Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
378 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 43 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 | #23775201 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #23765430 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #23762540 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23761568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23761554 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #23761553 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C79×#2205 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #19099379 | — | 2 | 1 | no | — |
| 9 | #19099378 | — | 2 | 1 | no | — |
| 10 | #19098942 | C22 | 1 | 1 | yes | characteristic |
| 11 | #19098858 | — | 2 | 1 | no | — |
| 12 | #19098837 | — | 2 | 1 | no | — |
| 13 | #19098836 | — | 2 | 1 | no | — |
| 14 | #19098747 | — | 2 | 1 | no | — |
| 15 | #19098745 | — | 2 | 1 | no | — |
| 16 | #19098745 | C22 | 1 | 1 | yes | characteristic |
| 17 | #19098677 | — | 2 | 1 | no | — |
| 18 | #19098362 | — | 2 | 1 | no | — |
| 19 | #19098362 | C22 | 1 | 1 | yes | characteristic |
| 20 | #19098312 | C22 | 1 | 1 | yes | characteristic |
| 21 | Q8⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 22 | Q82×C79 | C22 | 1 | 1 | yes | characteristic |
| 23 | #456×C79 | — | 2 | 1 | no | — |
| 24 | #456×C79 | C22 | 1 | 1 | yes | characteristic |
| 25 | #356×C79 | — | 2 | 1 | no | — |
| 26 | #356×C79 | C22 | 1 | 1 | yes | characteristic |
| 27 | #14579209 | D4 | 1 | 1 | yes | characteristic |
| 28 | #14579208 | — | 2 | 1 | no | — |
| 29 | #14579194 | — | 2 | 1 | no | — |
| 30 | #14579193 | — | 4 | 1 | no | — |
| 31 | #14579192 | — | 2 | 1 | no | — |
| 32 | #14579192 | — | 4 | 1 | no | — |
| 33 | #14579192 | — | 4 | 1 | no | — |
| 34 | #14579191 | — | 2 | 1 | no | — |
| 35 | #14579191 | — | 4 | 1 | no | — |
| 36 | #14579190 | — | 4 | 1 | no | — |
| 37 | #14579182 | — | 4 | 1 | no | — |
| 38 | #14579181 | — | 2 | 1 | no | — |
| 39 | #14579181 | — | 4 | 1 | no | — |
| 40 | C2×#11929614 | — | 2 | 1 | no | — |
| 41 | C2×#11929614 | — | 2 | 1 | no | — |
| 42 | C2×#11929614 | — | 4 | 1 | no | — |
| 43 | Q16×D79 | — | 4 | 1 | no | — |
| 44 | #14579169 | — | 2 | 1 | no | — |
| 45 | #14579168 | — | 2 | 1 | no | — |
| 46 | #14579161 | D4 | 1 | 1 | yes | characteristic |
| 47 | #14579096 | — | 2 | 1 | no | — |
| 48 | #14579094 | — | 4 | 1 | no | — |
| 49 | C4⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 50 | #14579089 | — | 2 | 1 | no | — |
| 51 | #14579089 | — | 4 | 1 | no | — |
| 52 | #14579085 | — | 4 | 1 | no | — |
| 53 | #14579080 | — | 2 | 1 | no | — |
| 54 | #14579080 | D4 | 1 | 1 | yes | characteristic |
| 55 | #14579079 | — | 2 | 1 | no | — |
| 56 | C4×C79⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 57 | 2−1+4×C79 | D4 | 1 | 1 | yes | characteristic |
| 58 | #137×C79 | — | 2 | 1 | no | — |
| 59 | #137×C79 | — | 4 | 1 | no | — |
| 60 | C4⋊Q8×C79 | — | 2 | 1 | no | — |
| 61 | C4⋊Q8×C79 | — | 2 | 1 | no | — |
| 62 | C4⋊Q8×C79 | — | 4 | 1 | no | — |
| 63 | C4⋊Q8×C79 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4×Q8×C79 | — | 2 | 1 | no | — |
| 65 | C4×Q8×C79 | — | 4 | 1 | no | — |
| 66 | #104×C79 | — | 2 | 1 | no | — |
| 67 | #104×C79 | — | 4 | 1 | no | — |
| 68 | #101×C79 | — | 2 | 1 | no | — |
| 69 | #101×C79 | D4 | 1 | 1 | yes | characteristic |
| 70 | #11929625 | — | 4 | 1 | no | — |
| 71 | #11929624 | — | 2 | 1 | no | — |
| 72 | #11929624 | — | 4 | 1 | no | — |
| 73 | #11929624 | — | 4 | 1 | no | — |
| 74 | #11929623 | — | 4 | 1 | no | — |
| 75 | #11929623 | — | 8 | 1 | no | — |
| 76 | C2×Dic158 | — | 2 | 1 | no | — |
| 77 | C2×Dic158 | — | 4 | 1 | no | — |
| 78 | Q8×D79 | — | 4 | 1 | no | — |
| 79 | Q8×D79 | — | 4 | 1 | no | — |
| 80 | Dic316 | — | 4 | 1 | no | — |
| 81 | #11929614 | — | 2 | 1 | no | — |
| 82 | #11929614 | — | 4 | 1 | no | — |
| 83 | #11929614 | — | 4 | 1 | no | — |
| 84 | #11929614 | — | 4 | 1 | no | — |
| 85 | #11929614 | — | 4 | 1 | no | — |
| 86 | #11929614 | — | 4 | 1 | no | — |
| 87 | #11929614 | — | 4 | 1 | no | — |
| 88 | #11929614 | — | 8 | 1 | no | — |
| 89 | #11929613 | — | 4 | 1 | no | — |
| 90 | #11929612 | — | 2 | 1 | no | — |
| 91 | #11929612 | — | 4 | 1 | no | — |
| 92 | #11929611 | — | 2 | 1 | no | — |
| 93 | #11929611 | — | 4 | 1 | no | — |
| 94 | #11929611 | — | 8 | 1 | no | — |
| 95 | #11929609 | — | 2 | 1 | no | — |
| 96 | #11929608 | — | 2 | 1 | no | — |
| 97 | #11929608 | — | 4 | 1 | no | — |
| 98 | #11929608 | — | 4 | 1 | no | — |
| 99 | #11929607 | — | 4 | 1 | no | — |
| 100 | C2×C79⋊C8 | — | 2 | 1 | no | — |
| 101 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 102 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 103 | C8×D79 | — | 4 | 1 | no | — |
| 104 | C4⋊Dic79 | — | 4 | 1 | no | — |
| 105 | #41×C79 | — | 2 | 1 | no | — |
| 106 | #41×C79 | — | 4 | 1 | no | — |
| 107 | #41×C79 | — | 4 | 1 | no | — |
| 108 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 109 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 110 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 111 | C2×Q8×C79 | — | 4 | 1 | no | — |
| 112 | C2×Q8×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×Q8×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | Q16×C79 | — | 4 | 1 | no | — |
| 115 | Q16×C79 | — | 8 | 1 | no | — |
| 116 | SD16×C79 | — | 4 | 1 | no | — |
| 117 | SD16×C79 | — | 8 | 1 | no | — |
| 118 | M16×C79 | — | 2 | 1 | no | — |
| 119 | M16×C79 | — | 4 | 1 | no | — |
| 120 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 121 | C4⋊C4×C79 | — | 4 | 1 | no | — |
| 122 | C4⋊C4×C79 | — | 4 | 1 | no | — |
| 123 | C4⋊C4×C79 | — | 4 | 1 | no | — |
| 124 | C4⋊C4×C79 | — | 4 | 1 | no | — |
| 125 | C42×C79 | — | 2 | 1 | no | — |
| 126 | C42×C79 | — | 2 | 1 | no | — |
| 127 | C42×C79 | — | 4 | 1 | no | — |
| 128 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | Q8×C79 | — | 2 | 1 | no | — |
| 130 | Q8×C79 | — | 2 | 2 | no | — |
| 131 | Q8×C79 | — | 4 | 1 | no | — |
| 132 | Q8×C79 | — | 4 | 1 | no | — |
| 133 | Q8×C79 | — | 4 | 1 | no | — |
| 134 | Q8×C79 | — | 4 | 1 | no | — |
| 135 | Q8×C79 | — | 8 | 1 | no | — |
| 136 | Q8×C79 | — | 8 | 1 | no | — |
| 137 | D4×C79 | — | 2 | 1 | no | — |
| 138 | D4×C79 | — | 4 | 1 | no | — |
| 139 | D4×C79 | — | 4 | 1 | no | — |
| 140 | C2×C4×C79 | — | 2 | 1 | no | — |
| 141 | C2×C4×C79 | — | 2 | 1 | no | — |
| 142 | C2×C4×C79 | — | 2 | 1 | no | — |
| 143 | C2×C4×C79 | — | 4 | 1 | no | — |
| 144 | C2×C4×C79 | — | 4 | 1 | no | — |
| 145 | C2×C4×C79 | — | 4 | 1 | no | — |
| 146 | C2×C4×C79 | — | 8 | 1 | no | — |
| 147 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 148 | C22⋊D79 | — | 4 | 1 | no | — |
| 149 | C22⋊D79 | — | 8 | 1 | no | — |
| 150 | C2×Dic79 | — | 4 | 1 | no | — |
| 151 | C2×Dic79 | — | 8 | 1 | no | — |
| 152 | D316 | — | 2 | 1 | no | — |
| 153 | D316 | — | 4 | 1 | no | — |
| 154 | C4×D79 | — | 4 | 1 | no | — |
| 155 | C4×D79 | — | 8 | 1 | no | — |
| 156 | C4×D79 | — | 8 | 1 | no | — |
| 157 | Dic158 | — | 2 | 1 | no | — |
| 158 | Dic158 | — | 4 | 1 | no | — |
| 159 | Dic158 | — | 4 | 1 | no | — |
| 160 | Dic158 | — | 4 | 1 | no | — |
| 161 | Dic158 | — | 8 | 1 | no | — |
| 162 | C8×C79 | — | 4 | 1 | no | — |
| 163 | C8×C79 | — | 8 | 1 | no | — |
| 164 | C79⋊C8 | — | 2 | 1 | no | — |
| 165 | C79⋊C8 | — | 2 | 1 | no | — |
| 166 | C79⋊C8 | — | 4 | 1 | no | — |
| 167 | C79⋊C8 | — | 8 | 1 | no | — |
| 168 | C79⋊C8 | — | 8 | 1 | no | — |
| 169 | C22×C79 | — | 4 | 1 | no | — |
| 170 | C22×C79 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 171 | C2×D79 | — | 4 | 1 | no | — |
| 172 | C4×C79 | — | 2 | 1 | no | — |
| 173 | C4×C79 | — | 2 | 1 | no | — |
| 174 | C4×C79 | — | 2 | 1 | no | — |
| 175 | C4×C79 | — | 4 | 2 | no | — |
| 176 | C4×C79 | — | 4 | 1 | no | — |
| 177 | C4×C79 | — | 4 | 1 | no | — |
| 178 | C4×C79 | — | 4 | 1 | no | — |
| 179 | C4×C79 | — | 8 | 1 | no | — |
| 180 | Dic79 | — | 4 | 1 | no | — |
| 181 | Dic79 | — | 8 | 1 | no | — |
| 182 | #13684 | — | 79 | 1 | no | maximal, Sylow |
| 183 | C2×C79 | — | 2 | 1 | no | — |
| 184 | C2×C79 | — | 8 | 1 | no | — |
| 185 | C2×C79 | #2196 | 1 | 1 | yes | characteristic |
| 186 | D79 | — | 8 | 1 | no | — |
| 187 | #3293 | — | 79 | 1 | no | — |
| 188 | #2205 | — | 79 | 1 | no | — |
| 189 | #2205 | D79 | 1 | 1 | yes | characteristic, complemented |
| 190 | #1633 | — | 79 | 1 | no | — |
| 191 | #1411 | — | 79 | 1 | no | — |
| 192 | #1405 | — | 79 | 1 | no | — |
| 193 | #1405 | — | 79 | 1 | no | — |
| 194 | C79 | #13684 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 195 | #578 | — | 158 | 1 | no | — |
| 196 | #578 | — | 158 | 1 | no | — |
| 197 | Q82 | C2×D79 | 1 | 1 | yes | characteristic |
| 198 | #494 | — | 79 | 1 | no | — |
| 199 | #477 | — | 158 | 1 | no | — |
| 200 | #473 | — | 158 | 1 | no | — |
| 201 | #473 | — | 158 | 1 | no | — |
| 202 | #456 | — | 2 | 1 | no | — |
| 203 | #456 | — | 79 | 1 | no | — |
| 204 | #456 | — | 158 | 1 | no | — |
| 205 | #456 | — | 158 | 1 | no | — |
| 206 | #456 | C2×D79 | 1 | 1 | yes | characteristic |
| 207 | #443 | — | 158 | 1 | no | — |
| 208 | #356 | — | 2 | 1 | no | — |
| 209 | #356 | — | 79 | 1 | no | — |
| 210 | #356 | — | 158 | 1 | no | — |
| 211 | #356 | C2×D79 | 1 | 1 | yes | characteristic |
| 212 | #333 | — | 79 | 1 | no | — |
| 213 | Q8⋊C8 | — | 158 | 1 | no | — |
| 214 | 2−1+4 | — | 79 | 1 | no | — |
| 215 | 2−1+4 | — | 158 | 1 | no | — |
| 216 | 2−1+4 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 217 | #137 | — | 2 | 1 | no | — |
| 218 | #137 | — | 4 | 1 | no | — |
| 219 | #137 | — | 316 | 1 | no | — |
| 220 | #137 | — | 316 | 1 | no | — |
| 221 | #137 | — | 316 | 1 | no | — |
| 222 | #137 | — | 316 | 1 | no | — |
| 223 | #137 | — | 316 | 1 | no | — |
| 224 | #137 | — | 158 | 1 | no | — |
| 225 | #137 | — | 158 | 1 | no | — |
| 226 | #137 | — | 158 | 1 | no | — |
| 227 | #135 | — | 316 | 1 | no | — |
| 228 | #135 | — | 316 | 1 | no | — |
| 229 | #135 | — | 158 | 1 | no | — |
| 230 | C2×Q16 | — | 316 | 1 | no | — |
| 231 | C2×Q16 | — | 316 | 1 | no | — |
| 232 | C2×Q16 | — | 158 | 1 | no | — |
| 233 | C2×Q16 | — | 158 | 1 | no | — |
| 234 | #131 | — | 158 | 1 | no | — |
| 235 | #131 | — | 158 | 1 | no | — |
| 236 | C4⋊Q8 | — | 2 | 1 | no | — |
| 237 | C4⋊Q8 | — | 2 | 1 | no | — |
| 238 | C4⋊Q8 | — | 4 | 1 | no | — |
| 239 | C4⋊Q8 | — | 79 | 1 | no | — |
| 240 | C4⋊Q8 | C22×D79 | 1 | 1 | yes | characteristic |
| 241 | C4×Q8 | — | 2 | 1 | no | — |
| 242 | C4×Q8 | — | 4 | 1 | no | — |
| 243 | #108 | — | 158 | 1 | no | — |
| 244 | #107 | — | 316 | 1 | no | — |
| 245 | C4⋊C8 | — | 158 | 1 | no | — |
| 246 | #104 | — | 2 | 1 | no | — |
| 247 | #104 | — | 4 | 1 | no | — |
| 248 | #104 | — | 316 | 1 | no | — |
| 249 | #104 | — | 158 | 1 | no | — |
| 250 | #103 | — | 316 | 1 | no | — |
| 251 | #101 | — | 2 | 1 | no | — |
| 252 | #101 | — | 79 | 1 | no | — |
| 253 | #101 | — | 158 | 1 | no | — |
| 254 | #101 | — | 158 | 1 | no | — |
| 255 | #101 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 256 | C4×C8 | — | 79 | 1 | no | — |
| 257 | #41 | — | 2 | 1 | no | — |
| 258 | #41 | — | 4 | 1 | no | — |
| 259 | #41 | — | 4 | 1 | no | — |
| 260 | #41 | — | 316 | 1 | no | — |
| 261 | #41 | — | 316 | 1 | no | — |
| 262 | #41 | — | 316 | 1 | no | — |
| 263 | #41 | — | 316 | 1 | no | — |
| 264 | #41 | — | 632 | 1 | no | — |
| 265 | #41 | — | 158 | 1 | no | — |
| 266 | C2×Q8 | — | 2 | 1 | no | — |
| 267 | C2×Q8 | — | 2 | 1 | no | — |
| 268 | C2×Q8 | — | 2 | 1 | no | — |
| 269 | C2×Q8 | — | 4 | 1 | no | — |
| 270 | C2×Q8 | — | 316 | 1 | no | — |
| 271 | C2×Q8 | — | 316 | 1 | no | — |
| 272 | C2×Q8 | — | 316 | 1 | no | — |
| 273 | C2×Q8 | — | 158 | 1 | no | — |
| 274 | C2×Q8 | D4×D79 | 1 | 1 | yes | characteristic |
| 275 | C2×Q8 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 276 | Q16 | — | 4 | 1 | no | — |
| 277 | Q16 | — | 8 | 1 | no | — |
| 278 | Q16 | — | 316 | 1 | no | — |
| 279 | Q16 | — | 316 | 1 | no | — |
| 280 | Q16 | — | 316 | 1 | no | — |
| 281 | Q16 | — | 316 | 1 | no | — |
| 282 | Q16 | — | 316 | 1 | no | — |
| 283 | Q16 | — | 316 | 1 | no | — |
| 284 | Q16 | — | 316 | 1 | no | — |
| 285 | Q16 | — | 632 | 1 | no | — |
| 286 | Q16 | — | 158 | 1 | no | — |
| 287 | SD16 | — | 4 | 1 | no | — |
| 288 | SD16 | — | 8 | 1 | no | — |
| 289 | SD16 | — | 316 | 1 | no | — |
| 290 | SD16 | — | 316 | 1 | no | — |
| 291 | SD16 | — | 316 | 1 | no | — |
| 292 | SD16 | — | 632 | 1 | no | — |
| 293 | SD16 | — | 158 | 1 | no | — |
| 294 | SD16 | — | 158 | 1 | no | — |
| 295 | D8 | — | 158 | 1 | no | — |
| 296 | M16 | — | 2 | 1 | no | — |
| 297 | M16 | — | 4 | 1 | no | — |
| 298 | M16 | — | 316 | 1 | no | — |
| 299 | M16 | — | 316 | 1 | no | — |
| 300 | M16 | — | 316 | 1 | no | — |
| 301 | M16 | — | 158 | 1 | no | — |
| 302 | C2×C8 | — | 316 | 1 | no | — |
| 303 | C2×C8 | — | 316 | 1 | no | — |
| 304 | C2×C8 | — | 316 | 1 | no | — |
| 305 | C2×C8 | — | 158 | 1 | no | — |
| 306 | C4⋊C4 | — | 2 | 1 | no | — |
| 307 | C4⋊C4 | — | 4 | 1 | no | — |
| 308 | C4⋊C4 | — | 4 | 1 | no | — |
| 309 | C4⋊C4 | — | 4 | 1 | no | — |
| 310 | C4⋊C4 | — | 4 | 1 | no | — |
| 311 | C4⋊C4 | — | 316 | 1 | no | — |
| 312 | C42 | — | 2 | 1 | no | — |
| 313 | C42 | — | 2 | 1 | no | — |
| 314 | C42 | — | 4 | 1 | no | — |
| 315 | C42 | D4×D79 | 1 | 1 | yes | characteristic |
| 316 | Q8 | — | 2 | 1 | no | — |
| 317 | Q8 | — | 2 | 2 | no | — |
| 318 | Q8 | — | 4 | 1 | no | — |
| 319 | Q8 | — | 4 | 1 | no | — |
| 320 | Q8 | — | 4 | 1 | no | — |
| 321 | Q8 | — | 4 | 1 | no | — |
| 322 | Q8 | — | 8 | 1 | no | — |
| 323 | Q8 | — | 8 | 1 | no | — |
| 324 | Q8 | — | 316 | 1 | no | — |
| 325 | Q8 | — | 316 | 1 | no | — |
| 326 | Q8 | — | 316 | 1 | no | — |
| 327 | Q8 | — | 632 | 1 | no | — |
| 328 | Q8 | — | 158 | 1 | no | — |
| 329 | D4 | — | 2 | 1 | no | — |
| 330 | D4 | — | 4 | 1 | no | — |
| 331 | D4 | — | 4 | 1 | no | — |
| 332 | D4 | — | 316 | 1 | no | — |
| 333 | D4 | — | 316 | 1 | no | — |
| 334 | D4 | — | 632 | 1 | no | — |
| 335 | D4 | — | 158 | 1 | no | — |
| 336 | C2×C4 | — | 2 | 1 | no | — |
| 337 | C2×C4 | — | 2 | 1 | no | — |
| 338 | C2×C4 | — | 2 | 1 | no | — |
| 339 | C2×C4 | — | 4 | 1 | no | — |
| 340 | C2×C4 | — | 4 | 1 | no | — |
| 341 | C2×C4 | — | 4 | 1 | no | — |
| 342 | C2×C4 | — | 8 | 1 | no | — |
| 343 | C2×C4 | — | 316 | 1 | no | — |
| 344 | C2×C4 | — | 316 | 1 | no | — |
| 345 | C2×C4 | — | 632 | 1 | no | — |
| 346 | C2×C4 | — | 632 | 1 | no | — |
| 347 | C2×C4 | — | 632 | 1 | no | — |
| 348 | C2×C4 | #14579129 | 1 | 1 | yes | characteristic |
| 349 | C8 | — | 4 | 1 | no | — |
| 350 | C8 | — | 8 | 1 | no | — |
| 351 | C8 | — | 316 | 1 | no | — |
| 352 | C8 | — | 632 | 1 | no | — |
| 353 | C8 | — | 632 | 1 | no | — |
| 354 | C8 | — | 158 | 1 | no | — |
| 355 | C8 | — | 158 | 1 | no | — |
| 356 | C22 | — | 4 | 1 | no | — |
| 357 | C22 | — | 316 | 1 | no | — |
| 358 | C22 | #19098749 | 1 | 1 | yes | characteristic |
| 359 | C4 | — | 2 | 1 | no | — |
| 360 | C4 | — | 2 | 1 | no | — |
| 361 | C4 | — | 2 | 1 | no | — |
| 362 | C4 | — | 4 | 2 | no | — |
| 363 | C4 | — | 4 | 1 | no | — |
| 364 | C4 | — | 4 | 1 | no | — |
| 365 | C4 | — | 4 | 1 | no | — |
| 366 | C4 | — | 8 | 1 | no | — |
| 367 | C4 | — | 316 | 1 | no | — |
| 368 | C4 | — | 632 | 1 | no | — |
| 369 | C2 | — | 2 | 1 | no | — |
| 370 | C2 | — | 8 | 1 | no | — |
| 371 | C2 | — | 632 | 1 | no | — |
| 372 | C2 | #23765382 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23765430 | C2 | semidirect |
| 3. #23762540 | C2 | semidirect |
| 4. #23761568 | C2 | semidirect |
| 5. #23761554 | C2 | semidirect |
| 6. #23761553 | C2 | semidirect |
| 7. C79×#2205 | C2 | semidirect |
| 189. #2205 | D79 | semidirect |
| 194. C79 | #13684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775201 | 2 |
| #23765430 | 2 |
| #23762540 | 2 |
| #23761568 | 2 |
| #23761554 | 2 |
| #23761553 | 2 |
| C79×#2205 | 2 |
| #13684 | 79 |