Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
642 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 128 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 | #11717520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11717462 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C5×#689 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C5×#4088 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11717069 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11717068 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11717063 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11717062 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11716951 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11716947 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11716935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×C52×Q8 | C22 | 1 | 1 | yes | characteristic |
| 13 | #87904 | — | 2 | 1 | no | — |
| 14 | #87904 | C22 | 1 | 2 | yes | — |
| 15 | Q8×C5⋊D5 | — | 2 | 1 | no | — |
| 16 | Q8×C5⋊D5 | C22 | 1 | 2 | yes | — |
| 17 | #87900 | — | 2 | 2 | no | — |
| 18 | #87900 | C22 | 1 | 1 | yes | characteristic |
| 19 | #87900 | C22 | 1 | 1 | yes | characteristic |
| 20 | C5×#709 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C5×Dic10 | C22 | 1 | 1 | yes | characteristic |
| 22 | #87879 | — | 2 | 2 | no | — |
| 23 | #87874 | — | 2 | 1 | no | — |
| 24 | #87872 | C22 | 1 | 2 | yes | — |
| 25 | #87871 | C22 | 1 | 2 | yes | — |
| 26 | D5×Dic10 | — | 2 | 1 | no | — |
| 27 | C5×#689 | C22 | 1 | 2 | yes | — |
| 28 | C5×#689 | C22 | 1 | 2 | yes | — |
| 29 | C5×#689 | C22 | 1 | 2 | yes | — |
| 30 | C5×#688 | C22 | 1 | 2 | yes | — |
| 31 | C5×#681 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×C5×#168 | C22 | 1 | 1 | yes | characteristic |
| 33 | #87776 | C22 | 1 | 1 | yes | characteristic |
| 34 | #87776 | C22 | 1 | 2 | yes | — |
| 35 | #87774 | C22 | 1 | 1 | yes | characteristic |
| 36 | #87774 | C22 | 1 | 2 | yes | — |
| 37 | #87773 | C22 | 1 | 1 | yes | characteristic |
| 38 | #87771 | C22 | 1 | 1 | yes | characteristic |
| 39 | #87769 | C22 | 1 | 2 | yes | — |
| 40 | #87767 | C22 | 1 | 2 | yes | — |
| 41 | #66113 | — | 5 | 1 | no | maximal |
| 42 | #66100 | — | 5 | 1 | no | maximal |
| 43 | C52×Q8 | — | 2 | 1 | no | — |
| 44 | C52×Q8 | C23 | 1 | 2 | yes | — |
| 45 | C2×C4×C52 | — | 2 | 1 | no | — |
| 46 | C2×C4×C52 | C23 | 1 | 1 | yes | characteristic |
| 47 | C22⋊(C5⋊D5) | — | 2 | 1 | no | — |
| 48 | C22⋊(C5⋊D5) | D4 | 1 | 2 | yes | — |
| 49 | C4⋊(C5⋊D5) | — | 2 | 2 | no | — |
| 50 | C4⋊(C5⋊D5) | D4 | 1 | 1 | yes | characteristic |
| 51 | C4⋊(C5⋊D5) | C23 | 1 | 1 | yes | characteristic |
| 52 | C4×C5⋊D5 | — | 2 | 2 | no | — |
| 53 | C4×C5⋊D5 | — | 2 | 1 | no | — |
| 54 | C4×C5⋊D5 | — | 2 | 2 | no | — |
| 55 | C4×C5⋊D5 | C23 | 1 | 2 | yes | — |
| 56 | #6045 | — | 2 | 2 | no | — |
| 57 | #6045 | D4 | 1 | 1 | yes | characteristic |
| 58 | #6045 | C23 | 1 | 1 | yes | characteristic |
| 59 | C5×C22⋊D5 | — | 2 | 1 | no | — |
| 60 | C2×C5×Dic5 | — | 2 | 1 | no | — |
| 61 | C5×D20 | C23 | 1 | 1 | yes | characteristic |
| 62 | C4×C5×D5 | — | 2 | 1 | no | — |
| 63 | C5×Dic10 | — | 2 | 1 | no | — |
| 64 | C5×Dic10 | C23 | 1 | 2 | yes | — |
| 65 | C5×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 66 | #6039 | — | 2 | 2 | no | — |
| 67 | #6038 | — | 2 | 2 | no | — |
| 68 | #6036 | — | 2 | 2 | no | — |
| 69 | D5×Dic5 | — | 2 | 2 | no | — |
| 70 | C5×#168 | C23 | 1 | 1 | yes | characteristic |
| 71 | C5×#168 | C23 | 1 | 2 | yes | — |
| 72 | C5×#168 | C23 | 1 | 1 | yes | characteristic |
| 73 | #4150 | — | 5 | 1 | no | — |
| 74 | #4147 | — | 5 | 1 | no | — |
| 75 | #4147 | — | 5 | 1 | no | — |
| 76 | #4147 | — | 5 | 1 | no | — |
| 77 | #4147 | — | 10 | 2 | no | — |
| 78 | C5×#137 | — | 5 | 1 | no | — |
| 79 | C2×C5×Q16 | — | 5 | 1 | no | — |
| 80 | #4096 | — | 5 | 1 | no | — |
| 81 | C2×#689 | D5 | 1 | 1 | yes | characteristic, complemented |
| 82 | #4088 | — | 5 | 1 | no | — |
| 83 | #4088 | D5 | 1 | 1 | yes | characteristic, complemented |
| 84 | #4065 | — | 5 | 2 | no | — |
| 85 | #4064 | — | 5 | 2 | no | — |
| 86 | #4064 | — | 5 | 2 | no | — |
| 87 | #4064 | — | 5 | 2 | no | — |
| 88 | D5×Q16 | — | 5 | 2 | no | — |
| 89 | D5×Q16 | — | 5 | 2 | no | — |
| 90 | #4062 | — | 5 | 2 | no | — |
| 91 | #4061 | — | 5 | 2 | no | — |
| 92 | #4055 | — | 5 | 1 | no | — |
| 93 | #4053 | — | 5 | 1 | no | — |
| 94 | #4050 | — | 5 | 1 | no | — |
| 95 | #4047 | — | 5 | 1 | no | — |
| 96 | C22×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 98 | C2×C5⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 99 | C2×C5×D5 | — | 2 | 1 | no | — |
| 100 | C4×C52 | — | 2 | 2 | no | — |
| 101 | C4×C52 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C4×C52 | C24 | 1 | 1 | yes | characteristic |
| 103 | #1039 | — | 2 | 1 | no | — |
| 104 | #1039 | C2×D4 | 1 | 2 | yes | — |
| 105 | C5×Dic5 | — | 2 | 2 | no | — |
| 106 | C5×Dic5 | — | 2 | 1 | no | — |
| 107 | C5×#41 | — | 5 | 1 | no | — |
| 108 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 109 | C2×C5×Q8 | — | 5 | 1 | no | — |
| 110 | C2×C5×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 111 | C2×C5×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 112 | #713 | — | 5 | 2 | no | — |
| 113 | #713 | — | 5 | 2 | no | — |
| 114 | #713 | — | 5 | 2 | no | — |
| 115 | #713 | — | 10 | 4 | no | — |
| 116 | #713 | — | 10 | 1 | no | — |
| 117 | #713 | — | 10 | 1 | no | — |
| 118 | #713 | — | 10 | 1 | no | — |
| 119 | #713 | — | 10 | 4 | no | — |
| 120 | Q8×D5 | — | 5 | 2 | no | — |
| 121 | Q8×D5 | — | 5 | 2 | no | — |
| 122 | Q8×D5 | — | 5 | 2 | no | — |
| 123 | Q8×D5 | — | 5 | 2 | no | — |
| 124 | Q8×D5 | — | 10 | 4 | no | — |
| 125 | Q8×D5 | — | 10 | 1 | no | — |
| 126 | Q8×D5 | — | 10 | 1 | no | — |
| 127 | Q8×D5 | — | 10 | 1 | no | — |
| 128 | Q8×D5 | — | 10 | 4 | no | — |
| 129 | #711 | — | 5 | 2 | no | — |
| 130 | #711 | — | 10 | 2 | no | — |
| 131 | #709 | — | 5 | 1 | no | — |
| 132 | #709 | — | 5 | 1 | no | — |
| 133 | #709 | — | 5 | 1 | no | — |
| 134 | #709 | — | 5 | 1 | no | — |
| 135 | #709 | — | 10 | 2 | no | — |
| 136 | #709 | — | 10 | 2 | no | — |
| 137 | #709 | — | 10 | 1 | no | — |
| 138 | #709 | — | 10 | 2 | no | — |
| 139 | #709 | — | 10 | 2 | no | — |
| 140 | #709 | — | 10 | 2 | no | — |
| 141 | #709 | — | 10 | 8 | no | — |
| 142 | #709 | C2×D5 | 1 | 1 | yes | characteristic |
| 143 | C2×Dic10 | — | 10 | 1 | no | — |
| 144 | C2×Dic10 | C2×D5 | 1 | 1 | yes | characteristic |
| 145 | C5×Q16 | — | 5 | 2 | no | — |
| 146 | C5×Q16 | — | 5 | 2 | no | — |
| 147 | C5×Q16 | — | 5 | 2 | no | — |
| 148 | C5×SD16 | — | 5 | 2 | no | — |
| 149 | C5×M16 | — | 5 | 1 | no | — |
| 150 | C2×C5×C8 | — | 5 | 1 | no | — |
| 151 | #689 | — | 5 | 1 | no | — |
| 152 | #689 | — | 5 | 2 | no | — |
| 153 | #689 | C2×D5 | 1 | 2 | yes | — |
| 154 | #689 | C2×D5 | 1 | 2 | yes | — |
| 155 | #689 | C2×D5 | 1 | 2 | yes | — |
| 156 | #688 | — | 5 | 1 | no | — |
| 157 | #688 | — | 5 | 2 | no | — |
| 158 | #688 | C2×D5 | 1 | 2 | yes | — |
| 159 | #687 | — | 5 | 1 | no | — |
| 160 | #686 | — | 5 | 1 | no | — |
| 161 | #681 | C2×D5 | 1 | 1 | yes | characteristic |
| 162 | C2×#168 | C2×D5 | 1 | 1 | yes | characteristic |
| 163 | Dic20 | — | 5 | 1 | no | — |
| 164 | Dic20 | — | 5 | 2 | no | — |
| 165 | D40 | — | 5 | 1 | no | — |
| 166 | #677 | — | 5 | 1 | no | — |
| 167 | #677 | — | 5 | 1 | no | — |
| 168 | #677 | — | 5 | 2 | no | — |
| 169 | #676 | — | 5 | 2 | no | — |
| 170 | #676 | — | 5 | 2 | no | — |
| 171 | C8×D5 | — | 5 | 2 | no | — |
| 172 | C8×D5 | — | 5 | 2 | no | — |
| 173 | #578 | — | 25 | 1 | no | Sylow |
| 174 | C2×C52 | — | 2 | 1 | no | — |
| 175 | C2×C52 | C22×D4 | 1 | 1 | yes | characteristic |
| 176 | C5⋊D5 | — | 2 | 2 | no | — |
| 177 | C5⋊D5 | — | 4 | 1 | no | — |
| 178 | C5×D5 | — | 4 | 1 | no | — |
| 179 | C5×Q8 | — | 2 | 4 | no | — |
| 180 | C5×Q8 | — | 2 | 1 | no | — |
| 181 | C5×Q8 | — | 2 | 1 | no | — |
| 182 | C5×Q8 | — | 2 | 4 | no | — |
| 183 | C5×Q8 | — | 5 | 1 | no | — |
| 184 | C5×Q8 | — | 5 | 2 | no | — |
| 185 | C5×Q8 | — | 10 | 1 | no | — |
| 186 | C5×Q8 | C22×D5 | 1 | 2 | yes | — |
| 187 | C5×Q8 | C22×D5 | 1 | 2 | yes | — |
| 188 | C5×D4 | — | 5 | 1 | no | — |
| 189 | C5×D4 | — | 10 | 1 | no | — |
| 190 | C2×C4×C5 | — | 2 | 4 | no | — |
| 191 | C2×C4×C5 | — | 2 | 1 | no | — |
| 192 | C2×C4×C5 | — | 2 | 1 | no | — |
| 193 | C2×C4×C5 | — | 2 | 2 | no | — |
| 194 | C2×C4×C5 | — | 10 | 1 | no | — |
| 195 | C2×C4×C5 | — | 10 | 1 | no | — |
| 196 | C2×C4×C5 | C22×D5 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×C5 | C22×D5 | 1 | 1 | yes | characteristic |
| 198 | C22⋊D5 | — | 2 | 1 | no | — |
| 199 | C22⋊D5 | — | 5 | 2 | no | — |
| 200 | C22⋊D5 | — | 5 | 2 | no | — |
| 201 | C22⋊D5 | — | 10 | 4 | no | — |
| 202 | C22⋊D5 | — | 10 | 2 | no | — |
| 203 | C22⋊D5 | — | 10 | 4 | no | — |
| 204 | C22⋊D5 | — | 10 | 1 | no | — |
| 205 | C22⋊D5 | — | 10 | 1 | no | — |
| 206 | C2×Dic5 | — | 2 | 1 | no | — |
| 207 | C2×Dic5 | — | 10 | 2 | no | — |
| 208 | D20 | — | 5 | 1 | no | — |
| 209 | D20 | — | 5 | 1 | no | — |
| 210 | D20 | — | 5 | 1 | no | — |
| 211 | D20 | — | 5 | 1 | no | — |
| 212 | D20 | — | 10 | 2 | no | — |
| 213 | D20 | — | 10 | 2 | no | — |
| 214 | D20 | — | 10 | 2 | no | — |
| 215 | D20 | — | 10 | 2 | no | — |
| 216 | D20 | — | 10 | 8 | no | — |
| 217 | D20 | — | 10 | 2 | no | — |
| 218 | D20 | C22×D5 | 1 | 1 | yes | characteristic |
| 219 | C4×D5 | — | 2 | 1 | no | — |
| 220 | C4×D5 | — | 5 | 2 | no | — |
| 221 | C4×D5 | — | 5 | 2 | no | — |
| 222 | C4×D5 | — | 10 | 4 | no | — |
| 223 | C4×D5 | — | 10 | 2 | no | — |
| 224 | C4×D5 | — | 10 | 2 | no | — |
| 225 | C4×D5 | — | 10 | 2 | no | — |
| 226 | C4×D5 | — | 10 | 2 | no | — |
| 227 | C4×D5 | — | 10 | 2 | no | — |
| 228 | C4×D5 | — | 10 | 2 | no | — |
| 229 | C4×D5 | — | 10 | 2 | no | — |
| 230 | C4×D5 | — | 10 | 8 | no | — |
| 231 | C4×D5 | — | 10 | 8 | no | — |
| 232 | C4×D5 | — | 10 | 4 | no | — |
| 233 | C4×D5 | — | 10 | 1 | no | — |
| 234 | C4×D5 | — | 10 | 1 | no | — |
| 235 | Dic10 | — | 2 | 1 | no | — |
| 236 | Dic10 | — | 5 | 1 | no | — |
| 237 | Dic10 | — | 5 | 1 | no | — |
| 238 | Dic10 | — | 5 | 1 | no | — |
| 239 | Dic10 | — | 5 | 1 | no | — |
| 240 | Dic10 | — | 10 | 2 | no | — |
| 241 | Dic10 | — | 10 | 2 | no | — |
| 242 | Dic10 | — | 10 | 2 | no | — |
| 243 | Dic10 | — | 10 | 2 | no | — |
| 244 | Dic10 | — | 10 | 2 | no | — |
| 245 | Dic10 | — | 10 | 2 | no | — |
| 246 | Dic10 | — | 10 | 8 | no | — |
| 247 | Dic10 | C22×D5 | 1 | 2 | yes | — |
| 248 | Dic10 | C22×D5 | 1 | 1 | yes | characteristic |
| 249 | C5×C8 | — | 5 | 1 | no | — |
| 250 | C5×C8 | — | 5 | 2 | no | — |
| 251 | C5×C8 | — | 5 | 1 | no | — |
| 252 | #168 | C22×D5 | 1 | 1 | yes | characteristic |
| 253 | #168 | C22×D5 | 1 | 2 | yes | — |
| 254 | #168 | C22×D5 | 1 | 1 | yes | characteristic |
| 255 | 2−1+4 | — | 25 | 1 | no | — |
| 256 | 2−1+4 | — | 25 | 1 | no | — |
| 257 | #137 | — | 5 | 1 | no | — |
| 258 | #137 | — | 25 | 1 | no | — |
| 259 | #137 | — | 25 | 2 | no | — |
| 260 | #137 | — | 25 | 2 | no | — |
| 261 | #135 | — | 25 | 1 | no | — |
| 262 | #135 | — | 25 | 2 | no | — |
| 263 | C2×Q16 | — | 5 | 1 | no | — |
| 264 | C2×Q16 | — | 25 | 2 | no | — |
| 265 | #131 | — | 25 | 1 | no | — |
| 266 | C52 | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 267 | C22×C5 | — | 2 | 2 | no | — |
| 268 | C22×C5 | — | 10 | 1 | no | — |
| 269 | C22×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 270 | C22×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 271 | C2×D5 | — | 2 | 1 | no | — |
| 272 | C2×D5 | — | 5 | 2 | no | — |
| 273 | C2×D5 | — | 5 | 2 | no | — |
| 274 | C2×D5 | — | 10 | 4 | no | — |
| 275 | C2×D5 | — | 10 | 4 | no | — |
| 276 | C2×D5 | — | 10 | 1 | no | — |
| 277 | C2×D5 | — | 10 | 1 | no | — |
| 278 | C4×C5 | — | 2 | 8 | no | — |
| 279 | C4×C5 | — | 2 | 2 | no | — |
| 280 | C4×C5 | — | 2 | 2 | no | — |
| 281 | C4×C5 | — | 2 | 2 | no | — |
| 282 | C4×C5 | — | 2 | 2 | no | — |
| 283 | C4×C5 | — | 10 | 1 | no | — |
| 284 | C4×C5 | — | 10 | 2 | no | — |
| 285 | C4×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 286 | C4×C5 | D4×D5 | 1 | 1 | yes | characteristic |
| 287 | C4×C5 | C23×D5 | 1 | 1 | yes | characteristic |
| 288 | C4×C5 | C23×D5 | 1 | 1 | yes | characteristic |
| 289 | Dic5 | — | 2 | 2 | no | — |
| 290 | Dic5 | — | 2 | 1 | no | — |
| 291 | Dic5 | — | 5 | 2 | no | — |
| 292 | Dic5 | — | 5 | 2 | no | — |
| 293 | Dic5 | — | 10 | 4 | no | — |
| 294 | Dic5 | — | 10 | 4 | no | — |
| 295 | Dic5 | — | 10 | 1 | no | — |
| 296 | Dic5 | — | 10 | 1 | no | — |
| 297 | #41 | — | 5 | 1 | no | — |
| 298 | #41 | — | 25 | 1 | no | — |
| 299 | #41 | — | 25 | 2 | no | — |
| 300 | #41 | — | 25 | 2 | no | — |
| 301 | #41 | — | 25 | 1 | no | — |
| 302 | #41 | — | 50 | 2 | no | — |
| 303 | #41 | — | 50 | 2 | no | — |
| 304 | #41 | — | 50 | 1 | no | — |
| 305 | #41 | — | 50 | 1 | no | — |
| 306 | C2×Q8 | — | 5 | 1 | no | — |
| 307 | C2×Q8 | — | 25 | 2 | no | — |
| 308 | C2×Q8 | — | 25 | 2 | no | — |
| 309 | C2×Q8 | — | 50 | 1 | no | — |
| 310 | C2×Q8 | — | 50 | 1 | no | — |
| 311 | C2×Q8 | D52 | 1 | 1 | yes | characteristic |
| 312 | Q16 | — | 5 | 2 | no | — |
| 313 | Q16 | — | 5 | 2 | no | — |
| 314 | Q16 | — | 5 | 2 | no | — |
| 315 | Q16 | — | 25 | 1 | no | — |
| 316 | Q16 | — | 25 | 2 | no | — |
| 317 | SD16 | — | 5 | 2 | no | — |
| 318 | SD16 | — | 25 | 1 | no | — |
| 319 | SD16 | — | 25 | 1 | no | — |
| 320 | SD16 | — | 25 | 2 | no | — |
| 321 | D8 | — | 25 | 1 | no | — |
| 322 | M16 | — | 5 | 1 | no | — |
| 323 | M16 | — | 25 | 2 | no | — |
| 324 | C2×C8 | — | 5 | 1 | no | — |
| 325 | C2×C8 | — | 25 | 2 | no | — |
| 326 | C2×C5 | — | 2 | 1 | no | — |
| 327 | C2×C5 | — | 2 | 1 | no | — |
| 328 | C2×C5 | — | 2 | 2 | no | — |
| 329 | C2×C5 | — | 4 | 2 | no | — |
| 330 | C2×C5 | — | 20 | 1 | no | — |
| 331 | C2×C5 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 332 | C2×C5 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 333 | D5 | — | 4 | 1 | no | — |
| 334 | D5 | — | 10 | 2 | no | — |
| 335 | D5 | — | 10 | 2 | no | — |
| 336 | D5 | — | 20 | 4 | no | — |
| 337 | D5 | — | 20 | 4 | no | — |
| 338 | D5 | — | 20 | 1 | no | — |
| 339 | D5 | — | 20 | 1 | no | — |
| 340 | Q8 | — | 2 | 1 | no | — |
| 341 | Q8 | — | 5 | 2 | no | — |
| 342 | Q8 | — | 5 | 1 | no | — |
| 343 | Q8 | — | 10 | 1 | no | — |
| 344 | Q8 | — | 25 | 1 | no | — |
| 345 | Q8 | — | 25 | 1 | no | — |
| 346 | Q8 | — | 50 | 2 | no | — |
| 347 | Q8 | — | 50 | 2 | no | — |
| 348 | Q8 | C2×D52 | 1 | 2 | yes | — |
| 349 | D4 | — | 5 | 1 | no | — |
| 350 | D4 | — | 10 | 1 | no | — |
| 351 | D4 | — | 25 | 2 | no | — |
| 352 | D4 | — | 25 | 1 | no | — |
| 353 | D4 | — | 25 | 1 | no | — |
| 354 | D4 | — | 50 | 2 | no | — |
| 355 | D4 | — | 50 | 2 | no | — |
| 356 | D4 | — | 50 | 1 | no | — |
| 357 | C2×C4 | — | 2 | 1 | no | — |
| 358 | C2×C4 | — | 10 | 1 | no | — |
| 359 | C2×C4 | — | 10 | 1 | no | — |
| 360 | C2×C4 | — | 25 | 2 | no | — |
| 361 | C2×C4 | — | 50 | 2 | no | — |
| 362 | C2×C4 | — | 50 | 2 | no | — |
| 363 | C2×C4 | — | 50 | 2 | no | — |
| 364 | C2×C4 | — | 50 | 2 | no | — |
| 365 | C2×C4 | — | 50 | 1 | no | — |
| 366 | C2×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 367 | C8 | — | 5 | 1 | no | — |
| 368 | C8 | — | 5 | 1 | no | — |
| 369 | C8 | — | 5 | 2 | no | — |
| 370 | C5 | — | 2 | 2 | no | — |
| 371 | C5 | #66100 | 1 | 1 | yes | characteristic, complemented |
| 372 | C5 | #66113 | 1 | 1 | yes | characteristic, complemented |
| 373 | C22 | — | 10 | 1 | no | — |
| 374 | C22 | — | 25 | 2 | no | — |
| 375 | C22 | — | 50 | 1 | no | — |
| 376 | C22 | #87886 | 1 | 1 | yes | characteristic |
| 377 | C4 | — | 2 | 2 | no | — |
| 378 | C4 | — | 10 | 1 | no | — |
| 379 | C4 | — | 10 | 2 | no | — |
| 380 | C4 | — | 25 | 2 | no | — |
| 381 | C4 | — | 50 | 1 | no | — |
| 382 | C4 | #87886 | 1 | 1 | yes | characteristic |
| 383 | C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 384 | C2 | — | 2 | 1 | no | — |
| 385 | C2 | — | 20 | 1 | no | — |
| 386 | C2 | — | 50 | 2 | no | — |
| 387 | C2 | — | 100 | 1 | no | — |
| 388 | C2 | C2×#87886 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#87886 |
| commutator, cosocle | C4×C52 | C24 |
| Frattini | C4 | C22×D52 |
| Fitting | C2×C52×Q8 | C22 |
| socle | C2×C52 | C22×D4 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #578 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717520 | C2 | semidirect |
| 2. #11717462 | C2 | semidirect |
| 3. C2×C5×#689 | C2 | semidirect |
| 4. C5×#4088 | C2 | semidirect |
| 5. #11717069 | C2 | semidirect |
| 6. #11717068 | C2 | semidirect |
| 7. #11717063 | C2 | semidirect |
| 8. #11717062 | C2 | semidirect |
| 9. #11716951 | C2 | semidirect |
| 10. #11716947 | C2 | semidirect |
| 11. #11716935 | C2 | semidirect |
| 81. C2×#689 | D5 | semidirect |
| 83. #4088 | D5 | semidirect |
| 266. C52 | #578 | semidirect |
| 371. C5 | #66100 | semidirect |
| 372. C5 | #66113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717520 | 2 |
| #11717462 | 2 |
| C2×C5×#689 | 2 |
| C5×#4088 | 2 |
| #11717069 | 2 |
| #11717068 | 2 |
| #11717063 | 2 |
| #11717062 | 2 |
| #11716951 | 2 |
| #11716947 | 2 |
| #11716935 | 2 |
| #66113 | 5 |
| #66100 | 5 |