Subgroups — C₄₁×C₃⋊#63120 #44544451

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#63120	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₁×Dic₃₉	—	5	1	no	maximal, Hall
5	D₅×C₁₃×C₄₁	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₄₁	—	5	1	no	—
7	C₅×C₁₃×C₄₁	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₄₁×ΓL(1,𝔽₁₆)	—	13	1	no	maximal, Hall
9	C₄₁×Dic₁₃	—	15	1	no	Hall
10	C₃×C₁₃×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃×D₅×C₄₁	D₁₃	1	1	yes	characteristic
12	C₂×C₁₃×C₄₁	—	5	1	no	—
13	AGL(1,𝔽₅)×C₄₁	—	39	1	no	Hall
14	C₃⋊#63120	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₅×C₄₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
16	C₁₃×C₄₁	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Hall
17	Dic₃×C₄₁	—	65	1	no	Hall
18	D₅×C₄₁	D₃₉	1	1	yes	characteristic
19	C₃×D₅×C₁₃	C₂×C₄₁	1	1	yes	characteristic
20	#63120	—	3	1	no	Hall
21	C₂×C₃×C₄₁	—	5	1	no	—
22	C₅×C₄₁	Dic₃₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
24	C₄×C₄₁	—	195	1	no	Hall
25	Dic₃₉	—	5	1	no	Hall
26	D₅×C₁₃	D₃×C₄₁	1	1	yes	characteristic
27	C₃×C₄₁	#63120	1	1	yes	characteristic, complemented, Hall
28	C₂×C₄₁	—	5	1	no	—
29	C₂×C₃×C₁₃	—	5	1	no	—
30	C₅×C₁₃	Dic₃×C₄₁	1	1	yes	characteristic, complemented, Hall
31	ΓL(1,𝔽₁₆)	—	13	1	no	Hall
32	Dic₁₃	—	15	1	no	Hall
33	C₄₁	C₃⋊#63120	1	1	yes	characteristic, direct product factor, Sylow
34	C₃×C₁₃	AGL(1,𝔽₅)×C₄₁	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	D₁₃×C₄₁	1	1	yes	characteristic
36	C₂×C₁₃	—	5	1	no	—
37	AGL(1,𝔽₅)	—	39	1	no	Hall
38	C₃×C₅	C₄₁×Dic₁₃	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₄₁×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
40	Dic₃	—	65	1	no	Hall
41	D₅	C₄₁×D₃₉	1	1	yes	characteristic
42	C₂×C₃	—	5	1	no	—
43	C₅	C₄₁×Dic₃₉	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	195	1	no	Sylow
45	C₃	C₄₁×#63120	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₄₁	C₃⋊#63120
commutator, hypocenter	C₃×C₅×C₁₃	C₄×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₁	C₄
prime radical	C₃×D₅×C₁₃×C₄₁	C₂
cosocle	C₃×D₅×C₁₃	C₂×C₄₁
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₄₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₃×C₄₁	C₄	semidirect
7. C₅×C₁₃×C₄₁	Dic₃	semidirect
10. C₃×C₁₃×C₄₁	AGL(1,𝔽₅)	semidirect
14. C₃⋊#63120	C₄₁	direct (N × H)
15. C₃×C₅×C₄₁	Dic₁₃	semidirect
16. C₁₃×C₄₁	ΓL(1,𝔽₁₆)	semidirect
22. C₅×C₄₁	Dic₃₉	semidirect
23. C₃×C₅×C₁₃	C₄×C₄₁	semidirect
27. C₃×C₄₁	#63120	semidirect
30. C₅×C₁₃	Dic₃×C₄₁	semidirect
33. C₄₁	C₃⋊#63120	direct (N × H)
34. C₃×C₁₃	AGL(1,𝔽₅)×C₄₁	semidirect
38. C₃×C₅	C₄₁×Dic₁₃	semidirect
39. C₁₃	C₄₁×ΓL(1,𝔽₁₆)	semidirect
43. C₅	C₄₁×Dic₃₉	semidirect
45. C₃	C₄₁×#63120	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₅×C₁₃×C₄₁	2
C₄₁×#63120	3
C₄₁×Dic₃₉	5
C₄₁×ΓL(1,𝔽₁₆)	13
C₃⋊#63120	41

Subgroups — C41×C3⋊#63120 #44544451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×C₃⋊#63120 #44544451