Subgroups — C₉×#3954 #13083783

Order 1440.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₉×#681	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#168	C₂	1	1	yes	maximal, characteristic
4	C₃×#3954	C₃	1	1	yes	maximal, characteristic
5	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₅×C₈×C₉	—	2	1	no	—
7	C₉×#168	—	2	1	no	—
8	C₉×#168	C₄	1	2	yes	—
9	C₉×#108	—	5	1	no	maximal, Hall
10	C₃×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
11	C₃×#681	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃×#168	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₅×C₉	Q₈	1	1	yes	characteristic
14	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₅×C₉	D₄	1	1	yes	characteristic
16	#3954	C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₉×M₁₆	—	5	1	no	—
18	C₉×M₁₆	D₅	1	1	yes	characteristic
19	C₂×C₈×C₉	—	5	1	no	—
20	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
21	C₃×C₅×C₈	—	2	1	no	—
22	C₃×#168	—	2	1	no	—
23	C₃×#168	C₃×C₄	1	2	yes	—
24	C₃×#108	—	5	1	no	—
25	C₂×C₅×C₉	—	2	1	no	—
26	C₂×C₅×C₉	C₄⋊C₄	1	1	yes	characteristic
27	C₅×M₁₆	C₂×C₉	1	1	yes	characteristic
28	#681	C₂×C₉	1	1	yes	characteristic
29	C₂×#168	C₂×C₉	1	1	yes	characteristic
30	C₂×C₄×C₉	C₂×D₅	1	1	yes	characteristic
31	C₈×C₉	—	2	1	no	—
32	C₈×C₉	—	5	2	no	—
33	C₈×C₉	—	10	1	no	—
34	C₂²×C₃×C₅	C₃×Q₈	1	1	yes	characteristic
35	C₃×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
36	C₃×C₄×C₅	C₃×D₄	1	1	yes	characteristic
37	C₃×M₁₆	—	5	1	no	—
38	C₃×M₁₆	C₃×D₅	1	1	yes	characteristic
39	C₂×C₃×C₈	—	5	1	no	—
40	C₅×C₉	#108	1	1	yes	characteristic, complemented, Hall
41	C₂×C₄×C₅	C₂²×C₉	1	1	yes	characteristic
42	C₅×C₈	—	2	1	no	—
43	#168	—	2	1	no	—
44	#168	C₄×C₉	1	2	yes	—
45	C₂²×C₉	Dic₁₀	1	1	yes	characteristic
46	C₄×C₉	C₄×D₅	1	1	yes	characteristic
47	C₄×C₉	C₂²⋊D₅	1	1	yes	characteristic
48	#108	—	5	1	no	Sylow
49	C₂×C₃×C₅	—	2	1	no	—
50	C₂×C₃×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₃×C₄	C₂×C₃×D₅	1	1	yes	characteristic
52	C₃×C₈	—	2	1	no	—
53	C₃×C₈	—	5	2	no	—
54	C₃×C₈	—	10	1	no	—
55	C₂²×C₅	Q₈×C₉	1	1	yes	characteristic
56	C₄×C₅	C₂×C₄×C₉	1	1	yes	characteristic
57	C₄×C₅	D₄×C₉	1	1	yes	characteristic
58	C₂×C₉	—	2	1	no	—
59	C₂×C₉	#683	1	1	yes	characteristic
60	M₁₆	—	5	1	no	—
61	M₁₆	C₉×D₅	1	1	yes	characteristic
62	C₂×C₈	—	5	1	no	—
63	C₃×C₅	C₃×#108	1	1	yes	characteristic
64	C₂²×C₃	C₃×Dic₁₀	1	1	yes	characteristic
65	C₃×C₄	C₃×C₄×D₅	1	1	yes	characteristic
66	C₃×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
67	C₂×C₅	—	2	1	no	—
68	C₂×C₅	C₉×C₄⋊C₄	1	1	yes	characteristic
69	C₉	#3954	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₄	C₂×C₉×D₅	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	5	2	no	—
73	C₈	—	10	1	no	—
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	C₃×#683	1	1	yes	characteristic
76	C₅	C₉×#108	1	1	yes	characteristic, complemented, Sylow
77	C₂²	C₉×Dic₁₀	1	1	yes	characteristic
78	C₄	C₄×C₉×D₅	1	1	yes	characteristic
79	C₄	C₉×C₂²⋊D₅	1	1	yes	characteristic
80	C₃	C₃×#3954	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	C₉×#683	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	C₂²⋊D₅
commutator	C₄×C₅	C₂×C₄×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₅
Fitting	C₅×C₉×M₁₆	C₂
socle	C₂×C₃×C₅	C₃×C₄⋊C₄
prime radical	C₂²×C₃×C₅	C₃×Q₈
cosocle	C₂×C₃×C₄×C₅	C₂²×C₃
hypercenter	C₉×M₁₆	D₅
hypocenter	C₅	C₉×#108
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₉ ◁ C₂×C₄×C₉ ◁ C₉×M₁₆

Complements

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

N	H ≅ G/N	type
16. #3954	C₉	direct (N × H)
40. C₅×C₉	#108	semidirect
69. C₉	#3954	direct (N × H)
76. 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
C₅×C₉×M₁₆	2
C₉×#681	2
C₂×C₉×#168	2
C₃×#3954	3
C₉×#108	5

Subgroups — C9×#3954 #13083783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3954 #13083783