Subgroups — C₂×C₉⋊#674 #13083985

Order 1440.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#168	C₂	1	1	yes	maximal, characteristic
2	C₉⋊#674	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊#674	—	3	1	no	maximal
4	C₂×C₄×C₅×C₉	C₄	1	1	yes	characteristic
5	C₉×#168	C₄	1	1	yes	characteristic
6	C₉×#168	C₂²	1	1	yes	characteristic
7	C₂×C₉⋊C₁₆	—	5	1	no	maximal, Hall
8	C₂×C₃×#168	D₃	1	1	yes	characteristic
9	C₃⋊#674	—	3	2	no	—
10	C₂²×C₅×C₉	C₈	1	1	yes	characteristic
11	C₄×C₅×C₉	C₈	1	1	yes	characteristic
12	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
13	C₂×#674	—	9	1	no	Hall
14	C₂×C₈×C₉	—	5	1	no	—
15	C₉⋊C₁₆	—	5	2	no	—
16	C₂×C₃×C₄×C₅	Dic₃	1	1	yes	characteristic
17	C₃×#168	Dic₃	1	1	yes	characteristic
18	C₃×#168	C₂×D₃	1	1	yes	characteristic
19	C₂×C₃⋊C₁₆	—	15	1	no	—
20	C₂×C₅×C₉	C₁₆	1	2	yes	complemented
21	C₂×C₅×C₉	C₂×C₈	1	1	yes	characteristic
22	C₂×#168	D₉	1	1	yes	characteristic
23	#674	—	9	2	no	—
24	C₂×C₄×C₉	AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₈×C₉	—	5	1	no	—
26	C₈×C₉	—	5	1	no	—
27	C₂²×C₃×C₅	C₃⋊C₈	1	1	yes	characteristic
28	C₃×C₄×C₅	C₃⋊C₈	1	1	yes	characteristic
29	C₃×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
30	C₂×C₃×C₈	—	5	1	no	—
31	C₃⋊C₁₆	—	15	2	no	—
32	C₅×C₉	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
33	C₂×C₄×C₅	Dic₉	1	1	yes	characteristic
34	#168	Dic₉	1	1	yes	characteristic
35	#168	C₂×D₉	1	1	yes	characteristic
36	C₂²×C₉	#170	1	1	yes	characteristic
37	C₄×C₉	#170	1	1	yes	characteristic
38	C₄×C₉	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₂×C₁₆	—	45	1	no	Sylow
40	C₂×C₃×C₅	C₃⋊C₁₆	1	2	yes	—
41	C₂×C₃×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
42	C₂×C₃×C₄	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
43	C₃×C₈	—	5	1	no	—
44	C₃×C₈	—	5	1	no	—
45	C₂²×C₅	C₉⋊C₈	1	1	yes	characteristic
46	C₄×C₅	C₉⋊C₈	1	1	yes	characteristic
47	C₄×C₅	C₂×Dic₉	1	1	yes	characteristic
48	C₂×C₉	#674	1	2	yes	complemented
49	C₂×C₉	C₂×#170	1	1	yes	characteristic
50	C₂×C₈	—	5	1	no	—
51	C₁₆	—	45	2	no	—
52	C₃×C₅	C₂×C₃⋊C₁₆	1	1	yes	characteristic
53	C₂²×C₃	C₃⋊#170	1	1	yes	characteristic
54	C₃×C₄	C₃⋊#170	1	1	yes	characteristic
55	C₃×C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
56	C₂×C₅	C₉⋊C₁₆	1	2	yes	complemented
57	C₂×C₅	C₂×C₉⋊C₈	1	1	yes	characteristic
58	C₉	C₂×#674	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₄	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic
60	C₈	—	5	1	no	—
61	C₈	—	5	1	no	—
62	C₂×C₃	C₃⋊#674	1	2	yes	—
63	C₂×C₃	C₂×C₃⋊#170	1	1	yes	characteristic
64	C₅	C₂×C₉⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
65	C₂²	C₉⋊#170	1	1	yes	characteristic
66	C₄	C₉⋊#170	1	1	yes	characteristic
67	C₄	C₂×C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic
68	C₃	C₂×C₃⋊#674	1	1	yes	characteristic
69	C₂	C₉⋊#674	1	2	yes	direct product factor
70	C₂	C₂×C₉⋊#170	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	C₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₉	C₂×C₁₆
Frattini	C₃×C₄	C₂×ΓL(1,𝔽₁₆)
Fitting	C₂×C₄×C₅×C₉	C₄
socle, prime radical	C₂²×C₃×C₅	C₃⋊C₈
cosocle	C₉×#168	C₂²
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₉⋊#674	C₂	direct (N × H)
20. C₂×C₅×C₉	C₁₆	semidirect
32. C₅×C₉	C₂×C₁₆	semidirect
48. C₂×C₉	#674	semidirect
56. C₂×C₅	C₉⋊C₁₆	semidirect
58. C₉	C₂×#674	semidirect
64. C₅	C₂×C₉⋊C₁₆	semidirect
69. C₂	C₉⋊#674	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#168	2
C₉⋊#674	2
C₂×C₃⋊#674	3
C₂×C₉⋊C₁₆	5

Subgroups — C2×C9⋊#674 #13083985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉⋊#674 #13083985