Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
384 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5⋊#1044 |
| commutator, hypocenter | C53 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | C2×C4 |
| prime radical | C2×D5×C5⋊D5 | C2 |
| cosocle | C5⋊(C5⋊D5) | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#92563 | C2 | semidirect |
| 3. D5⋊#1044 | C2 | direct (N × H) |
| 5. C2×C5×C5⋊D5 | C4 | semidirect |
| 6. C2×C52×D5 | C4 | semidirect |
| 7. D5×C5⋊D5 | C4 | semidirect |
| 9. #92563 | C22 | semidirect |
| 12. C2×C53 | C2×C4 | semidirect |
| 13. C5⋊(C5⋊D5) | C2×C4 | semidirect |
| 15. C5×C5⋊D5 | C2×C4 | semidirect |
| 16. C52×D5 | C2×C4 | semidirect |
| 26. C53 | C22×C4 | semidirect |
| 35. C2×C5⋊D5 | AGL(1,𝔽5) | semidirect |
| 39. C2×C5×D5 | AGL(1,𝔽5) | semidirect |
| 54. C2×C52 | C2×AGL(1,𝔽5) | semidirect |
| 55. C2×C52 | C2×AGL(1,𝔽5) | semidirect |
| 66. C5⋊D5 | C2×AGL(1,𝔽5) | semidirect |
| 70. C5×D5 | C2×AGL(1,𝔽5) | semidirect |
| 83. C52 | C22×AGL(1,𝔽5) | semidirect |
| 84. C52 | C22×AGL(1,𝔽5) | semidirect |
| 101. C2×D5 | #1044 | semidirect |
| 113. C2×C5 | D5⋊AGL(1,𝔽5) | semidirect |
| 114. C2×C5 | C2×#1044 | semidirect |
| 127. D5 | C2×#1044 | semidirect |
| 134. C5 | C2×D5⋊AGL(1,𝔽5) | semidirect |
| 135. C5 | C22×#1044 | semidirect |
| 146. C2 | D5⋊#1044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×C5⋊D5 | 2 |
| C2×#92563 | 2 |
| D5⋊#1044 | 2 |
| C22×#1044 | 5 |
| C2×D5⋊AGL(1,𝔽5) | 5 |