Subgroups — C₃×C₄₃⋊#63120 #46776544

Order 33540.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₃×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊#63120	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₅₅₉	—	5	1	no	maximal, Hall
5	D₅×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₄₃	—	5	1	no	—
7	C₅×C₁₃×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄₃⋊AGL(1,𝔽₅)	—	13	1	no	maximal, Hall
9	Dic₅₅₉	—	5	1	no	Hall
10	C₃×C₁₃×C₄₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃×D₅×C₄₃	D₁₃	1	1	yes	characteristic
12	C₂×C₁₃×C₄₃	—	5	1	no	—
13	C₄₃⋊AGL(1,𝔽₅)	—	13	1	no	Hall
14	C₃×#63120	—	43	1	no	maximal, Hall
15	C₃×C₅×C₄₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
16	C₁₃×C₄₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
17	C₃×Dic₄₃	—	65	1	no	Hall
18	D₅×C₄₃	C₃×D₁₃	1	1	yes	characteristic
19	C₃×D₅×C₁₃	D₄₃	1	1	yes	characteristic
20	#63120	—	43	1	no	Hall
21	C₂×C₃×C₄₃	—	5	1	no	—
22	C₅×C₄₃	C₃×Dic₁₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	Dic₄₃	1	1	yes	characteristic, complemented, Hall
24	Dic₄₃	—	65	1	no	Hall
25	C₃×Dic₁₃	—	215	1	no	Hall
26	D₅×C₁₃	C₃×D₄₃	1	1	yes	characteristic
27	C₃×C₄₃	#63120	1	1	yes	characteristic, complemented, Hall
28	C₂×C₄₃	—	5	1	no	—
29	C₂×C₃×C₁₃	—	5	1	no	—
30	C₅×C₁₃	C₃×Dic₄₃	1	1	yes	characteristic, complemented, Hall
31	C₃×AGL(1,𝔽₅)	—	559	1	no	Hall
32	Dic₁₃	—	215	1	no	Hall
33	C₄₃	C₃×#63120	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₃	C₄₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	D₅₅₉	1	1	yes	characteristic
36	C₂×C₁₃	—	5	1	no	—
37	AGL(1,𝔽₅)	—	559	1	no	Hall
38	C₃×C₅	Dic₅₅₉	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₃×C₄₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	2795	1	no	Hall
41	D₅	C₃×D₅₅₉	1	1	yes	characteristic
42	C₂×C₃	—	5	1	no	—
43	C₅	C₃×Dic₅₅₉	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2795	1	no	Sylow
45	C₃	C₄₃⋊#63120	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₄₃⋊#63120
commutator, hypocenter	C₅×C₁₃×C₄₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₃	C₄
prime radical	C₃×D₅×C₁₃×C₄₃	C₂
cosocle	D₅×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₄₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₄₃⋊#63120	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
15. C₃×C₅×C₄₃	Dic₁₃	semidirect
16. C₁₃×C₄₃	C₃×AGL(1,𝔽₅)	semidirect
22. C₅×C₄₃	C₃×Dic₁₃	semidirect
23. C₃×C₅×C₁₃	Dic₄₃	semidirect
27. C₃×C₄₃	#63120	semidirect
30. C₅×C₁₃	C₃×Dic₄₃	semidirect
33. C₄₃	C₃×#63120	semidirect
34. C₃×C₁₃	C₄₃⋊AGL(1,𝔽₅)	semidirect
38. C₃×C₅	Dic₅₅₉	semidirect
39. C₁₃	C₃×C₄₃⋊AGL(1,𝔽₅)	semidirect
43. C₅	C₃×Dic₅₅₉	semidirect
45. C₃	C₄₃⋊#63120	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×D₅×C₁₃×C₄₃	2
C₄₃⋊#63120	3
C₃×Dic₅₅₉	5
C₃×C₄₃⋊AGL(1,𝔽₅)	13
C₃×#63120	43

Subgroups — C3×C43⋊#63120 #46776544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₃⋊#63120 #46776544