Subgroups — C₃²×#4094 #13087873

Order 1440.

372 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₃²×#681	C₂	1	3	yes	maximal, complemented
3	C₂×C₃²×#168	C₂	1	3	yes	maximal, complemented
4	C₃×#4094	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₅×Q₈	C₄	1	1	yes	characteristic
6	C₃²×C₅×D₄	C₄	1	3	yes	—
7	C₂×C₃²×C₄×C₅	C₂²	1	3	yes	—
8	C₃²×#168	C₂²	1	1	yes	characteristic
9	C₃²×#168	C₂²	1	3	yes	—
10	C₃²×#131	—	5	1	no	maximal, Hall
11	C₃×C₅×#41	C₂×C₃	1	4	yes	—
12	C₃×#681	C₂×C₃	1	12	yes	complemented
13	C₂×C₃×#168	C₂×C₃	1	12	yes	complemented
14	C₂²×C₃²×C₅	C₂×C₄	1	3	yes	—
15	C₃²×C₄×C₅	C₂×C₄	1	3	yes	—
16	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
17	#4094	C₃²	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×#41	D₅	1	1	yes	characteristic
19	C₃²×M₁₆	—	5	3	no	—
20	C₂×C₃²×C₈	—	5	3	no	—
21	C₃×C₅×Q₈	C₃×C₄	1	4	yes	—
22	C₃×C₅×D₄	C₃×C₄	1	12	yes	—
23	C₂×C₃×C₄×C₅	C₂²×C₃	1	12	yes	—
24	C₃×#168	C₂²×C₃	1	4	yes	—
25	C₃×#168	C₂²×C₃	1	12	yes	—
26	C₃×#131	—	5	4	no	—
27	C₂×C₃²×C₅	—	2	3	no	—
28	C₂×C₃²×C₅	C₂²×C₄	1	1	yes	characteristic
29	C₅×#41	C₂×C₃²	1	1	yes	characteristic
30	#681	C₂×C₃²	1	3	yes	complemented
31	C₂×#168	C₂×C₃²	1	3	yes	complemented
32	C₃²×Q₈	Dic₅	1	1	yes	characteristic
33	C₃²×D₄	Dic₅	1	3	yes	—
34	C₂×C₃²×C₄	C₂×D₅	1	3	yes	—
35	C₃²×C₈	—	5	1	no	—
36	C₃²×C₈	—	5	3	no	—
37	C₂²×C₃×C₅	C₂×C₃×C₄	1	12	yes	—
38	C₃×C₄×C₅	C₂×C₃×C₄	1	12	yes	—
39	C₃×C₄×C₅	C₂³×C₃	1	4	yes	—
40	C₃×#41	C₃×D₅	1	4	yes	—
41	C₃×M₁₆	—	5	12	no	—
42	C₂×C₃×C₈	—	5	12	no	—
43	C₃²×C₅	#131	1	1	yes	characteristic, complemented, Hall
44	C₅×Q₈	C₃²×C₄	1	1	yes	characteristic
45	C₅×D₄	C₃²×C₄	1	3	yes	—
46	C₂×C₄×C₅	C₂²×C₃²	1	3	yes	—
47	#168	C₂²×C₃²	1	1	yes	characteristic
48	#168	C₂²×C₃²	1	3	yes	—
49	C₂²×C₃²	C₂×Dic₅	1	3	yes	—
50	C₃²×C₄	C₂×Dic₅	1	3	yes	—
51	C₃²×C₄	C₂²×D₅	1	1	yes	characteristic
52	#131	—	5	1	no	Sylow
53	C₂×C₃×C₅	—	2	12	no	—
54	C₂×C₃×C₅	C₂²×C₃×C₄	1	4	yes	—
55	C₃×Q₈	C₃×Dic₅	1	4	yes	—
56	C₃×D₄	C₃×Dic₅	1	12	yes	—
57	C₂×C₃×C₄	C₂×C₃×D₅	1	12	yes	—
58	C₃×C₈	—	5	4	no	—
59	C₃×C₈	—	5	12	no	—
60	C₂²×C₅	C₂×C₃²×C₄	1	3	yes	—
61	C₄×C₅	C₂×C₃²×C₄	1	3	yes	—
62	C₄×C₅	C₂³×C₃²	1	1	yes	characteristic
63	C₂×C₃²	—	2	3	no	—
64	C₂×C₃²	C₂²×Dic₅	1	1	yes	characteristic
65	#41	C₃²×D₅	1	1	yes	characteristic
66	M₁₆	—	5	3	no	—
67	C₂×C₈	—	5	3	no	—
68	C₃×C₅	C₃×#131	1	4	yes	complemented
69	C₂²×C₃	C₂×C₃×Dic₅	1	12	yes	—
70	C₃×C₄	C₂×C₃×Dic₅	1	12	yes	—
71	C₃×C₄	C₂²×C₃×D₅	1	4	yes	—
72	C₂×C₅	—	2	3	no	—
73	C₂×C₅	C₂²×C₃²×C₄	1	1	yes	characteristic
74	C₃²	#4094	1	1	yes	characteristic, direct product factor, Sylow
75	Q₈	C₃²×Dic₅	1	1	yes	characteristic
76	D₄	C₃²×Dic₅	1	3	yes	—
77	C₂×C₄	C₂×C₃²×D₅	1	3	yes	—
78	C₈	—	5	1	no	—
79	C₈	—	5	3	no	—
80	C₂×C₃	—	2	12	no	—
81	C₂×C₃	C₂²×C₃×Dic₅	1	4	yes	—
82	C₅	C₃²×#131	1	1	yes	characteristic, complemented, Sylow
83	C₂²	C₂×C₃²×Dic₅	1	3	yes	—
84	C₄	C₂×C₃²×Dic₅	1	3	yes	—
85	C₄	C₂²×C₃²×D₅	1	1	yes	characteristic
86	C₃	C₃×#4094	1	4	yes	direct product factor
87	C₂	—	2	3	no	—
88	C₂	C₂²×C₃²×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃²×C₄	C₂²×D₅
commutator	C₂×C₅	C₂²×C₃²×C₄
Frattini	C₄	C₂²×C₃²×D₅
Fitting, prime radical	C₃²×C₅×#41	C₂
socle	C₂×C₃²×C₅	C₂²×C₄
cosocle	C₄×C₅	C₂³×C₃²
hypercenter	C₃²×#41	D₅
hypocenter	C₅	C₃²×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃²×C₄ ◁ C₃²×#41

Complements

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

N	H ≅ G/N	type
2. C₃²×#681	C₂	semidirect
3. C₂×C₃²×#168	C₂	semidirect
4. C₃×#4094	C₃	direct (N × H)
12. C₃×#681	C₂×C₃	semidirect
13. C₂×C₃×#168	C₂×C₃	semidirect
17. #4094	C₃²	direct (N × H)
30. #681	C₂×C₃²	semidirect
31. C₂×#168	C₂×C₃²	semidirect
43. C₃²×C₅	#131	semidirect
68. C₃×C₅	C₃×#131	semidirect
74. C₃²	#4094	direct (N × H)
82. C₅	C₃²×#131	semidirect
86. C₃	C₃×#4094	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×#41	2
C₃²×#681	2
C₂×C₃²×#168	2
C₃×#4094	3
C₃²×#131	5

Subgroups — C32×#4094 #13087873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#4094 #13087873