← C22×D5×H(5,𝔽2) #13013185
Subgroups — C22×D5×H(5,𝔽2) #13013185
Order 1280.
65726 conjugacy classes of subgroups.
The subgroup lattice has 264 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×C5×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D5×H(5,𝔽2) | C2 | 1 | 96 | yes | maximal, direct product factor |
| 3 | C22×#4149 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C22×D5×#41 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C22×#4144 | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | C23×D4×D5 | C2 | 1 | 9 | yes | maximal, complemented |
| 7 | C25×D5 | C22 | 1 | 6 | yes | complemented |
| 8 | C2×C5×H(5,𝔽2) | C22 | 1 | 48 | yes | complemented |
| 9 | C22×C5×#41 | C22 | 1 | 6 | yes | complemented |
| 10 | C23×C5×D4 | C22 | 1 | 9 | yes | complemented |
| 11 | C23×C22⋊D5 | C22 | 1 | 18 | yes | complemented |
| 12 | D5×H(5,𝔽2) | C22 | 1 | 1024 | yes | direct product factor |
| 13 | C2×#4149 | C22 | 1 | 288 | yes | complemented |
| 14 | C2×D5×#41 | C22 | 1 | 288 | yes | complemented |
| 15 | C22×#713 | C22 | 1 | 6 | yes | complemented |
| 16 | C22×Q8×D5 | C22 | 1 | 2 | yes | complemented |
| 17 | C2×#4144 | C22 | 1 | 432 | yes | complemented |
| 18 | C22×#711 | C22 | 1 | 18 | yes | complemented |
| 19 | C22×D4×D5 | C22 | 1 | 18 | yes | complemented |
| 20 | C22×D4×D5 | C22 | 1 | 36 | yes | complemented |
| 21 | C22×D4×D5 | C22 | 1 | 432 | yes | complemented |
| 22 | C22×#709 | C22 | 1 | 18 | yes | complemented |
| 23 | C23×D20 | C22 | 1 | 9 | yes | complemented |
| 24 | C23×C4×D5 | C22 | 1 | 9 | yes | complemented |
| 25 | C23×H(5,𝔽2) | — | 5 | 1 | no | maximal, Sylow |
| 26 | C25×C5 | C23 | 1 | 6 | yes | complemented |
| 27 | C24×D5 | — | 4 | 48 | no | — |
| 28 | C24×D5 | C23 | 1 | 9 | yes | — |
| 29 | C24×D5 | C23 | 1 | 144 | yes | complemented |
| 30 | C24×D5 | C23 | 1 | 18 | yes | complemented |
| 31 | C5×H(5,𝔽2) | C23 | 1 | 256 | yes | complemented |
| 32 | C2×C5×#41 | C23 | 1 | 144 | yes | complemented |
| 33 | C22×C5×Q8 | C23 | 1 | 2 | yes | complemented |
| 34 | C22×C5×D4 | C23 | 1 | 18 | yes | complemented |
| 35 | C22×C5×D4 | C23 | 1 | 216 | yes | complemented |
| 36 | C23×C4×C5 | C23 | 1 | 9 | yes | complemented |
| 37 | C22×C22⋊D5 | C23 | 1 | 36 | yes | complemented |
| 38 | C22×C22⋊D5 | C23 | 1 | 432 | yes | complemented |
| 39 | C23×Dic5 | C23 | 1 | 9 | yes | complemented |
| 40 | #4149 | C23 | 1 | 1536 | yes | complemented |
| 41 | D5×#41 | C23 | 1 | 1536 | yes | complemented |
| 42 | C2×#713 | C23 | 1 | 144 | yes | complemented |
| 43 | C2×Q8×D5 | C23 | 1 | 48 | yes | complemented |
| 44 | #4144 | C23 | 1 | 2304 | yes | complemented |
| 45 | C2×#711 | C23 | 1 | 432 | yes | complemented |
| 46 | C2×D4×D5 | C23 | 1 | 432 | yes | complemented |
| 47 | C2×D4×D5 | C23 | 1 | 864 | yes | complemented |
| 48 | C2×D4×D5 | C23 | 1 | 2304 | yes | complemented |
| 49 | C2×#709 | C23 | 1 | 432 | yes | complemented |
| 50 | C22×D20 | C23 | 1 | 18 | yes | complemented |
| 51 | C22×D20 | C23 | 1 | 216 | yes | complemented |
| 52 | C22×C4×D5 | C23 | 1 | 6 | yes | — |
| 53 | C22×C4×D5 | C23 | 1 | 216 | yes | complemented |
| 54 | C22×C4×D5 | C23 | 1 | 18 | yes | complemented |
| 55 | C22×Dic10 | C23 | 1 | 6 | yes | complemented |
| 56 | C22×H(5,𝔽2) | — | 5 | 96 | no | — |
| 57 | C22×H(5,𝔽2) | — | 5 | 6 | no | — |
| 58 | C22×H(5,𝔽2) | — | 5 | 9 | no | — |
| 59 | C22×H(5,𝔽2) | D5 | 1 | 1 | yes | characteristic, direct product factor |
| 60 | C23×#41 | — | 5 | 6 | no | — |
| 61 | C24×D4 | — | 5 | 9 | no | — |
| 62 | C24×C5 | — | 4 | 24 | no | — |
| 63 | C24×C5 | C24 | 1 | 9 | yes | — |
| 64 | C24×C5 | C24 | 1 | 72 | yes | complemented |
| 65 | C23×D5 | — | 2 | 72 | no | — |
| 66 | C23×D5 | — | 4 | 576 | no | — |
| 67 | C23×D5 | — | 4 | 72 | no | — |
| 68 | C23×D5 | C24 | 1 | 9 | yes | — |
| 69 | C23×D5 | C24 | 1 | 108 | yes | — |
| 70 | C23×D5 | C24 | 1 | 1 | yes | characteristic |
| 71 | C23×D5 | C24 | 1 | 384 | yes | complemented |
| 72 | C23×D5 | C24 | 1 | 216 | yes | complemented |
| 73 | C5×#41 | C24 | 1 | 384 | yes | complemented |
| 74 | C2×C5×Q8 | C24 | 1 | 24 | yes | complemented |
| 75 | C2×C5×D4 | C24 | 1 | 216 | yes | complemented |
| 76 | C2×C5×D4 | C24 | 1 | 576 | yes | complemented |
| 77 | C22×C4×C5 | C24 | 1 | 6 | yes | — |
| 78 | C22×C4×C5 | C24 | 1 | 108 | yes | complemented |
| 79 | C2×C22⋊D5 | C24 | 1 | 432 | yes | complemented |
| 80 | C2×C22⋊D5 | C24 | 1 | 1152 | yes | complemented |
| 81 | C22×Dic5 | C24 | 1 | 6 | yes | — |
| 82 | C22×Dic5 | C24 | 1 | 108 | yes | complemented |
| 83 | #713 | C24 | 1 | 384 | yes | complemented |
| 84 | Q8×D5 | C24 | 1 | 128 | yes | complemented |
| 85 | #711 | C24 | 1 | 1152 | yes | complemented |
| 86 | D4×D5 | C24 | 1 | 1152 | yes | complemented |
| 87 | D4×D5 | C24 | 1 | 2304 | yes | complemented |
| 88 | #709 | C24 | 1 | 1152 | yes | complemented |
| 89 | C2×D20 | C24 | 1 | 216 | yes | complemented |
| 90 | C2×D20 | C24 | 1 | 576 | yes | complemented |
| 91 | C2×C4×D5 | C24 | 1 | 72 | yes | — |
| 92 | C2×C4×D5 | C24 | 1 | 576 | yes | complemented |
| 93 | C2×C4×D5 | C24 | 1 | 216 | yes | complemented |
| 94 | C2×Dic10 | C24 | 1 | 72 | yes | complemented |
| 95 | C26 | — | 5 | 6 | no | — |
| 96 | C2×H(5,𝔽2) | — | 5 | 1024 | no | — |
| 97 | C2×H(5,𝔽2) | — | 5 | 288 | no | — |
| 98 | C2×H(5,𝔽2) | — | 5 | 432 | no | — |
| 99 | C2×H(5,𝔽2) | C2×D5 | 1 | 48 | yes | direct product factor |
| 100 | C22×#41 | — | 5 | 288 | no | — |
| 101 | C22×#41 | — | 5 | 6 | no | — |
| 102 | C22×#41 | — | 5 | 18 | no | — |
| 103 | C22×#41 | — | 5 | 18 | no | — |
| 104 | C22×#41 | C2×D5 | 1 | 6 | yes | complemented |
| 105 | C23×Q8 | — | 5 | 2 | no | — |
| 106 | C23×D4 | — | 5 | 18 | no | — |
| 107 | C23×D4 | — | 5 | 18 | no | — |
| 108 | C23×D4 | — | 5 | 36 | no | — |
| 109 | C23×D4 | — | 5 | 432 | no | — |
| 110 | C23×D4 | — | 5 | 9 | no | — |
| 111 | C23×D4 | C2×D5 | 1 | 9 | yes | complemented |
| 112 | C24×C4 | — | 5 | 9 | no | — |
| 113 | C23×C5 | — | 2 | 36 | no | — |
| 114 | C23×C5 | — | 4 | 144 | no | — |
| 115 | C23×C5 | C25 | 1 | 54 | yes | — |
| 116 | C23×C5 | C25 | 1 | 1 | yes | characteristic |
| 117 | C23×C5 | C25 | 1 | 96 | yes | complemented |
| 118 | C22×D5 | — | 2 | 36 | no | — |
| 119 | C22×D5 | — | 2 | 432 | no | — |
| 120 | C22×D5 | — | 4 | 768 | no | — |
| 121 | C22×D5 | — | 4 | 432 | no | — |
| 122 | C22×D5 | H(5,𝔽2) | 1 | 8 | yes | direct product factor |
| 123 | C22×D5 | C25 | 1 | 54 | yes | — |
| 124 | C22×D5 | C25 | 1 | 144 | yes | — |
| 125 | C22×D5 | C25 | 1 | 6 | yes | — |
| 126 | C22×D5 | C25 | 1 | 288 | yes | complemented |
| 127 | C5×Q8 | C25 | 1 | 32 | yes | complemented |
| 128 | C5×D4 | C25 | 1 | 288 | yes | complemented |
| 129 | C2×C4×C5 | C25 | 1 | 36 | yes | — |
| 130 | C2×C4×C5 | C25 | 1 | 144 | yes | complemented |
| 131 | C22⋊D5 | C25 | 1 | 576 | yes | complemented |
| 132 | C2×Dic5 | C25 | 1 | 36 | yes | — |
| 133 | C2×Dic5 | C25 | 1 | 144 | yes | complemented |
| 134 | D20 | C25 | 1 | 288 | yes | complemented |
| 135 | C4×D5 | C25 | 1 | 96 | yes | — |
| 136 | C4×D5 | C25 | 1 | 288 | yes | complemented |
| 137 | Dic10 | C25 | 1 | 96 | yes | complemented |
| 138 | C25 | — | 5 | 9 | no | — |
| 139 | C25 | — | 5 | 18 | no | — |
| 140 | C25 | — | 5 | 144 | no | — |
| 141 | C25 | — | 20 | 48 | no | — |
| 142 | C25 | C22×D5 | 1 | 6 | yes | complemented |
| 143 | H(5,𝔽2) | — | 5 | 1536 | no | — |
| 144 | H(5,𝔽2) | — | 5 | 2304 | no | — |
| 145 | H(5,𝔽2) | C22×D5 | 1 | 256 | yes | direct product factor |
| 146 | C2×#41 | — | 5 | 1536 | no | — |
| 147 | C2×#41 | — | 5 | 144 | no | — |
| 148 | C2×#41 | — | 5 | 432 | no | — |
| 149 | C2×#41 | — | 5 | 432 | no | — |
| 150 | C2×#41 | C22×D5 | 1 | 144 | yes | complemented |
| 151 | C22×Q8 | — | 5 | 48 | no | — |
| 152 | C22×Q8 | — | 5 | 6 | no | — |
| 153 | C22×Q8 | C22×D5 | 1 | 2 | yes | complemented |
| 154 | C22×D4 | — | 5 | 36 | no | — |
| 155 | C22×D4 | — | 5 | 432 | no | — |
| 156 | C22×D4 | — | 5 | 432 | no | — |
| 157 | C22×D4 | — | 5 | 864 | no | — |
| 158 | C22×D4 | — | 5 | 2304 | no | — |
| 159 | C22×D4 | — | 5 | 18 | no | — |
| 160 | C22×D4 | — | 5 | 216 | no | — |
| 161 | C22×D4 | C22×D5 | 1 | 18 | yes | complemented |
| 162 | C22×D4 | C22×D5 | 1 | 216 | yes | complemented |
| 163 | C23×C4 | — | 5 | 9 | no | — |
| 164 | C23×C4 | — | 5 | 6 | no | — |
| 165 | C23×C4 | — | 5 | 18 | no | — |
| 166 | C23×C4 | — | 5 | 216 | no | — |
| 167 | C23×C4 | C22×D5 | 1 | 9 | yes | complemented |
| 168 | C22×C5 | — | 2 | 108 | no | — |
| 169 | C22×C5 | — | 4 | 96 | no | — |
| 170 | C22×C5 | C2×H(5,𝔽2) | 1 | 4 | yes | complemented |
| 171 | C22×C5 | C26 | 1 | 36 | yes | — |
| 172 | C22×C5 | C26 | 1 | 3 | yes | — |
| 173 | C2×D5 | — | 2 | 108 | no | — |
| 174 | C2×D5 | — | 2 | 288 | no | — |
| 175 | C2×D5 | — | 4 | 288 | no | — |
| 176 | C2×D5 | C2×H(5,𝔽2) | 1 | 24 | yes | direct product factor |
| 177 | C2×D5 | C26 | 1 | 36 | yes | — |
| 178 | C2×D5 | C26 | 1 | 4 | yes | — |
| 179 | C4×C5 | C26 | 1 | 24 | yes | — |
| 180 | Dic5 | C26 | 1 | 24 | yes | — |
| 181 | C24 | — | 4 | 24 | no | — |
| 182 | C24 | — | 5 | 1 | no | — |
| 183 | C24 | — | 5 | 108 | no | — |
| 184 | C24 | — | 5 | 9 | no | — |
| 185 | C24 | — | 5 | 216 | no | — |
| 186 | C24 | — | 5 | 384 | no | — |
| 187 | C24 | — | 10 | 72 | no | — |
| 188 | C24 | — | 20 | 72 | no | — |
| 189 | C24 | — | 20 | 576 | no | — |
| 190 | C24 | C23×D5 | 1 | 9 | yes | — |
| 191 | C24 | C23×D5 | 1 | 72 | yes | complemented |
| 192 | #41 | — | 5 | 384 | no | — |
| 193 | #41 | — | 5 | 1152 | no | — |
| 194 | #41 | — | 5 | 1152 | no | — |
| 195 | #41 | C23×D5 | 1 | 384 | yes | complemented |
| 196 | C2×Q8 | — | 5 | 128 | no | — |
| 197 | C2×Q8 | — | 5 | 72 | no | — |
| 198 | C2×Q8 | C23×D5 | 1 | 24 | yes | complemented |
| 199 | C2×D4 | — | 5 | 432 | no | — |
| 200 | C2×D4 | — | 5 | 1152 | no | — |
| 201 | C2×D4 | — | 5 | 1152 | no | — |
| 202 | C2×D4 | — | 5 | 2304 | no | — |
| 203 | C2×D4 | — | 5 | 216 | no | — |
| 204 | C2×D4 | — | 5 | 576 | no | — |
| 205 | C2×D4 | C23×D5 | 1 | 216 | yes | complemented |
| 206 | C2×D4 | C23×D5 | 1 | 576 | yes | complemented |
| 207 | C22×C4 | — | 5 | 108 | no | — |
| 208 | C22×C4 | — | 5 | 6 | no | — |
| 209 | C22×C4 | — | 5 | 72 | no | — |
| 210 | C22×C4 | — | 5 | 216 | no | — |
| 211 | C22×C4 | — | 5 | 576 | no | — |
| 212 | C22×C4 | C23×D5 | 1 | 6 | yes | — |
| 213 | C22×C4 | C23×D5 | 1 | 108 | yes | complemented |
| 214 | C2×C5 | — | 2 | 36 | no | — |
| 215 | C2×C5 | C22×H(5,𝔽2) | 1 | 6 | yes | complemented |
| 216 | C2×C5 | C27 | 1 | 1 | yes | characteristic |
| 217 | D5 | — | 2 | 36 | no | — |
| 218 | D5 | C22×H(5,𝔽2) | 1 | 8 | yes | direct product factor |
| 219 | C23 | — | 2 | 36 | no | — |
| 220 | C23 | — | 4 | 144 | no | — |
| 221 | C23 | — | 5 | 8 | no | — |
| 222 | C23 | — | 5 | 6 | no | — |
| 223 | C23 | — | 5 | 144 | no | — |
| 224 | C23 | — | 5 | 54 | no | — |
| 225 | C23 | — | 5 | 288 | no | — |
| 226 | C23 | — | 10 | 432 | no | — |
| 227 | C23 | — | 10 | 36 | no | — |
| 228 | C23 | — | 20 | 432 | no | — |
| 229 | C23 | — | 20 | 768 | no | — |
| 230 | C23 | C24×D5 | 1 | 54 | yes | — |
| 231 | C23 | C24×D5 | 1 | 1 | yes | characteristic |
| 232 | C23 | C24×D5 | 1 | 96 | yes | complemented |
| 233 | Q8 | — | 5 | 96 | no | — |
| 234 | Q8 | C24×D5 | 1 | 32 | yes | complemented |
| 235 | D4 | — | 5 | 576 | no | — |
| 236 | D4 | — | 5 | 288 | no | — |
| 237 | D4 | C24×D5 | 1 | 288 | yes | complemented |
| 238 | C2×C4 | — | 5 | 36 | no | — |
| 239 | C2×C4 | — | 5 | 144 | no | — |
| 240 | C2×C4 | — | 5 | 96 | no | — |
| 241 | C2×C4 | — | 5 | 288 | no | — |
| 242 | C2×C4 | C24×D5 | 1 | 36 | yes | — |
| 243 | C2×C4 | C24×D5 | 1 | 144 | yes | complemented |
| 244 | C5 | C23×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 245 | C22 | — | 2 | 108 | no | — |
| 246 | C22 | — | 4 | 96 | no | — |
| 247 | C22 | — | 5 | 24 | no | — |
| 248 | C22 | — | 5 | 4 | no | — |
| 249 | C22 | — | 5 | 36 | no | — |
| 250 | C22 | — | 10 | 288 | no | — |
| 251 | C22 | — | 10 | 108 | no | — |
| 252 | C22 | — | 20 | 288 | no | — |
| 253 | C22 | D5×H(5,𝔽2) | 1 | 4 | yes | direct product factor |
| 254 | C22 | C25×D5 | 1 | 36 | yes | — |
| 255 | C22 | C25×D5 | 1 | 3 | yes | — |
| 256 | C4 | — | 5 | 24 | no | — |
| 257 | C4 | C25×D5 | 1 | 24 | yes | — |
| 258 | C2 | — | 2 | 36 | no | — |
| 259 | C2 | — | 5 | 8 | no | — |
| 260 | C2 | — | 10 | 36 | no | — |
| 261 | C2 | C2×D5×H(5,𝔽2) | 1 | 6 | yes | direct product factor |
| 262 | C2 | C26×D5 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C22×C5×H(5,𝔽2) | C2 | semidirect |
| 2. C2×D5×H(5,𝔽2) | C2 | direct (N × H) |
| 3. C22×#4149 | C2 | semidirect |
| 4. C22×D5×#41 | C2 | semidirect |
| 5. C22×#4144 | C2 | semidirect |
| 6. C23×D4×D5 | C2 | semidirect |
| 7. C25×D5 | C22 | semidirect |
| 8. C2×C5×H(5,𝔽2) | C22 | semidirect |
| 9. C22×C5×#41 | C22 | semidirect |
| 10. C23×C5×D4 | C22 | semidirect |
| 11. C23×C22⋊D5 | C22 | semidirect |
| 12. D5×H(5,𝔽2) | C22 | direct (N × H) |
| 13. C2×#4149 | C22 | semidirect |
| 14. C2×D5×#41 | C22 | semidirect |
| 15. C22×#713 | C22 | semidirect |
| 16. C22×Q8×D5 | C22 | semidirect |
| 17. C2×#4144 | C22 | semidirect |
| 18. C22×#711 | C22 | semidirect |
| 19. C22×D4×D5 | C22 | semidirect |
| 20. C22×D4×D5 | C22 | semidirect |
| 21. C22×D4×D5 | C22 | semidirect |
| 22. C22×#709 | C22 | semidirect |
| 23. C23×D20 | C22 | semidirect |
| 24. C23×C4×D5 | C22 | semidirect |
| 26. C25×C5 | C23 | semidirect |
| 29. C24×D5 | C23 | semidirect |
| 30. C24×D5 | C23 | semidirect |
| 31. C5×H(5,𝔽2) | C23 | semidirect |
| 32. C2×C5×#41 | C23 | semidirect |
| 33. C22×C5×Q8 | C23 | semidirect |
| 34. C22×C5×D4 | C23 | semidirect |
| 35. C22×C5×D4 | C23 | semidirect |
| 36. C23×C4×C5 | C23 | semidirect |
| 37. C22×C22⋊D5 | C23 | semidirect |
| 38. C22×C22⋊D5 | C23 | semidirect |
| 39. C23×Dic5 | C23 | semidirect |
| 40. #4149 | C23 | semidirect |
| 41. D5×#41 | C23 | semidirect |
| 42. C2×#713 | C23 | semidirect |
| 43. C2×Q8×D5 | C23 | semidirect |
| 44. #4144 | C23 | semidirect |
| 45. C2×#711 | C23 | semidirect |
| 46. C2×D4×D5 | C23 | semidirect |
| 47. C2×D4×D5 | C23 | semidirect |
| 48. C2×D4×D5 | C23 | semidirect |
| 49. C2×#709 | C23 | semidirect |
| 50. C22×D20 | C23 | semidirect |
| 51. C22×D20 | C23 | semidirect |
| 53. C22×C4×D5 | C23 | semidirect |
| 54. C22×C4×D5 | C23 | semidirect |
| 55. C22×Dic10 | C23 | semidirect |
| 59. C22×H(5,𝔽2) | D5 | direct (N × H) |
| 64. C24×C5 | C24 | semidirect |
| 71. C23×D5 | C24 | semidirect |
| 72. C23×D5 | C24 | semidirect |
| 73. C5×#41 | C24 | semidirect |
| 74. C2×C5×Q8 | C24 | semidirect |
| 75. C2×C5×D4 | C24 | semidirect |
| 76. C2×C5×D4 | C24 | semidirect |
| 78. C22×C4×C5 | C24 | semidirect |
| 79. C2×C22⋊D5 | C24 | semidirect |
| 80. C2×C22⋊D5 | C24 | semidirect |
| 82. C22×Dic5 | C24 | semidirect |
| 83. #713 | C24 | semidirect |
| 84. Q8×D5 | C24 | semidirect |
| 85. #711 | C24 | semidirect |
| 86. D4×D5 | C24 | semidirect |
| 87. D4×D5 | C24 | semidirect |
| 88. #709 | C24 | semidirect |
| 89. C2×D20 | C24 | semidirect |
| 90. C2×D20 | C24 | semidirect |
| 92. C2×C4×D5 | C24 | semidirect |
| 93. C2×C4×D5 | C24 | semidirect |
| 94. C2×Dic10 | C24 | semidirect |
| 99. C2×H(5,𝔽2) | C2×D5 | direct (N × H) |
| 104. C22×#41 | C2×D5 | semidirect |
| 111. C23×D4 | C2×D5 | semidirect |
| 117. C23×C5 | C25 | semidirect |
| 122. C22×D5 | H(5,𝔽2) | direct (N × H) |
| 126. C22×D5 | C25 | semidirect |
| 127. C5×Q8 | C25 | semidirect |
| 128. C5×D4 | C25 | semidirect |
| 130. C2×C4×C5 | C25 | semidirect |
| 131. C22⋊D5 | C25 | semidirect |
| 133. C2×Dic5 | C25 | semidirect |
| 134. D20 | C25 | semidirect |
| 136. C4×D5 | C25 | semidirect |
| 137. Dic10 | C25 | semidirect |
| 142. C25 | C22×D5 | semidirect |
| 145. H(5,𝔽2) | C22×D5 | direct (N × H) |
| 150. C2×#41 | C22×D5 | semidirect |
| 153. C22×Q8 | C22×D5 | semidirect |
| 161. C22×D4 | C22×D5 | semidirect |
| 162. C22×D4 | C22×D5 | semidirect |
| 167. C23×C4 | C22×D5 | semidirect |
| 170. C22×C5 | C2×H(5,𝔽2) | semidirect |
| 176. C2×D5 | C2×H(5,𝔽2) | direct (N × H) |
| 191. C24 | C23×D5 | semidirect |
| 195. #41 | C23×D5 | semidirect |
| 198. C2×Q8 | C23×D5 | semidirect |
| 205. C2×D4 | C23×D5 | semidirect |
| 206. C2×D4 | C23×D5 | semidirect |
| 213. C22×C4 | C23×D5 | semidirect |
| 215. C2×C5 | C22×H(5,𝔽2) | semidirect |
| 218. D5 | C22×H(5,𝔽2) | direct (N × H) |
| 232. C23 | C24×D5 | semidirect |
| 234. Q8 | C24×D5 | semidirect |
| 237. D4 | C24×D5 | semidirect |
| 243. C2×C4 | C24×D5 | semidirect |
| 244. C5 | C23×H(5,𝔽2) | semidirect |
| 253. C22 | D5×H(5,𝔽2) | direct (N × H) |
| 261. C2 | C2×D5×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