Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1030 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10618944 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617208 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10617202 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10604624 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #10604621 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10604426 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10604423 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×Q8×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 9 | C5×Q82 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #66067 | — | 2 | 3 | no | — |
| 11 | #66064 | C4 | 1 | 3 | yes | complemented |
| 12 | #66060 | — | 2 | 3 | no | — |
| 13 | #66059 | C22 | 1 | 3 | yes | — |
| 14 | #65919 | C4 | 1 | 3 | yes | complemented |
| 15 | #65914 | C22 | 1 | 3 | yes | — |
| 16 | #65911 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #65910 | — | 2 | 1 | no | — |
| 18 | #65908 | — | 2 | 1 | no | — |
| 19 | C4×Q8×D5 | C22 | 1 | 1 | yes | characteristic |
| 20 | Q8×#170 | — | 2 | 1 | no | — |
| 21 | C4⋊C4×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 22 | #65709 | — | 2 | 3 | no | — |
| 23 | C4×C4⋊AGL(1,𝔽5) | C22 | 1 | 3 | yes | — |
| 24 | #65686 | C22 | 1 | 3 | yes | — |
| 25 | #65683 | C22 | 1 | 3 | yes | — |
| 26 | #65680 | C22 | 1 | 3 | yes | — |
| 27 | #64926 | C22 | 1 | 1 | yes | characteristic |
| 28 | #64926 | C22 | 1 | 3 | yes | — |
| 29 | #64868 | C22 | 1 | 3 | yes | — |
| 30 | #64868 | C22 | 1 | 6 | yes | — |
| 31 | #64868 | C22 | 1 | 3 | yes | — |
| 32 | #17550 | — | 5 | 1 | no | maximal, Sylow |
| 33 | C2×#713 | — | 2 | 1 | no | — |
| 34 | C2×#713 | — | 2 | 3 | no | — |
| 35 | C2×Q8×D5 | D4 | 1 | 1 | yes | characteristic |
| 36 | Q8×AGL(1,𝔽5) | — | 2 | 8 | no | — |
| 37 | C2×C4⋊AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 38 | C2×C4×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 39 | C2×C4×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 40 | C5×C4⋊Q8 | — | 2 | 3 | no | — |
| 41 | C5×C4⋊Q8 | C2×C4 | 1 | 3 | yes | — |
| 42 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 43 | C4×C5×Q8 | C2×C4 | 1 | 3 | yes | — |
| 44 | C4×C5×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #4093 | — | 2 | 3 | no | — |
| 46 | #4093 | C2×C4 | 1 | 3 | yes | — |
| 47 | #4092 | — | 2 | 6 | no | — |
| 48 | #4092 | C23 | 1 | 1 | yes | characteristic |
| 49 | Q8×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 50 | #4044 | — | 2 | 3 | no | — |
| 51 | #4043 | — | 2 | 3 | no | — |
| 52 | #4041 | — | 2 | 3 | no | — |
| 53 | #4041 | — | 2 | 3 | no | — |
| 54 | #4041 | C23 | 1 | 3 | yes | — |
| 55 | #4040 | — | 2 | 3 | no | — |
| 56 | #4040 | — | 2 | 6 | no | — |
| 57 | #4039 | — | 2 | 3 | no | — |
| 58 | #4039 | C2×C4 | 1 | 6 | yes | — |
| 59 | D5×C4⋊C4 | — | 2 | 3 | no | — |
| 60 | D5×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 61 | #4036 | C2×C4 | 1 | 3 | yes | — |
| 62 | #4033 | D4 | 1 | 3 | yes | — |
| 63 | #4021 | — | 2 | 3 | no | — |
| 64 | #4020 | C2×C4 | 1 | 3 | yes | — |
| 65 | C4×D20 | — | 2 | 3 | no | — |
| 66 | C4×D20 | — | 2 | 3 | no | — |
| 67 | C4×D20 | C2×C4 | 1 | 3 | yes | — |
| 68 | #4018 | — | 2 | 3 | no | — |
| 69 | C42×D5 | C23 | 1 | 3 | yes | — |
| 70 | C4×Dic10 | C2×C4 | 1 | 3 | yes | — |
| 71 | (C2×AGL(1,𝔽5))⋊C4 | — | 2 | 3 | no | — |
| 72 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 73 | (C2×AGL(1,𝔽5))⋊C4 | C23 | 1 | 3 | yes | — |
| 74 | #4003 | C23 | 1 | 1 | yes | characteristic |
| 75 | #4003 | C23 | 1 | 3 | yes | — |
| 76 | #4002 | — | 2 | 3 | no | — |
| 77 | C4⋊#170 | — | 2 | 3 | no | — |
| 78 | C4⋊#170 | — | 2 | 3 | no | — |
| 79 | C4×#170 | — | 2 | 3 | no | — |
| 80 | #3522 | — | 5 | 1 | no | — |
| 81 | #2984 | — | 5 | 1 | no | — |
| 82 | #2276 | — | 5 | 1 | no | — |
| 83 | #1509 | — | 5 | 3 | no | — |
| 84 | #1505 | — | 5 | 3 | no | — |
| 85 | #1502 | — | 5 | 3 | no | — |
| 86 | #1500 | — | 5 | 3 | no | — |
| 87 | C22×AGL(1,𝔽5) | — | 2 | 3 | no | — |
| 88 | C22×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 89 | C2×C5×Q8 | — | 2 | 3 | no | — |
| 90 | C2×C5×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 91 | C2×C5×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 92 | #713 | — | 4 | 4 | no | — |
| 93 | #713 | — | 8 | 3 | no | — |
| 94 | #713 | — | 8 | 3 | no | — |
| 95 | Q8×D5 | — | 2 | 4 | no | — |
| 96 | C2×D20 | — | 2 | 3 | no | — |
| 97 | C2×D20 | — | 2 | 3 | no | — |
| 98 | C2×D20 | — | 2 | 3 | no | — |
| 99 | C2×D20 | C22×C4 | 1 | 3 | yes | — |
| 100 | C2×C4×D5 | — | 2 | 3 | no | — |
| 101 | C2×C4×D5 | — | 2 | 6 | no | — |
| 102 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 103 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 104 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 105 | C2×Dic10 | C22⋊C4 | 1 | 3 | yes | — |
| 106 | C2×#170 | — | 2 | 1 | no | — |
| 107 | C2×#170 | — | 2 | 3 | no | — |
| 108 | C4⋊AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 109 | C4×AGL(1,𝔽5) | — | 2 | 12 | no | — |
| 110 | C4×AGL(1,𝔽5) | — | 8 | 3 | no | — |
| 111 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 112 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 113 | C5×C4⋊C4 | C22⋊C4 | 1 | 3 | yes | — |
| 114 | C5×C4⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 115 | C42×C5 | — | 2 | 3 | no | — |
| 116 | C42×C5 | C22×C4 | 1 | 3 | yes | — |
| 117 | #685 | — | 2 | 1 | no | — |
| 118 | #685 | — | 2 | 3 | no | — |
| 119 | #685 | — | 2 | 3 | no | — |
| 120 | #685 | — | 2 | 3 | no | — |
| 121 | #685 | — | 2 | 6 | no | — |
| 122 | #685 | — | 2 | 3 | no | — |
| 123 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 124 | C4⋊Dic5 | C22⋊C4 | 1 | 3 | yes | — |
| 125 | C4⋊Dic5 | C22×C4 | 1 | 1 | yes | characteristic |
| 126 | #683 | — | 2 | 3 | no | — |
| 127 | #683 | — | 2 | 1 | no | — |
| 128 | #683 | C22⋊C4 | 1 | 6 | yes | — |
| 129 | C4×Dic5 | C22×C4 | 1 | 3 | yes | — |
| 130 | C4×Dic5 | C2×D4 | 1 | 3 | yes | — |
| 131 | C4×Dic5 | C2×D4 | 1 | 3 | yes | — |
| 132 | #559 | — | 5 | 3 | no | — |
| 133 | Q82 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 134 | #554 | — | 5 | 3 | no | — |
| 135 | #550 | — | 5 | 1 | no | — |
| 136 | #548 | — | 10 | 1 | no | — |
| 137 | #547 | — | 10 | 3 | no | — |
| 138 | #542 | — | 10 | 3 | no | — |
| 139 | #532 | — | 5 | 3 | no | — |
| 140 | #529 | — | 5 | 3 | no | — |
| 141 | #520 | — | 10 | 1 | no | — |
| 142 | C2×C4×Q8 | — | 5 | 1 | no | — |
| 143 | C2×C4×Q8 | — | 10 | 1 | no | — |
| 144 | #446 | — | 10 | 3 | no | — |
| 145 | C8×Q8 | — | 10 | 1 | no | — |
| 146 | #432 | — | 5 | 3 | no | — |
| 147 | #431 | — | 5 | 3 | no | — |
| 148 | C4×C4⋊C4 | — | 5 | 3 | no | — |
| 149 | C4×C4⋊C4 | — | 10 | 3 | no | — |
| 150 | #376 | — | 5 | 3 | no | — |
| 151 | #328 | — | 5 | 1 | no | — |
| 152 | #328 | — | 5 | 3 | no | — |
| 153 | #327 | — | 5 | 3 | no | — |
| 154 | #327 | — | 5 | 3 | no | — |
| 155 | #327 | — | 5 | 6 | no | — |
| 156 | C22×D5 | — | 2 | 3 | no | — |
| 157 | C22×D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 159 | C2×AGL(1,𝔽5) | — | 2 | 6 | no | — |
| 160 | C2×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 161 | C2×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 162 | C2×AGL(1,𝔽5) | — | 4 | 3 | no | — |
| 163 | C2×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 164 | C5×Q8 | — | 4 | 1 | no | — |
| 165 | C5×Q8 | — | 8 | 3 | no | — |
| 166 | C5×Q8 | #104 | 1 | 4 | yes | — |
| 167 | C2×C4×C5 | — | 2 | 3 | no | — |
| 168 | C2×C4×C5 | — | 2 | 1 | no | — |
| 169 | C2×C4×C5 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 170 | C2×C4×C5 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 171 | C2×C4×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 172 | C2×Dic5 | — | 2 | 1 | no | — |
| 173 | C2×Dic5 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 174 | C2×Dic5 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 175 | C2×Dic5 | C22×D4 | 1 | 1 | yes | characteristic |
| 176 | D20 | — | 4 | 3 | no | — |
| 177 | D20 | — | 4 | 3 | no | — |
| 178 | D20 | — | 4 | 3 | no | — |
| 179 | D20 | — | 4 | 6 | no | — |
| 180 | D20 | — | 8 | 3 | no | — |
| 181 | C4×D5 | — | 2 | 3 | no | — |
| 182 | C4×D5 | — | 2 | 3 | no | — |
| 183 | C4×D5 | — | 2 | 6 | no | — |
| 184 | C4×D5 | — | 4 | 1 | no | — |
| 185 | C4×D5 | — | 4 | 6 | no | — |
| 186 | C4×D5 | — | 8 | 6 | no | — |
| 187 | Dic10 | — | 2 | 6 | no | — |
| 188 | #170 | — | 4 | 1 | no | — |
| 189 | #170 | — | 4 | 3 | no | — |
| 190 | C2×#41 | — | 10 | 3 | no | — |
| 191 | C2×#41 | — | 10 | 1 | no | — |
| 192 | C22×Q8 | — | 5 | 1 | no | — |
| 193 | C4⋊Q8 | — | 2 | 3 | no | — |
| 194 | C4⋊Q8 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 195 | #127 | — | 5 | 3 | no | — |
| 196 | #126 | — | 10 | 3 | no | — |
| 197 | #125 | — | 5 | 3 | no | — |
| 198 | #124 | — | 5 | 3 | no | — |
| 199 | #124 | — | 10 | 3 | no | — |
| 200 | #124 | — | 10 | 3 | no | — |
| 201 | #123 | — | 10 | 6 | no | — |
| 202 | #123 | — | 10 | 3 | no | — |
| 203 | C22⋊Q8 | — | 5 | 1 | no | — |
| 204 | C22⋊Q8 | — | 10 | 3 | no | — |
| 205 | C22⋊Q8 | — | 10 | 6 | no | — |
| 206 | #121 | — | 5 | 3 | no | — |
| 207 | #121 | — | 10 | 3 | no | — |
| 208 | #121 | — | 10 | 3 | no | — |
| 209 | C4×Q8 | — | 2 | 1 | no | — |
| 210 | C4×Q8 | — | 5 | 1 | no | — |
| 211 | C4×Q8 | — | 5 | 3 | no | — |
| 212 | C4×Q8 | — | 5 | 3 | no | — |
| 213 | C4×Q8 | — | 10 | 8 | no | — |
| 214 | C4×Q8 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 215 | C4×Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 216 | C4×D4 | — | 5 | 6 | no | — |
| 217 | C4×D4 | — | 5 | 3 | no | — |
| 218 | C4×D4 | — | 10 | 3 | no | — |
| 219 | C4×D4 | — | 10 | 3 | no | — |
| 220 | C4×D4 | — | 10 | 3 | no | — |
| 221 | #117 | — | 10 | 3 | no | — |
| 222 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 223 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 224 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 225 | C2×C42 | — | 5 | 3 | no | — |
| 226 | C2×C42 | — | 10 | 3 | no | — |
| 227 | C2×C42 | — | 10 | 3 | no | — |
| 228 | C4⋊C8 | — | 10 | 3 | no | — |
| 229 | C4⋊C8 | — | 10 | 3 | no | — |
| 230 | C22⋊C8 | — | 5 | 1 | no | — |
| 231 | C22⋊C8 | — | 5 | 3 | no | — |
| 232 | #97 | — | 10 | 3 | no | — |
| 233 | C4×C8 | — | 10 | 3 | no | — |
| 234 | #95 | — | 5 | 1 | no | — |
| 235 | #95 | — | 5 | 3 | no | — |
| 236 | #95 | — | 10 | 3 | no | — |
| 237 | C22×C5 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 238 | C2×D5 | — | 2 | 1 | no | — |
| 239 | C2×D5 | — | 2 | 1 | no | — |
| 240 | C2×D5 | — | 4 | 3 | no | — |
| 241 | C2×D5 | — | 4 | 3 | no | — |
| 242 | C2×D5 | — | 4 | 3 | no | — |
| 243 | C2×D5 | #576 | 1 | 1 | yes | characteristic |
| 244 | C2×D5 | #577 | 1 | 1 | yes | characteristic |
| 245 | AGL(1,𝔽5) | — | 4 | 6 | no | — |
| 246 | AGL(1,𝔽5) | — | 4 | 2 | no | — |
| 247 | C4×C5 | — | 2 | 1 | no | — |
| 248 | C4×C5 | — | 2 | 3 | no | — |
| 249 | C4×C5 | — | 4 | 1 | no | — |
| 250 | C4×C5 | — | 4 | 3 | no | — |
| 251 | C4×C5 | C2×#104 | 1 | 6 | yes | — |
| 252 | Dic5 | — | 2 | 1 | no | — |
| 253 | Dic5 | — | 2 | 3 | no | — |
| 254 | Dic5 | — | 2 | 3 | no | — |
| 255 | Dic5 | — | 4 | 1 | no | — |
| 256 | #41 | — | 20 | 4 | no | — |
| 257 | #41 | — | 40 | 3 | no | — |
| 258 | #41 | — | 40 | 3 | no | — |
| 259 | C2×Q8 | — | 2 | 3 | no | — |
| 260 | C2×Q8 | — | 5 | 3 | no | — |
| 261 | C2×Q8 | — | 10 | 4 | no | — |
| 262 | C2×Q8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 263 | C2×Q8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 264 | C2×D4 | — | 5 | 3 | no | — |
| 265 | C2×D4 | — | 10 | 3 | no | — |
| 266 | C2×D4 | — | 10 | 3 | no | — |
| 267 | C2×D4 | — | 10 | 3 | no | — |
| 268 | C22×C4 | — | 5 | 3 | no | — |
| 269 | C22×C4 | — | 5 | 3 | no | — |
| 270 | C22×C4 | — | 5 | 1 | no | — |
| 271 | C22×C4 | — | 10 | 6 | no | — |
| 272 | C22×C4 | — | 10 | 1 | no | — |
| 273 | C22×C4 | — | 10 | 3 | no | — |
| 274 | C22×C4 | — | 10 | 3 | no | — |
| 275 | C2×C8 | — | 10 | 1 | no | — |
| 276 | C2×C8 | — | 10 | 3 | no | — |
| 277 | C4⋊C4 | — | 2 | 3 | no | — |
| 278 | C4⋊C4 | — | 2 | 3 | no | — |
| 279 | C4⋊C4 | — | 5 | 3 | no | — |
| 280 | C4⋊C4 | — | 5 | 6 | no | — |
| 281 | C4⋊C4 | — | 5 | 1 | no | — |
| 282 | C4⋊C4 | — | 10 | 3 | no | — |
| 283 | C4⋊C4 | — | 10 | 1 | no | — |
| 284 | C4⋊C4 | — | 10 | 3 | no | — |
| 285 | C4⋊C4 | — | 10 | 12 | no | — |
| 286 | C4⋊C4 | C22⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 287 | C4⋊C4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 288 | C22⋊C4 | — | 10 | 3 | no | — |
| 289 | C22⋊C4 | — | 10 | 3 | no | — |
| 290 | C22⋊C4 | — | 10 | 6 | no | — |
| 291 | C22⋊C4 | — | 10 | 3 | no | — |
| 292 | C22⋊C4 | — | 10 | 1 | no | — |
| 293 | C22⋊C4 | — | 10 | 3 | no | — |
| 294 | C42 | — | 2 | 3 | no | — |
| 295 | C42 | — | 5 | 3 | no | — |
| 296 | C42 | — | 5 | 3 | no | — |
| 297 | C42 | — | 5 | 3 | no | — |
| 298 | C42 | — | 10 | 12 | no | — |
| 299 | C42 | — | 40 | 3 | no | — |
| 300 | C42 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 301 | C2×C5 | #2884 | 1 | 1 | yes | characteristic |
| 302 | C2×C5 | #2897 | 1 | 1 | yes | characteristic |
| 303 | C2×C5 | C22×#104 | 1 | 1 | yes | characteristic |
| 304 | D5 | — | 2 | 1 | no | — |
| 305 | D5 | — | 2 | 1 | no | — |
| 306 | D5 | — | 8 | 3 | no | — |
| 307 | C23 | — | 5 | 1 | no | — |
| 308 | C23 | — | 10 | 3 | no | — |
| 309 | Q8 | — | 4 | 1 | no | — |
| 310 | Q8 | — | 8 | 3 | no | — |
| 311 | Q8 | — | 10 | 6 | no | — |
| 312 | Q8 | #4010 | 1 | 4 | yes | — |
| 313 | D4 | — | 20 | 3 | no | — |
| 314 | D4 | — | 20 | 3 | no | — |
| 315 | D4 | — | 20 | 3 | no | — |
| 316 | D4 | — | 20 | 6 | no | — |
| 317 | D4 | — | 40 | 3 | no | — |
| 318 | C2×C4 | — | 2 | 1 | no | — |
| 319 | C2×C4 | — | 2 | 3 | no | — |
| 320 | C2×C4 | — | 5 | 1 | no | — |
| 321 | C2×C4 | — | 5 | 3 | no | — |
| 322 | C2×C4 | — | 5 | 3 | no | — |
| 323 | C2×C4 | — | 10 | 3 | no | — |
| 324 | C2×C4 | — | 10 | 3 | no | — |
| 325 | C2×C4 | — | 10 | 6 | no | — |
| 326 | C2×C4 | — | 10 | 2 | no | — |
| 327 | C2×C4 | — | 10 | 6 | no | — |
| 328 | C2×C4 | — | 10 | 1 | no | — |
| 329 | C2×C4 | — | 20 | 1 | no | — |
| 330 | C2×C4 | — | 20 | 3 | no | — |
| 331 | C2×C4 | — | 20 | 1 | no | — |
| 332 | C2×C4 | — | 20 | 1 | no | — |
| 333 | C2×C4 | — | 20 | 3 | no | — |
| 334 | C2×C4 | — | 20 | 6 | no | — |
| 335 | C2×C4 | — | 40 | 6 | no | — |
| 336 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 337 | C2×C4 | C2×C22⋊AGL(1,𝔽5) | 1 | 3 | yes | — |
| 338 | C2×C4 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 339 | C8 | — | 20 | 1 | no | — |
| 340 | C8 | — | 20 | 3 | no | — |
| 341 | C5 | #17550 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 342 | C22 | — | 5 | 1 | no | — |
| 343 | C22 | — | 5 | 1 | no | — |
| 344 | C22 | — | 10 | 1 | no | — |
| 345 | C22 | — | 10 | 1 | no | — |
| 346 | C22 | — | 20 | 3 | no | — |
| 347 | C22 | — | 20 | 3 | no | — |
| 348 | C22 | — | 20 | 3 | no | — |
| 349 | C22 | C22×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 350 | C4 | — | 2 | 1 | no | — |
| 351 | C4 | — | 2 | 3 | no | — |
| 352 | C4 | — | 4 | 1 | no | — |
| 353 | C4 | — | 4 | 3 | no | — |
| 354 | C4 | — | 10 | 3 | no | — |
| 355 | C4 | — | 10 | 1 | no | — |
| 356 | C4 | — | 10 | 3 | no | — |
| 357 | C4 | — | 20 | 6 | no | — |
| 358 | C4 | — | 20 | 2 | no | — |
| 359 | C4 | — | 20 | 1 | no | — |
| 360 | C4 | C2×#4010 | 1 | 6 | yes | — |
| 361 | C2 | — | 10 | 1 | no | — |
| 362 | C2 | — | 10 | 1 | no | — |
| 363 | C2 | — | 40 | 3 | no | — |
| 364 | C2 | C22×#4010 | 1 | 1 | yes | characteristic |
| 365 | C2 | #10617514 | 1 | 1 | yes | characteristic |
| 366 | C2 | #10617559 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10617208 | C2 | semidirect |
| 3. #10617202 | C2 | semidirect |
| 4. #10604624 | C2 | semidirect |
| 5. #10604621 | C2 | semidirect |
| 6. #10604426 | C2 | semidirect |
| 7. #10604423 | C2 | semidirect |
| 9. C5×Q82 | C4 | semidirect |
| 11. #66064 | C4 | semidirect |
| 14. #65919 | C4 | semidirect |
| 16. #65911 | C4 | semidirect |
| 133. Q82 | AGL(1,𝔽5) | semidirect |
| 341. C5 | #17550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618944 | 2 |
| #10617208 | 2 |
| #10617202 | 2 |
| #10604624 | 2 |
| #10604621 | 2 |
| #10604426 | 2 |
| #10604423 | 2 |
| #17550 | 5 |