Subgroups — C₉×#3951 #13083779

Order 1440.

90 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×#681	C₂	1	2	yes	maximal
3	C₃×#3951	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
5	C₅×C₈×C₉	C₄	1	2	yes	—
6	C₉×#168	—	2	2	no	—
7	C₉×#108	—	5	1	no	maximal, Hall
8	C₂×C₃×C₅×C₈	C₂×C₃	1	1	yes	characteristic
9	C₃×#681	C₂×C₃	1	2	yes	—
10	C₂²×C₅×C₉	Q₈	1	1	yes	characteristic
11	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₅×C₉	D₄	1	1	yes	characteristic
13	#3951	C₉	1	1	yes	characteristic, direct product factor, Hall
14	C₉×M₁₆	—	5	2	no	—
15	C₂×C₈×C₉	D₅	1	1	yes	characteristic
16	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
17	C₃×C₅×C₈	C₃×C₄	1	2	yes	—
18	C₃×#168	—	2	2	no	—
19	C₃×#108	—	5	1	no	—
20	C₂×C₅×C₉	—	2	1	no	—
21	C₂×C₅×C₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₅×C₈	C₂×C₉	1	1	yes	characteristic
23	#681	C₂×C₉	1	2	yes	—
24	C₂×C₄×C₉	C₂×D₅	1	1	yes	characteristic
25	C₈×C₉	—	10	2	no	—
26	C₈×C₉	Dic₅	1	2	yes	—
27	C₂²×C₃×C₅	C₃×Q₈	1	1	yes	characteristic
28	C₃×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
29	C₃×C₄×C₅	C₃×D₄	1	1	yes	characteristic
30	C₃×M₁₆	—	5	2	no	—
31	C₂×C₃×C₈	C₃×D₅	1	1	yes	characteristic
32	C₅×C₉	#108	1	1	yes	characteristic, complemented, Hall
33	C₂×C₄×C₅	C₂²×C₉	1	1	yes	characteristic
34	C₅×C₈	C₄×C₉	1	2	yes	—
35	#168	—	2	2	no	—
36	C₂²×C₉	Dic₁₀	1	1	yes	characteristic
37	C₄×C₉	D₂₀	1	1	yes	characteristic
38	C₄×C₉	C₂×Dic₅	1	1	yes	characteristic
39	#108	—	5	1	no	Sylow
40	C₂×C₃×C₅	—	2	1	no	—
41	C₂×C₃×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₃×C₄	C₂×C₃×D₅	1	1	yes	characteristic
43	C₃×C₈	—	10	2	no	—
44	C₃×C₈	C₃×Dic₅	1	2	yes	—
45	C₂²×C₅	Q₈×C₉	1	1	yes	characteristic
46	C₄×C₅	C₂×C₄×C₉	1	1	yes	characteristic
47	C₄×C₅	D₄×C₉	1	1	yes	characteristic
48	C₂×C₉	—	2	1	no	—
49	C₂×C₉	C₄⋊Dic₅	1	1	yes	characteristic
50	M₁₆	—	5	2	no	—
51	C₂×C₈	C₉×D₅	1	1	yes	characteristic
52	C₃×C₅	C₃×#108	1	1	yes	characteristic
53	C₂²×C₃	C₃×Dic₁₀	1	1	yes	characteristic
54	C₃×C₄	C₃×D₂₀	1	1	yes	characteristic
55	C₃×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
56	C₂×C₅	—	2	1	no	—
57	C₂×C₅	C₉×C₄⋊C₄	1	1	yes	characteristic
58	C₉	#3951	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₄	C₂×C₉×D₅	1	1	yes	characteristic
60	C₈	—	10	2	no	—
61	C₈	C₉×Dic₅	1	2	yes	—
62	C₂×C₃	—	2	1	no	—
63	C₂×C₃	C₃×C₄⋊Dic₅	1	1	yes	characteristic
64	C₅	C₉×#108	1	1	yes	characteristic, complemented, Sylow
65	C₂²	C₉×Dic₁₀	1	1	yes	characteristic
66	C₄	C₉×D₂₀	1	1	yes	characteristic
67	C₄	C₂×C₉×Dic₅	1	1	yes	characteristic
68	C₃	C₃×#3951	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	C₉×C₄⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	D₂₀
commutator	C₄×C₅	C₂×C₄×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₅
Fitting	C₂×C₅×C₈×C₉	C₂
socle	C₂×C₃×C₅	C₃×C₄⋊C₄
prime radical	C₂²×C₃×C₅	C₃×Q₈
cosocle	C₂×C₃×C₄×C₅	C₂²×C₃
hypercenter	C₂×C₈×C₉	D₅
hypocenter	C₅	C₉×#108
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₉ ◁ C₂×C₄×C₉ ◁ C₂×C₈×C₉

Complements

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

N	H ≅ G/N	type
13. #3951	C₉	direct (N × H)
32. C₅×C₉	#108	semidirect
58. C₉	#3951	direct (N × H)
64. C₅	C₉×#108	semidirect

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×#681	2
C₃×#3951	3
C₉×#108	5

Subgroups — C9×#3951 #13083779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3951 #13083779