Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
237 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C25 | C2×D4 |
| commutator | C2×C4 | C23×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle | C22×C5 | C2×C5×D4 |
| prime radical | C5×#121 | C2×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C25 ◁ C22×C4×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×C25 | C2 | semidirect |
| 2. C2×SD16×C25 | C2 | semidirect |
| 4. C25×#103 | C2 | semidirect |
| 5. C25×C22⋊C8 | C2 | semidirect |
| 22. Q8×C25 | D4 | semidirect |
| 42. C22×C25 | SD16 | semidirect |
| 59. #448 | C25 | direct (N × H) |
| 79. C22×Q8 | C2×C25 | semidirect |
| 80. C2×SD16 | C2×C25 | semidirect |
| 82. #103 | C2×C25 | semidirect |
| 83. C22⋊C8 | C2×C25 | semidirect |
| 84. C25 | #448 | direct (N × H) |
| 116. Q8 | D4×C25 | semidirect |
| 132. C22 | SD16×C25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C25 | 2 |
| C2×SD16×C25 | 2 |
| C25×#121 | 2 |
| C25×#103 | 2 |
| C25×C22⋊C8 | 2 |
| C5×#448 | 5 |