Subgroups — C₃₇⋊C₃×C₃⋊#1043 #45686315

Order 33300.

224 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	ΓL(1,𝔽₁₆)×C₃₇⋊C₃	—	5	6	no	maximal
6	C₃×C₃₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
7	C₅⋊D₅×C₃₇⋊C₃	—	2	1	no	—
8	C₅⋊D₅×C₃₇⋊C₃	D₃	1	1	yes	characteristic
9	C₃₇×#1043	—	3	1	no	Hall
10	C₃×D₅×C₃₇⋊C₃	—	5	6	no	—
11	C₅²×C₃₇⋊C₃	—	2	1	no	—
12	C₅²×C₃₇⋊C₃	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃₇×ΓL(1,𝔽₁₆)	—	5	6	no	—
15	AGL(1,𝔽₅)×C₃₇⋊C₃	—	15	6	no	—
16	C₃₇×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic
17	C₃×C₅×C₃₇⋊C₃	AGL(1,𝔽₅)	1	6	yes	complemented
18	Dic₃×C₃₇⋊C₃	—	25	1	no	Hall
19	C₃×D₅×C₃₇	—	5	6	no	—
20	D₅×C₃₇⋊C₃	—	5	6	no	—
21	D₅×C₃₇⋊C₃	—	10	6	no	—
22	C₅²×C₃₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₃⋊#1043	—	37	1	no	maximal, Hall
24	AGL(1,𝔽₅)×C₃₇	—	15	6	no	—
25	C₂×C₃×C₃₇⋊C₃	—	25	1	no	—
26	C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
27	C₅×C₃₇⋊C₃	—	2	6	no	—
28	C₅×C₃₇⋊C₃	ΓL(1,𝔽₁₆)	1	6	yes	complemented
29	C₃²×C₅⋊D₅	—	37	1	no	—
30	Dic₃×C₃₇	—	25	1	no	—
31	C₄×C₃₇⋊C₃	—	75	1	no	—
32	D₅×C₃₇	—	5	6	no	—
33	C₃×C₃₇⋊C₃	#1043	1	1	yes	characteristic, complemented, Hall
34	C₃⋊#1043	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
35	C₃×#1043	—	111	1	no	—
36	C₃²×C₅²	—	37	1	no	Hall
37	C₂×C₃×C₃₇	—	25	1	no	—
38	C₂×C₃₇⋊C₃	—	25	1	no	—
39	C₂×C₃₇⋊C₃	—	50	1	no	—
40	C₅×C₃₇	C₃×ΓL(1,𝔽₁₆)	1	6	yes	complemented
41	C₃×ΓL(1,𝔽₁₆)	—	185	6	no	—
42	C₃×C₅⋊D₅	—	37	1	no	—
43	C₃×C₅⋊D₅	—	74	1	no	—
44	C₃×C₅⋊D₅	C₂×C₃₇⋊C₃	1	1	yes	characteristic
45	C₄×C₃₇	—	75	1	no	Hall
46	C₃×C₃₇	C₃×#1043	1	1	yes	characteristic, complemented
47	C₃₇⋊C₃	—	2	1	no	—
48	C₃₇⋊C₃	C₃⋊#1043	1	1	yes	characteristic, direct product factor
49	#1043	—	3	1	no	Hall
50	C₃²×D₅	—	185	6	no	—
51	C₃×C₅²	—	37	1	no	—
52	C₃×C₅²	—	74	1	no	—
53	C₃×C₅²	C₄×C₃₇⋊C₃	1	1	yes	characteristic, complemented
54	C₂×C₃₇	—	25	1	no	—
55	ΓL(1,𝔽₁₆)	—	5	6	no	—
56	C₃×AGL(1,𝔽₅)	—	555	6	no	—
57	C₅⋊D₅	D₃×C₃₇⋊C₃	1	1	yes	characteristic
58	C₃²×C₅	—	37	6	no	—
59	C₃₇	C₃×C₃⋊#1043	1	1	yes	characteristic, complemented, Sylow
60	C₃×Dic₃	—	925	1	no	Hall
61	C₃×D₅	—	5	6	no	—
62	C₃×D₅	—	370	6	no	—
63	C₃×D₅	—	185	6	no	—
64	C₅²	Dic₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	AGL(1,𝔽₅)	—	15	6	no	—
66	C₂×C₃²	—	925	1	no	—
67	C₃×C₅	—	37	6	no	—
68	C₃×C₅	—	74	6	no	—
69	C₃×C₅	AGL(1,𝔽₅)×C₃₇⋊C₃	1	6	yes	complemented
70	C₃×C₄	—	2775	1	no	—
71	Dic₃	—	25	1	no	—
72	D₅	—	5	6	no	—
73	C₃²	—	37	1	no	Sylow
74	C₂×C₃	—	25	1	no	—
75	C₂×C₃	—	1850	1	no	—
76	C₂×C₃	—	925	1	no	—
77	C₅	ΓL(1,𝔽₁₆)×C₃₇⋊C₃	1	6	yes	complemented
78	C₄	—	75	1	no	Sylow
79	C₃	—	37	1	no	—
80	C₃	—	74	1	no	—
81	C₃	#1043×C₃₇⋊C₃	1	1	yes	characteristic, complemented
82	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
12. C₅²×C₃₇⋊C₃	Dic₃	semidirect
13. C₃×C₅²×C₃₇	C₃×C₄	semidirect
17. C₃×C₅×C₃₇⋊C₃	AGL(1,𝔽₅)	semidirect
22. C₅²×C₃₇	C₃×Dic₃	semidirect
26. C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)	semidirect
28. C₅×C₃₇⋊C₃	ΓL(1,𝔽₁₆)	semidirect
33. C₃×C₃₇⋊C₃	#1043	semidirect
34. C₃⋊#1043	C₃₇⋊C₃	direct (N × H)
40. C₅×C₃₇	C₃×ΓL(1,𝔽₁₆)	semidirect
46. C₃×C₃₇	C₃×#1043	semidirect
48. C₃₇⋊C₃	C₃⋊#1043	direct (N × H)
53. C₃×C₅²	C₄×C₃₇⋊C₃	semidirect
59. C₃₇	C₃×C₃⋊#1043	semidirect
64. C₅²	Dic₃×C₃₇⋊C₃	semidirect
69. C₃×C₅	AGL(1,𝔽₅)×C₃₇⋊C₃	semidirect
77. C₅	ΓL(1,𝔽₁₆)×C₃₇⋊C₃	semidirect
81. 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
ΓL(1,𝔽₁₆)×C₃₇⋊C₃	5
C₃×C₃⋊#1043	37

Subgroups — C37⋊C3×C3⋊#1043 #45686315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇⋊C₃×C₃⋊#1043 #45686315