Subgroups — C₄⋊(C₉⋊#168) #13083847

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	C₄⋊(C₃⋊#168)	—	3	1	no	maximal
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	C₄⋊(C₉⋊C₈)	—	5	1	no	maximal, Hall
9	C₃×C₄²×C₅	D₃	1	1	yes	characteristic
10	C₂×C₃⋊#168	—	3	2	no	—
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	—	9	1	no	Hall
17	C₄²×C₉	D₅	1	1	yes	characteristic
18	C₂×C₉⋊C₈	—	5	2	no	—
19	C₂×C₃×C₄×C₅	Dic₃	1	1	yes	characteristic
20	C₂×C₃×C₄×C₅	Dic₃	1	1	yes	characteristic
21	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
22	C₃⋊#168	—	6	2	no	—
23	C₄⋊(C₃⋊C₈)	—	15	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	D₉	1	1	yes	characteristic
28	C₂×#168	—	9	2	no	—
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	C₉⋊C₈	—	10	2	no	—
33	C₂²×C₃×C₅	C₂×Dic₃	1	1	yes	characteristic
34	C₃×C₄×C₅	—	2	1	no	—
35	C₃×C₄×C₅	C₃⋊C₈	1	2	yes	—
36	C₃×C₄×C₅	Dic₆	1	1	yes	characteristic
37	C₃×C₄×C₅	D₁₂	1	1	yes	characteristic
38	C₃×C₄²	D₁₅	1	1	yes	characteristic
39	C₂×C₃⋊C₈	—	15	2	no	—
40	C₅×C₉	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
41	C₂×C₄×C₅	Dic₉	1	1	yes	characteristic
42	C₂×C₄×C₅	Dic₉	1	1	yes	characteristic
43	C₂×C₄×C₅	C₂×D₉	1	1	yes	characteristic
44	#168	—	18	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	—	45	1	no	Sylow
51	C₂×C₃×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
52	C₂×C₃×C₅	#208	1	1	yes	characteristic
53	C₂×C₃×C₅	C₄⋊Dic₃	1	1	yes	characteristic
54	C₂×C₃×C₄	Dic₁₅	1	1	yes	characteristic
55	C₂×C₃×C₄	Dic₁₅	1	1	yes	characteristic
56	C₂×C₃×C₄	C₂×D₁₅	1	1	yes	characteristic
57	C₃⋊C₈	—	30	2	no	—
58	C₂²×C₅	C₂×Dic₉	1	1	yes	characteristic
59	C₄×C₅	—	2	1	no	—
60	C₄×C₅	C₉⋊C₈	1	2	yes	complemented
61	C₄×C₅	Dic₁₈	1	1	yes	characteristic
62	C₄×C₅	D₃₆	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	—	45	2	no	—
67	C₄²	D₄₅	1	1	yes	characteristic
68	C₃×C₅	C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
69	C₂²×C₃	C₂×Dic₁₅	1	1	yes	characteristic
70	C₃×C₄	—	2	1	no	—
71	C₃×C₄	C₃⋊#168	1	2	yes	—
72	C₃×C₄	Dic₃₀	1	1	yes	characteristic
73	C₃×C₄	D₆₀	1	1	yes	characteristic
74	C₂×C₅	C₂×C₉⋊C₈	1	1	yes	characteristic
75	C₂×C₅	#3667	1	1	yes	characteristic
76	C₂×C₅	C₄⋊Dic₉	1	1	yes	characteristic
77	C₉	C₄⋊#168	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₄	Dic₄₅	1	1	yes	characteristic
79	C₂×C₄	Dic₄₅	1	1	yes	characteristic
80	C₂×C₄	C₂×D₄₅	1	1	yes	characteristic
81	C₈	—	90	2	no	—
82	C₂×C₃	C₂×C₃⋊#168	1	1	yes	characteristic
83	C₂×C₃	#6710	1	1	yes	characteristic
84	C₂×C₃	C₄⋊Dic₁₅	1	1	yes	characteristic
85	C₅	C₄⋊(C₉⋊C₈)	1	1	yes	characteristic, complemented, Sylow
86	C₂²	C₂×Dic₄₅	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	C₉⋊#168	1	2	yes	complemented
89	C₄	Dic₉₀	1	1	yes	characteristic
90	C₄	D₁₈₀	1	1	yes	characteristic
91	C₃	C₄⋊(C₃⋊#168)	1	1	yes	characteristic
92	C₂	C₂×C₉⋊#168	1	1	yes	characteristic
93	C₂	#10623602	1	1	yes	characteristic
94	C₂	C₄⋊Dic₄₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄₅
commutator	C₂×C₅×C₉	C₂×C₈
Frattini	C₂×C₃×C₄	C₂×D₁₅
Fitting	C₄²×C₅×C₉	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×Dic₃
cosocle	C₂×C₄×C₅×C₉	C₂²
hypercenter	C₄²	D₄₅
hypocenter	C₅×C₉	C₄⋊C₈
LCS	G ▷ C₂×C₅×C₉ ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
13. C₄×C₅×C₉	C₈	semidirect
40. C₅×C₉	C₄⋊C₈	semidirect
47. C₄×C₉	#168	semidirect
60. C₄×C₅	C₉⋊C₈	semidirect
77. C₉	C₄⋊#168	semidirect
85. C₅	C₄⋊(C₉⋊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
C₄⋊(C₃⋊#168)	3
C₄⋊(C₉⋊C₈)	5

Subgroups — C4⋊(C9⋊#168) #13083847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₉⋊#168) #13083847