Subgroups — C₃×#15688301 #22580261

Order 8892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13093365	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉⋊#261	C₃	1	1	yes	maximal, characteristic, complemented
3	#15688301	C₃	1	3	yes	maximal, direct product factor
4	C₃×#10625203	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic
6	#13093365	C₂×C₃	1	3	yes	—
7	C₁₉⋊#261	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
9	#10625203	C₃×C₄	1	3	yes	complemented
10	C₃×(C₁₉⋊C₃)⋊C₄	—	13	1	no	maximal, Hall
11	C₁₉×D₁₃	C₂×C₃²	1	1	yes	characteristic
12	C₃×AGL(1,𝔽₁₃)	—	19	1	no	maximal, Hall
13	C₂×C₃×C₁₉⋊C₃	—	13	1	no	—
14	C₁₃×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₃×D₁₃⋊C₃	—	19	1	no	—
16	C₃×Dic₁₉	—	13	1	no	—
17	(C₁₉⋊C₃)⋊C₄	—	13	3	no	—
18	C₃×C₁₉⋊C₃	—	13	1	no	Hall
19	C₃×#261	—	19	1	no	—
20	AGL(1,𝔽₁₃)	—	19	3	no	—
21	C₃×C₁₃⋊C₃	—	19	1	no	Hall
22	C₂×C₃×C₁₉	—	13	1	no	—
23	C₂×C₁₉⋊C₃	—	13	3	no	—
24	C₃×D₁₃	D₁₉⋊C₃	1	1	yes	characteristic
25	D₁₃⋊C₃	—	19	3	no	—
26	Dic₁₉	—	13	1	no	Hall
27	C₃×C₁₉	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
28	C₁₉⋊C₃	—	13	3	no	—
29	#261	—	19	1	no	Hall
30	C₃×C₁₃	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
31	C₁₃⋊C₃	—	19	3	no	—
32	C₂×C₁₉	—	13	1	no	—
33	C₃²×C₄	—	247	1	no	Hall
34	D₁₃	C₃×D₁₉⋊C₃	1	1	yes	characteristic
35	C₁₉	C₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	—	247	1	no	—
37	C₁₃	C₃×(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₄	—	247	1	no	—
39	C₃×C₄	—	247	3	no	—
40	C₃²	—	247	1	no	Sylow
41	C₂×C₃	—	13	1	no	—
42	C₂×C₃	—	247	3	no	—
43	C₄	—	247	1	no	Sylow
44	C₃	—	247	3	no	—
45	C₃	#15688301	1	1	yes	characteristic, direct product factor
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#15688301
commutator, hypocenter	C₁₃×C₁₉	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₉	C₃×C₄
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₉⋊#261	C₃	semidirect
3. #15688301	C₃	direct (N × H)
4. C₃×#10625203	C₄	semidirect
7. C₁₉⋊#261	C₃²	semidirect
8. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
9. #10625203	C₃×C₄	semidirect
14. C₁₃×C₁₉	C₃²×C₄	semidirect
27. C₃×C₁₉	AGL(1,𝔽₁₃)	semidirect
30. C₃×C₁₃	(C₁₉⋊C₃)⋊C₄	semidirect
35. C₁₉	C₃×AGL(1,𝔽₁₃)	semidirect
37. C₁₃	C₃×(C₁₉⋊C₃)⋊C₄	semidirect
45. C₃	#15688301	direct (N × H)

Subgroups — C3×#15688301 #22580261

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#15688301 #22580261