Subgroups — C₄×C₉×#168 #13083763

Order 1440.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#168	C₂	1	2	yes	maximal
3	C₃×C₄×#168	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₉	C₄	1	2	yes	—
5	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₉×#168	C₄	1	4	yes	direct product factor
7	C₄×C₈×C₉	—	5	1	no	maximal, Hall
8	C₃×C₄²×C₅	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×#168	C₂×C₃	1	2	yes	—
10	C₂²×C₅×C₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₅×C₉	C₈	1	4	yes	complemented
12	C₄×C₅×C₉	C₂×C₄	1	2	yes	—
13	C₄×#168	C₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₈×C₉	—	5	2	no	—
15	C₄²×C₉	D₅	1	1	yes	characteristic
16	C₂×C₃×C₄×C₅	C₃×C₄	1	2	yes	—
17	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
18	C₃×#168	C₃×C₄	1	4	yes	—
19	C₃×C₄×C₈	—	5	1	no	—
20	C₂×C₅×C₉	C₄²	1	1	yes	characteristic
21	C₂×C₅×C₉	C₂×C₈	1	2	yes	—
22	C₄²×C₅	C₂×C₉	1	1	yes	characteristic
23	C₂×#168	C₂×C₉	1	2	yes	—
24	C₂×C₄×C₉	Dic₅	1	2	yes	—
25	C₂×C₄×C₉	C₂×D₅	1	1	yes	characteristic
26	C₈×C₉	—	5	4	no	—
27	C₂²×C₃×C₅	C₂×C₃×C₄	1	1	yes	characteristic
28	C₃×C₄×C₅	C₃×C₈	1	4	yes	—
29	C₃×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
30	C₂×C₃×C₈	—	5	2	no	—
31	C₃×C₄²	C₃×D₅	1	1	yes	characteristic
32	C₅×C₉	C₄×C₈	1	1	yes	characteristic, complemented, Hall
33	C₂×C₄×C₅	C₄×C₉	1	2	yes	—
34	C₂×C₄×C₅	C₂²×C₉	1	1	yes	characteristic
35	#168	C₄×C₉	1	4	yes	direct product factor
36	C₂²×C₉	C₂×Dic₅	1	1	yes	characteristic
37	C₄×C₉	#168	1	4	yes	direct product factor
38	C₄×C₉	C₄×D₅	1	2	yes	—
39	C₄×C₈	—	5	1	no	Sylow
40	C₂×C₃×C₅	C₃×C₄²	1	1	yes	characteristic
41	C₂×C₃×C₅	C₂×C₃×C₈	1	2	yes	—
42	C₂×C₃×C₄	C₃×Dic₅	1	2	yes	—
43	C₂×C₃×C₄	C₂×C₃×D₅	1	1	yes	characteristic
44	C₃×C₈	—	5	4	no	—
45	C₂²×C₅	C₂×C₄×C₉	1	1	yes	characteristic
46	C₄×C₅	C₈×C₉	1	4	yes	complemented
47	C₄×C₅	C₂×C₄×C₉	1	2	yes	—
48	C₂×C₉	C₂×#168	1	2	yes	—
49	C₂×C₉	C₄×Dic₅	1	1	yes	characteristic
50	C₂×C₈	—	5	2	no	—
51	C₄²	C₉×D₅	1	1	yes	characteristic
52	C₃×C₅	C₃×C₄×C₈	1	1	yes	characteristic
53	C₂²×C₃	C₂×C₃×Dic₅	1	1	yes	characteristic
54	C₃×C₄	C₃×#168	1	4	yes	—
55	C₃×C₄	C₃×C₄×D₅	1	2	yes	—
56	C₂×C₅	C₄²×C₉	1	1	yes	characteristic
57	C₂×C₅	C₂×C₈×C₉	1	2	yes	—
58	C₉	C₄×#168	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₄	C₉×Dic₅	1	2	yes	—
60	C₂×C₄	C₂×C₉×D₅	1	1	yes	characteristic
61	C₈	—	5	4	no	—
62	C₂×C₃	C₂×C₃×#168	1	2	yes	—
63	C₂×C₃	C₃×C₄×Dic₅	1	1	yes	characteristic
64	C₅	C₄×C₈×C₉	1	1	yes	characteristic, complemented, Sylow
65	C₂²	C₂×C₉×Dic₅	1	1	yes	characteristic
66	C₄	C₉×#168	1	4	yes	direct product factor
67	C₄	C₄×C₉×D₅	1	2	yes	—
68	C₃	C₃×C₄×#168	1	1	yes	characteristic
69	C₂	C₂×C₉×#168	1	2	yes	—
70	C₂	C₄×C₉×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄²×C₉	D₅
commutator, hypocenter	C₅	C₄×C₈×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₅
Fitting	C₄²×C₅×C₉	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₃×C₄
cosocle	C₂×C₃×C₄×C₅	C₂²×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₄²×C₉

Complements

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

N	H ≅ G/N	type
6. C₉×#168	C₄	direct (N × H)
11. C₄×C₅×C₉	C₈	semidirect
13. C₄×#168	C₉	direct (N × H)
32. C₅×C₉	C₄×C₈	semidirect
35. #168	C₄×C₉	direct (N × H)
37. C₄×C₉	#168	direct (N × H)
46. C₄×C₅	C₈×C₉	semidirect
58. C₉	C₄×#168	direct (N × H)
64. C₅	C₄×C₈×C₉	semidirect
66. C₄	C₉×#168	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×C₅×C₉	2
C₂×C₉×#168	2
C₃×C₄×#168	3
C₄×C₈×C₉	5

Subgroups — C4×C9×#168 #13083763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×#168 #13083763