Subgroups — C₃⋊D₃×#672 #13084700

Order 1440.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊#672)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#672	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×#672	—	3	4	no	maximal
5	C₄×C₅×C₃⋊D₃	C₄	1	1	yes	characteristic
6	C₃²×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₅×C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
8	C₁₆×C₃⋊D₃	—	5	1	no	maximal, Hall
9	C₅×D₃×C₈	—	3	4	no	—
10	C₃⋊#672	—	3	4	no	—
11	C₃×#672	D₃	1	4	yes	complemented
12	C₂×C₅×C₃⋊D₃	C₈	1	1	yes	characteristic
13	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₅×C₃⋊Dic₃	C₈	1	1	yes	characteristic
15	C₂×#672	—	9	1	no	Hall
16	C₈×C₃⋊D₃	D₅	1	1	yes	characteristic
17	C₃²×C₁₆	—	5	1	no	—
18	C₃⋊(C₃⋊C₁₆)	—	5	1	no	—
19	C₄×C₅×D₃	—	3	4	no	—
20	C₃×C₅×C₈	C₂×D₃	1	4	yes	—
21	C₅×C₃⋊C₈	—	3	4	no	—
22	D₃×C₁₆	—	15	4	no	—
23	C₂×C₃²×C₅	C₂×C₈	1	1	yes	characteristic
24	C₅×C₃⋊D₃	C₁₆	1	2	yes	complemented
25	C₂×C₅×C₈	—	9	1	no	—
26	#672	—	9	1	no	—
27	#672	C₃⋊D₃	1	1	yes	characteristic, direct product factor
28	C₄×C₃⋊D₃	Dic₅	1	1	yes	characteristic
29	C₃²×C₈	C₂×D₅	1	1	yes	characteristic
30	C₃⋊(C₃⋊C₈)	Dic₅	1	1	yes	characteristic
31	C₂×C₅×D₃	—	3	4	no	—
32	C₃×C₄×C₅	C₄×D₃	1	4	yes	—
33	C₅×Dic₃	—	3	4	no	—
34	D₃×C₈	—	3	4	no	—
35	C₃×C₁₆	—	5	4	no	—
36	C₃⋊C₁₆	—	15	4	no	—
37	C₃²×C₅	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
38	C₂×C₄×C₅	—	9	1	no	—
39	C₅×C₈	—	9	1	no	—
40	C₅×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
41	C₂×C₃⋊D₃	#168	1	1	yes	characteristic
42	C₃²×C₄	C₂×Dic₅	1	1	yes	characteristic
43	C₃⋊Dic₃	#168	1	1	yes	characteristic
44	C₂×C₁₆	—	45	1	no	Sylow
45	C₂×C₃×C₅	D₃×C₈	1	4	yes	—
46	C₅×D₃	—	3	8	no	—
47	C₄×D₃	—	3	4	no	—
48	C₃×C₈	D₃×D₅	1	4	yes	—
49	C₃⋊C₈	—	3	4	no	—
50	C₂²×C₅	—	9	1	no	—
51	C₄×C₅	—	9	1	no	—
52	C₄×C₅	C₄×C₃⋊D₃	1	1	yes	characteristic
53	C₂×C₃²	C₂×#168	1	1	yes	characteristic
54	C₃⋊D₃	#672	1	2	yes	direct product factor
55	C₂×C₈	—	9	1	no	—
56	C₁₆	—	5	1	no	—
57	C₁₆	—	45	1	no	—
58	C₃×C₅	D₃×C₁₆	1	4	yes	complemented
59	C₂×D₃	—	3	4	no	—
60	C₃×C₄	D₃×Dic₅	1	4	yes	—
61	Dic₃	—	3	4	no	—
62	C₂×C₅	—	9	2	no	—
63	C₂×C₅	C₈×C₃⋊D₃	1	1	yes	characteristic
64	C₃²	C₂×#672	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄	—	9	1	no	—
66	C₈	—	9	1	no	—
67	C₈	D₅×C₃⋊D₃	1	1	yes	characteristic
68	C₂×C₃	D₃×#168	1	4	yes	—
69	D₃	—	3	8	no	—
70	C₅	C₁₆×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	9	1	no	—
72	C₄	—	9	1	no	—
73	C₄	C₃⋊D₃×Dic₅	1	1	yes	characteristic
74	C₃	D₃×#672	1	4	yes	complemented
75	C₂	—	9	2	no	—
76	C₂	C₃⋊D₃×#168	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₅×C₃⋊D₃
commutator, hypocenter	C₃²×C₅	C₂×C₁₆
Fitting, cosocle	C₃²×C₅×C₈	C₂²
socle	C₂×C₃²×C₅	C₂×C₈
prime radical	C₂×C₅×C₃⋊D₃	C₈
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃⋊#672)	C₂	semidirect
3. C₃²×#672	C₂	semidirect
11. C₃×#672	D₃	semidirect
24. C₅×C₃⋊D₃	C₁₆	semidirect
27. #672	C₃⋊D₃	direct (N × H)
37. C₃²×C₅	C₂×C₁₆	semidirect
54. C₃⋊D₃	#672	direct (N × H)
58. C₃×C₅	D₃×C₁₆	semidirect
64. C₃²	C₂×#672	semidirect
70. C₅	C₁₆×C₃⋊D₃	semidirect
74. C₃	D₃×#672	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₈×C₃⋊D₃	2
C₃⋊(C₃⋊#672)	2
C₃²×#672	2
D₃×#672	3
C₁₆×C₃⋊D₃	5

Subgroups — C3⋊D3×#672 #13084700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#672 #13084700