Subgroups — C₃⋊(#1043⋊(C₃₇⋊C₃)) #45686274

Order 33300.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₅⋊D₅)⋊(C₃₇⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₃₇×C₃⋊#1043	C₃	1	1	yes	maximal, characteristic, complemented
3	#1043⋊(C₃₇⋊C₃)	—	3	1	no	maximal
4	C₃×C₅²⋊(C₃₇⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	(C₅⋊D₅)⋊(C₃₇⋊C₃)	—	2	1	no	—
7	(C₅⋊D₅)⋊(C₃₇⋊C₃)	D₃	1	1	yes	characteristic
8	C₃₇×#1043	—	3	1	no	Hall
9	C₅²⋊(C₃₇⋊C₃)	—	2	1	no	—
10	C₅²⋊(C₃₇⋊C₃)	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃₇×ΓL(1,𝔽₁₆)	—	15	2	no	—
13	C₃₇×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic
14	Dic₃×C₃₇⋊C₃	—	25	1	no	maximal, Hall
15	C₃×D₅×C₃₇	—	15	2	no	—
16	C₅²×C₃₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃⋊(#1043⋊C₃)	—	37	1	no	maximal, Hall
18	AGL(1,𝔽₅)×C₃₇	—	45	2	no	—
19	C₂×C₃×C₃₇⋊C₃	—	25	1	no	—
20	C₃×C₅×C₃₇	—	3	2	no	—
21	C₃×(C₅⋊D₅)⋊C₃	—	37	1	no	—
22	Dic₃×C₃₇	—	25	1	no	—
23	C₄×C₃₇⋊C₃	—	75	1	no	—
24	D₅×C₃₇	—	15	2	no	—
25	C₃×C₃₇⋊C₃	—	25	1	no	Hall
26	C₃⋊#1043	C₃₇⋊C₃	1	1	yes	characteristic, complemented
27	#1043⋊C₃	—	111	1	no	—
28	C₃×C₅²⋊C₃	—	37	1	no	Hall
29	C₂×C₃×C₃₇	—	25	1	no	—
30	C₂×C₃₇⋊C₃	—	25	1	no	—
31	C₂×C₃₇⋊C₃	—	50	1	no	—
32	C₅×C₃₇	—	3	2	no	—
33	C₃×C₅⋊D₅	C₂×C₃₇⋊C₃	1	1	yes	characteristic
34	(C₅⋊D₅)⋊C₃	—	37	1	no	—
35	(C₅⋊D₅)⋊C₃	—	74	1	no	—
36	C₄×C₃₇	—	75	1	no	Hall
37	C₃×C₃₇	#1043⋊C₃	1	1	yes	characteristic, complemented
38	C₃₇⋊C₃	—	25	1	no	—
39	C₃₇⋊C₃	—	50	1	no	—
40	#1043	—	3	1	no	Hall
41	C₃×C₅²	C₄×C₃₇⋊C₃	1	1	yes	characteristic, complemented
42	C₅²⋊C₃	—	37	1	no	—
43	C₅²⋊C₃	—	74	1	no	—
44	C₂×C₃₇	—	25	1	no	—
45	ΓL(1,𝔽₁₆)	—	15	2	no	—
46	C₅⋊D₅	D₃×C₃₇⋊C₃	1	1	yes	characteristic
47	C₃₇	C₃⋊(#1043⋊C₃)	1	1	yes	characteristic, complemented, Sylow
48	C₃×Dic₃	—	925	1	no	Hall
49	C₃×D₅	—	15	2	no	—
50	C₅²	Dic₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	AGL(1,𝔽₅)	—	45	2	no	—
52	C₂×C₃²	—	925	1	no	—
53	C₃×C₅	—	3	2	no	—
54	C₃×C₄	—	2775	1	no	—
55	Dic₃	—	25	1	no	—
56	D₅	—	15	2	no	—
57	C₃²	—	925	1	no	Sylow
58	C₂×C₃	—	25	1	no	—
59	C₂×C₃	—	1850	1	no	—
60	C₂×C₃	—	925	1	no	—
61	C₅	—	3	2	no	—
62	C₄	—	75	1	no	Sylow
63	C₃	—	1850	1	no	—
64	C₃	—	925	1	no	—
65	C₃	#1043⋊(C₃₇⋊C₃)	1	1	yes	characteristic, complemented
66	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₃₇	C₃×C₄
prime radical	C₃×(C₅⋊D₅)⋊(C₃₇⋊C₃)	C₂
cosocle	C₃×C₃₇×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₃×C₅²×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃₇×C₃⋊#1043	C₃	semidirect
4. C₃×C₅²⋊(C₃₇⋊C₃)	C₄	semidirect
10. C₅²⋊(C₃₇⋊C₃)	Dic₃	semidirect
11. C₃×C₅²×C₃₇	C₃×C₄	semidirect
16. C₅²×C₃₇	C₃×Dic₃	semidirect
26. C₃⋊#1043	C₃₇⋊C₃	semidirect
37. C₃×C₃₇	#1043⋊C₃	semidirect
41. C₃×C₅²	C₄×C₃₇⋊C₃	semidirect
47. C₃₇	C₃⋊(#1043⋊C₃)	semidirect
50. C₅²	Dic₃×C₃₇⋊C₃	semidirect
65. C₃	#1043⋊(C₃₇⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃×(C₅⋊D₅)⋊(C₃₇⋊C₃)	2
C₃₇×C₃⋊#1043	3
#1043⋊(C₃₇⋊C₃)	3
Dic₃×C₃₇⋊C₃	25
C₃⋊(#1043⋊C₃)	37

Subgroups — C3⋊(#1043⋊(C37⋊C3)) #45686274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#1043⋊(C₃₇⋊C₃)) #45686274