Subgroups — #20265534

Order 6464.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692243	C₂	1	1	yes	maximal, characteristic
2	#15692178	C₂	1	2	yes	maximal, complemented
3	#15692175	C₂	1	2	yes	maximal
4	C₄×#11717579	C₂	1	1	yes	maximal, characteristic, complemented
5	#125×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₀₂	C₂²	1	1	yes	characteristic
7	C₂×D₄₀₄	C₂²	1	1	yes	characteristic
8	C₂×#11717579	C₂²	1	2	yes	—
9	#13108051	—	2	2	no	—
10	C₄⋊C₄×C₁₀₁	—	2	2	no	—
11	C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
12	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×D₁₀₁	—	2	1	no	—
14	C₂×C₄×C₁₀₁	—	2	2	no	—
15	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
16	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₀₁	—	2	1	no	—
18	D₄₀₄	—	2	2	no	—
19	Dic₂₀₂	—	2	2	no	—
20	#11717579	—	2	2	no	—
21	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
22	C₂×D₁₀₁	—	4	1	no	—
23	C₂×D₁₀₁	—	4	2	no	—
24	C₄×C₁₀₁	—	2	2	no	—
25	C₄×C₁₀₁	—	4	2	no	—
26	C₄×C₁₀₁	#41	1	2	yes	—
27	Dic₁₀₁	—	4	1	no	—
28	C₂×C₁₀₁	#124	1	1	yes	characteristic
29	C₂×C₁₀₁	#135	1	2	yes	—
30	D₁₀₁	—	8	1	no	—
31	C₁₀₁	#488	1	1	yes	characteristic, complemented, Sylow
32	#488	—	101	1	no	maximal, Sylow
33	#125	D₁₀₁	1	1	yes	characteristic, complemented
34	#124	—	101	1	no	—
35	#103	—	101	2	no	—
36	#102	—	101	2	no	—
37	C₄×C₈	—	101	1	no	—
38	C₂×Q₈	—	101	1	no	—
39	C₂×D₄	—	101	1	no	—
40	C₂×C₈	—	101	2	no	—
41	C₄⋊C₄	—	2	2	no	—
42	C₄⋊C₄	C₂×D₁₀₁	1	2	yes	—
43	C₂²⋊C₄	—	202	2	no	—
44	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
45	C₂³	—	202	1	no	—
46	Q₈	—	202	2	no	—
47	D₄	—	202	2	no	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	202	1	no	—
50	C₂×C₄	C₂²⋊D₁₀₁	1	2	yes	—
51	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
52	C₈	—	202	2	no	—
53	C₂²	—	404	1	no	—
54	C₂²	—	404	2	no	—
55	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	4	2	no	—
58	C₄	—	404	1	no	—
59	C₄	#13108075	1	2	yes	—
60	C₂	—	808	1	no	—
61	C₂	#15692244	1	1	yes	characteristic
62	C₂	#15692275	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₁
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#125×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	#125	D₁₀₁
hypocenter	C₁₀₁	#488
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #15692178	C₂	semidirect
4. C₄×#11717579	C₂	semidirect
5. #125×C₁₀₁	C₂	semidirect
31. C₁₀₁	#488	semidirect
33. #125	D₁₀₁	semidirect