Subgroups — C₃×C₃⋊#16861528 #49147128

Order 36900.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×D₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16861528	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#16861528	—	3	1	no	maximal
4	C₃²×C₅²×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃⋊#11717964	—	5	6	no	maximal
6	C₃×C₅²×D₄₁	—	2	1	no	—
7	C₃×C₅²×D₄₁	D₃	1	1	yes	characteristic
8	C₃×C₅²×D₄₁	C₂×C₃	1	1	yes	characteristic
9	#16861528	—	3	1	no	Hall
10	C₃²×C₅×D₄₁	D₅	1	6	yes	—
11	C₃×C₅²×C₄₁	—	2	1	no	—
12	C₃×C₅²×C₄₁	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅²×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃⋊#11717964	—	5	6	no	—
15	C₃×#11717964	—	15	6	no	—
16	C₅²×D₄₁	C₃×D₃	1	1	yes	characteristic
17	C₃²×C₅×C₄₁	Dic₅	1	6	yes	complemented
18	C₃×C₃⋊#4223	—	25	1	no	Hall
19	C₃×C₅×D₄₁	—	2	6	no	—
20	C₃×C₅×D₄₁	C₃×D₅	1	6	yes	—
21	C₃×C₅×D₄₁	D₁₅	1	6	yes	—
22	C₅²×C₄₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₃⋊#1039	—	41	1	no	maximal, Hall
24	#11717964	—	15	6	no	—
25	C₃²×D₄₁	C₅⋊D₅	1	1	yes	characteristic
26	C₃×C₅×C₄₁	—	2	6	no	—
27	C₃×C₅×C₄₁	C₃×Dic₅	1	6	yes	complemented
28	C₃×C₅×C₄₁	Dic₁₅	1	6	yes	complemented
29	C₃⋊#4223	—	25	1	no	—
30	C₃×#4223	—	75	1	no	—
31	C₂×C₃²×C₅²	—	41	1	no	—
32	C₅×D₄₁	C₃×D₁₅	1	6	yes	—
33	C₃²×C₄₁	#1039	1	1	yes	characteristic, complemented, Hall
34	C₃⋊#1039	—	41	1	no	—
35	C₃×#1039	—	123	1	no	—
36	C₃×D₄₁	—	2	1	no	—
37	C₃×D₄₁	C₃×C₅⋊D₅	1	1	yes	characteristic
38	C₃×D₄₁	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
39	C₃²×C₅²	#4223	1	1	yes	characteristic, complemented, Hall
40	C₅×C₄₁	C₃×Dic₁₅	1	6	yes	complemented
41	C₃×Dic₁₅	—	205	6	no	—
42	#4223	—	75	1	no	Hall
43	C₂×C₃×C₅²	—	41	1	no	—
44	C₂×C₃×C₅²	—	41	1	no	—
45	C₂×C₃×C₅²	—	82	1	no	—
46	C₃×C₄₁	—	2	1	no	—
47	C₃×C₄₁	C₃×#1039	1	1	yes	characteristic, complemented
48	C₃×C₄₁	C₃⋊#1039	1	1	yes	characteristic, complemented
49	#1039	—	123	1	no	Hall
50	C₂×C₃²×C₅	—	41	6	no	—
51	D₄₁	C₃×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
52	C₃×C₅²	—	2	1	no	—
53	C₃×C₅²	C₃×#4223	1	1	yes	characteristic, complemented
54	C₃×C₅²	C₃⋊#4223	1	1	yes	characteristic, complemented
55	Dic₁₅	—	205	6	no	—
56	C₃×Dic₅	—	615	6	no	—
57	C₂×C₅²	—	41	1	no	—
58	C₃²×C₅	#11717964	1	6	yes	complemented
59	C₄₁	C₃×C₃⋊#1039	1	1	yes	characteristic, complemented, Sylow
60	C₃×Dic₃	—	1025	1	no	Hall
61	C₂×C₃×C₅	—	41	6	no	—
62	C₂×C₃×C₅	—	41	6	no	—
63	C₂×C₃×C₅	—	82	6	no	—
64	C₅²	C₃×C₃⋊#4223	1	1	yes	characteristic, complemented, Sylow
65	Dic₅	—	615	6	no	—
66	C₂×C₃²	—	41	1	no	—
67	C₃×C₅	—	2	6	no	—
68	C₃×C₅	C₃×#11717964	1	6	yes	complemented
69	C₃×C₅	C₃⋊#11717964	1	6	yes	complemented
70	C₃×C₄	—	3075	1	no	—
71	Dic₃	—	1025	1	no	—
72	C₂×C₅	—	41	6	no	—
73	C₃²	#16861528	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₃	—	41	1	no	—
75	C₂×C₃	—	41	1	no	—
76	C₂×C₃	—	82	1	no	—
77	C₅	C₃×C₃⋊#11717964	1	6	yes	complemented
78	C₄	—	3075	1	no	Sylow
79	C₃	—	2	1	no	—
80	C₃	C₃×#16861528	1	1	yes	characteristic, complemented
81	C₃	C₃⋊#16861528	1	1	yes	characteristic, direct product factor
82	C₂	—	41	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊#16861528
commutator, hypocenter	C₃×C₅²×C₄₁	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₄₁	C₄
prime radical	C₃²×C₅²×D₄₁	C₂
cosocle	C₃×C₅²×D₄₁	C₂×C₃
LCS	G ▷ C₃×C₅²×C₄₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊#16861528	C₃	direct (N × H)
4. C₃²×C₅²×C₄₁	C₄	semidirect
12. C₃×C₅²×C₄₁	Dic₃	semidirect
13. C₃×C₅²×C₄₁	C₃×C₄	semidirect
17. C₃²×C₅×C₄₁	Dic₅	semidirect
22. C₅²×C₄₁	C₃×Dic₃	semidirect
27. C₃×C₅×C₄₁	C₃×Dic₅	semidirect
28. C₃×C₅×C₄₁	Dic₁₅	semidirect
33. C₃²×C₄₁	#1039	semidirect
39. C₃²×C₅²	#4223	semidirect
40. C₅×C₄₁	C₃×Dic₁₅	semidirect
47. C₃×C₄₁	C₃×#1039	semidirect
48. C₃×C₄₁	C₃⋊#1039	semidirect
53. C₃×C₅²	C₃×#4223	semidirect
54. C₃×C₅²	C₃⋊#4223	semidirect
58. C₃²×C₅	#11717964	semidirect
59. C₄₁	C₃×C₃⋊#1039	semidirect
64. C₅²	C₃×C₃⋊#4223	semidirect
68. C₃×C₅	C₃×#11717964	semidirect
69. C₃×C₅	C₃⋊#11717964	semidirect
73. C₃²	#16861528	semidirect
77. C₅	C₃×C₃⋊#11717964	semidirect
80. C₃	C₃×#16861528	semidirect
81. C₃	C₃⋊#16861528	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×C₅²×D₄₁	2
C₃⋊#16861528	3
C₃×#16861528	3
C₃×C₃⋊#11717964	5
C₃×C₃⋊#1039	41

Subgroups — C3×C3⋊#16861528 #49147128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊#16861528 #49147128