Subgroups — C₉×#3961 #13083790

Order 1440.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₂₀	C₂	1	1	yes	maximal, characteristic
3	C₉×#672	C₂	1	1	yes	maximal, characteristic
4	C₃×#3961	C₃	1	1	yes	maximal, characteristic
5	C₅×Q₈×C₉	—	2	1	no	—
6	C₉×Dic₁₀	—	2	1	no	—
7	C₅×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₉×Q₃₂	—	5	1	no	maximal, Hall
9	C₃×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic
10	C₃×Dic₂₀	C₂×C₃	1	1	yes	characteristic
11	C₃×#672	C₂×C₃	1	1	yes	characteristic
12	C₄×C₅×C₉	—	4	1	no	—
13	C₄×C₅×C₉	D₄	1	1	yes	characteristic
14	C₉×Dic₅	—	4	1	no	—
15	#3961	C₉	1	1	yes	characteristic, direct product factor, Hall
16	C₉×Q₁₆	—	5	1	no	—
17	C₉×Q₁₆	D₅	1	1	yes	characteristic
18	C₉×C₁₆	—	5	1	no	—
19	C₃×C₅×Q₈	—	2	1	no	—
20	C₃×Dic₁₀	—	2	1	no	—
21	C₃×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
22	C₃×Q₃₂	—	5	1	no	—
23	C₂×C₅×C₉	D₈	1	1	yes	characteristic
24	C₅×Q₁₆	C₂×C₉	1	1	yes	characteristic
25	Dic₂₀	C₂×C₉	1	1	yes	characteristic
26	#672	C₂×C₉	1	1	yes	characteristic
27	Q₈×C₉	—	2	1	no	—
28	Q₈×C₉	—	10	1	no	—
29	C₈×C₉	C₂×D₅	1	1	yes	characteristic
30	C₃×C₄×C₅	—	4	1	no	—
31	C₃×C₄×C₅	C₃×D₄	1	1	yes	characteristic
32	C₃×Dic₅	—	4	1	no	—
33	C₃×Q₁₆	—	5	1	no	—
34	C₃×Q₁₆	C₃×D₅	1	1	yes	characteristic
35	C₃×C₁₆	—	5	1	no	—
36	C₅×C₉	Q₃₂	1	1	yes	characteristic, complemented, Hall
37	C₅×Q₈	—	2	1	no	—
38	Dic₁₀	—	2	1	no	—
39	C₅×C₈	C₂²×C₉	1	1	yes	characteristic
40	C₄×C₉	—	4	1	no	—
41	C₄×C₉	—	20	1	no	—
42	C₄×C₉	C₂²⋊D₅	1	1	yes	characteristic
43	Q₃₂	—	5	1	no	Sylow
44	C₂×C₃×C₅	C₃×D₈	1	1	yes	characteristic
45	C₃×Q₈	—	2	1	no	—
46	C₃×Q₈	—	10	1	no	—
47	C₃×C₈	C₂×C₃×D₅	1	1	yes	characteristic
48	C₄×C₅	—	4	1	no	—
49	C₄×C₅	D₄×C₉	1	1	yes	characteristic
50	Dic₅	—	4	1	no	—
51	C₂×C₉	#686	1	1	yes	characteristic
52	Q₁₆	—	5	1	no	—
53	Q₁₆	C₉×D₅	1	1	yes	characteristic
54	C₁₆	—	5	1	no	—
55	C₃×C₅	C₃×Q₃₂	1	1	yes	characteristic
56	C₃×C₄	—	4	1	no	—
57	C₃×C₄	—	20	1	no	—
58	C₃×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
59	C₂×C₅	C₉×D₈	1	1	yes	characteristic
60	C₉	#3961	1	1	yes	characteristic, direct product factor, Sylow
61	Q₈	—	2	1	no	—
62	Q₈	—	10	1	no	—
63	C₈	C₂×C₉×D₅	1	1	yes	characteristic
64	C₂×C₃	C₃×#686	1	1	yes	characteristic
65	C₅	C₉×Q₃₂	1	1	yes	characteristic, complemented, Sylow
66	C₄	—	4	1	no	—
67	C₄	—	20	1	no	—
68	C₄	C₉×C₂²⋊D₅	1	1	yes	characteristic
69	C₃	C₃×#3961	1	1	yes	characteristic
70	C₂	C₉×#686	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	#686
commutator	C₅×C₈	C₂²×C₉
Frattini	C₃×C₈	C₂×C₃×D₅
Fitting	C₅×C₉×Q₁₆	C₂
socle, prime radical	C₂×C₃×C₅	C₃×D₈
cosocle	C₃×C₅×C₈	C₂²×C₃
hypercenter	C₉×Q₁₆	D₅
hypocenter	C₅	C₉×Q₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₉ ◁ C₄×C₉ ◁ C₈×C₉ ◁ C₉×Q₁₆

Complements

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

N	H ≅ G/N	type
15. #3961	C₉	direct (N × H)
36. C₅×C₉	Q₃₂	semidirect
60. C₉	#3961	direct (N × H)
65. C₅	C₉×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×Q₁₆	2
C₉×Dic₂₀	2
C₉×#672	2
C₃×#3961	3
C₉×Q₃₂	5

Subgroups — C9×#3961 #13083790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3961 #13083790