Subgroups — #13083907

Order 1440.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10623539	C₂	1	1	yes	maximal, characteristic
2	C₉⋊#674	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#674	C₂	1	1	yes	maximal, characteristic, complemented
4	#91164	—	3	1	no	maximal
5	C₄×D₄₅	C₄	1	1	yes	characteristic
6	C₉×#168	C₂²	1	1	yes	characteristic
7	C₅×C₉⋊C₈	C₄	1	1	yes	characteristic
8	C₁₆×D₉	—	5	1	no	maximal, Hall
9	#6648	—	3	1	no	—
10	C₃⋊#674	—	3	1	no	—
11	C₃×#674	D₃	1	1	yes	characteristic
12	C₂×D₄₅	C₈	1	1	yes	characteristic
13	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
14	Dic₄₅	C₈	1	1	yes	characteristic
15	D₅⋊C₁₆	—	9	1	no	Hall
16	C₈×D₉	—	5	1	no	—
17	C₉×C₁₆	—	5	1	no	—
18	C₉⋊C₁₆	—	5	1	no	—
19	C₄×D₁₅	—	3	1	no	—
20	C₃×#168	C₂×D₃	1	1	yes	characteristic
21	C₅×C₃⋊C₈	—	3	1	no	—
22	D₃×C₁₆	—	15	1	no	—
23	C₂×C₅×C₉	C₂×C₈	1	1	yes	characteristic
24	D₄₅	C₁₆	1	2	yes	complemented
25	C₈×D₅	—	9	1	no	—
26	#674	—	9	1	no	—
27	#674	D₉	1	1	yes	characteristic, complemented
28	C₄×D₉	—	5	1	no	—
29	C₈×C₉	—	5	1	no	—
30	C₉⋊C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
31	C₂×D₁₅	—	3	1	no	—
32	C₃×C₄×C₅	C₄×D₃	1	1	yes	characteristic
33	Dic₁₅	—	3	1	no	—
34	D₃×C₈	—	15	1	no	—
35	C₃×C₁₆	—	5	1	no	—
36	C₃⋊C₁₆	—	15	1	no	—
37	C₅×C₉	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
38	C₄×D₅	—	9	1	no	—
39	C₅×C₈	—	9	1	no	—
40	#168	C₂×D₉	1	1	yes	characteristic
41	C₂×D₉	—	5	1	no	—
42	C₄×C₉	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
43	Dic₉	—	5	1	no	—
44	C₂×C₁₆	—	45	1	no	Sylow
45	C₂×C₃×C₅	D₃×C₈	1	1	yes	characteristic
46	D₁₅	—	3	2	no	—
47	C₄×D₃	—	15	1	no	—
48	C₃×C₈	—	5	1	no	—
49	C₃⋊C₈	—	3	1	no	—
50	C₂×D₅	—	9	1	no	—
51	C₄×C₅	C₄×D₉	1	1	yes	characteristic
52	Dic₅	—	9	1	no	—
53	C₂×C₉	D₅⋊C₈	1	1	yes	characteristic
54	D₉	—	5	2	no	—
55	C₂×C₈	—	45	1	no	—
56	C₁₆	—	5	1	no	—
57	C₁₆	—	45	1	no	—
58	C₃×C₅	D₃×C₁₆	1	1	yes	characteristic
59	C₂×D₃	—	15	1	no	—
60	C₃×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
61	Dic₃	—	15	1	no	—
62	C₂×C₅	C₈×D₉	1	1	yes	characteristic
63	D₅	—	9	2	no	—
64	C₉	D₅⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄	—	45	1	no	—
66	C₈	—	5	1	no	—
67	C₈	—	9	1	no	—
68	C₂×C₃	#6738	1	1	yes	characteristic
69	D₃	—	15	2	no	—
70	C₅	C₁₆×D₉	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	45	1	no	—
72	C₄	—	45	1	no	—
73	C₄	D₉×AGL(1,𝔽₅)	1	1	yes	characteristic
74	C₃	#91164	1	1	yes	characteristic
75	C₂	—	45	2	no	—
76	C₂	#10623627	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	D₉×AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₉	C₂×C₁₆
Frattini	C₃×C₄	D₃×AGL(1,𝔽₅)
Fitting	C₄×C₅×C₉	C₂×C₄
socle	C₂×C₃×C₅	D₃×C₈
prime radical	C₂×D₄₅	C₈
cosocle	C₉×#168	C₂²
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₉⋊#674	C₂	semidirect
3. C₉×#674	C₂	semidirect
24. D₄₅	C₁₆	semidirect
27. #674	D₉	semidirect
37. C₅×C₉	C₂×C₁₆	semidirect
64. C₉	D₅⋊C₁₆	semidirect
70. C₅	C₁₆×D₉	semidirect

Maximal subgroups

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

subgroup	index
#10623539	2
C₉⋊#674	2
C₉×#674	2
#91164	3
C₁₆×D₉	5