Finite Group DatabasebetaFinite Group DatabasebetaOrder 14700.
164 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52×#3862 | C22 |
| Fitting, socle | C52×C72 | C2×D3 |
| LCS | G ▷ C52×#3862 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5⋊(C5⋊#64418) | C2 | semidirect |
| 2. C5×C5⋊#64418 | C2 | semidirect |
| 3. C5×C5⋊#64425 | C2 | semidirect |
| 5. C52×#3862 | C22 | semidirect |
| 9. C5×C5⋊(C7⋊D7) | D3 | semidirect |
| 11. C5⋊#64425 | D5 | semidirect |
| 16. C5⋊#64418 | D5 | semidirect |
| 18. C52×C72 | C2×D3 | semidirect |
| 23. C5×#3862 | C2×D5 | semidirect |
| 24. C5×#3862 | C2×D5 | semidirect |
| 29. C5⋊(C7⋊D7) | D15 | semidirect |
| 48. C5×C72 | D3×D5 | semidirect |
| 49. C5×C72 | C2×D15 | semidirect |
| 59. #3862 | D52 | semidirect |
| 93. C72 | D5×D15 | semidirect |
| 113. C52 | #64418⋊C2 | semidirect |
| 142. C5 | #64418⋊D5 | semidirect |
| 143. C5 | #15668791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊(C5⋊#64418) | 2 |
| C5×C5⋊#64418 | 2 |
| C5×C5⋊#64425 | 2 |
| D35⋊D35 | 3 |
| #15668791 | 5 |
| #64418⋊D5 | 5 |
| D5×D15 | 49 |