Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
694 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C5 |
| Frattini | C22 | C23×C5×D5 |
| Fitting | C4×C52×Q8 | C2 |
| socle | C22×C52 | C24 |
| hypercenter | C4×C5×Q8 | D5 |
| hypocenter | C5 | C5×#550 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C5 ◁ C4×C5×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#713 | C2 | semidirect |
| 2. C4×C52×Q8 | C2 | semidirect |
| 3. C5×#4041 | C2 | semidirect |
| 4. C5×#4020 | C2 | semidirect |
| 5. C4×C5×D20 | C2 | semidirect |
| 17. #65911 | C5 | direct (N × H) |
| 19. C52×Q8 | D4 | semidirect |
| 29. C2×#713 | C2×C5 | semidirect |
| 33. C4×C5×Q8 | D5 | semidirect |
| 34. C4×C5×Q8 | C2×C5 | semidirect |
| 36. #4041 | C2×C5 | semidirect |
| 37. #4020 | C2×C5 | semidirect |
| 38. C4×D20 | C2×C5 | semidirect |
| 45. C4×C52 | #41 | semidirect |
| 78. C5×Q8 | D20 | semidirect |
| 79. C5×Q8 | C5×D4 | semidirect |
| 102. C4×Q8 | C5×D5 | semidirect |
| 104. C52 | #550 | semidirect |
| 121. C4×C5 | #713 | semidirect |
| 123. C4×C5 | C5×#41 | semidirect |
| 147. Q8 | C5×D20 | semidirect |
| 157. C5 | #65911 | direct (N × H) |
| 158. C5 | C5×#550 | semidirect |
| 166. C4 | C5×#713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C4×C52×Q8 | 2 |
| C5×#4041 | 2 |
| C5×#4020 | 2 |
| C4×C5×D20 | 2 |
| C5×#550 | 5 |
| #65911 | 5 |