Subgroups — C₃×C₃⋊#15691169 #43246367

Order 28260.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₇₈₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15691169	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#15691169	—	3	1	no	maximal
4	C₃²×C₅×C₁₅₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃⋊#10597845	—	5	1	no	maximal, Hall
6	C₃×D₇₈₅	—	2	1	no	—
7	C₃×D₇₈₅	D₃	1	1	yes	characteristic
8	C₃×D₇₈₅	C₂×C₃	1	1	yes	characteristic
9	#15691169	—	3	1	no	Hall
10	C₃²×D₁₅₇	—	5	1	no	—
11	C₃×C₅×C₁₅₇	—	2	1	no	—
12	C₃×C₅×C₁₅₇	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅×C₁₅₇	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃⋊#10597845	—	5	1	no	—
15	C₃×#10597845	—	15	1	no	—
16	D₇₈₅	C₃×D₃	1	1	yes	characteristic
17	C₃²×C₁₅₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
18	C₃×D₁₅₇	—	5	1	no	—
19	C₃×D₁₅₇	—	5	1	no	—
20	C₃×D₁₅₇	—	10	1	no	—
21	C₅×C₁₅₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
22	#10597845	—	15	1	no	Hall
23	C₃×C₁₅₇	—	2	1	no	—
24	C₃×C₁₅₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
25	C₃×C₁₅₇	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
26	D₁₅₇	—	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	#10597845	1	1	yes	characteristic, complemented, Hall
33	C₃×Dic₃	—	785	1	no	Hall
34	C₃×D₅	—	314	1	no	—
35	C₃×D₅	—	157	1	no	—
36	C₃×D₅	—	157	1	no	—
37	AGL(1,𝔽₅)	—	471	1	no	Hall
38	C₂×C₃²	—	785	1	no	—
39	C₃×C₅	—	2	1	no	—
40	C₃×C₅	C₃×#10597845	1	1	yes	characteristic, complemented
41	C₃×C₅	C₃⋊#10597845	1	1	yes	characteristic, complemented
42	C₃×C₄	—	2355	1	no	—
43	Dic₃	—	785	1	no	—
44	D₅	—	157	1	no	—
45	C₃²	#15691169	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	785	1	no	—
47	C₂×C₃	—	785	1	no	—
48	C₂×C₃	—	1570	1	no	—
49	C₅	C₃×C₃⋊#10597845	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	2355	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×#15691169	1	1	yes	characteristic, complemented
53	C₃	C₃⋊#15691169	1	1	yes	characteristic, direct product factor
54	C₂	—	785	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊#15691169
commutator, hypocenter	C₃×C₅×C₁₅₇	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₅₇	C₄
prime radical	C₃²×D₇₈₅	C₂
cosocle	C₃×D₇₈₅	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₅₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊#15691169	C₃	direct (N × H)
4. C₃²×C₅×C₁₅₇	C₄	semidirect
12. C₃×C₅×C₁₅₇	Dic₃	semidirect
13. C₃×C₅×C₁₅₇	C₃×C₄	semidirect
17. C₃²×C₁₅₇	AGL(1,𝔽₅)	semidirect
21. C₅×C₁₅₇	C₃×Dic₃	semidirect
24. C₃×C₁₅₇	C₃×AGL(1,𝔽₅)	semidirect
25. C₃×C₁₅₇	ΓL(1,𝔽₁₆)	semidirect
28. C₁₅₇	C₃×ΓL(1,𝔽₁₆)	semidirect
32. C₃²×C₅	#10597845	semidirect
40. C₃×C₅	C₃×#10597845	semidirect
41. C₃×C₅	C₃⋊#10597845	semidirect
45. C₃²	#15691169	semidirect
49. C₅	C₃×C₃⋊#10597845	semidirect
52. C₃	C₃×#15691169	semidirect
53. C₃	C₃⋊#15691169	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₇₈₅	2
C₃⋊#15691169	3
C₃×#15691169	3
C₃×C₃⋊#10597845	5
C₃×ΓL(1,𝔽₁₆)	157

Subgroups — C3×C3⋊#15691169 #43246367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊#15691169 #43246367