 36 | yes | — |
| 288 | C22×D5 | C26 | 1 | 3 | yes | — |
| 289 | C2×AGL(1,𝔽5) | — | 2 | 108 | no | — |
| 290 | C2×AGL(1,𝔽5) | — | 2 | 72 | no | — |
| 291 | C2×AGL(1,𝔽5) | — | 2 | 288 | no | — |
| 292 | C2×AGL(1,𝔽5) | — | 4 | 288 | no | — |
| 293 | C2×AGL(1,𝔽5) | — | 4 | 144 | no | — |
| 294 | C2×AGL(1,𝔽5) | C2×H(5,𝔽2) | 1 | 24 | yes | direct product factor |
| 295 | C2×AGL(1,𝔽5) | C26 | 1 | 24 | yes | — |
| 296 | C2×AGL(1,𝔽5) | C26 | 1 | 36 | yes | — |
| 297 | C2×AGL(1,𝔽5) | C26 | 1 | 4 | yes | — |
| 298 | C5×Q8 | C24×C4 | 1 | 32 | yes | complemented |
| 299 | C5×D4 | C24×C4 | 1 | 288 | yes | complemented |
| 300 | C2×C4×C5 | C24×C4 | 1 | 36 | yes | — |
| 301 | C2×C4×C5 | C24×C4 | 1 | 144 | yes | complemented |
| 302 | C22⋊D5 | C24×C4 | 1 | 576 | yes | complemented |
| 303 | C2×Dic5 | C24×C4 | 1 | 36 | yes | — |
| 304 | C2×Dic5 | C24×C4 | 1 | 144 | yes | complemented |
| 305 | D20 | C24×C4 | 1 | 288 | yes | complemented |
| 306 | C4×D5 | C24×C4 | 1 | 72 | yes | — |
| 307 | C4×D5 | C24×C4 | 1 | 288 | yes | complemented |
| 308 | C4×D5 | C26 | 1 | 24 | yes | — |
| 309 | Dic10 | C24×C4 | 1 | 96 | yes | complemented |
| 310 | C25 | — | 5 | 9 | no | — |
| 311 | C25 | — | 5 | 18 | no | — |
| 312 | C25 | — | 5 | 72 | no | — |
| 313 | C25 | — | 5 | 72 | no | — |
| 314 | C25 | — | 20 | 24 | no | — |
| 315 | C25 | — | 20 | 24 | no | — |
| 316 | C25 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 317 | H(5,𝔽2) | — | 5 | 1536 | no | — |
| 318 | H(5,𝔽2) | — | 5 | 2304 | no | — |
| 319 | H(5,𝔽2) | C22×AGL(1,𝔽5) | 1 | 256 | yes | direct product factor |
| 320 | C2×#41 | — | 5 | 384 | no | — |
| 321 | C2×#41 | — | 5 | 1152 | no | — |
| 322 | C2×#41 | — | 5 | 144 | no | — |
| 323 | C2×#41 | — | 5 | 432 | no | — |
| 324 | C2×#41 | — | 5 | 432 | no | — |
| 325 | C2×#41 | C22×AGL(1,𝔽5) | 1 | 144 | yes | complemented |
| 326 | C22×Q8 | — | 5 | 24 | no | — |
| 327 | C22×Q8 | — | 5 | 24 | no | — |
| 328 | C22×Q8 | — | 5 | 6 | no | — |
| 329 | C22×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 330 | C22×D4 | — | 5 | 36 | no | — |
| 331 | C22×D4 | — | 5 | 432 | no | — |
| 332 | C22×D4 | — | 5 | 216 | no | — |
| 333 | C22×D4 | — | 5 | 576 | no | — |
| 334 | C22×D4 | — | 5 | 216 | no | — |
| 335 | C22×D4 | — | 5 | 864 | no | — |
| 336 | C22×D4 | — | 5 | 1728 | no | — |
| 337 | C22×D4 | — | 5 | 18 | no | — |
| 338 | C22×D4 | — | 5 | 216 | no | — |
| 339 | C22×D4 | C22×AGL(1,𝔽5) | 1 | 18 | yes | complemented |
| 340 | C22×D4 | C22×AGL(1,𝔽5) | 1 | 216 | yes | complemented |
| 341 | C23×C4 | — | 5 | 1 | no | — |
| 342 | C23×C4 | — | 5 | 9 | no | — |
| 343 | C23×C4 | — | 5 | 6 | no | — |
| 344 | C23×C4 | — | 5 | 18 | no | — |
| 345 | C23×C4 | — | 5 | 108 | no | — |
| 346 | C23×C4 | — | 5 | 108 | no | — |
| 347 | C23×C4 | — | 5 | 6 | no | — |
| 348 | C23×C4 | — | 5 | 9 | no | — |
| 349 | C23×C4 | — | 5 | 108 | no | — |
| 350 | C23×C4 | — | 5 | 108 | no | — |
| 351 | C23×C4 | — | 5 | 216 | no | — |
| 352 | C23×C4 | — | 5 | 384 | no | — |
| 353 | C23×C4 | — | 10 | 72 | no | — |
| 354 | C23×C4 | — | 20 | 576 | no | — |
| 355 | C23×C4 | — | 20 | 36 | no | — |
| 356 | C23×C4 | — | 20 | 72 | no | — |
| 357 | C23×C4 | C22×AGL(1,𝔽5) | 1 | 9 | yes | complemented |
| 358 | C4×Q8 | — | 5 | 128 | no | — |
| 359 | C4×Q8 | — | 5 | 384 | no | — |
| 360 | C4×D4 | — | 5 | 1152 | no | — |
| 361 | C4×D4 | — | 5 | 2304 | no | — |
| 362 | C4×D4 | — | 5 | 1152 | no | — |
| 363 | #117 | — | 5 | 1152 | no | — |
| 364 | C2×C4⋊C4 | — | 5 | 216 | no | — |
| 365 | C2×C4⋊C4 | — | 5 | 576 | no | — |
| 366 | C2×C4⋊C4 | — | 5 | 72 | no | — |
| 367 | C2×C22⋊C4 | — | 5 | 432 | no | — |
| 368 | C2×C22⋊C4 | — | 5 | 1152 | no | — |
| 369 | C2×C42 | — | 5 | 216 | no | — |
| 370 | C2×C42 | — | 5 | 72 | no | — |
| 371 | C2×C42 | — | 5 | 576 | no | — |
| 372 | C22×C5 | — | 2 | 108 | no | — |
| 373 | C22×C5 | — | 4 | 96 | no | — |
| 374 | C22×C5 | C4×H(5,𝔽2) | 1 | 4 | yes | complemented |
| 375 | C22×C5 | C25×C4 | 1 | 36 | yes | — |
| 376 | C22×C5 | C25×C4 | 1 | 3 | yes | — |
| 377 | C2×D5 | — | 2 | 108 | no | — |
| 378 | C2×D5 | — | 2 | 36 | no | — |
| 379 | C2×D5 | — | 2 | 36 | no | — |
| 380 | C2×D5 | — | 2 | 216 | no | — |
| 381 | C2×D5 | — | 4 | 288 | no | — |
| 382 | C2×D5 | C4×H(5,𝔽2) | 1 | 12 | yes | complemented |
| 383 | C2×D5 | C25×C4 | 1 | 36 | yes | — |
| 384 | C2×D5 | C25×C4 | 1 | 3 | yes | — |
| 385 | C2×D5 | C22×H(5,𝔽2) | 1 | 6 | yes | — |
| 386 | C2×D5 | C2×#585 | 1 | 6 | yes | — |
| 387 | C2×D5 | C27 | 1 | 1 | yes | characteristic |
| 388 | AGL(1,𝔽5) | — | 2 | 36 | no | — |
| 389 | AGL(1,𝔽5) | — | 2 | 24 | no | — |
| 390 | AGL(1,𝔽5) | C22×H(5,𝔽2) | 1 | 8 | yes | direct product factor |
| 391 | C4×C5 | C25×C4 | 1 | 24 | yes | — |
| 392 | Dic5 | C25×C4 | 1 | 24 | yes | — |
| 393 | C24 | — | 4 | 24 | no | — |
| 394 | C24 | — | 5 | 1 | no | — |
| 395 | C24 | — | 5 | 54 | no | — |
| 396 | C24 | — | 5 | 54 | no | — |
| 397 | C24 | — | 5 | 9 | no | — |
| 398 | C24 | — | 5 | 216 | no | — |
| 399 | C24 | — | 5 | 96 | no | — |
| 400 | C24 | — | 5 | 288 | no | — |
| 401 | C24 | — | 10 | 36 | no | — |
| 402 | C24 | — | 10 | 36 | no | — |
| 403 | C24 | — | 20 | 72 | no | — |
| 404 | C24 | — | 20 | 144 | no | — |
| 405 | C24 | — | 20 | 144 | no | — |
| 406 | C24 | — | 20 | 288 | no | — |
| 407 | C24 | C23×AGL(1,𝔽5) | 1 | 9 | yes | — |
| 408 | C24 | C23×AGL(1,𝔽5) | 1 | 72 | yes | complemented |
| 409 | #41 | — | 5 | 384 | no | — |
| 410 | #41 | — | 5 | 1152 | no | — |
| 411 | #41 | — | 5 | 1152 | no | — |
| 412 | #41 | C23×AGL(1,𝔽5) | 1 | 384 | yes | complemented |
| 413 | C2×Q8 | — | 5 | 32 | no | — |
| 414 | C2×Q8 | — | 5 | 96 | no | — |
| 415 | C2×Q8 | — | 5 | 72 | no | — |
| 416 | C2×Q8 | C23×AGL(1,𝔽5) | 1 | 24 | yes | complemented |
| 417 | C2×D4 | — | 5 | 432 | no | — |
| 418 | C2×D4 | — | 5 | 1152 | no | — |
| 419 | C2×D4 | — | 5 | 288 | no | — |
| 420 | C2×D4 | — | 5 | 864 | no | — |
| 421 | C2×D4 | — | 5 | 2304 | no | — |
| 422 | C2×D4 | — | 5 | 216 | no | — |
| 423 | C2×D4 | — | 5 | 576 | no | — |
| 424 | C2×D4 | C23×AGL(1,𝔽5) | 1 | 216 | yes | complemented |
| 425 | C2×D4 | C23×AGL(1,𝔽5) | 1 | 576 | yes | complemented |
| 426 | C22×C4 | — | 5 | 6 | no | — |
| 427 | C22×C4 | — | 5 | 8 | no | — |
| 428 | C22×C4 | — | 5 | 108 | no | — |
| 429 | C22×C4 | — | 5 | 6 | no | — |
| 430 | C22×C4 | — | 5 | 36 | no | — |
| 431 | C22×C4 | — | 5 | 36 | no | — |
| 432 | C22×C4 | — | 5 | 216 | no | — |
| 433 | C22×C4 | — | 5 | 144 | no | — |
| 434 | C22×C4 | — | 5 | 432 | no | — |
| 435 | C22×C4 | — | 5 | 36 | no | — |
| 436 | C22×C4 | — | 5 | 54 | no | — |
| 437 | C22×C4 | — | 5 | 144 | no | — |
| 438 | C22×C4 | — | 5 | 144 | no | — |
| 439 | C22×C4 | — | 5 | 288 | no | — |
| 440 | C22×C4 | — | 10 | 432 | no | — |
| 441 | C22×C4 | — | 10 | 36 | no | — |
| 442 | C22×C4 | — | 10 | 24 | no | — |
| 443 | C22×C4 | — | 20 | 768 | no | — |
| 444 | C22×C4 | — | 20 | 432 | no | — |
| 445 | C22×C4 | — | 20 | 216 | no | — |
| 446 | C22×C4 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 447 | C22×C4 | C23×AGL(1,𝔽5) | 1 | 108 | yes | complemented |
| 448 | C4⋊C4 | — | 5 | 288 | no | — |
| 449 | C4⋊C4 | — | 5 | 96 | no | — |
| 450 | C22⋊C4 | — | 5 | 576 | no | — |
| 451 | C42 | — | 5 | 96 | no | — |
| 452 | C42 | — | 5 | 288 | no | — |
| 453 | C2×C5 | — | 2 | 36 | no | — |
| 454 | C2×C5 | C2×C4×H(5,𝔽2) | 1 | 6 | yes | complemented |
| 455 | C2×C5 | C26×C4 | 1 | 1 | yes | characteristic |
| 456 | D5 | — | 2 | 36 | no | — |
| 457 | D5 | C2×C4×H(5,𝔽2) | 1 | 6 | yes | complemented |
| 458 | D5 | C23×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 459 | D5 | C22×#585 | 1 | 1 | yes | characteristic |
| 460 | C23 | — | 2 | 36 | no | — |
| 461 | C23 | — | 4 | 144 | no | — |
| 462 | C23 | — | 5 | 4 | no | — |
| 463 | C23 | — | 5 | 4 | no | — |
| 464 | C23 | — | 5 | 3 | no | — |
| 465 | C23 | — | 5 | 3 | no | — |
| 466 | C23 | — | 5 | 36 | no | — |
| 467 | C23 | — | 5 | 108 | no | — |
| 468 | C23 | — | 5 | 54 | no | — |
| 469 | C23 | — | 5 | 288 | no | — |
| 470 | C23 | — | 10 | 108 | no | — |
| 471 | C23 | — | 10 | 108 | no | — |
| 472 | C23 | — | 10 | 216 | no | — |
| 473 | C23 | — | 10 | 36 | no | — |
| 474 | C23 | — | 20 | 432 | no | — |
| 475 | C23 | — | 20 | 96 | no | — |
| 476 | C23 | — | 20 | 96 | no | — |
| 477 | C23 | — | 20 | 576 | no | — |
| 478 | C23 | C24×AGL(1,𝔽5) | 1 | 54 | yes | — |
| 479 | C23 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 480 | C23 | C24×AGL(1,𝔽5) | 1 | 96 | yes | complemented |
| 481 | Q8 | — | 5 | 96 | no | — |
| 482 | Q8 | C24×AGL(1,𝔽5) | 1 | 32 | yes | complemented |
| 483 | D4 | — | 5 | 576 | no | — |
| 484 | D4 | — | 5 | 288 | no | — |
| 485 | D4 | C24×AGL(1,𝔽5) | 1 | 288 | yes | complemented |
| 486 | C2×C4 | — | 5 | 4 | no | — |
| 487 | C2×C4 | — | 5 | 24 | no | — |
| 488 | C2×C4 | — | 5 | 36 | no | — |
| 489 | C2×C4 | — | 5 | 144 | no | — |
| 490 | C2×C4 | — | 5 | 24 | no | — |
| 491 | C2×C4 | — | 5 | 72 | no | — |
| 492 | C2×C4 | — | 5 | 288 | no | — |
| 493 | C2×C4 | — | 5 | 24 | no | — |
| 494 | C2×C4 | — | 5 | 36 | no | — |
| 495 | C2×C4 | — | 10 | 288 | no | — |
| 496 | C2×C4 | — | 10 | 108 | no | — |
| 497 | C2×C4 | — | 10 | 72 | no | — |
| 498 | C2×C4 | — | 20 | 288 | no | — |
| 499 | C2×C4 | — | 20 | 144 | no | — |
| 500 | C2×C4 | C24×AGL(1,𝔽5) | 1 | 36 | yes | — |
| 501 | C2×C4 | C24×AGL(1,𝔽5) | 1 | 144 | yes | complemented |
| 502 | C5 | C22×C4×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 503 | C22 | — | 2 | 108 | no | — |
| 504 | C22 | — | 4 | 96 | no | — |
| 505 | C22 | — | 5 | 6 | no | — |
| 506 | C22 | — | 5 | 6 | no | — |
| 507 | C22 | — | 5 | 12 | no | — |
| 508 | C22 | — | 5 | 1 | no | — |
| 509 | C22 | — | 5 | 3 | no | — |
| 510 | C22 | — | 5 | 36 | no | — |
| 511 | C22 | — | 10 | 36 | no | — |
| 512 | C22 | — | 10 | 36 | no | — |
| 513 | C22 | — | 10 | 216 | no | — |
| 514 | C22 | — | 10 | 108 | no | — |
| 515 | C22 | — | 20 | 288 | no | — |
| 516 | C22 | AGL(1,𝔽5)×H(5,𝔽2) | 1 | 4 | yes | direct product factor |
| 517 | C22 | C25×AGL(1,𝔽5) | 1 | 36 | yes | — |
| 518 | C22 | C25×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 519 | C4 | — | 5 | 8 | no | — |
| 520 | C4 | — | 5 | 24 | no | — |
| 521 | C4 | — | 10 | 36 | no | — |
| 522 | C4 | — | 10 | 24 | no | — |
| 523 | C4 | C25×AGL(1,𝔽5) | 1 | 24 | yes | — |
| 524 | C2 | — | 2 | 36 | no | — |
| 525 | C2 | — | 5 | 1 | no | — |
| 526 | C2 | — | 5 | 1 | no | — |
| 527 | C2 | — | 5 | 6 | no | — |
| 528 | C2 | — | 10 | 36 | no | — |
| 529 | C2 | C2×AGL(1,𝔽5)×H(5,𝔽2) | 1 | 6 | yes | direct product factor |
| 530 | C2 | C26×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C2×AGL(1,𝔽5)×H(5,𝔽2) | C2 | direct (N × H) |
| 2. C22×#66266 | C2 | semidirect |
| 3. C22×#66258 | C2 | semidirect |
| 4. C22×#41×AGL(1,𝔽5) | C2 | semidirect |
| 5. C23×D4×AGL(1,𝔽5) | C2 | semidirect |
| 7. C25×AGL(1,𝔽5) | C22 | semidirect |
| 8. C22×C5×H(5,𝔽2) | C4 | semidirect |
| 9. C2×D5×H(5,𝔽2) | C4 | semidirect |
| 11. C22×#4149 | C4 | semidirect |
| 13. C22×#4144 | C4 | semidirect |
| 15. C23×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 16. AGL(1,𝔽5)×H(5,𝔽2) | C22 | direct (N × H) |
| 17. C2×#66266 | C22 | semidirect |
| 18. C2×#41×AGL(1,𝔽5) | C22 | semidirect |
| 19. C22×Q8×AGL(1,𝔽5) | C22 | semidirect |
| 20. C22×Q8×AGL(1,𝔽5) | C22 | semidirect |
| 21. C2×#66258 | C22 | semidirect |
| 22. C22×D4×AGL(1,𝔽5) | C22 | semidirect |
| 23. C22×D4×AGL(1,𝔽5) | C22 | semidirect |
| 24. C22×D4×AGL(1,𝔽5) | C22 | semidirect |
| 25. C22×D4×AGL(1,𝔽5) | C22 | semidirect |
| 26. C22×#4130 | C22 | semidirect |
| 27. C23×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 28. C23×C4×AGL(1,𝔽5) | C22 | semidirect |
| 35. C24×AGL(1,𝔽5) | C23 | semidirect |
| 36. C2×C5×H(5,𝔽2) | C2×C4 | semidirect |
| 37. C22×C5×#41 | C2×C4 | semidirect |
| 38. C23×C5×D4 | C2×C4 | semidirect |
| 39. C23×C22⋊D5 | C2×C4 | semidirect |
| 40. D5×H(5,𝔽2) | C2×C4 | semidirect |
| 42. C2×#4149 | C2×C4 | semidirect |
| 43. C2×D5×#41 | C2×C4 | semidirect |
| 45. C22×#713 | C2×C4 | semidirect |
| 47. C2×#4144 | C2×C4 | semidirect |
| 48. C22×#711 | C2×C4 | semidirect |
| 49. C22×D4×D5 | C2×C4 | semidirect |
| 50. C22×D4×D5 | C2×C4 | semidirect |
| 53. C22×#709 | C2×C4 | semidirect |
| 54. C23×D20 | C2×C4 | semidirect |
| 57. C22×C22⋊AGL(1,𝔽5) | C23 | semidirect |
| 58. #66266 | C23 | semidirect |
| 59. #41×AGL(1,𝔽5) | C23 | semidirect |
| 60. C2×Q8×AGL(1,𝔽5) | C23 | semidirect |
| 61. C2×Q8×AGL(1,𝔽5) | C23 | semidirect |
| 62. #66258 | C23 | semidirect |
| 63. C2×D4×AGL(1,𝔽5) | C23 | semidirect |
| 64. C2×D4×AGL(1,𝔽5) | C23 | semidirect |
| 65. C2×D4×AGL(1,𝔽5) | C23 | semidirect |
| 66. C2×D4×AGL(1,𝔽5) | C23 | semidirect |
| 67. C2×#4130 | C23 | semidirect |
| 70. C22×C4⋊AGL(1,𝔽5) | C23 | semidirect |
| 73. C22×C4×AGL(1,𝔽5) | C23 | semidirect |
| 80. C25×C5 | C22×C4 | semidirect |
| 83. C24×D5 | C22×C4 | semidirect |
| 84. C24×D5 | C22×C4 | semidirect |
| 97. C23×AGL(1,𝔽5) | C24 | semidirect |
| 98. C5×H(5,𝔽2) | C22×C4 | semidirect |
| 99. C2×C5×#41 | C22×C4 | semidirect |
| 100. C22×C5×Q8 | C22×C4 | semidirect |
| 101. C22×C5×D4 | C22×C4 | semidirect |
| 102. C22×C5×D4 | C22×C4 | semidirect |
| 103. C23×C4×C5 | C22×C4 | semidirect |
| 104. C22×C22⋊D5 | C22×C4 | semidirect |
| 105. C22×C22⋊D5 | C22×C4 | semidirect |
| 106. C23×Dic5 | C22×C4 | semidirect |
| 107. #4149 | C22×C4 | semidirect |
| 108. D5×#41 | C22×C4 | semidirect |
| 110. C2×#713 | C22×C4 | semidirect |
| 111. C2×Q8×D5 | C22×C4 | semidirect |
| 113. #4144 | C22×C4 | semidirect |
| 114. C2×#711 | C22×C4 | semidirect |
| 115. C2×D4×D5 | C22×C4 | semidirect |
| 116. C2×D4×D5 | C22×C4 | semidirect |
| 117. C2×D4×D5 | C22×C4 | semidirect |
| 120. C2×#709 | C22×C4 | semidirect |
| 121. C22×D20 | C22×C4 | semidirect |
| 122. C22×D20 | C22×C4 | semidirect |
| 123. C22×C4×D5 | C22×C4 | semidirect |
| 124. C22×C4×D5 | C22×C4 | semidirect |
| 127. C22×Dic10 | C22×C4 | semidirect |
| 129. C2×C22⋊AGL(1,𝔽5) | C24 | semidirect |
| 130. Q8×AGL(1,𝔽5) | C24 | semidirect |
| 131. Q8×AGL(1,𝔽5) | C24 | semidirect |
| 132. D4×AGL(1,𝔽5) | C24 | semidirect |
| 133. D4×AGL(1,𝔽5) | C24 | semidirect |
| 134. D4×AGL(1,𝔽5) | C24 | semidirect |
| 135. #4130 | C24 | semidirect |
| 138. C2×C4⋊AGL(1,𝔽5) | C24 | semidirect |
| 141. C2×C4×AGL(1,𝔽5) | C24 | semidirect |
| 146. C22×H(5,𝔽2) | AGL(1,𝔽5) | direct (N × H) |
| 166. C24×C5 | C23×C4 | semidirect |
| 175. C23×D5 | C23×C4 | semidirect |
| 176. C23×D5 | C23×C4 | semidirect |
| 186. C22×AGL(1,𝔽5) | H(5,𝔽2) | direct (N × H) |
| 193. C5×#41 | C23×C4 | semidirect |
| 194. C2×C5×Q8 | C23×C4 | semidirect |
| 195. C2×C5×D4 | C23×C4 | semidirect |
| 196. C2×C5×D4 | C23×C4 | semidirect |
| 198. C22×C4×C5 | C23×C4 | semidirect |
| 199. C2×C22⋊D5 | C23×C4 | semidirect |
| 200. C2×C22⋊D5 | C23×C4 | semidirect |
| 202. C22×Dic5 | C23×C4 | semidirect |
| 203. #713 | C23×C4 | semidirect |
| 204. Q8×D5 | C23×C4 | semidirect |
| 206. #711 | C23×C4 | semidirect |
| 207. D4×D5 | C23×C4 | semidirect |
| 208. D4×D5 | C23×C4 | semidirect |
| 210. #709 | C23×C4 | semidirect |
| 211. C2×D20 | C23×C4 | semidirect |
| 212. C2×D20 | C23×C4 | semidirect |
| 214. C2×C4×D5 | C23×C4 | semidirect |
| 215. C2×C4×D5 | C23×C4 | semidirect |
| 218. C2×Dic10 | C23×C4 | semidirect |
| 229. C2×H(5,𝔽2) | C2×AGL(1,𝔽5) | direct (N × H) |
| 235. C22×#41 | C2×AGL(1,𝔽5) | semidirect |
| 243. C23×D4 | C2×AGL(1,𝔽5) | semidirect |
| 272. C23×C5 | C24×C4 | semidirect |
| 284. C22×D5 | C24×C4 | semidirect |
| 294. C2×AGL(1,𝔽5) | C2×H(5,𝔽2) | direct (N × H) |
| 298. C5×Q8 | C24×C4 | semidirect |
| 299. C5×D4 | C24×C4 | semidirect |
| 301. C2×C4×C5 | C24×C4 | semidirect |
| 302. C22⋊D5 | C24×C4 | semidirect |
| 304. C2×Dic5 | C24×C4 | semidirect |
| 305. D20 | C24×C4 | semidirect |
| 307. C4×D5 | C24×C4 | semidirect |
| 309. Dic10 | C24×C4 | semidirect |
| 316. C25 | C22×AGL(1,𝔽5) | semidirect |
| 319. H(5,𝔽2) | C22×AGL(1,𝔽5) | direct (N × H) |
| 325. C2×#41 | C22×AGL(1,𝔽5) | semidirect |
| 329. C22×Q8 | C22×AGL(1,𝔽5) | semidirect |
| 339. C22×D4 | C22×AGL(1,𝔽5) | semidirect |
| 340. C22×D4 | C22×AGL(1,𝔽5) | semidirect |
| 357. C23×C4 | C22×AGL(1,𝔽5) | semidirect |
| 374. C22×C5 | C4×H(5,𝔽2) | semidirect |
| 382. C2×D5 | C4×H(5,𝔽2) | semidirect |
| 390. AGL(1,𝔽5) | C22×H(5,𝔽2) | direct (N × H) |
| 408. C24 | C23×AGL(1,𝔽5) | semidirect |
| 412. #41 | C23×AGL(1,𝔽5) | semidirect |
| 416. C2×Q8 | C23×AGL(1,𝔽5) | semidirect |
| 424. C2×D4 | C23×AGL(1,𝔽5) | semidirect |
| 425. C2×D4 | C23×AGL(1,𝔽5) | semidirect |
| 447. C22×C4 | C23×AGL(1,𝔽5) | semidirect |
| 454. C2×C5 | C2×C4×H(5,𝔽2) | semidirect |
| 457. D5 | C2×C4×H(5,𝔽2) | semidirect |
| 480. C23 | C24×AGL(1,𝔽5) | semidirect |
| 482. Q8 | C24×AGL(1,𝔽5) | semidirect |
| 485. D4 | C24×AGL(1,𝔽5) | semidirect |
| 501. C2×C4 | C24×AGL(1,𝔽5) | semidirect |
| 502. C5 | C22×C4×H(5,𝔽2) | semidirect |
| 516. C22 | AGL(1,𝔽5)×H(5,𝔽2) | direct (N × H) |
| 529. C2 | C2×AGL(1,𝔽5)×H(5,𝔽2) | direct (N × H) |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta