Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1008 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×#127 | C2 |
| hypercenter | #127 | C5⋊D5 |
| hypocenter | C52 | #560 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×#127 | C2 | semidirect |
| 2. #11717259 | C2 | semidirect |
| 3. #11717257 | C2 | semidirect |
| 4. #11717255 | C2 | semidirect |
| 5. #11717196 | C2 | semidirect |
| 8. C2×C52×D4 | C22 | semidirect |
| 10. C22×#1039 | C22 | semidirect |
| 11. C42×C52 | C22 | semidirect |
| 13. C22⋊#1039 | C22 | semidirect |
| 15. #87806 | C22 | semidirect |
| 27. C5×#127 | D5 | semidirect |
| 42. C2×C5×D4 | C2×D5 | semidirect |
| 45. C42×C5 | C2×D5 | semidirect |
| 65. #127 | C5⋊D5 | semidirect |
| 70. C52 | #560 | semidirect |
| 82. C2×D4 | C2×C5⋊D5 | semidirect |
| 88. C42 | C2×C5⋊D5 | semidirect |
| 103. C5 | #66054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#127 | 2 |
| #11717259 | 2 |
| #11717257 | 2 |
| #11717255 | 2 |
| #11717196 | 2 |
| #66054 | 5 |