Subgroups — C₉×C₄⋊#168 #13083765

Order 1440.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#168	C₂	1	2	yes	maximal
3	C₃×C₄⋊#168	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₉	C₄	1	1	yes	characteristic
5	C₂×C₄×C₅×C₉	C₄	1	1	yes	characteristic
6	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
7	C₉×#168	—	2	2	no	—
8	C₉×C₄⋊C₈	—	5	1	no	maximal, Hall
9	C₃×C₄²×C₅	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×#168	C₂×C₃	1	2	yes	—
11	C₂²×C₅×C₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₅×C₉	—	2	1	no	—
13	C₄×C₅×C₉	C₈	1	2	yes	complemented
14	C₄×C₅×C₉	D₄	1	1	yes	characteristic
15	C₄×C₅×C₉	Q₈	1	1	yes	characteristic
16	C₄⋊#168	C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₈×C₉	—	5	2	no	—
18	C₄²×C₉	D₅	1	1	yes	characteristic
19	C₂×C₃×C₄×C₅	C₃×C₄	1	1	yes	characteristic
20	C₂×C₃×C₄×C₅	C₃×C₄	1	1	yes	characteristic
21	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
22	C₃×#168	—	2	2	no	—
23	C₃×C₄⋊C₈	—	5	1	no	—
24	C₂×C₅×C₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₅×C₉	C₂×C₈	1	1	yes	characteristic
26	C₂×C₅×C₉	M₁₆	1	1	yes	characteristic
27	C₄²×C₅	C₂×C₉	1	1	yes	characteristic
28	C₂×#168	C₂×C₉	1	2	yes	—
29	C₂×C₄×C₉	Dic₅	1	1	yes	characteristic
30	C₂×C₄×C₉	Dic₅	1	1	yes	characteristic
31	C₂×C₄×C₉	C₂×D₅	1	1	yes	characteristic
32	C₈×C₉	—	10	2	no	—
33	C₂²×C₃×C₅	C₂×C₃×C₄	1	1	yes	characteristic
34	C₃×C₄×C₅	—	2	1	no	—
35	C₃×C₄×C₅	C₃×C₈	1	2	yes	—
36	C₃×C₄×C₅	C₃×D₄	1	1	yes	characteristic
37	C₃×C₄×C₅	C₃×Q₈	1	1	yes	characteristic
38	C₂×C₃×C₈	—	5	2	no	—
39	C₃×C₄²	C₃×D₅	1	1	yes	characteristic
40	C₅×C₉	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
41	C₂×C₄×C₅	C₄×C₉	1	1	yes	characteristic
42	C₂×C₄×C₅	C₄×C₉	1	1	yes	characteristic
43	C₂×C₄×C₅	C₂²×C₉	1	1	yes	characteristic
44	#168	—	2	2	no	—
45	C₂²×C₉	C₂×Dic₅	1	1	yes	characteristic
46	C₄×C₉	—	2	1	no	—
47	C₄×C₉	#168	1	2	yes	complemented
48	C₄×C₉	Dic₁₀	1	1	yes	characteristic
49	C₄×C₉	D₂₀	1	1	yes	characteristic
50	C₄⋊C₈	—	5	1	no	Sylow
51	C₂×C₃×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₃×C₅	C₂×C₃×C₈	1	1	yes	characteristic
53	C₂×C₃×C₅	C₃×M₁₆	1	1	yes	characteristic
54	C₂×C₃×C₄	C₃×Dic₅	1	1	yes	characteristic
55	C₂×C₃×C₄	C₃×Dic₅	1	1	yes	characteristic
56	C₂×C₃×C₄	C₂×C₃×D₅	1	1	yes	characteristic
57	C₃×C₈	—	10	2	no	—
58	C₂²×C₅	C₂×C₄×C₉	1	1	yes	characteristic
59	C₄×C₅	—	2	1	no	—
60	C₄×C₅	C₈×C₉	1	2	yes	complemented
61	C₄×C₅	D₄×C₉	1	1	yes	characteristic
62	C₄×C₅	Q₈×C₉	1	1	yes	characteristic
63	C₂×C₉	C₂×#168	1	1	yes	characteristic
64	C₂×C₉	#681	1	1	yes	characteristic
65	C₂×C₉	C₄⋊Dic₅	1	1	yes	characteristic
66	C₂×C₈	—	5	2	no	—
67	C₄²	C₉×D₅	1	1	yes	characteristic
68	C₃×C₅	C₃×C₄⋊C₈	1	1	yes	characteristic
69	C₂²×C₃	C₂×C₃×Dic₅	1	1	yes	characteristic
70	C₃×C₄	—	2	1	no	—
71	C₃×C₄	C₃×#168	1	2	yes	—
72	C₃×C₄	C₃×Dic₁₀	1	1	yes	characteristic
73	C₃×C₄	C₃×D₂₀	1	1	yes	characteristic
74	C₂×C₅	C₉×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₅	C₂×C₈×C₉	1	1	yes	characteristic
76	C₂×C₅	C₉×M₁₆	1	1	yes	characteristic
77	C₉	C₄⋊#168	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×C₄	C₉×Dic₅	1	1	yes	characteristic
79	C₂×C₄	C₉×Dic₅	1	1	yes	characteristic
80	C₂×C₄	C₂×C₉×D₅	1	1	yes	characteristic
81	C₈	—	10	2	no	—
82	C₂×C₃	C₂×C₃×#168	1	1	yes	characteristic
83	C₂×C₃	C₃×#681	1	1	yes	characteristic
84	C₂×C₃	C₃×C₄⋊Dic₅	1	1	yes	characteristic
85	C₅	C₉×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
86	C₂²	C₂×C₉×Dic₅	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	C₉×#168	1	2	yes	complemented
89	C₄	C₉×Dic₁₀	1	1	yes	characteristic
90	C₄	C₉×D₂₀	1	1	yes	characteristic
91	C₃	C₃×C₄⋊#168	1	1	yes	characteristic
92	C₂	C₂×C₉×#168	1	1	yes	characteristic
93	C₂	C₉×#681	1	1	yes	characteristic
94	C₂	C₉×C₄⋊Dic₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
13. C₄×C₅×C₉	C₈	semidirect
16. C₄⋊#168	C₉	direct (N × H)
40. C₅×C₉	C₄⋊C₈	semidirect
47. C₄×C₉	#168	semidirect
60. C₄×C₅	C₈×C₉	semidirect
77. C₉	C₄⋊#168	direct (N × H)
85. C₅	C₉×C₄⋊C₈	semidirect
88. C₄	C₉×#168	semidirect

Maximal subgroups

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

subgroup	index
C₄²×C₅×C₉	2
C₂×C₉×#168	2
C₃×C₄⋊#168	3
C₉×C₄⋊C₈	5

Subgroups — C9×C4⋊#168 #13083765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₄⋊#168 #13083765