Subgroups — #20265561

Order 6464.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₀₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13108063	C₂	1	2	yes	maximal, complemented
3	C₂×D₈₀₈	C₂	1	1	yes	maximal, characteristic
4	#15692243	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₀₂	C₂²	1	2	yes	—
7	C₂×D₄₀₄	C₂²	1	2	yes	—
8	Dic₄₀₄	—	2	2	no	—
9	#13108063	—	2	4	no	—
10	D₈₀₈	—	2	2	no	—
11	#13108051	—	2	4	no	—
12	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂²×D₁₀₁	—	2	2	no	—
16	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
17	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
18	C₂×Dic₁₀₁	—	2	2	no	—
19	D₄₀₄	—	2	2	no	—
20	D₄₀₄	—	2	2	no	—
21	Dic₂₀₂	—	2	2	no	—
22	Dic₂₀₂	—	2	2	no	—
23	C₈×C₁₀₁	D₄	1	2	yes	—
24	C₈×C₁₀₁	D₄	1	2	yes	—
25	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
26	C₂×D₁₀₁	—	4	2	no	—
27	C₂×D₁₀₁	—	4	4	no	—
28	C₄×C₁₀₁	—	2	2	no	—
29	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
31	Dic₁₀₁	—	4	2	no	—
32	C₂×C₁₀₁	#127	1	1	yes	characteristic
33	C₂×C₁₀₁	#135	1	2	yes	—
34	D₁₀₁	—	8	2	no	—
35	C₁₀₁	#495	1	1	yes	characteristic, complemented, Sylow
36	#495	—	101	1	no	maximal, Sylow
37	C₂×Q₁₆	—	101	1	no	—
38	C₂×SD₁₆	—	101	2	no	—
39	C₂×D₈	—	101	1	no	—
40	#124	—	101	2	no	—
41	C₄×C₈	D₁₀₁	1	1	yes	characteristic, complemented
42	C₂×Q₈	—	101	2	no	—
43	C₂×D₄	—	101	2	no	—
44	Q₁₆	—	202	2	no	—
45	SD₁₆	—	202	4	no	—
46	D₈	—	202	2	no	—
47	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
48	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
49	C₂²⋊C₄	—	202	4	no	—
50	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
51	C₂³	—	202	2	no	—
52	Q₈	—	202	2	no	—
53	Q₈	—	202	2	no	—
54	D₄	—	202	2	no	—
55	D₄	—	202	2	no	—
56	C₂×C₄	—	202	2	no	—
57	C₂×C₄	D₄₀₄	1	2	yes	—
58	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
59	C₈	D₄₀₄	1	2	yes	—
60	C₈	D₄₀₄	1	2	yes	—
61	C₂²	—	404	2	no	—
62	C₂²	—	404	4	no	—
63	C₂²	C₂×D₄₀₄	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	404	2	no	—
66	C₄	C₂×D₄₀₄	1	1	yes	characteristic
67	C₄	C₂×D₄₀₄	1	1	yes	characteristic
68	C₂	—	808	2	no	—
69	C₂	#15692252	1	1	yes	characteristic
70	C₂	#15692277	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₀₄
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₄×C₈×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	C₄×C₈	D₁₀₁
hypocenter	C₁₀₁	#495
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₄₀₄	C₂	semidirect
2. C₂×#13108063	C₂	semidirect
4. #15692243	C₂	semidirect
5. C₄×C₈×C₁₀₁	C₂	semidirect
35. C₁₀₁	#495	semidirect
41. C₄×C₈	D₁₀₁	semidirect