Subgroups — D₁₆×D₅₀₉ #45655657

Order 32576.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₅₀₉	C₂	1	2	yes	maximal, complemented
2	D₈₁₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#30654156	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₅₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₅₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₅₀₉	—	2	2	no	—
7	D₄₀₇₂	C₂²	1	2	yes	complemented
8	#22550846	—	2	2	no	—
9	C₈×D₅₀₉	C₂²	1	1	yes	characteristic
10	#22550836	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₅₀₉	C₂²	1	2	yes	complemented
12	C₁₆×C₅₀₉	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₅₀₉	—	4	2	no	—
14	D₂₀₃₆	—	2	2	no	—
15	C₂²⋊D₅₀₉	—	4	2	no	—
16	C₄×D₅₀₉	D₄	1	1	yes	characteristic
17	#16861325	D₄	1	1	yes	characteristic
18	D₄×C₅₀₉	—	2	2	no	—
19	C₈×C₅₀₉	C₂³	1	1	yes	characteristic
20	C₂²×C₅₀₉	—	4	2	no	—
21	C₂×D₅₀₉	—	4	2	no	—
22	C₂×D₅₀₉	—	8	4	no	—
23	C₂×D₅₀₉	D₈	1	1	yes	characteristic
24	C₄×C₅₀₉	C₂×D₄	1	1	yes	characteristic
25	Dic₅₀₉	D₈	1	1	yes	characteristic
26	C₂×C₅₀₉	—	8	2	no	—
27	C₂×C₅₀₉	C₂×D₈	1	1	yes	characteristic
28	D₅₀₉	—	8	2	no	—
29	D₅₀₉	D₁₆	1	2	yes	direct product factor
30	C₅₀₉	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	509	1	no	maximal, Sylow
32	C₂×D₈	—	509	2	no	—
33	D₁₆	—	509	2	no	—
34	D₁₆	—	509	1	no	—
35	D₁₆	D₅₀₉	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	509	1	no	—
37	C₂×D₄	—	1018	2	no	—
38	D₈	—	1018	2	no	—
39	D₈	—	509	2	no	—
40	D₈	C₂×D₅₀₉	1	2	yes	complemented
41	C₂×C₈	—	509	1	no	—
42	C₁₆	—	509	1	no	—
43	C₁₆	C₂×D₅₀₉	1	1	yes	characteristic, complemented
44	C₂³	—	2036	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	2036	2	no	—
47	D₄	—	1018	2	no	—
48	C₂×C₄	—	509	1	no	—
49	C₈	—	509	1	no	—
50	C₈	C₂²×D₅₀₉	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	4072	4	no	—
53	C₂²	—	2036	2	no	—
54	C₂²	—	509	1	no	—
55	C₄	—	509	1	no	—
56	C₄	D₄×D₅₀₉	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	4072	2	no	—
59	C₂	—	509	2	no	—
60	C₂	D₈×D₅₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₅₀₉
commutator, cosocle	C₈×C₅₀₉	C₂³
Frattini	C₈	C₂²×D₅₀₉
Fitting	D₁₆×C₅₀₉	C₂
socle	C₂×C₅₀₉	C₂×D₈
hypercenter	D₁₆	D₅₀₉
hypocenter	C₅₀₉	C₂×D₁₆
LCS	G ▷ C₈×C₅₀₉ ▷ C₄×C₅₀₉ ▷ C₂×C₅₀₉ ▷ C₅₀₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×D₅₀₉	C₂	semidirect
2. D₈₁₄₄	C₂	semidirect
3. #30654156	C₂	semidirect
4. C₁₆×D₅₀₉	C₂	semidirect
5. D₁₆×C₅₀₉	C₂	semidirect
7. D₄₀₇₂	C₂²	semidirect
10. #22550836	C₂²	semidirect
11. D₈×C₅₀₉	C₂²	semidirect
12. C₁₆×C₅₀₉	C₂²	semidirect
29. D₅₀₉	D₁₆	direct (N × H)
30. C₅₀₉	C₂×D₁₆	semidirect
35. D₁₆	D₅₀₉	direct (N × H)
40. D₈	C₂×D₅₀₉	semidirect
43. C₁₆	C₂×D₅₀₉	semidirect

Maximal subgroups

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

subgroup	index
D₈×D₅₀₉	2
D₈₁₄₄	2
#30654156	2
C₁₆×D₅₀₉	2
D₁₆×C₅₀₉	2
C₂×D₁₆	509

Subgroups — D16×D509 #45655657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₆×D₅₀₉ #45655657