Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
4778 conjugacy classes of subgroups; only the 727 normal subgroups are shown.
This group has 4778 conjugacy classes of subgroups — too many to draw. Only its 727 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 | #21438908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #21437755 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #21437751 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #21433499 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #21433490 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #21432559 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C59×#2884 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16838239 | — | 2 | 8 | no | — |
| 9 | #16838238 | — | 2 | 4 | no | — |
| 10 | #16838238 | C22 | 1 | 12 | yes | — |
| 11 | C2×#14273775 | — | 2 | 4 | no | — |
| 12 | C2×#14273775 | C22 | 1 | 2 | yes | — |
| 13 | 2−1+4×D59 | — | 2 | 8 | no | — |
| 14 | C22×#11745689 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #16838074 | — | 2 | 8 | no | — |
| 16 | #16838071 | — | 2 | 4 | no | — |
| 17 | #16838064 | — | 2 | 8 | no | — |
| 18 | #16838063 | — | 2 | 4 | no | — |
| 19 | #16837971 | C22 | 1 | 12 | yes | complemented |
| 20 | #16837966 | C22 | 1 | 6 | yes | complemented |
| 21 | #16837914 | C22 | 1 | 12 | yes | complemented |
| 22 | #16837909 | C22 | 1 | 6 | yes | complemented |
| 23 | #16837880 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #16837593 | C22 | 1 | 16 | yes | complemented |
| 25 | #16837590 | C22 | 1 | 48 | yes | complemented |
| 26 | #16837375 | C22 | 1 | 24 | yes | complemented |
| 27 | C2×2−1+4×C59 | C22 | 1 | 1 | yes | characteristic |
| 28 | C59×#519 | C22 | 1 | 2 | yes | complemented |
| 29 | C59×#410 | C22 | 1 | 12 | yes | complemented |
| 30 | #14273775 | — | 2 | 32 | no | — |
| 31 | #14273775 | — | 2 | 8 | no | — |
| 32 | #14273775 | — | 2 | 12 | no | — |
| 33 | #14273775 | — | 2 | 8 | no | — |
| 34 | #14273774 | — | 2 | 16 | no | — |
| 35 | #14273774 | — | 2 | 24 | no | — |
| 36 | #14273773 | — | 2 | 16 | no | — |
| 37 | #14273773 | — | 2 | 24 | no | — |
| 38 | #14273772 | — | 2 | 12 | no | — |
| 39 | #14273772 | C23 | 1 | 16 | yes | — |
| 40 | C2×#11745689 | — | 2 | 16 | no | — |
| 41 | C2×#11745689 | — | 2 | 4 | no | — |
| 42 | C2×#11745689 | — | 2 | 8 | no | — |
| 43 | C2×#11745689 | D4 | 1 | 8 | yes | complemented |
| 44 | C2×#11745685 | — | 2 | 24 | no | — |
| 45 | C2×#11745685 | C23 | 1 | 12 | yes | — |
| 46 | #41×D59 | — | 2 | 32 | no | — |
| 47 | #41×D59 | — | 2 | 48 | no | — |
| 48 | C2×Q8×D59 | — | 2 | 16 | no | — |
| 49 | C2×Q8×D59 | D4 | 1 | 8 | yes | complemented |
| 50 | C22×D236 | C23 | 1 | 3 | yes | — |
| 51 | C22×C4×D59 | C23 | 1 | 3 | yes | — |
| 52 | #14273724 | — | 2 | 12 | no | — |
| 53 | #14273723 | — | 2 | 6 | no | — |
| 54 | #14273716 | — | 2 | 6 | no | — |
| 55 | #14273715 | — | 2 | 12 | no | — |
| 56 | #14273711 | C23 | 1 | 8 | yes | — |
| 57 | #14273708 | C23 | 1 | 4 | yes | — |
| 58 | #14273707 | — | 2 | 12 | no | — |
| 59 | #14273703 | — | 2 | 6 | no | — |
| 60 | #14273702 | — | 2 | 12 | no | — |
| 61 | #14273702 | — | 2 | 24 | no | — |
| 62 | #14273701 | — | 2 | 12 | no | — |
| 63 | #14273698 | — | 2 | 6 | no | — |
| 64 | #14273697 | C23 | 1 | 24 | yes | — |
| 65 | #14273695 | C23 | 1 | 12 | yes | — |
| 66 | Q8×Dic59 | — | 2 | 4 | no | — |
| 67 | C4×D236 | — | 2 | 24 | no | — |
| 68 | C4×C22⋊D59 | — | 2 | 12 | no | — |
| 69 | #14273686 | C23 | 1 | 6 | yes | — |
| 70 | #14273641 | C23 | 1 | 32 | yes | — |
| 71 | 2−1+4×C59 | — | 2 | 8 | no | — |
| 72 | C2×#41×C59 | D4 | 1 | 4 | yes | complemented |
| 73 | C2×#41×C59 | C23 | 1 | 6 | yes | — |
| 74 | C22×Q8×C59 | D4 | 1 | 4 | yes | complemented |
| 75 | C22×Q8×C59 | C23 | 1 | 1 | yes | characteristic |
| 76 | C4×Q8×C59 | — | 2 | 8 | no | — |
| 77 | #117×C59 | C23 | 1 | 12 | yes | — |
| 78 | #99×C59 | C23 | 1 | 16 | yes | — |
| 79 | C23×D59 | C24 | 1 | 3 | yes | — |
| 80 | #41×C59 | — | 2 | 16 | no | — |
| 81 | #41×C59 | — | 2 | 24 | no | — |
| 82 | C2×Q8×C59 | — | 2 | 16 | no | — |
| 83 | C2×Q8×C59 | C2×D4 | 1 | 6 | yes | — |
| 84 | C2×Q8×C59 | C2×D4 | 1 | 4 | yes | — |
| 85 | C2×Q8×C59 | C2×D4 | 1 | 8 | yes | — |
| 86 | C2×D4×C59 | C2×D4 | 1 | 6 | yes | — |
| 87 | C2×D4×C59 | C24 | 1 | 4 | yes | — |
| 88 | C22×C4×C59 | C2×D4 | 1 | 12 | yes | — |
| 89 | C22×C4×C59 | C24 | 1 | 3 | yes | — |
| 90 | C2×C22⋊D59 | — | 2 | 16 | no | — |
| 91 | C2×C22⋊D59 | — | 2 | 12 | no | — |
| 92 | C2×C22⋊D59 | C24 | 1 | 8 | yes | — |
| 93 | C22×Dic59 | C24 | 1 | 1 | yes | characteristic |
| 94 | #11745689 | — | 2 | 48 | no | — |
| 95 | #11745689 | — | 2 | 32 | no | — |
| 96 | #11745689 | — | 4 | 16 | no | — |
| 97 | Q8×D59 | — | 2 | 48 | no | — |
| 98 | Q8×D59 | — | 2 | 32 | no | — |
| 99 | #11745687 | — | 2 | 48 | no | — |
| 100 | #11745687 | — | 2 | 32 | no | — |
| 101 | D4×D59 | — | 2 | 48 | no | — |
| 102 | D4×D59 | — | 2 | 32 | no | — |
| 103 | #11745685 | — | 2 | 48 | no | — |
| 104 | #11745685 | — | 2 | 48 | no | — |
| 105 | #11745685 | — | 2 | 24 | no | — |
| 106 | #11745685 | — | 2 | 16 | no | — |
| 107 | #11745685 | — | 2 | 24 | no | — |
| 108 | C2×D236 | — | 2 | 24 | no | — |
| 109 | C2×D236 | — | 2 | 6 | no | — |
| 110 | C2×D236 | — | 2 | 12 | no | — |
| 111 | C2×D236 | — | 2 | 24 | no | — |
| 112 | C2×D236 | C2×D4 | 1 | 12 | yes | — |
| 113 | C2×C4×D59 | — | 2 | 48 | no | — |
| 114 | C2×C4×D59 | — | 2 | 6 | no | — |
| 115 | C2×C4×D59 | — | 2 | 12 | no | — |
| 116 | C2×C4×D59 | C2×D4 | 1 | 24 | yes | — |
| 117 | C2×Dic118 | — | 2 | 24 | no | — |
| 118 | C2×Dic118 | C2×D4 | 1 | 12 | yes | — |
| 119 | C4⋊C4×C59 | — | 2 | 12 | no | — |
| 120 | C22⋊C4×C59 | C24 | 1 | 8 | yes | — |
| 121 | C42×C59 | — | 2 | 12 | no | — |
| 122 | C22⋊Dic59 | — | 2 | 4 | no | — |
| 123 | C22⋊Dic59 | C24 | 1 | 4 | yes | — |
| 124 | (C2×D59)⋊C4 | — | 2 | 8 | no | — |
| 125 | (C2×D59)⋊C4 | — | 2 | 12 | no | — |
| 126 | (C2×D59)⋊C4 | — | 2 | 24 | no | — |
| 127 | C4⋊Dic59 | — | 2 | 6 | no | — |
| 128 | C4⋊Dic59 | — | 2 | 8 | no | — |
| 129 | Dic59⋊C4 | — | 2 | 4 | no | — |
| 130 | C4×Dic59 | — | 2 | 6 | no | — |
| 131 | C23×C59 | C22×D4 | 1 | 4 | yes | — |
| 132 | C23×C59 | C25 | 1 | 1 | yes | characteristic |
| 133 | C22×D59 | — | 2 | 16 | no | — |
| 134 | C22×D59 | — | 2 | 6 | no | — |
| 135 | C22×D59 | — | 2 | 3 | no | — |
| 136 | C22×D59 | — | 8 | 3 | no | — |
| 137 | C22×D59 | C22×D4 | 1 | 8 | yes | — |
| 138 | Q8×C59 | — | 2 | 12 | no | — |
| 139 | Q8×C59 | #120 | 1 | 16 | yes | — |
| 140 | D4×C59 | — | 2 | 8 | no | — |
| 141 | D4×C59 | — | 2 | 12 | no | — |
| 142 | C2×C4×C59 | — | 2 | 24 | no | — |
| 143 | C2×C4×C59 | — | 2 | 8 | no | — |
| 144 | C2×C4×C59 | C22×D4 | 1 | 12 | yes | — |
| 145 | C2×C4×C59 | C22×D4 | 1 | 4 | yes | — |
| 146 | C2×C4×C59 | C22×D4 | 1 | 6 | yes | — |
| 147 | C22⋊D59 | — | 2 | 32 | no | — |
| 148 | C22⋊D59 | — | 2 | 8 | no | — |
| 149 | C22⋊D59 | — | 2 | 8 | no | — |
| 150 | C22⋊D59 | — | 8 | 12 | no | — |
| 151 | C2×Dic59 | — | 2 | 16 | no | — |
| 152 | C2×Dic59 | — | 2 | 4 | no | — |
| 153 | C2×Dic59 | — | 2 | 1 | no | — |
| 154 | C2×Dic59 | — | 2 | 2 | no | — |
| 155 | C2×Dic59 | C22×D4 | 1 | 8 | yes | — |
| 156 | D236 | — | 2 | 16 | no | — |
| 157 | D236 | — | 2 | 24 | no | — |
| 158 | D236 | — | 4 | 12 | no | — |
| 159 | D236 | — | 8 | 24 | no | — |
| 160 | C4×D59 | — | 2 | 32 | no | — |
| 161 | C4×D59 | — | 2 | 48 | no | — |
| 162 | C4×D59 | — | 4 | 12 | no | — |
| 163 | Dic118 | — | 2 | 16 | no | — |
| 164 | Dic118 | — | 2 | 24 | no | — |
| 165 | #60402 | — | 59 | 1 | no | maximal, Sylow |
| 166 | C22×C59 | — | 2 | 4 | no | — |
| 167 | C22×C59 | — | 4 | 1 | no | — |
| 168 | C22×C59 | — | 4 | 4 | no | — |
| 169 | C22×C59 | C23×D4 | 1 | 2 | yes | — |
| 170 | C22×C59 | C23×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×D59 | — | 2 | 8 | no | — |
| 172 | C2×D59 | — | 4 | 8 | no | — |
| 173 | C2×D59 | — | 4 | 12 | no | — |
| 174 | C2×D59 | — | 4 | 6 | no | — |
| 175 | C2×D59 | — | 4 | 3 | no | — |
| 176 | C2×D59 | — | 8 | 16 | no | — |
| 177 | C4×C59 | — | 2 | 4 | no | — |
| 178 | C4×C59 | — | 4 | 8 | no | — |
| 179 | C4×C59 | C2×#120 | 1 | 12 | yes | — |
| 180 | Dic59 | — | 2 | 8 | no | — |
| 181 | Dic59 | — | 4 | 4 | no | — |
| 182 | Dic59 | — | 4 | 1 | no | — |
| 183 | 2−1+6 | — | 59 | 1 | no | — |
| 184 | #3487 | — | 59 | 1 | no | — |
| 185 | #3487 | — | 59 | 2 | no | — |
| 186 | #3027 | — | 59 | 12 | no | — |
| 187 | #3025 | — | 59 | 12 | no | — |
| 188 | #2884 | — | 59 | 2 | no | — |
| 189 | #2884 | D59 | 1 | 1 | yes | characteristic, complemented |
| 190 | C2×C59 | — | 2 | 1 | no | — |
| 191 | C2×C59 | — | 2 | 2 | no | — |
| 192 | C2×C59 | — | 4 | 4 | no | — |
| 193 | C2×C59 | C22×#120 | 1 | 1 | yes | characteristic |
| 194 | D59 | — | 4 | 8 | no | — |
| 195 | D59 | — | 8 | 3 | no | — |
| 196 | #585 | — | 59 | 12 | no | — |
| 197 | #585 | — | 118 | 8 | no | — |
| 198 | #585 | — | 118 | 4 | no | — |
| 199 | C2×2−1+4 | — | 59 | 2 | no | — |
| 200 | C2×2−1+4 | — | 118 | 8 | no | — |
| 201 | C2×2−1+4 | — | 118 | 4 | no | — |
| 202 | C2×2−1+4 | C2×D59 | 1 | 1 | yes | characteristic |
| 203 | C22×#41 | — | 59 | 1 | no | — |
| 204 | #550 | — | 118 | 8 | no | — |
| 205 | #550 | — | 118 | 4 | no | — |
| 206 | #548 | — | 118 | 8 | no | — |
| 207 | #548 | — | 118 | 4 | no | — |
| 208 | #535 | — | 59 | 6 | no | — |
| 209 | #535 | — | 59 | 12 | no | — |
| 210 | #525 | — | 59 | 6 | no | — |
| 211 | #525 | — | 59 | 12 | no | — |
| 212 | #519 | — | 59 | 1 | no | — |
| 213 | #519 | C2×D59 | 1 | 2 | yes | complemented |
| 214 | #458 | — | 59 | 16 | no | — |
| 215 | B(4,𝔽2) | — | 59 | 48 | no | — |
| 216 | #410 | — | 59 | 24 | no | — |
| 217 | #410 | C2×D59 | 1 | 12 | yes | complemented |
| 218 | C59 | #60402 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 219 | 2−1+4 | — | 2 | 8 | no | — |
| 220 | 2−1+4 | — | 118 | 32 | no | — |
| 221 | 2−1+4 | — | 118 | 24 | no | — |
| 222 | 2−1+4 | — | 118 | 16 | no | — |
| 223 | 2−1+4 | — | 118 | 8 | no | — |
| 224 | 2−1+4 | — | 118 | 12 | no | — |
| 225 | 2−1+4 | — | 118 | 8 | no | — |
| 226 | H(5,𝔽2) | — | 59 | 16 | no | — |
| 227 | H(5,𝔽2) | — | 118 | 24 | no | — |
| 228 | H(5,𝔽2) | — | 118 | 16 | no | — |
| 229 | H(5,𝔽2) | — | 118 | 12 | no | — |
| 230 | C2×#41 | — | 59 | 8 | no | — |
| 231 | C2×#41 | — | 59 | 12 | no | — |
| 232 | C2×#41 | — | 118 | 48 | no | — |
| 233 | C2×#41 | — | 118 | 16 | no | — |
| 234 | C2×#41 | — | 118 | 32 | no | — |
| 235 | C2×#41 | — | 118 | 4 | no | — |
| 236 | C2×#41 | — | 118 | 8 | no | — |
| 237 | C2×#41 | — | 118 | 24 | no | — |
| 238 | C2×#41 | D236 | 1 | 4 | yes | complemented |
| 239 | C2×#41 | C22×D59 | 1 | 6 | yes | — |
| 240 | C22×Q8 | — | 59 | 8 | no | — |
| 241 | C22×Q8 | — | 118 | 16 | no | — |
| 242 | C22×Q8 | D236 | 1 | 4 | yes | complemented |
| 243 | C22×Q8 | C22×D59 | 1 | 1 | yes | characteristic |
| 244 | C22×D4 | — | 59 | 3 | no | — |
| 245 | C23×C4 | — | 59 | 3 | no | — |
| 246 | #127 | — | 118 | 12 | no | — |
| 247 | #127 | — | 118 | 6 | no | — |
| 248 | #124 | — | 118 | 12 | no | — |
| 249 | #124 | — | 118 | 6 | no | — |
| 250 | #123 | — | 59 | 4 | no | — |
| 251 | #123 | — | 59 | 8 | no | — |
| 252 | C22⋊Q8 | — | 118 | 12 | no | — |
| 253 | C22⋊Q8 | — | 118 | 6 | no | — |
| 254 | #121 | — | 118 | 24 | no | — |
| 255 | #121 | — | 118 | 12 | no | — |
| 256 | #121 | — | 118 | 6 | no | — |
| 257 | #121 | — | 118 | 12 | no | — |
| 258 | #120 | — | 59 | 12 | no | — |
| 259 | #120 | — | 59 | 24 | no | — |
| 260 | C4×Q8 | — | 2 | 8 | no | — |
| 261 | C4×Q8 | — | 118 | 4 | no | — |
| 262 | C4×D4 | — | 118 | 24 | no | — |
| 263 | C4×D4 | — | 118 | 12 | no | — |
| 264 | #117 | — | 59 | 6 | no | — |
| 265 | #117 | C22×D59 | 1 | 12 | yes | — |
| 266 | #99 | — | 59 | 32 | no | — |
| 267 | #99 | C22×D59 | 1 | 16 | yes | — |
| 268 | C24 | — | 59 | 3 | no | — |
| 269 | #41 | — | 2 | 16 | no | — |
| 270 | #41 | — | 2 | 24 | no | — |
| 271 | #41 | — | 118 | 48 | no | — |
| 272 | #41 | — | 118 | 48 | no | — |
| 273 | #41 | — | 118 | 32 | no | — |
| 274 | #41 | — | 118 | 48 | no | — |
| 275 | #41 | — | 118 | 48 | no | — |
| 276 | #41 | — | 118 | 32 | no | — |
| 277 | #41 | — | 118 | 24 | no | — |
| 278 | #41 | — | 118 | 24 | no | — |
| 279 | #41 | — | 118 | 16 | no | — |
| 280 | #41 | — | 236 | 16 | no | — |
| 281 | C2×Q8 | — | 2 | 16 | no | — |
| 282 | C2×Q8 | — | 59 | 12 | no | — |
| 283 | C2×Q8 | — | 118 | 24 | no | — |
| 284 | C2×Q8 | — | 118 | 48 | no | — |
| 285 | C2×Q8 | — | 118 | 32 | no | — |
| 286 | C2×Q8 | C2×D236 | 1 | 6 | yes | — |
| 287 | C2×Q8 | C2×D236 | 1 | 4 | yes | — |
| 288 | C2×Q8 | D4×D59 | 1 | 8 | yes | — |
| 289 | C2×D4 | — | 59 | 8 | no | — |
| 290 | C2×D4 | — | 59 | 12 | no | — |
| 291 | C2×D4 | — | 118 | 24 | no | — |
| 292 | C2×D4 | — | 118 | 24 | no | — |
| 293 | C2×D4 | — | 118 | 32 | no | — |
| 294 | C2×D4 | — | 118 | 48 | no | — |
| 295 | C2×D4 | — | 118 | 16 | no | — |
| 296 | C2×D4 | — | 118 | 12 | no | — |
| 297 | C2×D4 | — | 118 | 12 | no | — |
| 298 | C2×D4 | — | 118 | 6 | no | — |
| 299 | C2×D4 | C2×D236 | 1 | 6 | yes | — |
| 300 | C2×D4 | C23×D59 | 1 | 4 | yes | — |
| 301 | C22×C4 | — | 59 | 24 | no | — |
| 302 | C22×C4 | — | 59 | 1 | no | — |
| 303 | C22×C4 | — | 118 | 48 | no | — |
| 304 | C22×C4 | — | 118 | 12 | no | — |
| 305 | C22×C4 | — | 118 | 6 | no | — |
| 306 | C22×C4 | C2×D236 | 1 | 12 | yes | — |
| 307 | C22×C4 | C23×D59 | 1 | 3 | yes | — |
| 308 | C4⋊C4 | — | 2 | 12 | no | — |
| 309 | C4⋊C4 | — | 118 | 8 | no | — |
| 310 | C4⋊C4 | — | 118 | 6 | no | — |
| 311 | C4⋊C4 | — | 118 | 4 | no | — |
| 312 | C22⋊C4 | — | 59 | 4 | no | — |
| 313 | C22⋊C4 | — | 118 | 24 | no | — |
| 314 | C22⋊C4 | — | 118 | 8 | no | — |
| 315 | C22⋊C4 | — | 118 | 4 | no | — |
| 316 | C22⋊C4 | — | 118 | 12 | no | — |
| 317 | C22⋊C4 | C23×D59 | 1 | 8 | yes | — |
| 318 | C42 | — | 2 | 12 | no | — |
| 319 | C42 | — | 118 | 6 | no | — |
| 320 | C23 | — | 59 | 8 | no | — |
| 321 | C23 | — | 118 | 16 | no | — |
| 322 | C23 | — | 118 | 6 | no | — |
| 323 | C23 | — | 118 | 3 | no | — |
| 324 | C23 | — | 472 | 3 | no | — |
| 325 | C23 | C22×D236 | 1 | 4 | yes | — |
| 326 | C23 | C24×D59 | 1 | 1 | yes | characteristic |
| 327 | Q8 | — | 2 | 12 | no | — |
| 328 | Q8 | — | 118 | 16 | no | — |
| 329 | Q8 | — | 118 | 24 | no | — |
| 330 | Q8 | #14273697 | 1 | 16 | yes | — |
| 331 | D4 | — | 2 | 8 | no | — |
| 332 | D4 | — | 2 | 12 | no | — |
| 333 | D4 | — | 118 | 16 | no | — |
| 334 | D4 | — | 118 | 32 | no | — |
| 335 | D4 | — | 118 | 8 | no | — |
| 336 | D4 | — | 118 | 8 | no | — |
| 337 | D4 | — | 118 | 24 | no | — |
| 338 | D4 | — | 472 | 24 | no | — |
| 339 | D4 | — | 472 | 12 | no | — |
| 340 | D4 | — | 236 | 12 | no | — |
| 341 | C2×C4 | — | 2 | 24 | no | — |
| 342 | C2×C4 | — | 2 | 8 | no | — |
| 343 | C2×C4 | — | 59 | 8 | no | — |
| 344 | C2×C4 | — | 118 | 32 | no | — |
| 345 | C2×C4 | — | 118 | 16 | no | — |
| 346 | C2×C4 | — | 118 | 48 | no | — |
| 347 | C2×C4 | — | 118 | 2 | no | — |
| 348 | C2×C4 | — | 118 | 4 | no | — |
| 349 | C2×C4 | — | 118 | 1 | no | — |
| 350 | C2×C4 | — | 236 | 12 | no | — |
| 351 | C2×C4 | C2×D4×D59 | 1 | 12 | yes | — |
| 352 | C2×C4 | C22×D236 | 1 | 4 | yes | — |
| 353 | C2×C4 | C22×D236 | 1 | 6 | yes | — |
| 354 | C22 | — | 2 | 4 | no | — |
| 355 | C22 | — | 4 | 1 | no | — |
| 356 | C22 | — | 4 | 4 | no | — |
| 357 | C22 | — | 118 | 8 | no | — |
| 358 | C22 | — | 472 | 16 | no | — |
| 359 | C22 | — | 236 | 12 | no | — |
| 360 | C22 | — | 236 | 6 | no | — |
| 361 | C22 | — | 236 | 8 | no | — |
| 362 | C22 | — | 236 | 3 | no | — |
| 363 | C22 | C22×D4×D59 | 1 | 2 | yes | — |
| 364 | C22 | C23×D236 | 1 | 1 | yes | characteristic |
| 365 | C4 | — | 2 | 4 | no | — |
| 366 | C4 | — | 4 | 8 | no | — |
| 367 | C4 | — | 118 | 8 | no | — |
| 368 | C4 | — | 236 | 4 | no | — |
| 369 | C4 | — | 236 | 1 | no | — |
| 370 | C4 | C2×#14273697 | 1 | 12 | yes | — |
| 371 | C2 | — | 2 | 2 | no | — |
| 372 | C2 | — | 2 | 1 | no | — |
| 373 | C2 | — | 4 | 4 | no | — |
| 374 | C2 | — | 472 | 3 | no | — |
| 375 | C2 | — | 236 | 8 | no | — |
| 376 | C2 | C22×#14273697 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21438908 | C2 | semidirect |
| 2. #21437755 | C2 | semidirect |
| 3. #21437751 | C2 | semidirect |
| 4. #21433499 | C2 | semidirect |
| 5. #21433490 | C2 | semidirect |
| 6. #21432559 | C2 | semidirect |
| 7. C59×#2884 | C2 | semidirect |
| 14. C22×#11745689 | C22 | semidirect |
| 19. #16837971 | C22 | semidirect |
| 20. #16837966 | C22 | semidirect |
| 21. #16837914 | C22 | semidirect |
| 22. #16837909 | C22 | semidirect |
| 23. #16837880 | C22 | semidirect |
| 24. #16837593 | C22 | semidirect |
| 25. #16837590 | C22 | semidirect |
| 26. #16837375 | C22 | semidirect |
| 28. C59×#519 | C22 | semidirect |
| 29. C59×#410 | C22 | semidirect |
| 43. C2×#11745689 | D4 | semidirect |
| 49. C2×Q8×D59 | D4 | semidirect |
| 72. C2×#41×C59 | D4 | semidirect |
| 74. C22×Q8×C59 | D4 | semidirect |
| 189. #2884 | D59 | semidirect |
| 213. #519 | C2×D59 | semidirect |
| 217. #410 | C2×D59 | semidirect |
| 218. C59 | #60402 | semidirect |
| 238. C2×#41 | D236 | semidirect |
| 242. C22×Q8 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438908 | 2 |
| #21437755 | 2 |
| #21437751 | 2 |
| #21433499 | 2 |
| #21433490 | 2 |
| #21432559 | 2 |
| C59×#2884 | 2 |
| #60402 | 59 |