Subgroups — #95×D₁₆₃ #23781508

Order 10432.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₁₆₃	C₂	1	3	yes	maximal
2	C₁₆₃⋊#95	C₂	1	3	yes	maximal, complemented
3	#95×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₁₆₃	C₂²	1	1	yes	characteristic
5	C₂²×Dic₁₆₃	C₂²	1	3	yes	—
6	C₂×C₄×D₁₆₃	—	2	12	no	—
7	C₂×C₄×D₁₆₃	C₄	1	12	yes	complemented
8	C₂²×C₄×C₁₆₃	C₂²	1	3	yes	—
9	C₂²×D₁₆₃	C₂×C₄	1	6	yes	—
10	C₂²×D₁₆₃	D₄	1	6	yes	—
11	C₂²×D₁₆₃	Q₈	1	2	yes	—
12	C₂×Dic₁₆₃	—	2	6	no	—
13	C₂×Dic₁₆₃	C₂×C₄	1	6	yes	complemented
14	C₄×D₁₆₃	—	2	24	no	—
15	C₂³×C₁₆₃	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₁₆₃	—	2	6	no	—
17	C₂×C₄×C₁₆₃	C₂×C₄	1	6	yes	complemented
18	C₂²×C₁₆₃	C₂²×C₄	1	3	yes	—
19	C₂²×C₁₆₃	C₂×D₄	1	3	yes	—
20	C₂²×C₁₆₃	C₂×Q₈	1	1	yes	characteristic
21	C₂×D₁₆₃	C₄²	1	4	yes	—
22	C₂×D₁₆₃	C₂²⋊C₄	1	12	yes	—
23	C₂×D₁₆₃	C₄⋊C₄	1	12	yes	—
24	C₄×C₁₆₃	—	2	6	no	—
25	Dic₁₆₃	—	2	6	no	—
26	C₂×C₁₆₃	C₂×C₄²	1	1	yes	characteristic
27	C₂×C₁₆₃	C₂×C₂²⋊C₄	1	3	yes	—
28	C₂×C₁₆₃	C₂×C₄⋊C₄	1	3	yes	—
29	D₁₆₃	#95	1	8	yes	direct product factor
30	C₁₆₃	C₂×#95	1	1	yes	characteristic, complemented, Sylow
31	C₂×#95	—	163	1	no	maximal, Sylow
32	C₂³×C₄	—	163	3	no	—
33	#95	—	163	3	no	—
34	#95	D₁₆₃	1	1	yes	characteristic, direct product factor
35	C₂⁴	—	163	1	no	—
36	C₂²×C₄	—	326	12	no	—
37	C₂²×C₄	—	163	3	no	—
38	C₂²×C₄	—	163	12	no	—
39	C₂²×C₄	C₂×D₁₆₃	1	3	yes	—
40	C₂³	—	163	6	no	—
41	C₂³	—	163	6	no	—
42	C₂³	—	163	2	no	—
43	C₂³	C₂²×D₁₆₃	1	1	yes	characteristic
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	326	24	no	—
46	C₂×C₄	—	326	6	no	—
47	C₂×C₄	—	163	6	no	—
48	C₂×C₄	C₄×D₁₆₃	1	6	yes	complemented
49	C₂²	—	163	4	no	—
50	C₂²	—	163	12	no	—
51	C₂²	—	163	12	no	—
52	C₂²	C₂×C₄×D₁₆₃	1	3	yes	—
53	C₂²	D₄×D₁₆₃	1	3	yes	—
54	C₂²	Q₈×D₁₆₃	1	1	yes	characteristic
55	C₄	—	2	6	no	—
56	C₄	—	326	6	no	—
57	C₂	—	163	8	no	—
58	C₂	C₄²×D₁₆₃	1	1	yes	characteristic
59	C₂	C₂²⋊C₄×D₁₆₃	1	3	yes	—
60	C₂	C₄⋊C₄×D₁₆₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₆₃
commutator	C₂×C₁₆₃	C₂×C₄²
Fitting	#95×C₁₆₃	C₂
socle, cosocle	C₂³×C₁₆₃	C₂³
prime radical	C₂³×D₁₆₃	C₂²
hypercenter	#95	D₁₆₃
hypocenter	C₁₆₃	C₂×#95
LCS	G ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₁₆₃⋊#95	C₂	semidirect
3. #95×C₁₆₃	C₂	semidirect
7. C₂×C₄×D₁₆₃	C₄	semidirect
13. C₂×Dic₁₆₃	C₂×C₄	semidirect
17. C₂×C₄×C₁₆₃	C₂×C₄	semidirect
29. D₁₆₃	#95	direct (N × H)
30. C₁₆₃	C₂×#95	semidirect
34. #95	D₁₆₃	direct (N × H)
48. C₂×C₄	C₄×D₁₆₃	semidirect

Subgroups — #95×D163 #23781508

Conjugacy classes of subgroups

Complements

Subgroups — #95×D₁₆₃ #23781508