Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
788 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 226 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 | C2×C52×#41 | C2 |
| socle | C22×C52 | C24 |
| hypercenter | C2×C5×#41 | D5 |
| hypocenter | C5 | C5×#550 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C5×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C52×#41 | C2 | semidirect |
| 2. C2×C5×#713 | C2 | semidirect |
| 3. C5×Q8×Dic5 | C2 | semidirect |
| 4. C5×#4086 | C2 | semidirect |
| 5. C5×#4084 | C2 | semidirect |
| 6. C5×#4076 | C2 | semidirect |
| 7. C4×C5×C22⋊D5 | C2 | semidirect |
| 23. #66168 | C5 | direct (N × H) |
| 26. C52×Q8 | D4 | semidirect |
| 40. C2×C5×#41 | D5 | semidirect |
| 41. C2×C5×#41 | C2×C5 | semidirect |
| 42. C2×#713 | C2×C5 | semidirect |
| 48. Q8×Dic5 | C2×C5 | semidirect |
| 49. #4086 | C2×C5 | semidirect |
| 50. #4084 | C2×C5 | semidirect |
| 51. #4076 | C2×C5 | semidirect |
| 52. C4×C22⋊D5 | C2×C5 | semidirect |
| 64. C5×Dic5 | #41 | semidirect |
| 109. C5×Q8 | C22⋊D5 | semidirect |
| 110. C5×Q8 | C5×D4 | semidirect |
| 138. C2×#41 | C5×D5 | semidirect |
| 144. C52 | #550 | semidirect |
| 174. Dic5 | C5×#41 | semidirect |
| 205. Q8 | C5×C22⋊D5 | semidirect |
| 218. C5 | #66168 | direct (N × H) |
| 219. C5 | C5×#550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| C2×C5×#713 | 2 |
| C5×Q8×Dic5 | 2 |
| C5×#4086 | 2 |
| C5×#4084 | 2 |
| C5×#4076 | 2 |
| C4×C5×C22⋊D5 | 2 |
| C5×#550 | 5 |
| #66168 | 5 |