Subgroups — C₄₇×Dic₁₆₅ #44526613

Order 31020.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×Dic₅₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₇×Dic₃₃	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₁×C₄₇	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₄₇	D₅	1	1	yes	characteristic
7	C₄₇×Dic₁₅	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₄₇	Dic₃	1	1	yes	characteristic, complemented, Hall
9	Dic₁₁×C₄₇	—	15	1	no	Hall
10	C₃×C₁₁×C₄₇	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₄₇	D₁₁	1	1	yes	characteristic
12	C₂×C₁₁×C₄₇	D₁₅	1	1	yes	characteristic
13	Dic₅×C₄₇	—	33	1	no	Hall
14	C₃×C₅×C₄₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
15	Dic₁₆₅	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	Dic₃×C₄₇	—	55	1	no	Hall
17	C₁₁×C₄₇	Dic₁₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₄₇	D₃₃	1	1	yes	characteristic
19	C₂×C₃×C₅×C₁₁	C₂×C₄₇	1	1	yes	characteristic
20	C₂×C₃×C₄₇	D₅₅	1	1	yes	characteristic
21	C₅×C₄₇	Dic₃₃	1	1	yes	characteristic, complemented, Hall
22	Dic₅₅	—	3	1	no	Hall
23	C₄×C₄₇	—	165	1	no	Hall
24	C₃×C₅×C₁₁	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₇	Dic₅₅	1	1	yes	characteristic, complemented, Hall
26	Dic₃₃	—	5	1	no	Hall
27	C₂×C₅×C₁₁	D₃×C₄₇	1	1	yes	characteristic
28	C₂×C₄₇	D₁₆₅	1	1	yes	characteristic
29	C₂×C₃×C₁₁	D₅×C₄₇	1	1	yes	characteristic
30	Dic₁₅	—	11	1	no	Hall
31	C₅×C₁₁	Dic₃×C₄₇	1	1	yes	characteristic, complemented, Hall
32	C₄₇	Dic₁₆₅	1	1	yes	characteristic, direct product factor, Sylow
33	Dic₁₁	—	15	1	no	Hall
34	C₃×C₁₁	Dic₅×C₄₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	D₁₁×C₄₇	1	1	yes	characteristic
36	C₂×C₁₁	D₁₅×C₄₇	1	1	yes	characteristic
37	Dic₅	—	33	1	no	Hall
38	C₃×C₅	Dic₁₁×C₄₇	1	1	yes	characteristic, complemented, Hall
39	Dic₃	—	55	1	no	Hall
40	C₁₁	C₄₇×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	C₄₇×D₃₃	1	1	yes	characteristic
42	C₂×C₃	C₄₇×D₅₅	1	1	yes	characteristic
43	C₅	C₄₇×Dic₃₃	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	165	1	no	Sylow
45	C₃	C₄₇×Dic₅₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₄₇×D₁₆₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄₇	D₁₆₅
commutator, hypocenter	C₃×C₅×C₁₁	C₄×C₄₇
Frattini	C₂	C₄₇×D₁₆₅
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₁×C₄₇	C₂
cosocle	C₂×C₃×C₅×C₁₁	C₂×C₄₇
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₂×C₄₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₄₇	C₄	semidirect
8. C₅×C₁₁×C₄₇	Dic₃	semidirect
10. C₃×C₁₁×C₄₇	Dic₅	semidirect
14. C₃×C₅×C₄₇	Dic₁₁	semidirect
15. Dic₁₆₅	C₄₇	direct (N × H)
17. C₁₁×C₄₇	Dic₁₅	semidirect
21. C₅×C₄₇	Dic₃₃	semidirect
24. C₃×C₅×C₁₁	C₄×C₄₇	semidirect
25. C₃×C₄₇	Dic₅₅	semidirect
31. C₅×C₁₁	Dic₃×C₄₇	semidirect
32. C₄₇	Dic₁₆₅	direct (N × H)
34. C₃×C₁₁	Dic₅×C₄₇	semidirect
38. C₃×C₅	Dic₁₁×C₄₇	semidirect
40. C₁₁	C₄₇×Dic₁₅	semidirect
43. C₅	C₄₇×Dic₃₃	semidirect
45. C₃	C₄₇×Dic₅₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₁₁×C₄₇	2
C₄₇×Dic₅₅	3
C₄₇×Dic₃₃	5
C₄₇×Dic₁₅	11
Dic₁₆₅	47

Subgroups — C47×Dic165 #44526613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×Dic₁₆₅ #44526613