Subgroups — #20265367

Order 6464.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692236	C₂	1	3	yes	maximal, complemented
2	#15692170	C₂	1	3	yes	maximal, complemented
3	H(5,𝔽₂)×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
5	#13108053	—	2	3	no	—
6	C₂²⋊Dic₁₀₁	—	2	3	no	—
7	C₂²⋊Dic₁₀₁	C₂²	1	3	yes	complemented
8	#41×C₁₀₁	—	2	3	no	—
9	C₂×D₄×C₁₀₁	—	2	3	no	—
10	C₂×D₄×C₁₀₁	C₂²	1	3	yes	—
11	C₂³×C₁₀₁	—	2	1	no	—
12	C₂³×C₁₀₁	D₄	1	3	yes	—
13	C₂³×C₁₀₁	C₂³	1	1	yes	characteristic
14	Q₈×C₁₀₁	—	2	1	no	—
15	D₄×C₁₀₁	—	2	3	no	—
16	D₄×C₁₀₁	—	2	6	no	—
17	C₂×C₄×C₁₀₁	—	2	3	no	—
18	C₂×C₄×C₁₀₁	D₄	1	3	yes	—
19	C₂×Dic₁₀₁	—	2	3	no	—
20	C₂×Dic₁₀₁	—	2	3	no	—
21	C₂²×C₁₀₁	—	2	3	no	—
22	C₂²×C₁₀₁	—	4	1	no	—
23	C₂²×C₁₀₁	—	4	3	no	—
24	C₂²×C₁₀₁	—	8	1	no	—
25	C₂²×C₁₀₁	C₂×D₄	1	3	yes	—
26	C₄×C₁₀₁	—	2	3	no	—
27	Dic₁₀₁	—	4	3	no	—
28	Dic₁₀₁	—	4	1	no	—
29	C₂×C₁₀₁	—	2	3	no	—
30	C₂×C₁₀₁	—	4	3	no	—
31	C₂×C₁₀₁	#120	1	1	yes	characteristic
32	C₁₀₁	#458	1	1	yes	characteristic, complemented, Sylow
33	#458	—	101	1	no	maximal, Sylow
34	H(5,𝔽₂)	D₁₀₁	1	1	yes	characteristic
35	#123	—	101	3	no	—
36	#99	—	101	3	no	—
37	#41	—	2	3	no	—
38	C₂×D₄	—	2	3	no	—
39	C₂×D₄	C₂×D₁₀₁	1	3	yes	—
40	C₂²×C₄	—	101	1	no	—
41	C₄⋊C₄	—	202	3	no	—
42	C₂²⋊C₄	—	101	3	no	—
43	C₂²⋊C₄	—	202	3	no	—
44	C₂³	—	2	1	no	—
45	C₂³	C₂²⋊D₁₀₁	1	3	yes	—
46	C₂³	C₂²×D₁₀₁	1	1	yes	characteristic
47	Q₈	—	2	1	no	—
48	D₄	—	2	3	no	—
49	D₄	—	2	6	no	—
50	C₂×C₄	—	2	3	no	—
51	C₂×C₄	—	202	3	no	—
52	C₂×C₄	—	202	3	no	—
53	C₂×C₄	C₂²⋊D₁₀₁	1	3	yes	—
54	C₂²	—	2	3	no	—
55	C₂²	—	4	1	no	—
56	C₂²	—	4	3	no	—
57	C₂²	—	8	1	no	—
58	C₂²	C₂×C₂²⋊D₁₀₁	1	3	yes	—
59	C₄	—	2	3	no	—
60	C₄	—	404	3	no	—
61	C₄	—	404	1	no	—
62	C₂	—	2	3	no	—
63	C₂	—	4	3	no	—
64	C₂	#15692224	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692224
commutator	C₂³×C₁₀₁	C₂³
Frattini	C₂³	C₂²×D₁₀₁
Fitting	H(5,𝔽₂)×C₁₀₁	C₂
socle	C₂×C₁₀₁	#120
hypercenter	H(5,𝔽₂)	D₁₀₁
hypocenter	C₁₀₁	#458
LCS	G ▷ C₂³×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. #15692236	C₂	semidirect
2. #15692170	C₂	semidirect
4. C₂²×Dic₁₀₁	C₂²	semidirect
7. C₂²⋊Dic₁₀₁	C₂²	semidirect
32. C₁₀₁	#458	semidirect