Subgroups — C₂×#30654203 #45655755

Order 32576.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀₁₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₂₀₃₆	C₂	1	1	yes	maximal, characteristic
3	#30654203	C₂	1	8	yes	maximal, direct product factor
4	C₂×#22550838	C₂	1	4	yes	maximal, complemented
5	C₂×C₄²×C₅₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₅₀₉	C₂²	1	2	yes	—
7	C₂×Dic₁₀₁₈	—	2	4	no	—
8	C₂×Dic₁₀₁₈	C₂²	1	4	yes	complemented
9	C₂×D₂₀₃₆	—	2	4	no	—
10	C₂×D₂₀₃₆	C₂²	1	4	yes	—
11	C₂²×Dic₅₀₉	C₂²	1	2	yes	—
12	#22550838	C₂²	1	16	yes	complemented
13	C₂²×C₄×C₅₀₉	C₂²	1	2	yes	—
14	C₂²×C₄×C₅₀₉	C₂²	1	1	yes	characteristic
15	C₄²×C₅₀₉	C₂²	1	4	yes	complemented
16	C₂²×D₅₀₉	—	2	4	no	—
17	C₂²×D₅₀₉	—	2	8	no	—
18	C₂²×D₅₀₉	C₂³	1	4	yes	—
19	Dic₁₀₁₈	—	2	8	no	—
20	D₂₀₃₆	—	2	8	no	—
21	C₂×Dic₅₀₉	—	2	4	no	—
22	C₂×Dic₅₀₉	C₂³	1	4	yes	—
23	C₂³×C₅₀₉	C₂³	1	1	yes	characteristic
24	C₂×C₄×C₅₀₉	—	2	4	no	—
25	C₂×C₄×C₅₀₉	D₄	1	4	yes	—
26	C₂×C₄×C₅₀₉	C₂³	1	4	yes	—
27	C₂×C₄×C₅₀₉	C₂³	1	2	yes	—
28	C₂²×C₅₀₉	C₂×D₄	1	2	yes	—
29	C₂²×C₅₀₉	#41	1	4	yes	—
30	C₂²×C₅₀₉	C₂⁴	1	1	yes	characteristic
31	C₂×D₅₀₉	—	2	4	no	—
32	C₂×D₅₀₉	—	2	8	no	—
33	C₂×D₅₀₉	—	4	8	no	—
34	C₄×C₅₀₉	—	2	4	no	—
35	C₄×C₅₀₉	C₂×D₄	1	4	yes	—
36	Dic₅₀₉	—	2	4	no	—
37	C₂×C₅₀₉	#124	1	4	yes	complemented
38	C₂×C₅₀₉	C₂²×D₄	1	1	yes	characteristic
39	C₂×C₅₀₉	C₂×#41	1	2	yes	—
40	D₅₀₉	—	4	4	no	—
41	C₅₀₉	C₂×#124	1	1	yes	characteristic, complemented, Sylow
42	C₂×#124	—	509	1	no	maximal, Sylow
43	C₂²×Q₈	—	509	1	no	—
44	C₂²×D₄	—	509	1	no	—
45	#124	—	509	8	no	—
46	C₂×C₂²⋊C₄	—	509	4	no	—
47	C₂×C₄²	D₅₀₉	1	1	yes	characteristic, complemented
48	C₂⁴	—	509	2	no	—
49	C₂×Q₈	—	1018	4	no	—
50	C₂×Q₈	—	509	4	no	—
51	C₂×D₄	—	1018	4	no	—
52	C₂×D₄	—	509	4	no	—
53	C₂²×C₄	—	509	2	no	—
54	C₂²×C₄	C₂×D₅₀₉	1	2	yes	—
55	C₂²×C₄	C₂×D₅₀₉	1	1	yes	characteristic
56	C₂²⋊C₄	—	509	16	no	—
57	C₄²	C₂×D₅₀₉	1	4	yes	complemented
58	C₂³	—	1018	4	no	—
59	C₂³	—	1018	8	no	—
60	C₂³	—	509	4	no	—
61	C₂³	C₂²×D₅₀₉	1	1	yes	characteristic
62	Q₈	—	1018	8	no	—
63	D₄	—	1018	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	1018	4	no	—
66	C₂×C₄	—	509	4	no	—
67	C₂×C₄	D₂₀₃₆	1	4	yes	—
68	C₂×C₄	C₂²×D₅₀₉	1	4	yes	—
69	C₂×C₄	C₂²×D₅₀₉	1	2	yes	—
70	C₂²	—	2036	8	no	—
71	C₂²	—	1018	4	no	—
72	C₂²	—	1018	8	no	—
73	C₂²	C₂×D₂₀₃₆	1	2	yes	—
74	C₂²	#22550861	1	4	yes	—
75	C₂²	C₂³×D₅₀₉	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	1018	4	no	—
78	C₄	C₂×D₂₀₃₆	1	4	yes	—
79	C₂	—	2036	4	no	—
80	C₂	#30654203	1	4	yes	direct product factor
81	C₂	C₂²×D₂₀₃₆	1	1	yes	characteristic
82	C₂	C₂×#22550861	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₅₀₉
commutator, cosocle	C₂²×C₅₀₉	C₂⁴
Frattini	C₂²	C₂³×D₅₀₉
Fitting	C₂×C₄²×C₅₀₉	C₂
socle	C₂³×C₅₀₉	C₂³
prime radical	C₂²×D₂₀₃₆	C₂
hypercenter	C₂×C₄²	D₅₀₉
hypocenter	C₅₀₉	C₂×#124
LCS	G ▷ C₂²×C₅₀₉ ▷ C₅₀₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₁₀₁₈	C₂	semidirect
3. #30654203	C₂	direct (N × H)
4. C₂×#22550838	C₂	semidirect
5. C₂×C₄²×C₅₀₉	C₂	semidirect
8. C₂×Dic₁₀₁₈	C₂²	semidirect
12. #22550838	C₂²	semidirect
15. C₄²×C₅₀₉	C₂²	semidirect
37. C₂×C₅₀₉	#124	semidirect
41. C₅₀₉	C₂×#124	semidirect
47. C₂×C₄²	D₅₀₉	semidirect
57. C₄²	C₂×D₅₀₉	semidirect
80. C₂	#30654203	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₁₀₁₈	2
C₂²×D₂₀₃₆	2
#30654203	2
C₂×#22550838	2
C₂×C₄²×C₅₀₉	2
C₂×#124	509

Subgroups — C2×#30654203 #45655755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30654203 #45655755