Subgroups — C₃×C₃⋊#16814877 #45686436

Order 33300.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅⋊D₁₈₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16814877	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#16814877	—	3	1	no	maximal
4	C₃²×C₅²×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃⋊#10625191	—	5	6	no	maximal
6	C₃×C₅⋊D₁₈₅	—	2	1	no	—
7	C₃×C₅⋊D₁₈₅	D₃	1	1	yes	characteristic
8	C₃×C₅⋊D₁₈₅	C₂×C₃	1	1	yes	characteristic
9	#16814877	—	3	1	no	Hall
10	C₃²×D₁₈₅	—	5	6	no	—
11	C₃×C₅²×C₃₇	—	2	1	no	—
12	C₃×C₅²×C₃₇	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃⋊#10625191	—	5	6	no	—
15	C₃×#10625191	—	15	6	no	—
16	C₅⋊D₁₈₅	C₃×D₃	1	1	yes	characteristic
17	C₃²×C₅×C₃₇	AGL(1,𝔽₅)	1	6	yes	complemented
18	C₃×C₃⋊#3866	—	25	1	no	Hall
19	C₃×D₁₈₅	—	5	6	no	—
20	C₃×D₁₈₅	—	5	6	no	—
21	C₃×D₁₈₅	—	10	6	no	—
22	C₅²×C₃₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₃⋊#1043	—	37	1	no	maximal, Hall
24	#10625191	—	15	6	no	—
25	C₃²×D₃₇	—	25	1	no	—
26	C₃×C₅×C₃₇	—	2	6	no	—
27	C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
28	C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	1	6	yes	complemented
29	C₃²×C₅⋊D₅	—	37	1	no	—
30	C₃⋊#3866	—	25	1	no	—
31	C₃×#3866	—	75	1	no	—
32	D₁₈₅	—	5	6	no	—
33	C₃²×C₃₇	#1043	1	1	yes	characteristic, complemented, Hall
34	C₃⋊#1043	—	37	1	no	—
35	C₃×#1043	—	111	1	no	—
36	C₃²×C₅²	#3866	1	1	yes	characteristic, complemented, Hall
37	C₃×D₃₇	—	25	1	no	—
38	C₃×D₃₇	—	25	1	no	—
39	C₃×D₃₇	—	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	—	37	1	no	—
44	C₃×C₅⋊D₅	—	74	1	no	—
45	#3866	—	75	1	no	Hall
46	C₃×C₃₇	—	2	1	no	—
47	C₃×C₃₇	C₃×#1043	1	1	yes	characteristic, complemented
48	C₃×C₃₇	C₃⋊#1043	1	1	yes	characteristic, complemented
49	#1043	—	111	1	no	Hall
50	C₃²×D₅	—	185	6	no	—
51	C₃×C₅²	—	2	1	no	—
52	C₃×C₅²	C₃×#3866	1	1	yes	characteristic, complemented
53	C₃×C₅²	C₃⋊#3866	1	1	yes	characteristic, complemented
54	D₃₇	—	25	1	no	—
55	ΓL(1,𝔽₁₆)	—	185	6	no	—
56	C₃×AGL(1,𝔽₅)	—	555	6	no	—
57	C₅⋊D₅	—	37	1	no	—
58	C₃²×C₅	#10625191	1	6	yes	complemented
59	C₃₇	C₃×C₃⋊#1043	1	1	yes	characteristic, complemented, Sylow
60	C₃×Dic₃	—	925	1	no	Hall
61	C₃×D₅	—	370	6	no	—
62	C₃×D₅	—	185	6	no	—
63	C₃×D₅	—	185	6	no	—
64	C₅²	C₃×C₃⋊#3866	1	1	yes	characteristic, complemented, Sylow
65	AGL(1,𝔽₅)	—	555	6	no	—
66	C₂×C₃²	—	925	1	no	—
67	C₃×C₅	—	2	6	no	—
68	C₃×C₅	C₃×#10625191	1	6	yes	complemented
69	C₃×C₅	C₃⋊#10625191	1	6	yes	complemented
70	C₃×C₄	—	2775	1	no	—
71	Dic₃	—	925	1	no	—
72	D₅	—	185	6	no	—
73	C₃²	#16814877	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₃	—	1850	1	no	—
75	C₂×C₃	—	925	1	no	—
76	C₂×C₃	—	925	1	no	—
77	C₅	C₃×C₃⋊#10625191	1	6	yes	complemented
78	C₄	—	2775	1	no	Sylow
79	C₃	—	2	1	no	—
80	C₃	C₃×#16814877	1	1	yes	characteristic, complemented
81	C₃	C₃⋊#16814877	1	1	yes	characteristic, direct product factor
82	C₂	—	925	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊#16814877
commutator, hypocenter	C₃×C₅²×C₃₇	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₃₇	C₄
prime radical	C₃²×C₅⋊D₁₈₅	C₂
cosocle	C₃×C₅⋊D₁₈₅	C₂×C₃
LCS	G ▷ C₃×C₅²×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊#16814877	C₃	direct (N × H)
4. C₃²×C₅²×C₃₇	C₄	semidirect
12. C₃×C₅²×C₃₇	Dic₃	semidirect
13. C₃×C₅²×C₃₇	C₃×C₄	semidirect
17. C₃²×C₅×C₃₇	AGL(1,𝔽₅)	semidirect
22. C₅²×C₃₇	C₃×Dic₃	semidirect
27. C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)	semidirect
28. C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	semidirect
33. C₃²×C₃₇	#1043	semidirect
36. C₃²×C₅²	#3866	semidirect
40. C₅×C₃₇	C₃×ΓL(1,𝔽₁₆)	semidirect
47. C₃×C₃₇	C₃×#1043	semidirect
48. C₃×C₃₇	C₃⋊#1043	semidirect
52. C₃×C₅²	C₃×#3866	semidirect
53. C₃×C₅²	C₃⋊#3866	semidirect
58. C₃²×C₅	#10625191	semidirect
59. C₃₇	C₃×C₃⋊#1043	semidirect
64. C₅²	C₃×C₃⋊#3866	semidirect
68. C₃×C₅	C₃×#10625191	semidirect
69. C₃×C₅	C₃⋊#10625191	semidirect
73. C₃²	#16814877	semidirect
77. C₅	C₃×C₃⋊#10625191	semidirect
80. C₃	C₃×#16814877	semidirect
81. C₃	C₃⋊#16814877	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅⋊D₁₈₅	2
C₃⋊#16814877	3
C₃×#16814877	3
C₃×C₃⋊#10625191	5
C₃×C₃⋊#1043	37

Subgroups — C3×C3⋊#16814877 #45686436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊#16814877 #45686436