Subgroups — D₅₀₉⋊#131 #45656314

Order 32576.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654303	C₂	1	2	yes	maximal, complemented
2	#30654302	C₂	1	6	yes	maximal, complemented
3	D₅₀₉⋊M₁₆	C₂	1	3	yes	maximal, complemented
4	C₂×D₅₀₉⋊C₈	C₂	1	3	yes	maximal, complemented
5	#41×D₅₀₉	C₂	1	1	yes	maximal, characteristic
6	#22550871	C₂²	1	6	yes	complemented
7	#22550870	C₂²	1	6	yes	complemented
8	D₅₀₉⋊C₈	C₂²	1	1	yes	characteristic
9	D₅₀₉⋊C₈	C₂²	1	3	yes	—
10	D₅₀₉⋊C₈	C₂²	1	6	yes	complemented
11	C₂×#16861332	C₂²	1	6	yes	complemented
12	#22550862	C₂²	1	1	yes	characteristic
13	#22550861	C₄	1	3	yes	—
14	#22550860	C₂²	1	3	yes	—
15	Q₈×D₅₀₉	C₄	1	1	yes	characteristic
16	D₄×D₅₀₉	C₄	1	3	yes	—
17	C₂×C₄×D₅₀₉	C₂²	1	3	yes	—
18	#41×C₅₀₉	C₄	1	1	yes	characteristic
19	#16861332	C₂³	1	2	yes	—
20	#16861332	C₂³	1	6	yes	—
21	C₂²×D₅₀₉	C₂×C₄	1	3	yes	—
22	Dic₁₀₁₈	C₂×C₄	1	3	yes	—
23	D₂₀₃₆	C₂×C₄	1	3	yes	—
24	C₂²⋊D₅₀₉	C₂×C₄	1	6	yes	—
25	C₂×Dic₅₀₉	C₂³	1	3	yes	—
26	C₄×D₅₀₉	C₂×C₄	1	3	yes	—
27	C₄×D₅₀₉	C₂×C₄	1	3	yes	—
28	C₄×D₅₀₉	C₂³	1	1	yes	characteristic
29	C₄×D₅₀₉	C₂³	1	3	yes	—
30	Q₈×C₅₀₉	C₂×C₄	1	1	yes	characteristic
31	D₄×C₅₀₉	C₂×C₄	1	3	yes	—
32	C₂×C₄×C₅₀₉	C₂×C₄	1	3	yes	—
33	C₂²×C₅₀₉	C₂²×C₄	1	3	yes	—
34	C₂×D₅₀₉	—	2	6	no	—
35	C₂×D₅₀₉	C₂²×C₄	1	3	yes	—
36	C₂×D₅₀₉	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₅₀₉	C₂²×C₄	1	3	yes	—
38	C₄×C₅₀₉	C₂²×C₄	1	1	yes	characteristic
39	Dic₅₀₉	C₂²×C₄	1	3	yes	—
40	Dic₅₀₉	C₂⁴	1	1	yes	characteristic
41	C₂×C₅₀₉	—	2	3	no	—
42	C₂×C₅₀₉	C₂³×C₄	1	1	yes	characteristic
43	D₅₀₉	—	2	3	no	—
44	D₅₀₉	#131	1	2	yes	complemented
45	C₅₀₉	C₂×#131	1	1	yes	characteristic, complemented, Sylow
46	C₂×#131	—	509	1	no	maximal, Sylow
47	C₂×#41	—	509	1	no	—
48	#131	—	509	6	no	—
49	#131	—	509	2	no	—
50	C₂×M₁₆	—	509	3	no	—
51	C₂²×C₈	—	509	3	no	—
52	#41	—	509	1	no	—
53	#41	—	509	3	no	—
54	#41	—	509	3	no	—
55	#41	#14523266	1	1	yes	characteristic
56	C₂×Q₈	—	509	1	no	—
57	C₂×D₄	—	509	3	no	—
58	C₂²×C₄	—	509	3	no	—
59	M₁₆	—	509	6	no	—
60	M₁₆	—	509	6	no	—
61	C₂×C₈	—	509	6	no	—
62	C₂×C₈	—	509	1	no	—
63	C₂×C₈	—	509	3	no	—
64	C₂×C₈	—	509	6	no	—
65	C₂³	—	509	3	no	—
66	Q₈	—	509	3	no	—
67	Q₈	C₂×#14523266	1	1	yes	characteristic
68	D₄	—	509	6	no	—
69	D₄	—	509	3	no	—
70	D₄	C₂×#14523266	1	3	yes	—
71	C₂×C₄	—	509	3	no	—
72	C₂×C₄	—	509	3	no	—
73	C₂×C₄	—	509	3	no	—
74	C₂×C₄	—	509	1	no	—
75	C₂×C₄	—	509	3	no	—
76	C₂×C₄	C₂×#14523266	1	3	yes	—
77	C₈	—	509	2	no	—
78	C₈	—	509	6	no	—
79	C₂²	—	1018	6	no	—
80	C₂²	—	509	3	no	—
81	C₂²	—	509	1	no	—
82	C₂²	C₂²×#14523266	1	3	yes	—
83	C₄	—	509	1	no	—
84	C₄	—	509	3	no	—
85	C₄	C₂²×#14523266	1	3	yes	—
86	C₄	C₂²×#14523266	1	1	yes	characteristic
87	C₂	—	2	3	no	—
88	C₂	—	1018	3	no	—
89	C₂	—	509	2	no	—
90	C₂	C₂³×#14523266	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×#14523266
commutator, socle	C₂×C₅₀₉	C₂³×C₄
Frattini	C₂	C₂³×#14523266
Fitting	#41×C₅₀₉	C₄
prime radical	#41×D₅₀₉	C₂
cosocle	Dic₅₀₉	C₂⁴
hypercenter	#41	#14523266
hypocenter	C₅₀₉	C₂×#131
LCS	G ▷ C₂×C₅₀₉ ▷ C₅₀₉
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #30654303	C₂	semidirect
2. #30654302	C₂	semidirect
3. D₅₀₉⋊M₁₆	C₂	semidirect
4. C₂×D₅₀₉⋊C₈	C₂	semidirect
6. #22550871	C₂²	semidirect
7. #22550870	C₂²	semidirect
10. D₅₀₉⋊C₈	C₂²	semidirect
11. C₂×#16861332	C₂²	semidirect
44. D₅₀₉	#131	semidirect
45. C₅₀₉	C₂×#131	semidirect

Maximal subgroups

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

subgroup	index
#30654303	2
#30654302	2
D₅₀₉⋊M₁₆	2
C₂×D₅₀₉⋊C₈	2
#41×D₅₀₉	2
C₂×#131	509

Subgroups — D509⋊#131 #45656314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₀₉⋊#131 #45656314