← C5×AGL(1,𝔽5)×H(5,𝔽2) #72275706
Order 3200.
3403 conjugacy classes of subgroups.
The subgroup lattice has 333 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C5×D5×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#66266 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | C5×#41×AGL(1,𝔽5) | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C5×#66258 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | C2×C5×D4×AGL(1,𝔽5) | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | C23×C5×AGL(1,𝔽5) | C22 | 1 | 6 | yes | complemented |
| 7 | C52×H(5,𝔽2) | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C5×#4149 | C4 | 1 | 6 | yes | complemented |
| 9 | C5×D5×#41 | C22 | 1 | 6 | yes | — |
| 10 | C5×#4144 | C4 | 1 | 9 | yes | complemented |
| 11 | C2×C5×D4×D5 | C22 | 1 | 9 | yes | — |
| 12 | C2×C5×C22⋊AGL(1,𝔽5) | C22 | 1 | 18 | yes | complemented |
| 13 | C5×Q8×AGL(1,𝔽5) | C22 | 1 | 2 | yes | complemented |
| 14 | C5×Q8×AGL(1,𝔽5) | C22 | 1 | 6 | yes | complemented |
| 15 | C5×D4×AGL(1,𝔽5) | C22 | 1 | 18 | yes | complemented |
| 16 | C5×D4×AGL(1,𝔽5) | C22 | 1 | 36 | yes | complemented |
| 17 | C5×D4×AGL(1,𝔽5) | C22 | 1 | 18 | yes | complemented |
| 18 | C5×#4130 | C22 | 1 | 18 | yes | complemented |
| 19 | C2×C5×C4⋊AGL(1,𝔽5) | C22 | 1 | 9 | yes | complemented |
| 20 | C2×C4×C5×AGL(1,𝔽5) | C22 | 1 | 9 | yes | complemented |
| 21 | AGL(1,𝔽5)×H(5,𝔽2) | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 22 | C4×C5×H(5,𝔽2) | — | 5 | 1 | no | maximal |
| 23 | C23×C5×D5 | C23 | 1 | 6 | yes | — |
| 24 | C22×C5×AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 25 | C22×C5×AGL(1,𝔽5) | C23 | 1 | 9 | yes | — |
| 26 | C22×C5×AGL(1,𝔽5) | C23 | 1 | 9 | yes | — |
| 27 | C22×C5×AGL(1,𝔽5) | C23 | 1 | 18 | yes | — |
| 28 | C52×#41 | C2×C4 | 1 | 6 | yes | complemented |
| 29 | C2×C52×D4 | C2×C4 | 1 | 9 | yes | complemented |
| 30 | C2×C5×C22⋊D5 | C2×C4 | 1 | 18 | yes | complemented |
| 31 | C5×#713 | C2×C4 | 1 | 6 | yes | complemented |
| 32 | C5×Q8×D5 | C23 | 1 | 2 | yes | — |
| 33 | C5×#711 | C2×C4 | 1 | 18 | yes | complemented |
| 34 | C5×D4×D5 | C2×C4 | 1 | 36 | yes | complemented |
| 35 | C5×D4×D5 | C23 | 1 | 18 | yes | — |
| 36 | C5×#709 | C2×C4 | 1 | 18 | yes | complemented |
| 37 | C2×C5×D20 | C2×C4 | 1 | 9 | yes | complemented |
| 38 | C2×C4×C5×D5 | C23 | 1 | 9 | yes | — |
| 39 | C5×C22⋊AGL(1,𝔽5) | C23 | 1 | 36 | yes | — |
| 40 | C5×C4⋊AGL(1,𝔽5) | C23 | 1 | 18 | yes | — |
| 41 | C5×C4⋊AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 42 | C4×C5×AGL(1,𝔽5) | C23 | 1 | 6 | yes | — |
| 43 | C4×C5×AGL(1,𝔽5) | C23 | 1 | 18 | yes | — |
| 44 | C2×C5×H(5,𝔽2) | — | 5 | 1 | no | — |
| 45 | D5×H(5,𝔽2) | C2×C5 | 1 | 1 | yes | characteristic |
| 46 | #66266 | C2×C5 | 1 | 6 | yes | complemented |
| 47 | #41×AGL(1,𝔽5) | C2×C5 | 1 | 6 | yes | complemented |
| 48 | #66258 | C2×C5 | 1 | 9 | yes | complemented |
| 49 | C2×D4×AGL(1,𝔽5) | C2×C5 | 1 | 9 | yes | complemented |
| 50 | C5×#520 | — | 5 | 6 | no | — |
| 51 | C5×#518 | — | 5 | 9 | no | — |
| 52 | C4×C5×#41 | — | 5 | 6 | no | — |
| 53 | C2×C4×C5×D4 | — | 5 | 9 | no | — |
| 54 | C23×C52 | C22×C4 | 1 | 6 | yes | complemented |
| 55 | C22×C5×D5 | — | 4 | 6 | no | — |
| 56 | C22×C5×D5 | — | 4 | 6 | no | — |
| 57 | C22×C5×D5 | C22×C4 | 1 | 18 | yes | complemented |
| 58 | C22×C5×D5 | C24 | 1 | 9 | yes | — |
| 59 | C2×C5×AGL(1,𝔽5) | — | 2 | 18 | no | — |
| 60 | C2×C5×AGL(1,𝔽5) | — | 4 | 18 | no | — |
| 61 | C2×C5×AGL(1,𝔽5) | — | 4 | 9 | no | — |
| 62 | C2×C5×AGL(1,𝔽5) | C24 | 1 | 6 | yes | — |
| 63 | C2×C5×AGL(1,𝔽5) | C24 | 1 | 9 | yes | — |
| 64 | C2×C5×AGL(1,𝔽5) | C24 | 1 | 1 | yes | characteristic |
| 65 | C52×Q8 | C22×C4 | 1 | 2 | yes | complemented |
| 66 | C52×D4 | C22×C4 | 1 | 18 | yes | complemented |
| 67 | C2×C4×C52 | C22×C4 | 1 | 9 | yes | complemented |
| 68 | C5×C22⋊D5 | C22×C4 | 1 | 36 | yes | complemented |
| 69 | C2×C5×Dic5 | C22×C4 | 1 | 9 | yes | complemented |
| 70 | C5×D20 | C22×C4 | 1 | 18 | yes | complemented |
| 71 | C4×C5×D5 | C22×C4 | 1 | 18 | yes | complemented |
| 72 | C4×C5×D5 | C24 | 1 | 6 | yes | — |
| 73 | C5×Dic10 | C22×C4 | 1 | 6 | yes | complemented |
| 74 | C23×AGL(1,𝔽5) | C22×C5 | 1 | 6 | yes | complemented |
| 75 | C5×H(5,𝔽2) | — | 4 | 1 | no | — |
| 76 | C5×H(5,𝔽2) | — | 5 | 6 | no | — |
| 77 | C5×H(5,𝔽2) | — | 5 | 9 | no | — |
| 78 | C5×H(5,𝔽2) | C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 79 | C5×H(5,𝔽2) | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 80 | C2×C5×#41 | — | 5 | 6 | no | — |
| 81 | C22×C5×D4 | — | 5 | 9 | no | — |
| 82 | C23×C4×C5 | — | 5 | 6 | no | — |
| 83 | #4149 | C4×C5 | 1 | 6 | yes | complemented |
| 84 | D5×#41 | C22×C5 | 1 | 6 | yes | — |
| 85 | #4144 | C4×C5 | 1 | 9 | yes | complemented |
| 86 | C2×D4×D5 | C22×C5 | 1 | 9 | yes | — |
| 87 | C2×C22⋊AGL(1,𝔽5) | C22×C5 | 1 | 18 | yes | complemented |
| 88 | Q8×AGL(1,𝔽5) | C22×C5 | 1 | 2 | yes | complemented |
| 89 | Q8×AGL(1,𝔽5) | C22×C5 | 1 | 6 | yes | complemented |
| 90 | D4×AGL(1,𝔽5) | C22×C5 | 1 | 18 | yes | complemented |
| 91 | D4×AGL(1,𝔽5) | C22×C5 | 1 | 36 | yes | complemented |
| 92 | D4×AGL(1,𝔽5) | C22×C5 | 1 | 18 | yes | complemented |
| 93 | #4130 | C22×C5 | 1 | 18 | yes | complemented |
| 94 | C2×C4⋊AGL(1,𝔽5) | C22×C5 | 1 | 9 | yes | complemented |
| 95 | C2×C4×AGL(1,𝔽5) | C22×C5 | 1 | 9 | yes | complemented |
| 96 | C4×C5×Q8 | — | 5 | 2 | no | — |
| 97 | C4×C5×Q8 | — | 5 | 6 | no | — |
| 98 | C4×C5×D4 | — | 5 | 18 | no | — |
| 99 | C4×C5×D4 | — | 5 | 36 | no | — |
| 100 | C4×C5×D4 | — | 5 | 18 | no | — |
| 101 | C5×#117 | — | 5 | 18 | no | — |
| 102 | C2×C5×C4⋊C4 | — | 5 | 9 | no | — |
| 103 | C2×C5×C22⋊C4 | — | 5 | 18 | no | — |
| 104 | C2×C42×C5 | — | 5 | 9 | no | — |
| 105 | C4×H(5,𝔽2) | — | 5 | 1 | no | Sylow |
| 106 | C22×C52 | — | 4 | 6 | no | — |
| 107 | C22×C52 | C23×C4 | 1 | 9 | yes | — |
| 108 | C2×C5×D5 | — | 2 | 9 | no | — |
| 109 | C2×C5×D5 | — | 2 | 9 | no | — |
| 110 | C2×C5×D5 | — | 4 | 18 | no | — |
| 111 | C2×C5×D5 | C23×C4 | 1 | 9 | yes | — |
| 112 | C2×C5×D5 | C25 | 1 | 1 | yes | characteristic |
| 113 | C5×AGL(1,𝔽5) | — | 2 | 9 | no | — |
| 114 | C5×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 115 | C5×AGL(1,𝔽5) | H(5,𝔽2) | 1 | 2 | yes | direct product factor |
| 116 | C4×C52 | C23×C4 | 1 | 6 | yes | — |
| 117 | C5×Dic5 | C23×C4 | 1 | 6 | yes | — |
| 118 | C24×C5 | — | 5 | 6 | no | — |
| 119 | C23×D5 | C23×C5 | 1 | 6 | yes | — |
| 120 | C22×AGL(1,𝔽5) | — | 4 | 12 | no | — |
| 121 | C22×AGL(1,𝔽5) | C23×C5 | 1 | 9 | yes | — |
| 122 | C22×AGL(1,𝔽5) | C23×C5 | 1 | 9 | yes | — |
| 123 | C22×AGL(1,𝔽5) | C23×C5 | 1 | 18 | yes | — |
| 124 | C5×#41 | — | 4 | 6 | no | — |
| 125 | C5×#41 | — | 5 | 6 | no | — |
| 126 | C5×#41 | — | 5 | 18 | no | — |
| 127 | C5×#41 | — | 5 | 18 | no | — |
| 128 | C5×#41 | C2×C4×C5 | 1 | 6 | yes | complemented |
| 129 | C5×#41 | C2×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 130 | C2×C5×Q8 | — | 5 | 2 | no | — |
| 131 | C2×C5×D4 | — | 4 | 9 | no | — |
| 132 | C2×C5×D4 | — | 5 | 18 | no | — |
| 133 | C2×C5×D4 | — | 5 | 18 | no | — |
| 134 | C2×C5×D4 | — | 5 | 36 | no | — |
| 135 | C2×C5×D4 | — | 5 | 9 | no | — |
| 136 | C2×C5×D4 | C2×C4×C5 | 1 | 9 | yes | complemented |
| 137 | C2×C5×D4 | C2×AGL(1,𝔽5) | 1 | 9 | yes | complemented |
| 138 | C22×C4×C5 | — | 5 | 9 | no | — |
| 139 | C22×C4×C5 | — | 5 | 9 | no | — |
| 140 | C22×C4×C5 | — | 5 | 9 | no | — |
| 141 | C22×C4×C5 | — | 5 | 18 | no | — |
| 142 | C22×C4×C5 | — | 20 | 12 | no | — |
| 143 | C2×C22⋊D5 | C2×C4×C5 | 1 | 18 | yes | complemented |
| 144 | #713 | C2×C4×C5 | 1 | 6 | yes | complemented |
| 145 | Q8×D5 | C23×C5 | 1 | 2 | yes | — |
| 146 | #711 | C2×C4×C5 | 1 | 18 | yes | complemented |
| 147 | D4×D5 | C2×C4×C5 | 1 | 36 | yes | complemented |
| 148 | D4×D5 | C23×C5 | 1 | 18 | yes | — |
| 149 | #709 | C2×C4×C5 | 1 | 18 | yes | complemented |
| 150 | C2×D20 | C2×C4×C5 | 1 | 9 | yes | complemented |
| 151 | C2×C4×D5 | C23×C5 | 1 | 9 | yes | — |
| 152 | C22⋊AGL(1,𝔽5) | C23×C5 | 1 | 36 | yes | — |
| 153 | C4⋊AGL(1,𝔽5) | C23×C5 | 1 | 18 | yes | — |
| 154 | C4⋊AGL(1,𝔽5) | C23×C5 | 1 | 6 | yes | — |
| 155 | C4×AGL(1,𝔽5) | C23×C5 | 1 | 6 | yes | — |
| 156 | C4×AGL(1,𝔽5) | C23×C5 | 1 | 18 | yes | — |
| 157 | C5×C4⋊C4 | — | 5 | 18 | no | — |
| 158 | C5×C4⋊C4 | — | 5 | 6 | no | — |
| 159 | C5×C22⋊C4 | — | 5 | 36 | no | — |
| 160 | C42×C5 | — | 5 | 6 | no | — |
| 161 | C42×C5 | — | 5 | 18 | no | — |
| 162 | C2×H(5,𝔽2) | — | 5 | 1 | no | — |
| 163 | #520 | — | 5 | 6 | no | — |
| 164 | #518 | — | 5 | 9 | no | — |
| 165 | C4×#41 | — | 5 | 6 | no | — |
| 166 | C2×C4×D4 | — | 5 | 9 | no | — |
| 167 | C2×C52 | — | 2 | 9 | no | — |
| 168 | C2×C52 | C24×C4 | 1 | 1 | yes | characteristic |
| 169 | C5×D5 | — | 2 | 9 | no | — |
| 170 | C5×D5 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 171 | C5×D5 | #585 | 1 | 1 | yes | characteristic |
| 172 | C23×C5 | — | 4 | 6 | no | — |
| 173 | C23×C5 | — | 5 | 9 | no | — |
| 174 | C23×C5 | — | 5 | 18 | no | — |
| 175 | C23×C5 | — | 20 | 6 | no | — |
| 176 | C23×C5 | — | 20 | 6 | no | — |
| 177 | C23×C5 | C22×C4×C5 | 1 | 6 | yes | complemented |
| 178 | C23×C5 | C22×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 179 | C22×D5 | — | 4 | 6 | no | — |
| 180 | C22×D5 | — | 4 | 6 | no | — |
| 181 | C22×D5 | C22×C4×C5 | 1 | 18 | yes | complemented |
| 182 | C22×D5 | C24×C5 | 1 | 9 | yes | — |
| 183 | C2×AGL(1,𝔽5) | — | 2 | 18 | no | — |
| 184 | C2×AGL(1,𝔽5) | — | 4 | 18 | no | — |
| 185 | C2×AGL(1,𝔽5) | — | 4 | 9 | no | — |
| 186 | C2×AGL(1,𝔽5) | C24×C5 | 1 | 6 | yes | — |
| 187 | C2×AGL(1,𝔽5) | C24×C5 | 1 | 9 | yes | — |
| 188 | C2×AGL(1,𝔽5) | C24×C5 | 1 | 1 | yes | characteristic |
| 189 | C5×Q8 | — | 4 | 2 | no | — |
| 190 | C5×Q8 | — | 5 | 6 | no | — |
| 191 | C5×Q8 | C22×C4×C5 | 1 | 2 | yes | complemented |
| 192 | C5×Q8 | C22×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 193 | C5×D4 | — | 4 | 18 | no | — |
| 194 | C5×D4 | — | 5 | 36 | no | — |
| 195 | C5×D4 | — | 5 | 18 | no | — |
| 196 | C5×D4 | C22×C4×C5 | 1 | 18 | yes | complemented |
| 197 | C5×D4 | C22×AGL(1,𝔽5) | 1 | 18 | yes | complemented |
| 198 | C2×C4×C5 | — | 4 | 9 | no | — |
| 199 | C2×C4×C5 | — | 5 | 1 | no | — |
| 200 | C2×C4×C5 | — | 5 | 9 | no | — |
| 201 | C2×C4×C5 | — | 5 | 18 | no | — |
| 202 | C2×C4×C5 | — | 5 | 6 | no | — |
| 203 | C2×C4×C5 | — | 5 | 6 | no | — |
| 204 | C2×C4×C5 | — | 5 | 9 | no | — |
| 205 | C2×C4×C5 | — | 10 | 18 | no | — |
| 206 | C2×C4×C5 | — | 20 | 9 | no | — |
| 207 | C2×C4×C5 | — | 20 | 18 | no | — |
| 208 | C2×C4×C5 | C22×C4×C5 | 1 | 9 | yes | complemented |
| 209 | C2×C4×C5 | C22×AGL(1,𝔽5) | 1 | 9 | yes | complemented |
| 210 | C22⋊D5 | C22×C4×C5 | 1 | 36 | yes | complemented |
| 211 | C2×Dic5 | C22×C4×C5 | 1 | 9 | yes | complemented |
| 212 | D20 | C22×C4×C5 | 1 | 18 | yes | complemented |
| 213 | C4×D5 | C22×C4×C5 | 1 | 18 | yes | complemented |
| 214 | C4×D5 | C24×C5 | 1 | 6 | yes | — |
| 215 | Dic10 | C22×C4×C5 | 1 | 6 | yes | complemented |
| 216 | H(5,𝔽2) | — | 5 | 6 | no | — |
| 217 | H(5,𝔽2) | — | 5 | 9 | no | — |
| 218 | H(5,𝔽2) | C5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor |
| 219 | C2×#41 | — | 5 | 6 | no | — |
| 220 | C22×D4 | — | 5 | 9 | no | — |
| 221 | C23×C4 | — | 5 | 6 | no | — |
| 222 | C4×Q8 | — | 5 | 2 | no | — |
| 223 | C4×Q8 | — | 5 | 6 | no | — |
| 224 | C4×D4 | — | 5 | 18 | no | — |
| 225 | C4×D4 | — | 5 | 36 | no | — |
| 226 | C4×D4 | — | 5 | 18 | no | — |
| 227 | #117 | — | 5 | 18 | no | — |
| 228 | C2×C4⋊C4 | — | 5 | 9 | no | — |
| 229 | C2×C22⋊C4 | — | 5 | 18 | no | — |
| 230 | C2×C42 | — | 5 | 9 | no | — |
| 231 | C52 | C4×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 232 | C22×C5 | — | 4 | 6 | no | — |
| 233 | C22×C5 | — | 4 | 6 | no | — |
| 234 | C22×C5 | — | 4 | 9 | no | — |
| 235 | C22×C5 | — | 5 | 1 | no | — |
| 236 | C22×C5 | — | 5 | 9 | no | — |
| 237 | C22×C5 | — | 10 | 9 | no | — |
| 238 | C22×C5 | — | 10 | 9 | no | — |
| 239 | C22×C5 | — | 16 | 6 | no | — |
| 240 | C22×C5 | — | 20 | 18 | no | — |
| 241 | C22×C5 | C23×C4×C5 | 1 | 9 | yes | — |
| 242 | C22×C5 | C23×AGL(1,𝔽5) | 1 | 9 | yes | — |
| 243 | C2×D5 | — | 2 | 9 | no | — |
| 244 | C2×D5 | — | 2 | 9 | no | — |
| 245 | C2×D5 | — | 4 | 18 | no | — |
| 246 | C2×D5 | C23×C4×C5 | 1 | 9 | yes | — |
| 247 | C2×D5 | C25×C5 | 1 | 1 | yes | characteristic |
| 248 | AGL(1,𝔽5) | — | 2 | 9 | no | — |
| 249 | AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 250 | AGL(1,𝔽5) | C5×H(5,𝔽2) | 1 | 2 | yes | direct product factor |
| 251 | C4×C5 | — | 4 | 6 | no | — |
| 252 | C4×C5 | — | 5 | 2 | no | — |
| 253 | C4×C5 | — | 5 | 6 | no | — |
| 254 | C4×C5 | — | 10 | 9 | no | — |
| 255 | C4×C5 | — | 10 | 6 | no | — |
| 256 | C4×C5 | C23×C4×C5 | 1 | 6 | yes | — |
| 257 | C4×C5 | C23×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 258 | Dic5 | C23×C4×C5 | 1 | 6 | yes | — |
| 259 | C24 | — | 5 | 6 | no | — |
| 260 | #41 | — | 5 | 6 | no | — |
| 261 | #41 | — | 5 | 18 | no | — |
| 262 | #41 | — | 5 | 18 | no | — |
| 263 | #41 | C2×C5×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 264 | C2×Q8 | — | 5 | 2 | no | — |
| 265 | C2×D4 | — | 5 | 18 | no | — |
| 266 | C2×D4 | — | 5 | 18 | no | — |
| 267 | C2×D4 | — | 5 | 36 | no | — |
| 268 | C2×D4 | — | 5 | 9 | no | — |
| 269 | C2×D4 | C2×C5×AGL(1,𝔽5) | 1 | 9 | yes | complemented |
| 270 | C22×C4 | — | 5 | 9 | no | — |
| 271 | C22×C4 | — | 5 | 9 | no | — |
| 272 | C22×C4 | — | 5 | 9 | no | — |
| 273 | C22×C4 | — | 5 | 18 | no | — |
| 274 | C22×C4 | — | 20 | 12 | no | — |
| 275 | C4⋊C4 | — | 5 | 18 | no | — |
| 276 | C4⋊C4 | — | 5 | 6 | no | — |
| 277 | C22⋊C4 | — | 5 | 36 | no | — |
| 278 | C42 | — | 5 | 6 | no | — |
| 279 | C42 | — | 5 | 18 | no | — |
| 280 | C2×C5 | — | 2 | 9 | no | — |
| 281 | C2×C5 | — | 2 | 9 | no | — |
| 282 | C2×C5 | — | 4 | 1 | no | — |
| 283 | C2×C5 | — | 5 | 1 | no | — |
| 284 | C2×C5 | — | 5 | 1 | no | — |
| 285 | C2×C5 | — | 8 | 9 | no | — |
| 286 | C2×C5 | — | 10 | 9 | no | — |
| 287 | C2×C5 | C24×C4×C5 | 1 | 1 | yes | characteristic |
| 288 | C2×C5 | C24×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 289 | D5 | — | 2 | 9 | no | — |
| 290 | D5 | C2×C5×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 291 | D5 | C5×#585 | 1 | 1 | yes | characteristic |
| 292 | C23 | — | 5 | 9 | no | — |
| 293 | C23 | — | 5 | 18 | no | — |
| 294 | C23 | — | 20 | 6 | no | — |
| 295 | C23 | — | 20 | 6 | no | — |
| 296 | C23 | C22×C5×AGL(1,𝔽5) | 1 | 6 | yes | complemented |
| 297 | Q8 | — | 5 | 6 | no | — |
| 298 | Q8 | C22×C5×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 299 | D4 | — | 5 | 36 | no | — |
| 300 | D4 | — | 5 | 18 | no | — |
| 301 | D4 | C22×C5×AGL(1,𝔽5) | 1 | 18 | yes | complemented |
| 302 | C2×C4 | — | 5 | 1 | no | — |
| 303 | C2×C4 | — | 5 | 9 | no | — |
| 304 | C2×C4 | — | 5 | 6 | no | — |
| 305 | C2×C4 | — | 5 | 18 | no | — |
| 306 | C2×C4 | — | 5 | 6 | no | — |
| 307 | C2×C4 | — | 5 | 9 | no | — |
| 308 | C2×C4 | — | 10 | 18 | no | — |
| 309 | C2×C4 | — | 20 | 18 | no | — |
| 310 | C2×C4 | — | 20 | 9 | no | — |
| 311 | C2×C4 | C22×C5×AGL(1,𝔽5) | 1 | 9 | yes | complemented |
| 312 | C5 | — | 4 | 1 | no | — |
| 313 | C5 | C4×C5×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 314 | C5 | AGL(1,𝔽5)×H(5,𝔽2) | 1 | 1 | yes | characteristic, direct product factor |
| 315 | C22 | — | 4 | 6 | no | — |
| 316 | C22 | — | 5 | 1 | no | — |
| 317 | C22 | — | 5 | 9 | no | — |
| 318 | C22 | — | 10 | 9 | no | — |
| 319 | C22 | — | 10 | 9 | no | — |
| 320 | C22 | — | 20 | 18 | no | — |
| 321 | C22 | C23×C5×AGL(1,𝔽5) | 1 | 9 | yes | — |
| 322 | C4 | — | 5 | 2 | no | — |
| 323 | C4 | — | 5 | 6 | no | — |
| 324 | C4 | — | 10 | 9 | no | — |
| 325 | C4 | — | 10 | 6 | no | — |
| 326 | C4 | C23×C5×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 327 | C2 | — | 2 | 9 | no | — |
| 328 | C2 | — | 5 | 1 | no | — |
| 329 | C2 | — | 5 | 1 | no | — |
| 330 | C2 | — | 10 | 9 | no | — |
| 331 | C2 | C24×C5×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 2. C5×#66266 | C2 | semidirect |
| 3. C5×#41×AGL(1,𝔽5) | C2 | semidirect |
| 4. C5×#66258 | C2 | semidirect |
| 5. C2×C5×D4×AGL(1,𝔽5) | C2 | semidirect |
| 6. C23×C5×AGL(1,𝔽5) | C22 | semidirect |
| 7. C52×H(5,𝔽2) | C4 | semidirect |
| 8. C5×#4149 | C4 | semidirect |
| 10. C5×#4144 | C4 | semidirect |
| 12. C2×C5×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 13. C5×Q8×AGL(1,𝔽5) | C22 | semidirect |
| 14. C5×Q8×AGL(1,𝔽5) | C22 | semidirect |
| 15. C5×D4×AGL(1,𝔽5) | C22 | semidirect |
| 16. C5×D4×AGL(1,𝔽5) | C22 | semidirect |
| 17. C5×D4×AGL(1,𝔽5) | C22 | semidirect |
| 18. C5×#4130 | C22 | semidirect |
| 19. C2×C5×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 20. C2×C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 21. AGL(1,𝔽5)×H(5,𝔽2) | C5 | direct (N × H) |
| 28. C52×#41 | C2×C4 | semidirect |
| 29. C2×C52×D4 | C2×C4 | semidirect |
| 30. C2×C5×C22⋊D5 | C2×C4 | semidirect |
| 31. C5×#713 | C2×C4 | semidirect |
| 33. C5×#711 | C2×C4 | semidirect |
| 34. C5×D4×D5 | C2×C4 | semidirect |
| 36. C5×#709 | C2×C4 | semidirect |
| 37. C2×C5×D20 | C2×C4 | semidirect |
| 46. #66266 | C2×C5 | semidirect |
| 47. #41×AGL(1,𝔽5) | C2×C5 | semidirect |
| 48. #66258 | C2×C5 | semidirect |
| 49. C2×D4×AGL(1,𝔽5) | C2×C5 | semidirect |
| 54. C23×C52 | C22×C4 | semidirect |
| 57. C22×C5×D5 | C22×C4 | semidirect |
| 65. C52×Q8 | C22×C4 | semidirect |
| 66. C52×D4 | C22×C4 | semidirect |
| 67. C2×C4×C52 | C22×C4 | semidirect |
| 68. C5×C22⋊D5 | C22×C4 | semidirect |
| 69. C2×C5×Dic5 | C22×C4 | semidirect |
| 70. C5×D20 | C22×C4 | semidirect |
| 71. C4×C5×D5 | C22×C4 | semidirect |
| 73. C5×Dic10 | C22×C4 | semidirect |
| 74. C23×AGL(1,𝔽5) | C22×C5 | semidirect |
| 78. C5×H(5,𝔽2) | C4×C5 | semidirect |
| 79. C5×H(5,𝔽2) | AGL(1,𝔽5) | direct (N × H) |
| 83. #4149 | C4×C5 | semidirect |
| 85. #4144 | C4×C5 | semidirect |
| 87. C2×C22⋊AGL(1,𝔽5) | C22×C5 | semidirect |
| 88. Q8×AGL(1,𝔽5) | C22×C5 | semidirect |
| 89. Q8×AGL(1,𝔽5) | C22×C5 | semidirect |
| 90. D4×AGL(1,𝔽5) | C22×C5 | semidirect |
| 91. D4×AGL(1,𝔽5) | C22×C5 | semidirect |
| 92. D4×AGL(1,𝔽5) | C22×C5 | semidirect |
| 93. #4130 | C22×C5 | semidirect |
| 94. C2×C4⋊AGL(1,𝔽5) | C22×C5 | semidirect |
| 95. C2×C4×AGL(1,𝔽5) | C22×C5 | semidirect |
| 115. C5×AGL(1,𝔽5) | H(5,𝔽2) | direct (N × H) |
| 128. C5×#41 | C2×C4×C5 | semidirect |
| 129. C5×#41 | C2×AGL(1,𝔽5) | semidirect |
| 136. C2×C5×D4 | C2×C4×C5 | semidirect |
| 137. C2×C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 143. C2×C22⋊D5 | C2×C4×C5 | semidirect |
| 144. #713 | C2×C4×C5 | semidirect |
| 146. #711 | C2×C4×C5 | semidirect |
| 147. D4×D5 | C2×C4×C5 | semidirect |
| 149. #709 | C2×C4×C5 | semidirect |
| 150. C2×D20 | C2×C4×C5 | semidirect |
| 177. C23×C5 | C22×C4×C5 | semidirect |
| 178. C23×C5 | C22×AGL(1,𝔽5) | semidirect |
| 181. C22×D5 | C22×C4×C5 | semidirect |
| 191. C5×Q8 | C22×C4×C5 | semidirect |
| 192. C5×Q8 | C22×AGL(1,𝔽5) | semidirect |
| 196. C5×D4 | C22×C4×C5 | semidirect |
| 197. C5×D4 | C22×AGL(1,𝔽5) | semidirect |
| 208. C2×C4×C5 | C22×C4×C5 | semidirect |
| 209. C2×C4×C5 | C22×AGL(1,𝔽5) | semidirect |
| 210. C22⋊D5 | C22×C4×C5 | semidirect |
| 211. C2×Dic5 | C22×C4×C5 | semidirect |
| 212. D20 | C22×C4×C5 | semidirect |
| 213. C4×D5 | C22×C4×C5 | semidirect |
| 215. Dic10 | C22×C4×C5 | semidirect |
| 218. H(5,𝔽2) | C5×AGL(1,𝔽5) | direct (N × H) |
| 231. C52 | C4×H(5,𝔽2) | semidirect |
| 250. AGL(1,𝔽5) | C5×H(5,𝔽2) | direct (N × H) |
| 263. #41 | C2×C5×AGL(1,𝔽5) | semidirect |
| 269. C2×D4 | C2×C5×AGL(1,𝔽5) | semidirect |
| 296. C23 | C22×C5×AGL(1,𝔽5) | semidirect |
| 298. Q8 | C22×C5×AGL(1,𝔽5) | semidirect |
| 301. D4 | C22×C5×AGL(1,𝔽5) | semidirect |
| 311. C2×C4 | C22×C5×AGL(1,𝔽5) | semidirect |
| 313. C5 | C4×C5×H(5,𝔽2) | semidirect |
| 314. C5 | 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