Subgroups — D₅₁×D₁₅₇ #44545112

Order 32028.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₀₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅₁×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₇×D₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₁₅₇	—	3	1	no	maximal, Hall
5	C₃×C₁₇×C₁₅₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₆₆₉	—	3	1	no	—
7	C₁₇×D₁₅₇	D₃	1	1	yes	characteristic, complemented
8	D₁₇×C₁₅₇	—	3	1	no	—
9	C₁₇×C₁₅₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₁₅₇	—	17	1	no	maximal, Hall
11	D₄₇₁	—	17	1	no	—
12	C₃×D₁₅₇	D₁₇	1	1	yes	characteristic, complemented
13	D₃×C₁₅₇	—	17	1	no	—
14	C₂×D₁₅₇	—	51	1	no	Hall
15	C₃×C₁₅₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₅₇	—	51	1	no	—
17	D₁₅₇	—	51	1	no	—
18	D₁₅₇	D₅₁	1	1	yes	characteristic, direct product factor
19	C₂×D₅₁	—	157	1	no	maximal, Hall
20	C₁₅₇	C₂×D₅₁	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₇	—	157	1	no	—
22	D₅₁	—	157	1	no	—
23	D₅₁	D₁₅₇	1	1	yes	characteristic, direct product factor
24	C₂×D₁₇	—	471	1	no	Hall
25	C₃×C₁₇	C₂×D₁₅₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₇	—	157	1	no	—
27	D₁₇	—	3	1	no	—
28	D₁₇	—	471	1	no	—
29	C₁₇	D₃×D₁₅₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2669	1	no	Hall
31	C₂×C₃	—	157	1	no	—
32	D₃	—	17	1	no	—
33	D₃	—	2669	1	no	—
34	C₂²	—	8007	1	no	Sylow
35	C₃	D₁₇×D₁₅₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	51	1	no	—
37	C₂	—	8007	1	no	—
38	C₂	—	157	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₇×C₁₅₇	C₂²
LCS	G ▷ C₃×C₁₇×C₁₅₇
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₈₀₀₇	C₂	semidirect
2. D₅₁×C₁₅₇	C₂	semidirect
3. C₃×C₁₇×D₁₅₇	C₂	semidirect
5. C₃×C₁₇×C₁₅₇	C₂²	semidirect
7. C₁₇×D₁₅₇	D₃	semidirect
9. C₁₇×C₁₅₇	C₂×D₃	semidirect
12. C₃×D₁₅₇	D₁₇	semidirect
15. C₃×C₁₅₇	C₂×D₁₇	semidirect
18. D₁₅₇	D₅₁	direct (N × H)
20. C₁₅₇	C₂×D₅₁	semidirect
23. D₅₁	D₁₅₇	direct (N × H)
25. C₃×C₁₇	C₂×D₁₅₇	semidirect
29. C₁₇	D₃×D₁₅₇	semidirect
35. C₃	D₁₇×D₁₅₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₈₀₀₇	2
D₅₁×C₁₅₇	2
C₃×C₁₇×D₁₅₇	2
D₁₇×D₁₅₇	3
D₃×D₁₅₇	17
C₂×D₅₁	157

Subgroups — D51×D157 #44545112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₁×D₁₅₇ #44545112