Subgroups — C₂×#15692180 #20265169

Order 6464.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₀₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#15692180	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₀₂	—	2	1	no	—
6	C₂×Dic₂₀₂	—	2	2	no	—
7	C₂×Dic₂₀₂	C₄	1	4	yes	complemented
8	C₂×Dic₂₀₂	C₂²	1	2	yes	—
9	C₂²×Dic₁₀₁	—	2	1	no	—
10	C₂²×Dic₁₀₁	—	2	1	no	—
11	C₄⋊Dic₁₀₁	—	2	1	no	—
12	C₄⋊Dic₁₀₁	C₂²	1	2	yes	—
13	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₀₁	—	2	2	no	—
15	C₂×C₈×C₁₀₁	C₂²	1	2	yes	—
16	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
20	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₀₁	—	2	4	no	—
22	C₂×Dic₁₀₁	—	2	2	no	—
23	C₂×Dic₁₀₁	—	2	2	no	—
24	C₂×Dic₁₀₁	—	4	2	no	—
25	Dic₂₀₂	—	2	4	no	—
26	Dic₂₀₂	—	2	2	no	—
27	Dic₂₀₂	C₂×C₄	1	4	yes	complemented
28	C₈×C₁₀₁	—	2	2	no	—
29	C₂²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₁₀₁	SD₁₆	1	2	yes	—
31	C₂²×C₁₀₁	Q₁₆	1	2	yes	—
32	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
34	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
36	Dic₁₀₁	—	2	4	no	—
37	Dic₁₀₁	—	4	2	no	—
38	C₂×C₁₀₁	#103	1	4	yes	complemented
39	C₂×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₁₀₁	C₂×Q₁₆	1	1	yes	characteristic
42	C₁₀₁	C₂×#103	1	1	yes	characteristic, complemented, Sylow
43	C₂×#103	—	101	1	no	maximal, Sylow
44	C₂²×Q₈	—	101	1	no	—
45	C₂²×C₈	D₁₀₁	1	1	yes	characteristic
46	C₂×C₄⋊C₄	—	101	1	no	—
47	#103	—	101	4	no	—
48	C₂×Q₈	—	101	4	no	—
49	C₂×Q₈	—	101	2	no	—
50	C₂×Q₈	—	202	1	no	—
51	C₂×Q₈	—	202	2	no	—
52	C₂²×C₄	—	202	1	no	—
53	C₂²×C₄	—	202	1	no	—
54	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	C₂×D₁₀₁	1	2	yes	—
57	C₄⋊C₄	—	101	2	no	—
58	C₄⋊C₄	—	202	1	no	—
59	C₂³	D₄₀₄	1	1	yes	characteristic
60	Q₈	—	101	4	no	—
61	Q₈	—	202	4	no	—
62	Q₈	—	202	2	no	—
63	C₂×C₄	—	404	2	no	—
64	C₂×C₄	—	202	2	no	—
65	C₂×C₄	—	202	4	no	—
66	C₂×C₄	—	202	2	no	—
67	C₂×C₄	C₄×D₁₀₁	1	2	yes	—
68	C₂×C₄	D₄₀₄	1	1	yes	characteristic
69	C₂×C₄	C₂²⋊D₁₀₁	1	2	yes	—
70	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₂²	#13108051	1	2	yes	—
73	C₂²	#13108063	1	2	yes	—
74	C₂²	Dic₄₀₄	1	2	yes	—
75	C₂²	C₂×D₄₀₄	1	1	yes	characteristic
76	C₄	—	404	2	no	—
77	C₄	—	202	4	no	—
78	C₄	#13108051	1	2	yes	—
79	C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
80	C₄	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
81	C₂	#15692180	1	4	yes	direct product factor
82	C₂	C₂×#13108051	1	1	yes	characteristic
83	C₂	C₂×#13108063	1	1	yes	characteristic
84	C₂	C₂×Dic₄₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄₀₄
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₂²×C₈×C₁₀₁	C₂
socle	C₂³×C₁₀₁	D₄
hypercenter	C₂²×C₈	D₁₀₁
hypocenter	C₁₀₁	C₂×#103
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #15692180	C₂	direct (N × H)
7. C₂×Dic₂₀₂	C₄	semidirect
27. Dic₂₀₂	C₂×C₄	semidirect
38. C₂×C₁₀₁	#103	semidirect
42. C₁₀₁	C₂×#103	semidirect
81. C₂	#15692180	direct (N × H)

Subgroups — C2×#15692180 #20265169

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692180 #20265169