Finite Group DatabasebetaFinite Group DatabasebetaOrder 14700.
240 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 50 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, Fitting, socle, cosocle, hypocenter | C52×C72 | C22×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5⋊D5×#3862 | C2 | semidirect |
| 2. C5×D5×#3862 | C2 | semidirect |
| 3. C72×D52 | C3 | semidirect |
| 4. C52×#3862 | C22 | semidirect |
| 6. C72×C5⋊D5 | C2×C3 | semidirect |
| 7. C5×C72×D5 | C2×C3 | semidirect |
| 12. D5×#3862 | D5 | direct (N × H) |
| 13. C52×C72 | C22×C3 | semidirect |
| 18. C5×#3862 | C2×D5 | semidirect |
| 20. C7×D52 | ΓL(1,𝔽8) | semidirect |
| 26. C72×D5 | C3×D5 | semidirect |
| 29. C7×C5⋊D5 | C2×ΓL(1,𝔽8) | semidirect |
| 31. C5×C7×D5 | C2×ΓL(1,𝔽8) | semidirect |
| 36. C5×C72 | C2×C3×D5 | semidirect |
| 43. C52×C7 | C22×ΓL(1,𝔽8) | semidirect |
| 46. #3862 | D52 | direct (N × H) |
| 51. D52 | #3862 | direct (N × H) |
| 63. C7×D5 | D5×ΓL(1,𝔽8) | semidirect |
| 65. C5⋊D5 | C2×#3862 | semidirect |
| 66. C5×D5 | C2×#3862 | semidirect |
| 67. C72 | C3×D52 | semidirect |
| 73. C5×C7 | C2×D5×ΓL(1,𝔽8) | semidirect |
| 80. C52 | C22×#3862 | semidirect |
| 93. D5 | D5×#3862 | direct (N × H) |
| 95. C7 | D52×ΓL(1,𝔽8) | semidirect |
| 99. C5 | C2×D5×#3862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊D5×#3862 | 2 |
| C5×D5×#3862 | 2 |
| C72×D52 | 3 |
| C2×D5×#3862 | 5 |
| D52×ΓL(1,𝔽8) | 7 |