Subgroups — C₁₅₇⋊#401 #23757216

Order 10048.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097678	C₂	1	3	yes	maximal
2	#19097678	C₂	1	3	yes	maximal
3	#95×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₅₇	C₂²	1	3	yes	—
5	C₂²×Dic₁₅₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₁₅₇	C₂²	1	3	yes	—
7	C₂×Dic₁₅₇	—	2	3	no	—
8	C₂×Dic₁₅₇	—	2	3	no	—
9	C₂×Dic₁₅₇	—	2	3	no	—
10	C₂×Dic₁₅₇	—	2	3	no	—
11	C₂³×C₁₅₇	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₁₅₇	—	2	6	no	—
13	C₂×C₄×C₁₅₇	—	2	3	no	—
14	C₂²×C₁₅₇	#41	1	3	yes	—
15	C₂²×C₁₅₇	#41	1	3	yes	—
16	C₂²×C₁₅₇	#41	1	1	yes	characteristic
17	C₄×C₁₅₇	—	4	3	no	—
18	Dic₁₅₇	—	4	1	no	—
19	Dic₁₅₇	—	4	3	no	—
20	C₂×C₁₅₇	#126	1	3	yes	—
21	C₂×C₁₅₇	#126	1	1	yes	characteristic
22	C₂×C₁₅₇	#126	1	3	yes	—
23	C₁₅₇	#401	1	1	yes	characteristic, complemented, Sylow
24	#401	—	157	1	no	maximal, Sylow
25	#95	—	157	3	no	—
26	#95	—	157	3	no	—
27	#95	D₁₅₇	1	1	yes	characteristic
28	C₂²×C₄	—	157	3	no	—
29	C₂²×C₄	—	157	1	no	—
30	C₂²×C₄	C₂×D₁₅₇	1	3	yes	—
31	C₂³	C₂²×D₁₅₇	1	1	yes	characteristic
32	C₂×C₄	—	2	6	no	—
33	C₂×C₄	—	2	3	no	—
34	C₂×C₄	—	314	3	no	—
35	C₂×C₄	—	314	3	no	—
36	C₂×C₄	—	314	3	no	—
37	C₂×C₄	—	314	3	no	—
38	C₂²	#14578953	1	3	yes	—
39	C₂²	#14578954	1	3	yes	—
40	C₂²	#14578955	1	1	yes	characteristic
41	C₄	—	4	3	no	—
42	C₄	—	628	1	no	—
43	C₄	—	628	3	no	—
44	C₂	#19097764	1	3	yes	—
45	C₂	#19097765	1	1	yes	characteristic
46	C₂	#19097766	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₅₇
commutator, socle, prime radical, cosocle	C₂³×C₁₅₇	C₂³
Fitting	#95×C₁₅₇	C₂
hypercenter	#95	D₁₅₇
hypocenter	C₁₅₇	#401
LCS	G ▷ C₂³×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂³ ◁ #95

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

N	H ≅ G/N	type
23. C₁₅₇	#401	semidirect