Subgroups — C₅×C₁₁×Dic₃×C₄₇ #44526607

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	C₄×C₅×C₁₁×C₄₇	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×Dic₃×C₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×C₄₇	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₄₇	C₂×C₅	1	1	yes	characteristic
7	C₅×Dic₃×C₄₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₄₇	Dic₃	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₁₁×C₄₇	—	3	1	no	Hall
10	C₃×C₁₁×C₄₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₄₇	C₂×C₁₁	1	1	yes	characteristic
12	C₂×C₁₁×C₄₇	C₅×D₃	1	1	yes	characteristic
13	C₄×C₅×C₄₇	—	3	1	no	Hall
14	C₃×C₅×C₄₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₁×Dic₃	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	Dic₃×C₄₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₁₁×C₄₇	C₅×Dic₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×C₄₇	D₃×C₁₁	1	1	yes	characteristic
19	C₂×C₃×C₅×C₁₁	C₂×C₄₇	1	1	yes	characteristic
20	C₂×C₃×C₄₇	C₂×C₅×C₁₁	1	1	yes	characteristic
21	C₅×C₄₇	C₁₁×Dic₃	1	1	yes	characteristic, direct product factor, Hall
22	C₄×C₅×C₁₁	—	3	1	no	Hall
23	C₄×C₄₇	—	3	1	no	Hall
24	C₃×C₅×C₁₁	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₇	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
26	C₁₁×Dic₃	C₅×C₄₇	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₁₁	D₃×C₄₇	1	1	yes	characteristic
28	C₂×C₄₇	C₅×D₃×C₁₁	1	1	yes	characteristic
29	C₂×C₃×C₁₁	C₂×C₅×C₄₇	1	1	yes	characteristic
30	C₅×Dic₃	C₁₁×C₄₇	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₁₁	Dic₃×C₄₇	1	1	yes	characteristic, direct product factor, Hall
32	C₄₇	C₅×C₁₁×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₄×C₁₁	—	3	1	no	Hall
34	C₃×C₁₁	C₄×C₅×C₄₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	C₂×C₁₁×C₄₇	1	1	yes	characteristic
36	C₂×C₁₁	C₅×D₃×C₄₇	1	1	yes	characteristic
37	C₄×C₅	—	3	1	no	Hall
38	C₃×C₅	C₄×C₁₁×C₄₇	1	1	yes	characteristic, complemented, Hall
39	Dic₃	C₅×C₁₁×C₄₇	1	1	yes	characteristic, direct product factor, Hall
40	C₁₁	C₅×Dic₃×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	D₃×C₁₁×C₄₇	1	1	yes	characteristic
42	C₂×C₃	C₂×C₅×C₁₁×C₄₇	1	1	yes	characteristic
43	C₅	C₁₁×Dic₃×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	3	1	no	Sylow
45	C₃	C₄×C₅×C₁₁×C₄₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₅×D₃×C₁₁×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁×C₄₇	D₃
commutator, hypocenter	C₃	C₄×C₅×C₁₁×C₄₇
Frattini	C₂	C₅×D₃×C₁₁×C₄₇
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₁×C₄₇	C₂
cosocle	C₂×C₃	C₂×C₅×C₁₁×C₄₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₁₁×C₄₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₄₇	C₄	semidirect
4. C₁₁×Dic₃×C₄₇	C₅	direct (N × H)
7. C₅×Dic₃×C₄₇	C₁₁	direct (N × H)
8. C₅×C₁₁×C₄₇	Dic₃	direct (N × H)
10. C₃×C₁₁×C₄₇	C₄×C₅	semidirect
14. C₃×C₅×C₄₇	C₄×C₁₁	semidirect
15. C₅×C₁₁×Dic₃	C₄₇	direct (N × H)
16. Dic₃×C₄₇	C₅×C₁₁	direct (N × H)
17. C₁₁×C₄₇	C₅×Dic₃	direct (N × H)
21. C₅×C₄₇	C₁₁×Dic₃	direct (N × H)
24. C₃×C₅×C₁₁	C₄×C₄₇	semidirect
25. C₃×C₄₇	C₄×C₅×C₁₁	semidirect
26. C₁₁×Dic₃	C₅×C₄₇	direct (N × H)
30. C₅×Dic₃	C₁₁×C₄₇	direct (N × H)
31. C₅×C₁₁	Dic₃×C₄₇	direct (N × H)
32. C₄₇	C₅×C₁₁×Dic₃	direct (N × H)
34. C₃×C₁₁	C₄×C₅×C₄₇	semidirect
38. C₃×C₅	C₄×C₁₁×C₄₇	semidirect
39. Dic₃	C₅×C₁₁×C₄₇	direct (N × H)
40. C₁₁	C₅×Dic₃×C₄₇	direct (N × H)
43. C₅	C₁₁×Dic₃×C₄₇	direct (N × H)
45. C₃	C₄×C₅×C₁₁×C₄₇	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
C₄×C₅×C₁₁×C₄₇	3
C₁₁×Dic₃×C₄₇	5
C₅×Dic₃×C₄₇	11
C₅×C₁₁×Dic₃	47

Subgroups — C5×C11×Dic3×C47 #44526607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×Dic₃×C₄₇ #44526607