Subgroups — C₂×C₉×#672 #13083772

Order 1440.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×#672	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×#672	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₉	C₄	1	1	yes	characteristic
5	C₅×C₈×C₉	C₄	1	1	yes	characteristic
6	C₅×C₈×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₉×C₁₆	—	5	1	no	maximal, Hall
8	C₂×C₃×C₅×C₈	C₂×C₃	1	1	yes	characteristic
9	C₃×#672	C₂×C₃	1	2	yes	—
10	C₂²×C₅×C₉	C₈	1	1	yes	characteristic
11	C₄×C₅×C₉	C₈	1	1	yes	characteristic
12	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
13	C₂×#672	C₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₈×C₉	D₅	1	1	yes	characteristic
15	C₉×C₁₆	—	5	2	no	—
16	C₂×C₃×C₄×C₅	C₃×C₄	1	1	yes	characteristic
17	C₃×C₅×C₈	C₃×C₄	1	1	yes	characteristic
18	C₃×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
19	C₂×C₃×C₁₆	—	5	1	no	—
20	C₂×C₅×C₉	C₁₆	1	2	yes	complemented
21	C₂×C₅×C₉	C₂×C₈	1	1	yes	characteristic
22	C₂×C₅×C₈	C₂×C₉	1	1	yes	characteristic
23	#672	C₂×C₉	1	2	yes	direct product factor
24	C₂×C₄×C₉	Dic₅	1	1	yes	characteristic
25	C₈×C₉	Dic₅	1	1	yes	characteristic
26	C₈×C₉	C₂×D₅	1	1	yes	characteristic
27	C₂²×C₃×C₅	C₃×C₈	1	1	yes	characteristic
28	C₃×C₄×C₅	C₃×C₈	1	1	yes	characteristic
29	C₃×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
30	C₂×C₃×C₈	C₃×D₅	1	1	yes	characteristic
31	C₃×C₁₆	—	5	2	no	—
32	C₅×C₉	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
33	C₂×C₄×C₅	C₄×C₉	1	1	yes	characteristic
34	C₅×C₈	C₄×C₉	1	1	yes	characteristic
35	C₅×C₈	C₂²×C₉	1	1	yes	characteristic
36	C₂²×C₉	#168	1	1	yes	characteristic
37	C₄×C₉	#168	1	1	yes	characteristic
38	C₄×C₉	C₂×Dic₅	1	1	yes	characteristic
39	C₂×C₁₆	—	5	1	no	Sylow
40	C₂×C₃×C₅	C₃×C₁₆	1	2	yes	—
41	C₂×C₃×C₅	C₂×C₃×C₈	1	1	yes	characteristic
42	C₂×C₃×C₄	C₃×Dic₅	1	1	yes	characteristic
43	C₃×C₈	C₃×Dic₅	1	1	yes	characteristic
44	C₃×C₈	C₂×C₃×D₅	1	1	yes	characteristic
45	C₂²×C₅	C₈×C₉	1	1	yes	characteristic
46	C₄×C₅	C₈×C₉	1	1	yes	characteristic
47	C₄×C₅	C₂×C₄×C₉	1	1	yes	characteristic
48	C₂×C₉	#672	1	2	yes	direct product factor
49	C₂×C₉	C₂×#168	1	1	yes	characteristic
50	C₂×C₈	C₉×D₅	1	1	yes	characteristic
51	C₁₆	—	5	2	no	—
52	C₃×C₅	C₂×C₃×C₁₆	1	1	yes	characteristic
53	C₂²×C₃	C₃×#168	1	1	yes	characteristic
54	C₃×C₄	C₃×#168	1	1	yes	characteristic
55	C₃×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
56	C₂×C₅	C₉×C₁₆	1	2	yes	complemented
57	C₂×C₅	C₂×C₈×C₉	1	1	yes	characteristic
58	C₉	C₂×#672	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₄	C₉×Dic₅	1	1	yes	characteristic
60	C₈	C₉×Dic₅	1	1	yes	characteristic
61	C₈	C₂×C₉×D₅	1	1	yes	characteristic
62	C₂×C₃	C₃×#672	1	2	yes	—
63	C₂×C₃	C₂×C₃×#168	1	1	yes	characteristic
64	C₅	C₂×C₉×C₁₆	1	1	yes	characteristic, complemented, Sylow
65	C₂²	C₉×#168	1	1	yes	characteristic
66	C₄	C₉×#168	1	1	yes	characteristic
67	C₄	C₂×C₉×Dic₅	1	1	yes	characteristic
68	C₃	C₂×C₃×#672	1	1	yes	characteristic
69	C₂	C₉×#672	1	2	yes	direct product factor
70	C₂	C₂×C₉×#168	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈×C₉	D₅
commutator, hypocenter	C₅	C₂×C₉×C₁₆
Frattini	C₃×C₈	C₂×C₃×D₅
Fitting	C₂×C₅×C₈×C₉	C₂
socle, prime radical	C₂²×C₃×C₅	C₃×C₈
cosocle	C₃×C₅×C₈	C₂²×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₈×C₉

Complements

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

N	H ≅ G/N	type
2. C₉×#672	C₂	direct (N × H)
13. C₂×#672	C₉	direct (N × H)
20. C₂×C₅×C₉	C₁₆	semidirect
23. #672	C₂×C₉	direct (N × H)
32. C₅×C₉	C₂×C₁₆	semidirect
48. C₂×C₉	#672	direct (N × H)
56. C₂×C₅	C₉×C₁₆	semidirect
58. C₉	C₂×#672	direct (N × H)
64. C₅	C₂×C₉×C₁₆	semidirect
69. C₂	C₉×#672	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₈×C₉	2
C₉×#672	2
C₂×C₃×#672	3
C₂×C₉×C₁₆	5

Subgroups — C2×C9×#672 #13083772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#672 #13083772