Subgroups — C₅×C₃⋊(C₃₁⋊#595) #44539356

Order 31620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₃₁×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁⋊#595	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃₁⋊#595)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₃₁×D₁₇	D₃	1	1	yes	characteristic
6	C₃×C₃₁×D₁₇	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₇×C₃₁	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₃₁⋊#595	—	3	1	no	Hall
9	C₅×Dic₉₃	—	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×C₅×C₃₁	—	17	1	no	—
14	C₅×Dic₃₁	—	51	1	no	Hall
15	C₁₇×C₃₁	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅×D₁₇	D₃₁	1	1	yes	characteristic
17	C₃×C₅×C₃₁	#595	1	1	yes	characteristic, complemented, Hall
18	Dic₉₃	—	17	1	no	Hall
19	C₅×#595	—	93	1	no	Hall
20	C₂×C₅×C₃₁	—	17	1	no	—
21	C₃×C₅×C₁₇	Dic₃₁	1	1	yes	characteristic, complemented, Hall
22	C₃⋊#595	—	31	1	no	Hall
23	C₂×C₃×C₃₁	—	17	1	no	—
24	C₅×D₁₇	D₉₃	1	1	yes	characteristic
25	C₅×C₃₁	C₃⋊#595	1	1	yes	characteristic, complemented, Hall
26	Dic₃₁	—	51	1	no	Hall
27	C₃×D₁₇	C₅×D₃₁	1	1	yes	characteristic
28	C₃×C₃₁	C₅×#595	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	Dic₉₃	1	1	yes	characteristic, complemented, Hall
30	#595	—	93	1	no	Hall
31	C₂×C₃₁	—	17	1	no	—
32	C₅×Dic₃	—	527	1	no	Hall
33	C₃×C₁₇	C₅×Dic₃₁	1	1	yes	characteristic, complemented, Hall
34	D₁₇	C₅×D₉₃	1	1	yes	characteristic
35	C₃₁	C₅×C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	—	17	1	no	—
37	C₄×C₅	—	1581	1	no	Hall
38	C₁₇	C₅×Dic₉₃	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₃₁⋊#595	1	1	yes	characteristic, complemented, Hall
40	Dic₃	—	527	1	no	Hall
41	C₂×C₅	—	17	1	no	—
42	C₂×C₃	—	17	1	no	—
43	C₅	C₃⋊(C₃₁⋊#595)	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	1581	1	no	Sylow
45	C₃	C₅×C₃₁⋊#595	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(C₃₁⋊#595)
commutator, hypocenter	C₃×C₁₇×C₃₁	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₁	C₄
prime radical	C₃×C₅×C₃₁×D₁₇	C₂
cosocle	C₃×C₃₁×D₁₇	C₂×C₅
LCS	G ▷ C₃×C₁₇×C₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₇×C₃₁	C₄	semidirect
4. C₃⋊(C₃₁⋊#595)	C₅	direct (N × H)
7. C₅×C₁₇×C₃₁	Dic₃	semidirect
10. C₃×C₁₇×C₃₁	C₄×C₅	semidirect
15. C₁₇×C₃₁	C₅×Dic₃	semidirect
17. C₃×C₅×C₃₁	#595	semidirect
21. C₃×C₅×C₁₇	Dic₃₁	semidirect
25. C₅×C₃₁	C₃⋊#595	semidirect
28. C₃×C₃₁	C₅×#595	semidirect
29. C₅×C₁₇	Dic₉₃	semidirect
33. C₃×C₁₇	C₅×Dic₃₁	semidirect
35. C₃₁	C₅×C₃⋊#595	semidirect
38. C₁₇	C₅×Dic₉₃	semidirect
39. C₃×C₅	C₃₁⋊#595	semidirect
43. C₅	C₃⋊(C₃₁⋊#595)	direct (N × H)
45. C₃	C₅×C₃₁⋊#595	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₃₁×D₁₇	2
C₅×C₃₁⋊#595	3
C₃⋊(C₃₁⋊#595)	5
C₅×Dic₉₃	17
C₅×C₃⋊#595	31

Subgroups — C5×C3⋊(C31⋊#595) #44539356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊(C₃₁⋊#595) #44539356