Subgroups — #127×D₁₀₁ #20265715

Order 6464.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×D₁₀₁	C₂	1	6	yes	maximal, complemented
2	#15692252	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692251	C₂	1	6	yes	maximal, complemented
4	C₄²×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#127×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₁₀₁	C₂²	1	4	yes	—
7	C₂×D₄₀₄	C₂²	1	6	yes	complemented
8	C₂×C₂²⋊D₁₀₁	C₂²	1	12	yes	complemented
9	D₄×D₁₀₁	—	2	24	no	—
10	C₂×C₄×D₁₀₁	C₂²	1	3	yes	—
11	C₄×Dic₁₀₁	C₂²	1	3	yes	complemented
12	C₂×D₄×C₁₀₁	C₂²	1	6	yes	complemented
13	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₁₀₁	C₂³	1	4	yes	—
15	C₂²×D₁₀₁	—	2	24	no	—
16	C₂²×D₁₀₁	C₂³	1	4	yes	—
17	C₂²×D₁₀₁	C₂³	1	1	yes	characteristic
18	D₄×C₁₀₁	—	2	12	no	—
19	C₂×C₄×C₁₀₁	C₂³	1	3	yes	—
20	C₂²⋊D₁₀₁	—	2	24	no	—
21	C₂×Dic₁₀₁	C₂³	1	3	yes	—
22	D₄₀₄	—	2	12	no	—
23	C₄×D₁₀₁	D₄	1	12	yes	complemented
24	C₂²×C₁₀₁	—	2	12	no	—
25	C₂²×C₁₀₁	C₂⁴	1	1	yes	characteristic
26	C₂×D₁₀₁	—	2	12	no	—
27	C₂×D₁₀₁	—	4	16	no	—
28	C₂×D₁₀₁	C₂×D₄	1	6	yes	—
29	C₄×C₁₀₁	C₂×D₄	1	6	yes	complemented
30	Dic₁₀₁	C₂×D₄	1	6	yes	complemented
31	C₂×C₁₀₁	—	4	4	no	—
32	C₂×C₁₀₁	C₂²×D₄	1	3	yes	—
33	D₁₀₁	—	4	4	no	—
34	D₁₀₁	#127	1	4	yes	direct product factor
35	C₁₀₁	C₂×#127	1	1	yes	characteristic, complemented, Sylow
36	C₂×#127	—	101	1	no	maximal, Sylow
37	C₂²×D₄	—	101	6	no	—
38	#127	—	101	6	no	—
39	#127	—	101	1	no	—
40	#127	D₁₀₁	1	1	yes	characteristic, direct product factor
41	C₂×C₄²	—	101	1	no	—
42	C₂⁴	—	101	4	no	—
43	C₂×D₄	—	101	12	no	—
44	C₂×D₄	—	101	6	no	—
45	C₂×D₄	—	202	24	no	—
46	C₂×D₄	C₂×D₁₀₁	1	6	yes	complemented
47	C₂²×C₄	—	101	3	no	—
48	C₄²	—	101	3	no	—
49	C₄²	C₂×D₁₀₁	1	1	yes	characteristic, complemented
50	C₂³	—	101	1	no	—
51	C₂³	—	101	4	no	—
52	C₂³	—	202	24	no	—
53	C₂³	C₂²×D₁₀₁	1	4	yes	—
54	D₄	—	2	12	no	—
55	D₄	—	202	24	no	—
56	D₄	—	202	12	no	—
57	C₂×C₄	—	101	3	no	—
58	C₂×C₄	—	101	12	no	—
59	C₂×C₄	C₂²×D₁₀₁	1	3	yes	—
60	C₂²	—	2	12	no	—
61	C₂²	—	101	6	no	—
62	C₂²	—	404	16	no	—
63	C₂²	—	202	12	no	—
64	C₂²	C₂³×D₁₀₁	1	1	yes	characteristic
65	C₄	—	101	6	no	—
66	C₄	D₄×D₁₀₁	1	6	yes	complemented
67	C₂	—	4	4	no	—
68	C₂	—	101	4	no	—
69	C₂	—	404	4	no	—
70	C₂	C₂×D₄×D₁₀₁	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₀₁
commutator, socle	C₂²×C₁₀₁	C₂⁴
Fitting	#127×C₁₀₁	C₂
hypercenter	#127	D₁₀₁
hypocenter	C₁₀₁	C₂×#127
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×D₁₀₁	C₂	semidirect
2. #15692252	C₂	semidirect
3. #15692251	C₂	semidirect
4. C₄²×D₁₀₁	C₂	semidirect
5. #127×C₁₀₁	C₂	semidirect
7. C₂×D₄₀₄	C₂²	semidirect
8. C₂×C₂²⋊D₁₀₁	C₂²	semidirect
11. C₄×Dic₁₀₁	C₂²	semidirect
12. C₂×D₄×C₁₀₁	C₂²	semidirect
13. C₄²×C₁₀₁	C₂²	semidirect
23. C₄×D₁₀₁	D₄	semidirect
29. C₄×C₁₀₁	C₂×D₄	semidirect
30. Dic₁₀₁	C₂×D₄	semidirect
34. D₁₀₁	#127	direct (N × H)
35. C₁₀₁	C₂×#127	semidirect
40. #127	D₁₀₁	direct (N × H)
46. C₂×D₄	C₂×D₁₀₁	semidirect
49. C₄²	C₂×D₁₀₁	semidirect
66. C₄	D₄×D₁₀₁	semidirect

Subgroups — #127×D101 #20265715

Conjugacy classes of subgroups

Complements

Subgroups — #127×D₁₀₁ #20265715