Subgroups — C₃×C₄₃×#63122 #46776539

Order 33540.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#63122	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄₃×#261	—	5	1	no	maximal, Hall
5	C₄₃×D₆₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₁₃×C₄₃	—	5	1	no	—
7	C₅×C₁₃×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×AGL(1,𝔽₅)×C₄₃	—	13	1	no	maximal, Hall
9	C₄₃×#261	—	5	1	no	Hall
10	C₃×C₁₃×C₄₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃×D₅×C₄₃	—	13	1	no	—
12	D₁₃×C₄₃	—	5	1	no	—
13	AGL(1,𝔽₅)×C₄₃	—	13	1	no	Hall
14	C₃×#63122	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₅×C₄₃	#261	1	1	yes	characteristic, complemented, Hall
16	C₁₃×C₄₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄×C₄₃	—	65	1	no	Hall
18	D₅×C₄₃	—	13	1	no	—
19	C₃×D₆₅	C₂×C₄₃	1	1	yes	characteristic
20	#63122	C₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₄₃	—	65	1	no	—
22	C₅×C₄₃	C₃×#261	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
24	C₄×C₄₃	—	65	1	no	Hall
25	C₃×#261	—	5	1	no	Hall
26	D₆₅	C₂×C₃×C₄₃	1	1	yes	characteristic
27	C₃×C₄₃	#63122	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₄₃	—	65	1	no	—
29	C₃×D₁₃	—	5	1	no	—
30	C₅×C₁₃	C₃×C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
31	C₃×AGL(1,𝔽₅)	—	13	1	no	Hall
32	#261	—	5	1	no	Hall
33	C₄₃	C₃×#63122	1	1	yes	characteristic, direct product factor, Sylow
34	C₃×C₁₃	AGL(1,𝔽₅)×C₄₃	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	—	13	1	no	—
36	D₁₃	—	5	1	no	—
37	AGL(1,𝔽₅)	—	13	1	no	Hall
38	C₃×C₅	C₄₃×#261	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₃×AGL(1,𝔽₅)×C₄₃	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	65	1	no	Hall
41	D₅	—	13	1	no	—
42	C₂×C₃	—	65	1	no	—
43	C₅	C₃×C₄₃×#261	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	65	1	no	Sylow
45	C₃	C₄₃×#63122	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₄₃	#63122
commutator, hypocenter	C₅×C₁₃	C₃×C₄×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₃	C₄
prime radical	C₃×C₄₃×D₆₅	C₂
cosocle	D₆₅	C₂×C₃×C₄₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₄₃

Complements

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

N	H ≅ G/N	type
2. C₄₃×#63122	C₃	direct (N × H)
3. C₃×C₅×C₁₃×C₄₃	C₄	semidirect
7. C₅×C₁₃×C₄₃	C₃×C₄	semidirect
10. C₃×C₁₃×C₄₃	AGL(1,𝔽₅)	semidirect
14. C₃×#63122	C₄₃	direct (N × H)
15. C₃×C₅×C₄₃	#261	semidirect
16. C₁₃×C₄₃	C₃×AGL(1,𝔽₅)	semidirect
20. #63122	C₃×C₄₃	direct (N × H)
22. C₅×C₄₃	C₃×#261	semidirect
23. C₃×C₅×C₁₃	C₄×C₄₃	semidirect
27. C₃×C₄₃	#63122	direct (N × H)
30. C₅×C₁₃	C₃×C₄×C₄₃	semidirect
33. C₄₃	C₃×#63122	direct (N × H)
34. C₃×C₁₃	AGL(1,𝔽₅)×C₄₃	semidirect
38. C₃×C₅	C₄₃×#261	semidirect
39. C₁₃	C₃×AGL(1,𝔽₅)×C₄₃	semidirect
43. C₅	C₃×C₄₃×#261	semidirect
45. C₃	C₄₃×#63122	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄₃×D₆₅	2
C₄₃×#63122	3
C₃×C₄₃×#261	5
C₃×AGL(1,𝔽₅)×C₄₃	13
C₃×#63122	43

Subgroups — C3×C43×#63122 #46776539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₃×#63122 #46776539