Subgroups — C₅×C₇×C₃⋊#3866 #29509671

Order 15540.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×D₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×#3866	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₃⋊#3866	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇×D₃₇	D₃	1	1	yes	characteristic
6	C₅×C₃⋊#3866	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇×D₃₇	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇×C₃₇	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×D₃₇	C₂×C₇	1	1	yes	characteristic
10	C₇×#3866	—	3	1	no	Hall
11	C₃×C₇×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅×#3866	—	3	1	no	Hall
13	C₃×C₅×C₃₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	C₇×D₃₇	C₅×D₃	1	1	yes	characteristic
15	C₃⋊#3866	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₇×Dic₃	—	37	1	no	maximal, Hall
17	C₅×D₃₇	D₃×C₇	1	1	yes	characteristic
18	C₇×C₃₇	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₃×D₃₇	C₂×C₅×C₇	1	1	yes	characteristic
20	C₂×C₃×C₅×C₇	—	37	1	no	—
21	C₅×C₃₇	C₇×Dic₃	1	1	yes	characteristic, complemented, Hall
22	#3866	—	3	1	no	Hall
23	C₄×C₅×C₇	—	111	1	no	Hall
24	C₃×C₃₇	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅×C₇	#3866	1	1	yes	characteristic, complemented, Hall
26	C₇×Dic₃	—	37	1	no	Hall
27	D₃₇	C₅×D₃×C₇	1	1	yes	characteristic
28	C₂×C₅×C₇	—	37	1	no	—
29	C₅×Dic₃	—	37	1	no	Hall
30	C₂×C₃×C₇	—	37	1	no	—
31	C₃₇	C₅×C₇×Dic₃	1	1	yes	characteristic, complemented, Sylow
32	C₅×C₇	C₃⋊#3866	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₅	—	37	1	no	—
34	C₄×C₇	—	111	1	no	Hall
35	C₃×C₇	C₅×#3866	1	1	yes	characteristic, complemented, Hall
36	C₄×C₅	—	111	1	no	Hall
37	C₃×C₅	C₇×#3866	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	—	37	1	no	—
39	Dic₃	—	37	1	no	Hall
40	C₂×C₅	—	37	1	no	—
41	C₇	C₅×C₃⋊#3866	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	—	37	1	no	—
43	C₅	C₇×C₃⋊#3866	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	111	1	no	Sylow
45	C₃	C₅×C₇×#3866	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	37	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇	C₃⋊#3866
commutator, hypocenter	C₃×C₃₇	C₄×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₃₇	C₄
prime radical	C₃×C₅×C₇×D₃₇	C₂
cosocle	C₃×D₃₇	C₂×C₅×C₇
LCS	G ▷ C₃×C₃₇
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇×C₃₇	C₄	semidirect
4. C₇×C₃⋊#3866	C₅	direct (N × H)
6. C₅×C₃⋊#3866	C₇	direct (N × H)
8. C₅×C₇×C₃₇	Dic₃	semidirect
11. C₃×C₇×C₃₇	C₄×C₅	semidirect
13. C₃×C₅×C₃₇	C₄×C₇	semidirect
15. C₃⋊#3866	C₅×C₇	direct (N × H)
18. C₇×C₃₇	C₅×Dic₃	semidirect
21. C₅×C₃₇	C₇×Dic₃	semidirect
24. C₃×C₃₇	C₄×C₅×C₇	semidirect
25. C₃×C₅×C₇	#3866	semidirect
31. C₃₇	C₅×C₇×Dic₃	semidirect
32. C₅×C₇	C₃⋊#3866	direct (N × H)
35. C₃×C₇	C₅×#3866	semidirect
37. C₃×C₅	C₇×#3866	semidirect
41. C₇	C₅×C₃⋊#3866	direct (N × H)
43. C₅	C₇×C₃⋊#3866	direct (N × H)
45. C₃	C₅×C₇×#3866	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×D₃₇	2
C₅×C₇×#3866	3
C₇×C₃⋊#3866	5
C₅×C₃⋊#3866	7
C₅×C₇×Dic₃	37

Subgroups — C5×C7×C3⋊#3866 #29509671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₃⋊#3866 #29509671