Subgroups — C₃×#14523157 #20258879

Order 6084.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#10621730	C₃	1	1	yes	maximal, characteristic, complemented
3	#14523157	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₁₃×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×D₁₃	C₂×C₃	1	1	yes	characteristic
6	D₁₃×C₁₃⋊C₃	C₂×C₃	1	3	yes	—
7	#10621730	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented
9	C₁₃×C₁₃⋊C₃	C₃×C₄	1	3	yes	complemented
10	C₃²×#261	—	13	1	no	maximal
11	C₃×Dic₁₃⋊C₃	—	13	1	no	maximal
12	C₁₃×D₁₃	C₂×C₃²	1	1	yes	characteristic
13	C₃²×D₁₃	—	13	1	no	—
14	C₂×C₃×C₁₃⋊C₃	—	13	1	no	—
15	C₁₃²	C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₃×#261	—	13	3	no	—
17	C₃×#261	—	13	1	no	—
18	C₃×Dic₁₃	—	13	1	no	—
19	Dic₁₃⋊C₃	—	13	3	no	—
20	C₃²×C₁₃	—	13	1	no	—
21	C₃×C₁₃⋊C₃	#261	1	1	yes	characteristic, complemented
22	C₂×C₃×C₁₃	—	13	1	no	—
23	C₃×D₁₃	—	13	3	no	—
24	C₃×D₁₃	D₁₃⋊C₃	1	1	yes	characteristic
25	C₂×C₁₃⋊C₃	—	13	3	no	—
26	#261	—	13	1	no	—
27	Dic₁₃	—	13	1	no	—
28	C₃×C₁₃	—	12	1	no	—
29	C₃×C₁₃	—	13	3	no	—
30	C₃×C₁₃	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₃×C₁₃	C₃×#261	1	1	yes	characteristic, complemented
32	C₁₃⋊C₃	C₃×#261	1	3	yes	complemented
33	C₃²×C₄	—	169	1	no	Hall
34	C₂×C₁₃	—	13	1	no	—
35	D₁₃	C₃×D₁₃⋊C₃	1	1	yes	characteristic
36	C₂×C₃²	—	169	1	no	—
37	C₁₃	—	12	1	no	—
38	C₁₃	C₃×Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
39	C₁₃	C₃²×#261	1	1	yes	characteristic, complemented
40	C₃×C₄	—	169	1	no	—
41	C₃×C₄	—	169	3	no	—
42	C₃²	—	13	1	no	Sylow
43	C₂×C₃	—	13	1	no	—
44	C₂×C₃	—	169	3	no	—
45	C₄	—	169	1	no	Sylow
46	C₃	—	13	3	no	—
47	C₃	#14523157	1	1	yes	characteristic, direct product factor
48	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#14523157
commutator, hypocenter	C₁₃²	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²	C₃×C₄
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×#10621730	C₃	semidirect
3. #14523157	C₃	direct (N × H)
4. C₃×C₁₃×C₁₃⋊C₃	C₄	semidirect
7. #10621730	C₃²	semidirect
8. C₃×C₁₃²	C₃×C₄	semidirect
9. C₁₃×C₁₃⋊C₃	C₃×C₄	semidirect
15. C₁₃²	C₃²×C₄	semidirect
21. C₃×C₁₃⋊C₃	#261	semidirect
30. C₃×C₁₃	Dic₁₃⋊C₃	semidirect
31. C₃×C₁₃	C₃×#261	semidirect
32. C₁₃⋊C₃	C₃×#261	semidirect
38. C₁₃	C₃×Dic₁₃⋊C₃	semidirect
39. C₁₃	C₃²×#261	semidirect
47. C₃	#14523157	direct (N × H)

Subgroups — C3×#14523157 #20258879

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#14523157 #20258879