Subgroups — C₃×Dic₂₅₈₅ #44526606

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	Dic₂₅₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₁×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₅₁₇	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₁×C₄₇	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₄₇	D₅	1	1	yes	characteristic
7	C₃×Dic₂₃₅	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₄₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	Dic₅₁₇	—	5	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	C₃×D₅	1	1	yes	characteristic
13	Dic₂₃₅	—	11	1	no	Hall
14	C₃×C₅×C₄₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×Dic₅₅	—	47	1	no	maximal, Hall
16	C₃×Dic₄₇	—	55	1	no	Hall
17	C₁₁×C₄₇	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₄₇	C₃×D₁₁	1	1	yes	characteristic
19	C₂×C₃×C₅×C₁₁	D₄₇	1	1	yes	characteristic
20	C₂×C₃×C₄₇	D₅₅	1	1	yes	characteristic
21	C₅×C₄₇	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
22	Dic₅₅	—	47	1	no	Hall
23	Dic₄₇	—	55	1	no	Hall
24	C₃×C₅×C₁₁	Dic₄₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₇	Dic₅₅	1	1	yes	characteristic, complemented, Hall
26	C₃×Dic₁₁	—	235	1	no	Hall
27	C₂×C₅×C₁₁	C₃×D₄₇	1	1	yes	characteristic
28	C₂×C₄₇	C₃×D₅₅	1	1	yes	characteristic
29	C₂×C₃×C₁₁	D₂₃₅	1	1	yes	characteristic
30	C₃×Dic₅	—	517	1	no	Hall
31	C₅×C₁₁	C₃×Dic₄₇	1	1	yes	characteristic, complemented, Hall
32	C₄₇	C₃×Dic₅₅	1	1	yes	characteristic, complemented, Sylow
33	Dic₁₁	—	235	1	no	Hall
34	C₃×C₁₁	Dic₂₃₅	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	D₅₁₇	1	1	yes	characteristic
36	C₂×C₁₁	C₃×D₂₃₅	1	1	yes	characteristic
37	Dic₅	—	517	1	no	Hall
38	C₃×C₅	Dic₅₁₇	1	1	yes	characteristic, complemented, Hall
39	C₃×C₄	—	2585	1	no	Hall
40	C₁₁	C₃×Dic₂₃₅	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	C₃×D₅₁₇	1	1	yes	characteristic
42	C₂×C₃	D₂₅₈₅	1	1	yes	characteristic
43	C₅	C₃×Dic₅₁₇	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2585	1	no	Sylow
45	C₃	Dic₂₅₈₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×D₂₅₈₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₅₈₅
commutator, hypocenter	C₅×C₁₁×C₄₇	C₃×C₄
Frattini	C₂	C₃×D₂₅₈₅
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₁×C₄₇	C₂
cosocle	C₂×C₅×C₁₁×C₄₇	C₂×C₃
LCS	G ▷ C₅×C₁₁×C₄₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₂₅₈₅	C₃	direct (N × H)
3. C₃×C₅×C₁₁×C₄₇	C₄	semidirect
8. C₅×C₁₁×C₄₇	C₃×C₄	semidirect
10. C₃×C₁₁×C₄₇	Dic₅	semidirect
14. C₃×C₅×C₄₇	Dic₁₁	semidirect
17. C₁₁×C₄₇	C₃×Dic₅	semidirect
21. C₅×C₄₇	C₃×Dic₁₁	semidirect
24. C₃×C₅×C₁₁	Dic₄₇	semidirect
25. C₃×C₄₇	Dic₅₅	semidirect
31. C₅×C₁₁	C₃×Dic₄₇	semidirect
32. C₄₇	C₃×Dic₅₅	semidirect
34. C₃×C₁₁	Dic₂₃₅	semidirect
38. C₃×C₅	Dic₅₁₇	semidirect
40. C₁₁	C₃×Dic₂₃₅	semidirect
43. C₅	C₃×Dic₅₁₇	semidirect
45. C₃	Dic₂₅₈₅	direct (N × H)

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
Dic₂₅₈₅	3
C₃×Dic₅₁₇	5
C₃×Dic₂₃₅	11
C₃×Dic₅₅	47

Subgroups — C3×Dic2585 #44526606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₂₅₈₅ #44526606