Subgroups — C₃×C₄₁×#63118 #44544417

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#63118	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄₁×#261	—	5	1	no	maximal, Hall
5	C₅×D₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic
6	C₃×D₁₃×C₄₁	D₅	1	1	yes	characteristic
7	C₅×C₁₃×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×Dic₅×C₄₁	—	13	1	no	maximal, Hall
9	C₄₁×#261	—	5	1	no	Hall
10	C₃×C₁₃×C₄₁	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₄₁	—	13	1	no	—
12	D₁₃×C₄₁	C₃×D₅	1	1	yes	characteristic
13	Dic₅×C₄₁	—	13	1	no	Hall
14	C₃×#63118	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₅×C₄₁	#261	1	1	yes	characteristic, complemented, Hall
16	C₁₃×C₄₁	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄×C₄₁	—	65	1	no	Hall
18	C₂×C₅×C₄₁	—	13	1	no	—
19	C₃×C₅×D₁₃	C₂×C₄₁	1	1	yes	characteristic
20	#63118	C₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₄₁	—	13	1	no	—
22	C₅×C₄₁	C₃×#261	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
24	C₄×C₄₁	—	65	1	no	Hall
25	C₃×#261	—	5	1	no	Hall
26	C₅×D₁₃	C₂×C₃×C₄₁	1	1	yes	characteristic
27	C₃×C₄₁	#63118	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₄₁	—	13	1	no	—
29	C₃×D₁₃	D₅×C₄₁	1	1	yes	characteristic
30	C₅×C₁₃	C₃×C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
31	C₃×Dic₅	—	13	1	no	Hall
32	#261	—	5	1	no	Hall
33	C₄₁	C₃×#63118	1	1	yes	characteristic, direct product factor, Sylow
34	C₃×C₁₃	Dic₅×C₄₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	—	13	1	no	—
36	D₁₃	C₃×D₅×C₄₁	1	1	yes	characteristic
37	Dic₅	—	13	1	no	Hall
38	C₃×C₅	C₄₁×#261	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₃×Dic₅×C₄₁	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	65	1	no	Hall
41	C₂×C₅	—	13	1	no	—
42	C₂×C₃	—	13	1	no	—
43	C₅	C₃×C₄₁×#261	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	65	1	no	Sylow
45	C₃	C₄₁×#63118	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₄₁	#63118
commutator, hypocenter	C₅×C₁₃	C₃×C₄×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₁	C₄
prime radical	C₃×C₅×D₁₃×C₄₁	C₂
cosocle	C₅×D₁₃	C₂×C₃×C₄₁
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₄₁

Complements

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

N	H ≅ G/N	type
2. C₄₁×#63118	C₃	direct (N × H)
3. C₃×C₅×C₁₃×C₄₁	C₄	semidirect
7. C₅×C₁₃×C₄₁	C₃×C₄	semidirect
10. C₃×C₁₃×C₄₁	Dic₅	semidirect
14. C₃×#63118	C₄₁	direct (N × H)
15. C₃×C₅×C₄₁	#261	semidirect
16. C₁₃×C₄₁	C₃×Dic₅	semidirect
20. #63118	C₃×C₄₁	direct (N × H)
22. C₅×C₄₁	C₃×#261	semidirect
23. C₃×C₅×C₁₃	C₄×C₄₁	semidirect
27. C₃×C₄₁	#63118	direct (N × H)
30. C₅×C₁₃	C₃×C₄×C₄₁	semidirect
33. C₄₁	C₃×#63118	direct (N × H)
34. C₃×C₁₃	Dic₅×C₄₁	semidirect
38. C₃×C₅	C₄₁×#261	semidirect
39. C₁₃	C₃×Dic₅×C₄₁	semidirect
43. C₅	C₃×C₄₁×#261	semidirect
45. C₃	C₄₁×#63118	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×C₅×D₁₃×C₄₁	2
C₄₁×#63118	3
C₃×C₄₁×#261	5
C₃×Dic₅×C₄₁	13
C₃×#63118	41

Subgroups — C3×C41×#63118 #44544417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₁×#63118 #44544417