Subgroups — C₃₁×C₃⋊#66772 #44539371

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	C₃₁×#66772	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₁×C₃⋊#595	—	5	1	no	maximal, Hall
5	C₅×C₃₁×D₁₇	D₃	1	1	yes	characteristic
6	C₃×C₃₁×D₁₇	D₅	1	1	yes	characteristic
7	C₅×C₁₇×C₃₁	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₃₁×#595	—	15	1	no	Hall
9	C₃₁×Dic₁₅	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₃₁	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₃₁×D₁₇	D₁₅	1	1	yes	characteristic
12	C₃⋊#66772	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×C₃₁	—	17	1	no	—
14	Dic₅×C₃₁	—	51	1	no	Hall
15	C₁₇×C₃₁	Dic₁₅	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅×D₁₇	C₂×C₃₁	1	1	yes	characteristic
17	C₃×C₅×C₃₁	#595	1	1	yes	characteristic, complemented, Hall
18	Dic₃×C₃₁	—	85	1	no	Hall
19	#66772	—	3	1	no	Hall
20	C₂×C₅×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	—	17	1	no	—
24	C₅×D₁₇	D₃×C₃₁	1	1	yes	characteristic
25	C₅×C₃₁	C₃⋊#595	1	1	yes	characteristic, complemented, Hall
26	C₄×C₃₁	—	255	1	no	Hall
27	C₃×D₁₇	D₅×C₃₁	1	1	yes	characteristic
28	C₃×C₃₁	#66772	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	Dic₃×C₃₁	1	1	yes	characteristic, complemented, Hall
30	#595	—	15	1	no	Hall
31	C₂×C₃₁	—	17	1	no	—
32	Dic₁₅	—	17	1	no	Hall
33	C₃×C₁₇	Dic₅×C₃₁	1	1	yes	characteristic, complemented, Hall
34	D₁₇	D₁₅×C₃₁	1	1	yes	characteristic
35	C₃₁	C₃⋊#66772	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃×C₅	—	17	1	no	—
37	Dic₅	—	51	1	no	Hall
38	C₁₇	C₃₁×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₃₁×#595	1	1	yes	characteristic, complemented, Hall
40	Dic₃	—	85	1	no	Hall
41	C₂×C₅	—	17	1	no	—
42	C₂×C₃	—	17	1	no	—
43	C₅	C₃₁×C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	255	1	no	Sylow
45	C₃	C₃₁×#66772	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	C₃⋊#66772
commutator, hypocenter	C₃×C₅×C₁₇	C₄×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₁	C₄
prime radical	C₃×C₅×C₃₁×D₁₇	C₂
cosocle	C₃×C₅×D₁₇	C₂×C₃₁
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₇×C₃₁	C₄	semidirect
7. C₅×C₁₇×C₃₁	Dic₃	semidirect
10. C₃×C₁₇×C₃₁	Dic₅	semidirect
12. C₃⋊#66772	C₃₁	direct (N × H)
15. C₁₇×C₃₁	Dic₁₅	semidirect
17. C₃×C₅×C₃₁	#595	semidirect
21. C₃×C₅×C₁₇	C₄×C₃₁	semidirect
25. C₅×C₃₁	C₃⋊#595	semidirect
28. C₃×C₃₁	#66772	semidirect
29. C₅×C₁₇	Dic₃×C₃₁	semidirect
33. C₃×C₁₇	Dic₅×C₃₁	semidirect
35. C₃₁	C₃⋊#66772	direct (N × H)
38. C₁₇	C₃₁×Dic₁₅	semidirect
39. C₃×C₅	C₃₁×#595	semidirect
43. C₅	C₃₁×C₃⋊#595	semidirect
45. C₃	C₃₁×#66772	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
C₃₁×#66772	3
C₃₁×C₃⋊#595	5
C₃₁×Dic₁₅	17
C₃⋊#66772	31

Subgroups — C31×C3⋊#66772 #44539371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×C₃⋊#66772 #44539371