Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
165 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 165 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×C4×C25 | D4 |
| commutator | C4 | C22×C4×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle, prime radical | C22×C5 | C2×C5×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C25 ◁ C42×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. Q16×C25 | C4 | direct (N × H) |
| 33. C4×C25 | Q16 | direct (N × H) |
| 44. C4×Q16 | C25 | direct (N × H) |
| 62. C25 | C4×Q16 | direct (N × H) |
| 71. Q16 | C4×C25 | direct (N × H) |
| 95. C4 | Q16×C25 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C25 | 2 |
| C4×Q8×C25 | 2 |
| C25×#107 | 2 |
| C25×#103 | 2 |
| C4×C8×C25 | 2 |
| C4×C5×Q16 | 5 |