Subgroups — C₃×C₃₁×#66775 #44539340

Order 31620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#66775	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₁×#595	—	5	1	no	maximal, Hall
5	C₃₁×D₈₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₃₁×D₁₇	—	5	1	no	—
7	C₅×C₁₇×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃₁×#595	—	5	1	no	Hall
9	C₃×AGL(1,𝔽₅)×C₃₁	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₃₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃₁×D₁₇	—	5	1	no	—
12	C₃×#66775	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×C₃₁	—	17	1	no	—
14	AGL(1,𝔽₅)×C₃₁	—	17	1	no	Hall
15	C₁₇×C₃₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
16	C₃×D₈₅	C₂×C₃₁	1	1	yes	characteristic
17	C₃×C₅×C₃₁	#595	1	1	yes	characteristic, complemented, Hall
18	C₃×C₄×C₃₁	—	85	1	no	Hall
19	#66775	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
20	D₅×C₃₁	—	17	1	no	—
21	C₃×C₅×C₁₇	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
22	C₃×#595	—	5	1	no	Hall
23	C₂×C₃×C₃₁	—	85	1	no	—
24	D₈₅	C₂×C₃×C₃₁	1	1	yes	characteristic
25	C₅×C₃₁	C₃×#595	1	1	yes	characteristic, complemented, Hall
26	C₄×C₃₁	—	85	1	no	Hall
27	C₃×D₁₇	—	5	1	no	—
28	C₃×C₃₁	#66775	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₁₇	C₃×C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
30	#595	—	5	1	no	Hall
31	C₂×C₃₁	—	85	1	no	—
32	C₃×AGL(1,𝔽₅)	—	17	1	no	Hall
33	C₃×C₁₇	AGL(1,𝔽₅)×C₃₁	1	1	yes	characteristic, complemented, Hall
34	D₁₇	—	5	1	no	—
35	C₃₁	C₃×#66775	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×D₅	—	17	1	no	—
37	AGL(1,𝔽₅)	—	17	1	no	Hall
38	C₁₇	C₃×AGL(1,𝔽₅)×C₃₁	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₃₁×#595	1	1	yes	characteristic, complemented, Hall
40	C₃×C₄	—	85	1	no	Hall
41	D₅	—	17	1	no	—
42	C₂×C₃	—	85	1	no	—
43	C₅	C₃×C₃₁×#595	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	85	1	no	Sylow
45	C₃	C₃₁×#66775	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	85	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₃₁	#66775
commutator, hypocenter	C₅×C₁₇	C₃×C₄×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₁	C₄
prime radical	C₃×C₃₁×D₈₅	C₂
cosocle	D₈₅	C₂×C₃×C₃₁
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₃×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₃₁×#66775	C₃	direct (N × H)
3. C₃×C₅×C₁₇×C₃₁	C₄	semidirect
7. C₅×C₁₇×C₃₁	C₃×C₄	semidirect
10. C₃×C₁₇×C₃₁	AGL(1,𝔽₅)	semidirect
12. C₃×#66775	C₃₁	direct (N × H)
15. C₁₇×C₃₁	C₃×AGL(1,𝔽₅)	semidirect
17. C₃×C₅×C₃₁	#595	semidirect
19. #66775	C₃×C₃₁	direct (N × H)
21. C₃×C₅×C₁₇	C₄×C₃₁	semidirect
25. C₅×C₃₁	C₃×#595	semidirect
28. C₃×C₃₁	#66775	direct (N × H)
29. C₅×C₁₇	C₃×C₄×C₃₁	semidirect
33. C₃×C₁₇	AGL(1,𝔽₅)×C₃₁	semidirect
35. C₃₁	C₃×#66775	direct (N × H)
38. C₁₇	C₃×AGL(1,𝔽₅)×C₃₁	semidirect
39. C₃×C₅	C₃₁×#595	semidirect
43. C₅	C₃×C₃₁×#595	semidirect
45. C₃	C₃₁×#66775	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×C₃₁×D₈₅	2
C₃₁×#66775	3
C₃×C₃₁×#595	5
C₃×AGL(1,𝔽₅)×C₃₁	17
C₃×#66775	31

Subgroups — C3×C31×#66775 #44539340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₁×#66775 #44539340