Subgroups — C₃⋊#27160387 #49179882

Order 37740.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×D₃₇	C₂	1	1	yes	maximal, characteristic
2	#27160387	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#14578982	—	5	1	no	maximal, Hall
5	C₅×C₁₇×D₃₇	D₃	1	1	yes	characteristic
6	C₃×C₁₇×D₃₇	D₅	1	1	yes	characteristic
7	C₅×C₁₇×C₃₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#14578982	—	15	1	no	Hall
9	C₃⋊#10625194	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₃₇	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₁₇×D₃₇	D₁₅	1	1	yes	characteristic
12	C₃×C₅×D₃₇	D₁₇	1	1	yes	characteristic
13	Dic₂₅₅	—	37	1	no	maximal, Hall
14	#10625194	—	51	1	no	Hall
15	C₁₇×C₃₇	Dic₁₅	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅×C₃₇	Dic₁₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅×C₁₇	—	37	1	no	—
18	C₃⋊#3866	—	85	1	no	Hall
19	C₅×D₃₇	D₅₁	1	1	yes	characteristic
20	Dic₈₅	—	111	1	no	Hall
21	C₃×C₅×C₁₇	#3866	1	1	yes	characteristic, complemented, Hall
22	C₃×D₃₇	D₈₅	1	1	yes	characteristic
23	Dic₅₁	—	185	1	no	Hall
24	C₅×C₃₇	Dic₅₁	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₁₇	—	37	1	no	—
26	#3866	—	255	1	no	Hall
27	C₃×C₃₇	Dic₈₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₇	—	37	1	no	—
29	C₅×C₁₇	C₃⋊#3866	1	1	yes	characteristic, complemented, Hall
30	D₃₇	D₂₅₅	1	1	yes	characteristic
31	Dic₁₇	—	555	1	no	Hall
32	Dic₁₅	—	629	1	no	Hall
33	C₃×C₁₇	#10625194	1	1	yes	characteristic, complemented, Hall
34	C₃₇	Dic₂₅₅	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₁₇	—	37	1	no	—
36	C₂×C₃×C₅	—	37	1	no	—
37	Dic₅	—	1887	1	no	Hall
38	C₁₇	C₃⋊#10625194	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	#14578982	1	1	yes	characteristic, complemented, Hall
40	Dic₃	—	3145	1	no	Hall
41	C₂×C₅	—	37	1	no	—
42	C₂×C₃	—	37	1	no	—
43	C₅	C₃⋊#14578982	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	9435	1	no	Sylow
45	C₃	#27160387	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	37	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₁₇×C₃₇	C₄
prime radical, cosocle	C₃×C₅×C₁₇×D₃₇	C₂
LCS	G ▷ C₃×C₅×C₁₇×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₇×C₃₇	C₄	semidirect
7. C₅×C₁₇×C₃₇	Dic₃	semidirect
10. C₃×C₁₇×C₃₇	Dic₅	semidirect
15. C₁₇×C₃₇	Dic₁₅	semidirect
16. C₃×C₅×C₃₇	Dic₁₇	semidirect
21. C₃×C₅×C₁₇	#3866	semidirect
24. C₅×C₃₇	Dic₅₁	semidirect
27. C₃×C₃₇	Dic₈₅	semidirect
29. C₅×C₁₇	C₃⋊#3866	semidirect
33. C₃×C₁₇	#10625194	semidirect
34. C₃₇	Dic₂₅₅	semidirect
38. C₁₇	C₃⋊#10625194	semidirect
39. C₃×C₅	#14578982	semidirect
43. C₅	C₃⋊#14578982	semidirect
45. C₃	#27160387	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₇×D₃₇	2
#27160387	3
C₃⋊#14578982	5
C₃⋊#10625194	17
Dic₂₅₅	37

Subgroups — C3⋊#27160387 #49179882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#27160387 #49179882