Finite Group DatabasebetaFinite Group DatabasebetaOrder 4800.
2064 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 2064 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11925533 | C2 | semidirect |
| 2. C2×C4⋊(C3⋊#1043) | C2 | semidirect |
| 4. C2×C4×C3⋊#1043 | C2 | semidirect |
| 9. C2×C3×C52×D4 | C4 | semidirect |
| 10. C2×C3×C22⋊(C5⋊D5) | C4 | semidirect |
| 13. C2×C3×C4⋊(C5⋊D5) | C4 | semidirect |
| 34. C2×C3⋊#1043 | D4 | semidirect |
| 49. C2×C52×D4 | Dic3 | semidirect |
| 50. C2×C22⋊(C5⋊D5) | Dic3 | semidirect |
| 53. C2×C4⋊(C5⋊D5) | Dic3 | semidirect |
| 73. C3×C4×C52 | C22⋊C4 | semidirect |
| 74. C3×#1039 | C22⋊C4 | semidirect |
| 78. C2×C3×C5×D4 | AGL(1,𝔽5) | semidirect |
| 151. C4×C52 | #217 | semidirect |
| 152. #1039 | #217 | semidirect |
| 160. C2×C5×D4 | ΓL(1,𝔽16) | semidirect |
| 169. C3×C52 | #390 | semidirect |
| 185. C3×C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 199. C2×C3×D4 | #1043 | semidirect |
| 236. C52 | #5221 | semidirect |
| 270. C4×C5 | #6763 | semidirect |
| 277. C2×D4 | C3⋊#1043 | semidirect |
| 284. C3×C5 | #65780 | semidirect |
| 298. C3×C4 | C22⋊#1043 | semidirect |
| 334. C5 | #11752439 | semidirect |
| 350. C4 | #11925533 | semidirect |
| 351. C3 | #13104792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11925533 | 2 |
| C2×C4⋊(C3⋊#1043) | 2 |
| C2×C3×D4×C5⋊D5 | 2 |
| C2×C4×C3⋊#1043 | 2 |
| #13104792 | 3 |
| #11752439 | 5 |