Subgroups — C₉×#3947 #13083776

Order 1440.

120 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	C₄×C₉×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#168	C₂	1	1	yes	maximal, characteristic
4	C₃×#3947	C₃	1	1	yes	maximal, characteristic
5	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₂×C₉×Dic₅	C₄	1	2	yes	—
7	C₅×C₈×C₉	C₄	1	2	yes	complemented
8	C₉×#168	C₄	1	2	yes	complemented
9	C₉×#97	—	5	1	no	maximal, Hall
10	C₂×C₃×C₅×C₈	C₂×C₃	1	1	yes	characteristic
11	C₃×C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃×#168	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₅×C₉	C₂×C₄	1	1	yes	characteristic
14	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
16	C₉×Dic₅	—	2	2	no	—
17	#3947	C₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₈×C₉	—	5	1	no	—
19	C₂×C₈×C₉	D₅	1	1	yes	characteristic
20	C₄²×C₉	—	5	1	no	—
21	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₃×Dic₅	C₃×C₄	1	2	yes	—
23	C₃×C₅×C₈	C₃×C₄	1	2	yes	—
24	C₃×#168	C₃×C₄	1	2	yes	—
25	C₃×#97	—	5	1	no	—
26	C₂×C₅×C₉	C₄²	1	1	yes	characteristic
27	C₂×C₅×C₉	M₁₆	1	2	yes	—
28	C₂×C₅×C₈	C₂×C₉	1	1	yes	characteristic
29	C₄×Dic₅	C₂×C₉	1	1	yes	characteristic
30	C₂×#168	C₂×C₉	1	1	yes	characteristic
31	C₂×C₄×C₉	—	5	2	no	—
32	C₂×C₄×C₉	C₂×D₅	1	1	yes	characteristic
33	C₈×C₉	—	5	2	no	—
34	C₈×C₉	Dic₅	1	2	yes	complemented
35	C₂²×C₃×C₅	C₂×C₃×C₄	1	1	yes	characteristic
36	C₃×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
37	C₃×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
38	C₃×Dic₅	—	2	2	no	—
39	C₂×C₃×C₈	—	5	1	no	—
40	C₂×C₃×C₈	C₃×D₅	1	1	yes	characteristic
41	C₃×C₄²	—	5	1	no	—
42	C₅×C₉	#97	1	1	yes	characteristic, complemented, Hall
43	C₂×C₄×C₅	C₂²×C₉	1	1	yes	characteristic
44	C₂×Dic₅	C₄×C₉	1	2	yes	—
45	C₅×C₈	C₄×C₉	1	2	yes	complemented
46	#168	C₄×C₉	1	2	yes	complemented
47	C₂²×C₉	C₄×D₅	1	1	yes	characteristic
48	C₄×C₉	—	10	2	no	—
49	C₄×C₉	C₄×D₅	1	1	yes	characteristic
50	C₄×C₉	C₂×Dic₅	1	1	yes	characteristic
51	#97	—	5	1	no	Sylow
52	C₂×C₃×C₅	C₃×C₄²	1	1	yes	characteristic
53	C₂×C₃×C₅	C₃×M₁₆	1	2	yes	—
54	C₂×C₃×C₄	—	5	2	no	—
55	C₂×C₃×C₄	C₂×C₃×D₅	1	1	yes	characteristic
56	C₃×C₈	—	5	2	no	—
57	C₃×C₈	C₃×Dic₅	1	2	yes	—
58	C₂²×C₅	C₂×C₄×C₉	1	1	yes	characteristic
59	C₄×C₅	C₂×C₄×C₉	1	1	yes	characteristic
60	C₄×C₅	C₂×C₄×C₉	1	1	yes	characteristic
61	Dic₅	—	2	2	no	—
62	C₂×C₉	#676	1	2	yes	—
63	C₂×C₉	C₄×Dic₅	1	1	yes	characteristic
64	C₂×C₈	—	5	1	no	—
65	C₂×C₈	C₉×D₅	1	1	yes	characteristic
66	C₄²	—	5	1	no	—
67	C₃×C₅	C₃×#97	1	1	yes	characteristic
68	C₂²×C₃	C₃×C₄×D₅	1	1	yes	characteristic
69	C₃×C₄	—	10	2	no	—
70	C₃×C₄	C₃×C₄×D₅	1	1	yes	characteristic
71	C₃×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
72	C₂×C₅	C₄²×C₉	1	1	yes	characteristic
73	C₂×C₅	C₉×M₁₆	1	2	yes	—
74	C₉	#3947	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×C₄	—	5	2	no	—
76	C₂×C₄	C₂×C₉×D₅	1	1	yes	characteristic
77	C₈	—	5	2	no	—
78	C₈	C₉×Dic₅	1	2	yes	complemented
79	C₂×C₃	C₃×#676	1	2	yes	—
80	C₂×C₃	C₃×C₄×Dic₅	1	1	yes	characteristic
81	C₅	C₉×#97	1	1	yes	characteristic, complemented, Sylow
82	C₂²	C₄×C₉×D₅	1	1	yes	characteristic
83	C₄	—	10	2	no	—
84	C₄	C₄×C₉×D₅	1	1	yes	characteristic
85	C₄	C₂×C₉×Dic₅	1	1	yes	characteristic
86	C₃	C₃×#3947	1	1	yes	characteristic
87	C₂	C₉×#676	1	2	yes	—
88	C₂	C₄×C₉×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂×D₅
commutator	C₂×C₅	C₄²×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₅
Fitting	C₂×C₅×C₈×C₉	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₃×C₄
cosocle	C₂×C₃×C₄×C₅	C₂²×C₃
hypercenter	C₂×C₈×C₉	D₅
hypocenter	C₅	C₉×#97
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂×C₈×C₉

Complements

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

N	H ≅ G/N	type
7. C₅×C₈×C₉	C₄	semidirect
8. C₉×#168	C₄	semidirect
17. #3947	C₉	direct (N × H)
34. C₈×C₉	Dic₅	semidirect
42. C₅×C₉	#97	semidirect
45. C₅×C₈	C₄×C₉	semidirect
46. #168	C₄×C₉	semidirect
74. C₉	#3947	direct (N × H)
78. C₈	C₉×Dic₅	semidirect
81. C₅	C₉×#97	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
C₄×C₉×Dic₅	2
C₂×C₉×#168	2
C₃×#3947	3
C₉×#97	5

Subgroups — C9×#3947 #13083776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3947 #13083776