Subgroups — D₃×C₃⋊#1039 #14268290

Order 1800.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊#1039)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊#1039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃⋊#1039	—	3	1	no	maximal
5	D₃×#1039	—	3	1	no	maximal
6	C₂×C₃²×C₅²	C₂²	1	1	yes	characteristic
7	C₃×C₅²×D₃	C₄	1	2	yes	complemented
8	D₃×Dic₁₅	—	5	6	no	maximal
9	C₂²×C₃×C₅²	—	3	1	no	—
10	C₂×C₅²×D₃	D₃	1	1	yes	characteristic
11	C₃⋊#1039	—	3	1	no	—
12	C₃⋊#1039	—	3	1	no	—
13	C₃⋊#1039	—	6	1	no	—
14	C₃⋊#1039	D₃	1	1	yes	characteristic, direct product factor
15	C₃×#1039	—	3	1	no	—
16	C₃²×C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
17	C₂×#1039	—	9	1	no	Hall
18	C₂×C₃×C₅×D₃	D₅	1	6	yes	—
19	C₃⋊Dic₁₅	—	5	6	no	—
20	C₃×Dic₁₅	—	5	6	no	—
21	C₂×C₃×C₅²	—	2	1	no	—
22	C₂×C₃×C₅²	—	3	2	no	—
23	C₂×C₃×C₅²	C₂×D₃	1	1	yes	characteristic
24	C₂×C₃×C₅²	C₂×D₃	1	1	yes	characteristic
25	C₅²×D₃	Dic₃	1	2	yes	complemented
26	C₂×Dic₁₅	—	15	6	no	—
27	D₃×Dic₅	—	15	6	no	—
28	C₂²×C₅²	—	3	1	no	—
29	#1039	—	3	1	no	—
30	#1039	—	9	1	no	—
31	C₂×C₃²×C₅	C₂×D₅	1	6	yes	—
32	C₃×C₅×D₃	Dic₅	1	12	yes	complemented
33	C₃×C₅²	—	2	1	no	—
34	C₃×C₅²	C₄×D₃	1	1	yes	characteristic, complemented
35	C₃×C₅²	C₂×Dic₃	1	1	yes	characteristic, complemented
36	D₃×Dic₃	—	25	1	no	Hall
37	C₂²×C₃×C₅	—	3	6	no	—
38	C₂×C₅×D₃	D₁₅	1	6	yes	—
39	Dic₁₅	—	5	6	no	—
40	Dic₁₅	—	15	6	no	—
41	Dic₁₅	—	15	6	no	—
42	Dic₁₅	—	30	6	no	—
43	C₃×Dic₅	—	15	6	no	—
44	C₂×C₅²	—	3	2	no	—
45	C₂×C₅²	D₃²	1	1	yes	characteristic
46	C₃²×C₅	C₂×Dic₅	1	6	yes	complemented
47	C₂×Dic₅	—	45	6	no	—
48	C₂×C₃×D₃	C₅⋊D₅	1	1	yes	characteristic
49	C₃⋊Dic₃	—	25	1	no	—
50	C₃×Dic₃	—	25	1	no	—
51	C₂×C₃×C₅	—	2	6	no	—
52	C₂×C₃×C₅	—	3	12	no	—
53	C₂×C₃×C₅	D₃×D₅	1	6	yes	—
54	C₂×C₃×C₅	C₂×D₁₅	1	6	yes	—
55	C₅×D₃	Dic₁₅	1	12	yes	complemented
56	C₅²	D₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×Dic₃	—	75	1	no	—
58	C₄×D₃	—	75	1	no	—
59	C₂²×C₅	—	3	6	no	—
60	Dic₅	—	15	6	no	—
61	Dic₅	—	45	6	no	—
62	C₂×C₃²	C₂×C₅⋊D₅	1	1	yes	characteristic
63	C₃×D₃	#1039	1	2	yes	complemented
64	C₃×C₅	—	2	6	no	—
65	C₃×C₅	D₃×Dic₅	1	6	yes	complemented
66	C₃×C₅	C₂×Dic₁₅	1	6	yes	complemented
67	C₂²×C₃	—	3	1	no	—
68	C₂×D₃	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
69	C₃×C₄	—	75	1	no	—
70	Dic₃	—	25	1	no	—
71	Dic₃	—	75	1	no	—
72	Dic₃	—	75	1	no	—
73	Dic₃	—	150	1	no	—
74	C₂×C₅	—	3	12	no	—
75	C₂×C₅	D₃×D₁₅	1	6	yes	—
76	C₃²	C₂×#1039	1	1	yes	characteristic, complemented, Sylow
77	C₂×C₄	—	225	1	no	Sylow
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	—	3	2	no	—
80	C₂×C₃	D₃×C₅⋊D₅	1	1	yes	characteristic
81	C₂×C₃	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
82	D₃	C₃⋊#1039	1	2	yes	direct product factor
83	C₅	D₃×Dic₁₅	1	6	yes	complemented
84	C₂²	—	3	1	no	—
85	C₄	—	75	1	no	—
86	C₄	—	225	1	no	—
87	C₃	—	2	1	no	—
88	C₃	D₃×#1039	1	1	yes	characteristic, complemented
89	C₃	C₂×C₃⋊#1039	1	1	yes	characteristic, complemented
90	C₂	—	3	2	no	—
91	C₂	D₃×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₃⋊(C₅⋊D₅)
commutator, hypocenter	C₃²×C₅²	C₂×C₄
Fitting, socle, cosocle	C₂×C₃²×C₅²	C₂²
prime radical	C₂×C₃×C₅²×D₃	C₂
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃⋊#1039)	C₂	semidirect
3. C₃×C₃⋊#1039	C₂	semidirect
7. C₃×C₅²×D₃	C₄	semidirect
14. C₃⋊#1039	D₃	direct (N × H)
16. C₃²×C₅²	C₂×C₄	semidirect
25. C₅²×D₃	Dic₃	semidirect
32. C₃×C₅×D₃	Dic₅	semidirect
34. C₃×C₅²	C₄×D₃	semidirect
35. C₃×C₅²	C₂×Dic₃	semidirect
46. C₃²×C₅	C₂×Dic₅	semidirect
55. C₅×D₃	Dic₁₅	semidirect
56. C₅²	D₃×Dic₃	semidirect
63. C₃×D₃	#1039	semidirect
65. C₃×C₅	D₃×Dic₅	semidirect
66. C₃×C₅	C₂×Dic₁₅	semidirect
76. C₃²	C₂×#1039	semidirect
82. D₃	C₃⋊#1039	direct (N × H)
83. C₅	D₃×Dic₁₅	semidirect
88. C₃	D₃×#1039	semidirect
89. C₃	C₂×C₃⋊#1039	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²×D₃	2
C₃⋊(C₃⋊#1039)	2
C₃×C₃⋊#1039	2
C₂×C₃⋊#1039	3
D₃×#1039	3
D₃×Dic₁₅	5

Subgroups — D3×C3⋊#1039 #14268290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₃⋊#1039 #14268290