Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
792 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11717202 |
| commutator, cosocle | C23×C52 | C23 |
| Frattini | C23 | C22×C5⋊D5 |
| Fitting | C52×#99 | C2 |
| socle | C2×C52 | #120 |
| hypercenter | #99 | C5⋊D5 |
| hypocenter | C52 | B(4,𝔽2) |
| LCS | G ▷ C23×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #99 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717517 | C2 | semidirect |
| 2. #11717257 | C2 | semidirect |
| 3. #11717202 | C2 | semidirect |
| 4. C52×#99 | C2 | semidirect |
| 5. #11716673 | C2 | semidirect |
| 6. C23×C5⋊D5 | C22 | semidirect |
| 15. C52×C22⋊C4 | C22 | semidirect |
| 16. C22⋊#1039 | C22 | semidirect |
| 20. C23×C52 | D4 | semidirect |
| 26. C22×C5⋊D5 | D4 | semidirect |
| 29. C2×C4×C52 | D4 | semidirect |
| 36. C2×#1039 | D4 | semidirect |
| 44. C5×#99 | D5 | semidirect |
| 72. C5×C22⋊C4 | C2×D5 | semidirect |
| 83. C23×C5 | D20 | semidirect |
| 92. C2×C4×C5 | D20 | semidirect |
| 108. #99 | C5⋊D5 | semidirect |
| 109. C52 | B(4,𝔽2) | semidirect |
| 139. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 151. C23 | C4⋊(C5⋊D5) | semidirect |
| 166. C2×C4 | C4⋊(C5⋊D5) | semidirect |
| 167. C5 | #65030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717517 | 2 |
| #11717257 | 2 |
| #11717202 | 2 |
| C52×#99 | 2 |
| #11716673 | 2 |
| #65030 | 5 |