Subgroups — #20265022

Order 6464.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₁₀₁	C₂	1	3	yes	maximal
2	#15692162	C₂	1	3	yes	maximal
3	#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₀₁	C₂²	1	3	yes	—
5	C₂²×Dic₁₀₁	C₂²	1	1	yes	characteristic
6	C₄×Dic₁₀₁	C₄	1	12	yes	complemented
7	C₂²×C₄×C₁₀₁	C₂²	1	3	yes	—
8	C₂³×C₁₀₁	C₂³	1	1	yes	characteristic
9	C₂×C₄×C₁₀₁	—	2	6	no	—
10	C₂×C₄×C₁₀₁	C₂×C₄	1	6	yes	—
11	C₂×Dic₁₀₁	—	2	3	no	—
12	C₂×Dic₁₀₁	—	2	3	no	—
13	C₂×Dic₁₀₁	C₂×C₄	1	6	yes	—
14	C₂×Dic₁₀₁	C₂×C₄	1	6	yes	—
15	C₂²×C₁₀₁	C₂²×C₄	1	3	yes	—
16	C₂²×C₁₀₁	#41	1	3	yes	—
17	C₂²×C₁₀₁	#41	1	1	yes	characteristic
18	C₄×C₁₀₁	—	2	6	no	—
19	Dic₁₀₁	—	2	6	no	—
20	Dic₁₀₁	C₄²	1	4	yes	—
21	C₂×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
22	C₂×C₁₀₁	#117	1	3	yes	—
23	C₂×C₁₀₁	#117	1	3	yes	—
24	C₁₀₁	#376	1	1	yes	characteristic, complemented, Sylow
25	#376	—	101	1	no	maximal, Sylow
26	C₂×C₄²	—	101	3	no	—
27	#95	—	101	3	no	—
28	#95	D₁₀₁	1	1	yes	characteristic
29	C₂²×C₄	—	101	1	no	—
30	C₂²×C₄	—	101	3	no	—
31	C₂²×C₄	C₂×D₁₀₁	1	3	yes	—
32	C₄²	—	101	12	no	—
33	C₂³	C₂²×D₁₀₁	1	1	yes	characteristic
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	—	101	6	no	—
36	C₂×C₄	—	101	6	no	—
37	C₂×C₄	—	202	3	no	—
38	C₂×C₄	—	202	3	no	—
39	C₂×C₄	C₄×D₁₀₁	1	6	yes	—
40	C₂²	C₂×C₄×D₁₀₁	1	3	yes	—
41	C₂²	#13108073	1	3	yes	—
42	C₂²	#13108075	1	1	yes	characteristic
43	C₄	—	2	6	no	—
44	C₄	—	101	4	no	—
45	C₄	—	202	6	no	—
46	C₂	C₄²×D₁₀₁	1	1	yes	characteristic
47	C₂	#15692211	1	3	yes	—
48	C₂	#15692213	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₁
commutator	C₂×C₁₀₁	C₂×C₄²
Fitting	#95×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂³
hypercenter	#95	D₁₀₁
hypocenter	C₁₀₁	#376
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
6. C₄×Dic₁₀₁	C₄	semidirect
24. C₁₀₁	#376	semidirect