Subgroups — C₃⋊(ΓL(1,𝔽₃₂)⋊#595) #44539291

Order 31620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₇×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic
2	ΓL(1,𝔽₃₂)⋊#595	—	3	1	no	maximal, Hall
3	C₃×C₁₇×ΓL(1,𝔽₃₂)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃₁⋊#595)	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	D₁₇×ΓL(1,𝔽₃₂)	D₃	1	1	yes	characteristic
6	C₃×C₃₁×D₁₇	C₂×C₅	1	1	yes	characteristic
7	C₁₇×ΓL(1,𝔽₃₂)	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₃₁⋊#595	—	3	1	no	Hall
9	C₃⋊(Dic₃₁⋊C₅)	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃₁×D₁₇	C₅×D₃	1	1	yes	characteristic
12	C₅×C₃⋊#595	—	31	1	no	maximal, Hall
13	C₂×C₃×ΓL(1,𝔽₃₂)	—	17	1	no	—
14	Dic₃₁⋊C₅	—	51	1	no	Hall
15	C₁₇×C₃₁	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅×D₁₇	—	31	1	no	—
17	C₃×ΓL(1,𝔽₃₂)	#595	1	1	yes	characteristic, complemented, Hall
18	Dic₉₃	—	17	1	no	Hall
19	C₅×#595	—	93	1	no	Hall
20	C₂×ΓL(1,𝔽₃₂)	—	17	1	no	—
21	C₃×C₅×C₁₇	—	31	1	no	Hall
22	C₃⋊#595	—	31	1	no	Hall
23	C₂×C₃×C₃₁	—	17	1	no	—
24	C₅×D₁₇	—	31	1	no	—
25	ΓL(1,𝔽₃₂)	C₃⋊#595	1	1	yes	characteristic, complemented, Hall
26	Dic₃₁	—	51	1	no	Hall
27	C₃×D₁₇	D₃₁⋊C₅	1	1	yes	characteristic
28	C₃×C₃₁	C₅×#595	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	—	31	1	no	Hall
30	#595	—	93	1	no	Hall
31	C₂×C₃₁	—	17	1	no	—
32	C₅×Dic₃	—	527	1	no	Hall
33	C₃×C₁₇	Dic₃₁⋊C₅	1	1	yes	characteristic, complemented, Hall
34	D₁₇	C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic
35	C₃₁	C₅×C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	—	527	1	no	—
37	C₄×C₅	—	1581	1	no	Hall
38	C₁₇	C₃⋊(Dic₃₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	31	1	no	Hall
40	Dic₃	—	527	1	no	Hall
41	C₂×C₅	—	527	1	no	—
42	C₂×C₃	—	17	1	no	—
43	C₅	—	31	1	no	Sylow
44	C₄	—	1581	1	no	Sylow
45	C₃	ΓL(1,𝔽₃₂)⋊#595	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₇×C₃₁	C₄×C₅
prime radical	C₃×D₁₇×ΓL(1,𝔽₃₂)	C₂
cosocle	C₃×C₃₁×D₁₇	C₂×C₅
LCS	G ▷ C₃×C₁₇×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₇×ΓL(1,𝔽₃₂)	C₄	semidirect
4. C₃⋊(C₃₁⋊#595)	C₅	semidirect
7. C₁₇×ΓL(1,𝔽₃₂)	Dic₃	semidirect
10. C₃×C₁₇×C₃₁	C₄×C₅	semidirect
15. C₁₇×C₃₁	C₅×Dic₃	semidirect
17. C₃×ΓL(1,𝔽₃₂)	#595	semidirect
25. ΓL(1,𝔽₃₂)	C₃⋊#595	semidirect
28. C₃×C₃₁	C₅×#595	semidirect
33. C₃×C₁₇	Dic₃₁⋊C₅	semidirect
35. C₃₁	C₅×C₃⋊#595	semidirect
38. C₁₇	C₃⋊(Dic₃₁⋊C₅)	semidirect
45. C₃	ΓL(1,𝔽₃₂)⋊#595	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₁₇×ΓL(1,𝔽₃₂)	2
ΓL(1,𝔽₃₂)⋊#595	3
C₃⋊(C₃₁⋊#595)	5
C₃⋊(Dic₃₁⋊C₅)	17
C₅×C₃⋊#595	31

Subgroups — C3⋊(ΓL(1,𝔽32)⋊#595) #44539291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(ΓL(1,𝔽₃₂)⋊#595) #44539291