Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
950 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 143 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 | #10617719 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#1801 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10602427 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10601296 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10601291 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#4147 | — | 2 | 1 | no | — |
| 7 | C2×C4×C5×Q8 | C22 | 1 | 1 | yes | characteristic |
| 8 | #65911 | — | 2 | 2 | no | — |
| 9 | #65910 | — | 2 | 4 | no | — |
| 10 | Q8×D20 | — | 2 | 2 | no | — |
| 11 | #65844 | — | 2 | 1 | no | — |
| 12 | #65844 | C4 | 1 | 4 | yes | — |
| 13 | #65811 | — | 2 | 2 | no | — |
| 14 | #65811 | C22 | 1 | 2 | yes | — |
| 15 | C5×#423 | C22 | 1 | 2 | yes | — |
| 16 | C2×C5×#101 | — | 2 | 1 | no | — |
| 17 | C2×C4⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C4×#168 | C22 | 1 | 1 | yes | characteristic |
| 19 | C5×#343 | — | 2 | 1 | no | — |
| 20 | #64744 | — | 2 | 2 | no | — |
| 21 | #64705 | — | 2 | 2 | no | — |
| 22 | #64703 | — | 2 | 4 | no | — |
| 23 | #64702 | — | 2 | 2 | no | — |
| 24 | #8354 | — | 5 | 1 | no | maximal, Sylow |
| 25 | C22×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 26 | #4147 | — | 4 | 4 | no | — |
| 27 | #4147 | — | 4 | 2 | no | — |
| 28 | #4147 | — | 4 | 2 | no | — |
| 29 | C2×#713 | — | 2 | 4 | no | — |
| 30 | C2×Q8×D5 | — | 2 | 4 | no | — |
| 31 | C2×#709 | — | 2 | 4 | no | — |
| 32 | C2×#709 | — | 2 | 2 | no | — |
| 33 | C2×C5×M16 | — | 2 | 2 | no | — |
| 34 | C4×C5×Q8 | — | 2 | 2 | no | — |
| 35 | C4×C5×Q8 | — | 2 | 2 | no | — |
| 36 | C2×C5×C4⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 37 | C2×C5×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×C42×C5 | D4 | 1 | 2 | yes | — |
| 39 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 40 | #4076 | — | 2 | 4 | no | — |
| 41 | #4076 | — | 2 | 2 | no | — |
| 42 | #4076 | C2×C4 | 1 | 4 | yes | — |
| 43 | C22×#168 | — | 2 | 1 | no | — |
| 44 | C22×#168 | — | 2 | 1 | no | — |
| 45 | #4043 | — | 2 | 4 | no | — |
| 46 | #4043 | — | 2 | 8 | no | — |
| 47 | #4041 | — | 2 | 4 | no | — |
| 48 | #4041 | — | 2 | 8 | no | — |
| 49 | #4021 | — | 2 | 4 | no | — |
| 50 | #4021 | — | 2 | 2 | no | — |
| 51 | #4020 | — | 2 | 2 | no | — |
| 52 | #4020 | D4 | 1 | 2 | yes | — |
| 53 | C4×D20 | — | 2 | 4 | no | — |
| 54 | C4×D20 | — | 2 | 4 | no | — |
| 55 | C4×D20 | — | 2 | 2 | no | — |
| 56 | C4×D20 | D4 | 1 | 4 | yes | — |
| 57 | #4015 | — | 2 | 2 | no | — |
| 58 | #4015 | D4 | 1 | 2 | yes | — |
| 59 | C5×C4⋊C8 | — | 2 | 2 | no | — |
| 60 | C5×C4⋊C8 | — | 2 | 2 | no | — |
| 61 | C5×#101 | — | 4 | 2 | no | — |
| 62 | C4⋊#168 | — | 2 | 2 | no | — |
| 63 | C4×#168 | — | 2 | 2 | no | — |
| 64 | #3497 | — | 5 | 1 | no | — |
| 65 | #1984 | — | 5 | 1 | no | — |
| 66 | #1801 | D5 | 1 | 1 | yes | characteristic, complemented |
| 67 | #1547 | — | 5 | 2 | no | — |
| 68 | #1492 | — | 5 | 2 | no | — |
| 69 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 70 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 71 | C2×C5×Q8 | D8 | 1 | 2 | yes | — |
| 72 | C2×C5×Q8 | SD16 | 1 | 2 | yes | — |
| 73 | C22×C4×C5 | C22⋊C4 | 1 | 2 | yes | — |
| 74 | C22×C4×C5 | C22⋊C4 | 1 | 2 | yes | — |
| 75 | C22×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 76 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 78 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 79 | #713 | — | 4 | 8 | no | — |
| 80 | #713 | — | 4 | 8 | no | — |
| 81 | Q8×D5 | — | 4 | 8 | no | — |
| 82 | Q8×D5 | — | 4 | 8 | no | — |
| 83 | #709 | — | 4 | 8 | no | — |
| 84 | #709 | — | 4 | 8 | no | — |
| 85 | #709 | — | 4 | 2 | no | — |
| 86 | #709 | — | 4 | 2 | no | — |
| 87 | #709 | — | 4 | 2 | no | — |
| 88 | #709 | — | 4 | 2 | no | — |
| 89 | C2×D20 | — | 2 | 4 | no | — |
| 90 | C2×D20 | — | 2 | 2 | no | — |
| 91 | C2×D20 | — | 2 | 2 | no | — |
| 92 | C2×D20 | — | 2 | 4 | no | — |
| 93 | C2×D20 | C22⋊C4 | 1 | 4 | yes | — |
| 94 | C2×C4×D5 | — | 2 | 8 | no | — |
| 95 | C2×C4×D5 | — | 2 | 4 | no | — |
| 96 | C2×Dic10 | — | 2 | 4 | no | — |
| 97 | C2×Dic10 | — | 2 | 2 | no | — |
| 98 | C5×M16 | — | 4 | 2 | no | — |
| 99 | C5×M16 | — | 4 | 2 | no | — |
| 100 | C2×C5×C8 | — | 4 | 2 | no | — |
| 101 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 102 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 103 | C42×C5 | — | 2 | 2 | no | — |
| 104 | C42×C5 | — | 2 | 2 | no | — |
| 105 | C42×C5 | C2×D4 | 1 | 2 | yes | — |
| 106 | C42×C5 | C2×D4 | 1 | 2 | yes | — |
| 107 | #685 | — | 2 | 8 | no | — |
| 108 | #685 | — | 2 | 4 | no | — |
| 109 | #685 | — | 2 | 4 | no | — |
| 110 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 111 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 112 | C4⋊Dic5 | C22⋊C4 | 1 | 4 | yes | — |
| 113 | C2×#168 | — | 2 | 2 | no | — |
| 114 | C2×#168 | — | 4 | 1 | no | — |
| 115 | C2×#168 | — | 4 | 1 | no | — |
| 116 | C2×#168 | — | 4 | 2 | no | — |
| 117 | C2×#168 | — | 4 | 1 | no | — |
| 118 | C2×2−1+4 | — | 10 | 1 | no | — |
| 119 | #550 | — | 10 | 2 | no | — |
| 120 | D4×Q8 | — | 10 | 2 | no | — |
| 121 | #548 | — | 10 | 4 | no | — |
| 122 | #537 | — | 5 | 4 | no | — |
| 123 | #537 | — | 10 | 1 | no | — |
| 124 | #532 | — | 5 | 2 | no | — |
| 125 | #532 | — | 10 | 2 | no | — |
| 126 | C2×C4×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 127 | #423 | C2×D5 | 1 | 2 | yes | — |
| 128 | C2×C4⋊C8 | — | 5 | 1 | no | — |
| 129 | C2×#101 | — | 2 | 1 | no | — |
| 130 | C2×C4×C8 | — | 5 | 1 | no | — |
| 131 | #343 | — | 2 | 1 | no | — |
| 132 | #336 | — | 10 | 2 | no | — |
| 133 | #332 | — | 10 | 2 | no | — |
| 134 | #331 | — | 10 | 2 | no | — |
| 135 | D4⋊C8 | — | 10 | 4 | no | — |
| 136 | C23×C5 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 137 | C22×D5 | — | 2 | 4 | no | — |
| 138 | C5×Q8 | — | 2 | 4 | no | — |
| 139 | C5×Q8 | — | 2 | 4 | no | — |
| 140 | C2×C4×C5 | — | 2 | 2 | no | — |
| 141 | C2×C4×C5 | — | 2 | 2 | no | — |
| 142 | C2×C4×C5 | — | 2 | 1 | no | — |
| 143 | C2×C4×C5 | — | 2 | 1 | no | — |
| 144 | C2×C4×C5 | — | 2 | 2 | no | — |
| 145 | C2×C4×C5 | — | 4 | 1 | no | — |
| 146 | C2×C4×C5 | — | 4 | 2 | no | — |
| 147 | C2×C4×C5 | #102 | 1 | 4 | yes | — |
| 148 | C2×C4×C5 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 149 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 151 | C2×C4×C5 | #120 | 1 | 2 | yes | — |
| 152 | C2×C4×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C5 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 155 | C22⋊D5 | — | 4 | 4 | no | — |
| 156 | C22⋊D5 | — | 4 | 4 | no | — |
| 157 | C2×Dic5 | — | 2 | 4 | no | — |
| 158 | D20 | — | 4 | 4 | no | — |
| 159 | D20 | — | 4 | 8 | no | — |
| 160 | D20 | — | 4 | 2 | no | — |
| 161 | D20 | — | 4 | 2 | no | — |
| 162 | D20 | — | 4 | 2 | no | — |
| 163 | D20 | — | 4 | 2 | no | — |
| 164 | D20 | — | 8 | 4 | no | — |
| 165 | C4×D5 | — | 4 | 16 | no | — |
| 166 | C4×D5 | — | 4 | 4 | no | — |
| 167 | C4×D5 | — | 4 | 4 | no | — |
| 168 | Dic10 | — | 4 | 8 | no | — |
| 169 | Dic10 | — | 4 | 2 | no | — |
| 170 | Dic10 | — | 4 | 2 | no | — |
| 171 | C5×C8 | — | 8 | 2 | no | — |
| 172 | #168 | — | 4 | 2 | no | — |
| 173 | #168 | — | 8 | 1 | no | — |
| 174 | 2−1+4 | — | 20 | 4 | no | — |
| 175 | 2−1+4 | — | 20 | 2 | no | — |
| 176 | 2−1+4 | — | 20 | 2 | no | — |
| 177 | C2×#41 | — | 10 | 4 | no | — |
| 178 | C2×#41 | — | 10 | 4 | no | — |
| 179 | C2×#41 | — | 10 | 2 | no | — |
| 180 | C22×Q8 | — | 10 | 4 | no | — |
| 181 | C22×Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 182 | C2×M16 | — | 2 | 2 | no | — |
| 183 | C22×C8 | — | 10 | 1 | no | — |
| 184 | C22×C8 | — | 10 | 1 | no | — |
| 185 | C4⋊Q8 | — | 5 | 2 | no | — |
| 186 | C4⋊Q8 | — | 10 | 2 | no | — |
| 187 | #127 | — | 5 | 2 | no | — |
| 188 | #127 | — | 10 | 2 | no | — |
| 189 | #124 | — | 10 | 4 | no | — |
| 190 | #124 | — | 10 | 2 | no | — |
| 191 | C22⋊Q8 | — | 10 | 8 | no | — |
| 192 | C22⋊Q8 | — | 10 | 4 | no | — |
| 193 | #121 | — | 5 | 4 | no | — |
| 194 | #121 | — | 10 | 8 | no | — |
| 195 | #121 | — | 10 | 4 | no | — |
| 196 | #121 | — | 10 | 4 | no | — |
| 197 | #121 | — | 10 | 2 | no | — |
| 198 | C4×Q8 | — | 2 | 2 | no | — |
| 199 | C4×Q8 | — | 2 | 2 | no | — |
| 200 | C4×D4 | — | 5 | 4 | no | — |
| 201 | C4×D4 | — | 10 | 4 | no | — |
| 202 | C4×D4 | — | 10 | 4 | no | — |
| 203 | C4×D4 | — | 10 | 2 | no | — |
| 204 | C2×C4⋊C4 | C4×D5 | 1 | 2 | yes | — |
| 205 | C2×C4⋊C4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 206 | C2×C42 | D20 | 1 | 2 | yes | — |
| 207 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 208 | C4⋊C8 | — | 2 | 2 | no | — |
| 209 | C4⋊C8 | — | 2 | 2 | no | — |
| 210 | C4⋊C8 | — | 10 | 2 | no | — |
| 211 | #101 | — | 4 | 2 | no | — |
| 212 | C4×C8 | — | 10 | 2 | no | — |
| 213 | C22×C5 | — | 2 | 1 | no | — |
| 214 | C22×C5 | — | 2 | 1 | no | — |
| 215 | C22×C5 | #379 | 1 | 1 | yes | characteristic |
| 216 | C22×C5 | C2×#102 | 1 | 1 | yes | characteristic |
| 217 | C22×C5 | #418 | 1 | 1 | yes | characteristic |
| 218 | C2×D5 | — | 4 | 4 | no | — |
| 219 | C2×D5 | — | 4 | 4 | no | — |
| 220 | C2×D5 | — | 4 | 4 | no | — |
| 221 | C4×C5 | — | 2 | 1 | no | — |
| 222 | C4×C5 | — | 2 | 4 | no | — |
| 223 | C4×C5 | — | 2 | 2 | no | — |
| 224 | C4×C5 | — | 4 | 2 | no | — |
| 225 | C4×C5 | #447 | 1 | 2 | yes | — |
| 226 | C4×C5 | #450 | 1 | 2 | yes | — |
| 227 | C4×C5 | #454 | 1 | 1 | yes | characteristic |
| 228 | C4×C5 | #456 | 1 | 1 | yes | characteristic |
| 229 | Dic5 | — | 4 | 4 | no | — |
| 230 | #41 | — | 20 | 8 | no | — |
| 231 | #41 | — | 20 | 8 | no | — |
| 232 | #41 | — | 20 | 8 | no | — |
| 233 | #41 | — | 20 | 8 | no | — |
| 234 | #41 | — | 20 | 2 | no | — |
| 235 | #41 | — | 20 | 2 | no | — |
| 236 | #41 | — | 20 | 2 | no | — |
| 237 | #41 | — | 20 | 2 | no | — |
| 238 | C2×Q8 | — | 2 | 2 | no | — |
| 239 | C2×Q8 | — | 2 | 2 | no | — |
| 240 | C2×Q8 | — | 10 | 4 | no | — |
| 241 | C2×Q8 | — | 10 | 2 | no | — |
| 242 | C2×Q8 | — | 20 | 8 | no | — |
| 243 | C2×Q8 | — | 20 | 8 | no | — |
| 244 | C2×Q8 | #686 | 1 | 2 | yes | — |
| 245 | C2×Q8 | #688 | 1 | 2 | yes | — |
| 246 | C2×D4 | — | 5 | 4 | no | — |
| 247 | C2×D4 | — | 10 | 4 | no | — |
| 248 | C2×D4 | — | 10 | 4 | no | — |
| 249 | C2×D4 | — | 10 | 4 | no | — |
| 250 | C2×D4 | — | 10 | 2 | no | — |
| 251 | C2×D4 | — | 10 | 2 | no | — |
| 252 | C22×C4 | — | 10 | 8 | no | — |
| 253 | C22×C4 | — | 10 | 4 | no | — |
| 254 | C22×C4 | #685 | 1 | 2 | yes | — |
| 255 | C22×C4 | #685 | 1 | 2 | yes | — |
| 256 | C22×C4 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 257 | C22×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 258 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 259 | M16 | — | 4 | 2 | no | — |
| 260 | M16 | — | 4 | 2 | no | — |
| 261 | C2×C8 | — | 4 | 2 | no | — |
| 262 | C2×C8 | — | 10 | 2 | no | — |
| 263 | C2×C8 | — | 20 | 1 | no | — |
| 264 | C2×C8 | — | 20 | 1 | no | — |
| 265 | C2×C8 | — | 20 | 2 | no | — |
| 266 | C2×C8 | — | 20 | 1 | no | — |
| 267 | C4⋊C4 | — | 2 | 4 | no | — |
| 268 | C4⋊C4 | — | 2 | 2 | no | — |
| 269 | C4⋊C4 | — | 5 | 4 | no | — |
| 270 | C4⋊C4 | — | 10 | 4 | no | — |
| 271 | C4⋊C4 | — | 10 | 2 | no | — |
| 272 | C22⋊C4 | — | 10 | 8 | no | — |
| 273 | C22⋊C4 | — | 10 | 4 | no | — |
| 274 | C22⋊C4 | — | 10 | 4 | no | — |
| 275 | C42 | — | 2 | 2 | no | — |
| 276 | C42 | — | 2 | 2 | no | — |
| 277 | C42 | D4×D5 | 1 | 2 | yes | — |
| 278 | C42 | D4×D5 | 1 | 2 | yes | — |
| 279 | C2×C5 | — | 2 | 1 | no | — |
| 280 | C2×C5 | — | 2 | 1 | no | — |
| 281 | C2×C5 | #1786 | 1 | 1 | yes | characteristic |
| 282 | C2×C5 | #1791 | 1 | 1 | yes | characteristic |
| 283 | C2×C5 | #1793 | 1 | 1 | yes | characteristic |
| 284 | D5 | — | 8 | 4 | no | — |
| 285 | C23 | — | 10 | 4 | no | — |
| 286 | C23 | C2×#685 | 1 | 1 | yes | characteristic |
| 287 | Q8 | — | 2 | 4 | no | — |
| 288 | Q8 | — | 2 | 4 | no | — |
| 289 | Q8 | — | 20 | 8 | no | — |
| 290 | Q8 | — | 20 | 2 | no | — |
| 291 | Q8 | — | 20 | 2 | no | — |
| 292 | D4 | — | 20 | 4 | no | — |
| 293 | D4 | — | 20 | 8 | no | — |
| 294 | D4 | — | 20 | 4 | no | — |
| 295 | D4 | — | 20 | 4 | no | — |
| 296 | D4 | — | 20 | 2 | no | — |
| 297 | D4 | — | 20 | 2 | no | — |
| 298 | D4 | — | 20 | 2 | no | — |
| 299 | D4 | — | 20 | 2 | no | — |
| 300 | D4 | — | 40 | 4 | no | — |
| 301 | C2×C4 | — | 2 | 2 | no | — |
| 302 | C2×C4 | — | 2 | 2 | no | — |
| 303 | C2×C4 | — | 2 | 1 | no | — |
| 304 | C2×C4 | — | 2 | 1 | no | — |
| 305 | C2×C4 | — | 2 | 2 | no | — |
| 306 | C2×C4 | — | 4 | 1 | no | — |
| 307 | C2×C4 | — | 4 | 2 | no | — |
| 308 | C2×C4 | — | 10 | 4 | no | — |
| 309 | C2×C4 | — | 20 | 16 | no | — |
| 310 | C2×C4 | — | 20 | 4 | no | — |
| 311 | C2×C4 | — | 20 | 4 | no | — |
| 312 | C2×C4 | #3941 | 1 | 4 | yes | — |
| 313 | C2×C4 | D5×C22⋊C4 | 1 | 2 | yes | — |
| 314 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 315 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 316 | C2×C4 | C2×#686 | 1 | 1 | yes | characteristic |
| 317 | C2×C4 | #4083 | 1 | 2 | yes | — |
| 318 | C2×C4 | C2×#688 | 1 | 1 | yes | characteristic |
| 319 | C2×C4 | #4095 | 1 | 2 | yes | — |
| 320 | C8 | — | 8 | 2 | no | — |
| 321 | C8 | — | 20 | 2 | no | — |
| 322 | C8 | — | 40 | 1 | no | — |
| 323 | C5 | #8354 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 324 | C22 | — | 2 | 1 | no | — |
| 325 | C22 | — | 2 | 1 | no | — |
| 326 | C22 | — | 20 | 4 | no | — |
| 327 | C22 | — | 20 | 4 | no | — |
| 328 | C22 | — | 20 | 4 | no | — |
| 329 | C22 | #65244 | 1 | 1 | yes | characteristic |
| 330 | C22 | C2×#3941 | 1 | 1 | yes | characteristic |
| 331 | C22 | #65290 | 1 | 1 | yes | characteristic |
| 332 | C4 | — | 2 | 4 | no | — |
| 333 | C4 | — | 2 | 1 | no | — |
| 334 | C4 | — | 2 | 2 | no | — |
| 335 | C4 | — | 4 | 2 | no | — |
| 336 | C4 | — | 20 | 4 | no | — |
| 337 | C4 | #65041 | 1 | 1 | yes | characteristic |
| 338 | C4 | #65042 | 1 | 1 | yes | characteristic |
| 339 | C4 | #65325 | 1 | 2 | yes | — |
| 340 | C4 | #65335 | 1 | 2 | yes | — |
| 341 | C2 | — | 2 | 1 | no | — |
| 342 | C2 | — | 2 | 1 | no | — |
| 343 | C2 | — | 40 | 4 | no | — |
| 344 | C2 | #10600314 | 1 | 1 | yes | characteristic |
| 345 | C2 | #10600914 | 1 | 1 | yes | characteristic |
| 346 | C2 | #10600936 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1801 | C2 | semidirect |
| 3. #10602427 | C2 | semidirect |
| 4. #10601296 | C2 | semidirect |
| 5. #10601291 | C2 | semidirect |
| 66. #1801 | D5 | semidirect |
| 323. C5 | #8354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617719 | 2 |
| C5×#1801 | 2 |
| #10602427 | 2 |
| #10601296 | 2 |
| #10601291 | 2 |
| #8354 | 5 |