Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1288 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 1288 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×C5⋊D5 |
| commutator, socle, cosocle | C23×C52 | C23 |
| Fitting | C52×#95 | C2 |
| hypercenter | #95 | C5⋊D5 |
| hypocenter | C52 | #392 |
| LCS | G ▷ C23×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 2. C2×#87808 | C2 | semidirect |
| 3. C52×#95 | C2 | semidirect |
| 16. C22×C5⋊D5 | D4 | semidirect |
| 18. C2×C4×C52 | D4 | semidirect |
| 23. C5×#95 | D5 | semidirect |
| 52. C2×C4×C5 | D20 | semidirect |
| 57. #95 | C5⋊D5 | semidirect |
| 58. C52 | #392 | semidirect |
| 88. C2×C4 | C4⋊(C5⋊D5) | semidirect |
| 89. C5 | #64960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C2×#87808 | 2 |
| C52×#95 | 2 |
| #64960 | 5 |