Subgroups — C₃⋊(#15691171⋊C₃) #43246331

Order 28260.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₅₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15691171	C₃	1	1	yes	maximal, characteristic, complemented
3	#15691171⋊C₃	—	3	1	no	maximal
4	C₃×C₅×C₁₅₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃⋊(Dic₁₅₇⋊C₃)	—	5	1	no	maximal, Hall
6	D₅×C₁₅₇⋊C₃	—	2	1	no	—
7	D₅×C₁₅₇⋊C₃	D₃	1	1	yes	characteristic
8	C₃×D₅×C₁₅₇	C₂×C₃	1	1	yes	characteristic
9	#15691171	—	3	1	no	Hall
10	C₂×C₃×C₁₅₇⋊C₃	—	5	1	no	—
11	C₃×C₅×C₁₅₇	C₃×C₄	1	1	yes	characteristic, complemented
12	C₅×C₁₅₇⋊C₃	—	2	1	no	—
13	C₅×C₁₅₇⋊C₃	Dic₃	1	1	yes	characteristic, complemented
14	Dic₄₇₁	—	5	1	no	—
15	Dic₁₅₇⋊C₃	—	15	1	no	—
16	D₅×C₁₅₇	C₃×D₃	1	1	yes	characteristic
17	C₃×C₁₅₇⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₁₅₇	—	5	1	no	—
19	C₂×C₁₅₇⋊C₃	—	5	1	no	—
20	C₂×C₁₅₇⋊C₃	—	10	1	no	—
21	C₅×C₁₅₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
22	Dic₁₅₇	—	15	1	no	Hall
23	C₃×C₁₅₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
24	C₁₅₇⋊C₃	—	2	1	no	—
25	C₁₅₇⋊C₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
26	C₂×C₁₅₇	—	5	1	no	—
27	C₃×ΓL(1,𝔽₁₆)	—	157	1	no	maximal, Hall
28	C₁₅₇	C₃×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
29	C₃²×D₅	—	157	1	no	—
30	ΓL(1,𝔽₁₆)	—	157	1	no	—
31	C₃×AGL(1,𝔽₅)	—	471	1	no	—
32	C₃²×C₅	—	157	1	no	Hall
33	C₃×Dic₃	—	785	1	no	Hall
34	C₃×D₅	—	314	1	no	—
35	C₃×D₅	—	314	1	no	—
36	C₃×D₅	D₁₅₇⋊C₃	1	1	yes	characteristic
37	AGL(1,𝔽₅)	—	471	1	no	Hall
38	C₂×C₃²	—	785	1	no	—
39	C₃×C₅	—	314	1	no	—
40	C₃×C₅	—	314	1	no	—
41	C₃×C₅	Dic₁₅₇⋊C₃	1	1	yes	characteristic, complemented
42	C₃×C₄	—	2355	1	no	—
43	Dic₃	—	785	1	no	—
44	D₅	C₃⋊(D₁₅₇⋊C₃)	1	1	yes	characteristic
45	C₃²	—	157	1	no	Sylow
46	C₂×C₃	—	5	1	no	—
47	C₂×C₃	—	1570	1	no	—
48	C₂×C₃	—	1570	1	no	—
49	C₅	C₃⋊(Dic₁₅₇⋊C₃)	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	2355	1	no	Sylow
51	C₃	—	314	1	no	—
52	C₃	—	314	1	no	—
53	C₃	#15691171⋊C₃	1	1	yes	characteristic, complemented
54	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₁₅₇	C₃×C₄
prime radical	C₃×D₅×C₁₅₇⋊C₃	C₂
cosocle	C₃×D₅×C₁₅₇	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₅₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃⋊#15691171	C₃	semidirect
4. C₃×C₅×C₁₅₇⋊C₃	C₄	semidirect
11. C₃×C₅×C₁₅₇	C₃×C₄	semidirect
13. C₅×C₁₅₇⋊C₃	Dic₃	semidirect
17. C₃×C₁₅₇⋊C₃	AGL(1,𝔽₅)	semidirect
21. C₅×C₁₅₇	C₃×Dic₃	semidirect
23. C₃×C₁₅₇	C₃×AGL(1,𝔽₅)	semidirect
25. C₁₅₇⋊C₃	ΓL(1,𝔽₁₆)	semidirect
28. C₁₅₇	C₃×ΓL(1,𝔽₁₆)	semidirect
41. C₃×C₅	Dic₁₅₇⋊C₃	semidirect
49. C₅	C₃⋊(Dic₁₅₇⋊C₃)	semidirect
53. C₃	#15691171⋊C₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₅×C₁₅₇⋊C₃	2
C₃⋊#15691171	3
#15691171⋊C₃	3
C₃⋊(Dic₁₅₇⋊C₃)	5
C₃×ΓL(1,𝔽₁₆)	157

Subgroups — C3⋊(#15691171⋊C3) #43246331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#15691171⋊C₃) #43246331