Subgroups — D₄₅×D₁₆₃ #44440010

Order 29340.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₅×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₉×D₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅×D₁₆₃	—	3	1	no	maximal
5	C₅×C₉×C₁₆₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₉×D₁₆₃	—	5	1	no	maximal, Hall
7	D₂₄₄₅	—	3	1	no	—
8	D₁₅×C₁₆₃	—	3	1	no	—
9	C₃×C₅×D₁₆₃	D₃	1	1	yes	characteristic
10	D₅×D₁₆₃	—	9	1	no	Hall
11	D₁₄₆₇	—	5	1	no	—
12	C₉×D₁₆₃	D₅	1	1	yes	characteristic, complemented
13	D₉×C₁₆₃	—	5	1	no	—
14	C₃×C₅×C₁₆₃	C₂×D₃	1	1	yes	characteristic
15	D₃×D₁₆₃	—	15	1	no	—
16	D₈₁₅	—	9	1	no	—
17	C₅×D₁₆₃	D₉	1	1	yes	characteristic, complemented
18	D₅×C₁₆₃	—	9	1	no	—
19	C₉×C₁₆₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₄₈₉	—	15	1	no	—
21	C₃×D₁₆₃	D₁₅	1	1	yes	characteristic
22	D₃×C₁₆₃	—	15	1	no	—
23	C₅×C₁₆₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₆₃	—	45	1	no	Hall
25	C₃×C₁₆₃	C₂×D₁₅	1	1	yes	characteristic
26	C₂×C₁₆₃	—	45	1	no	—
27	D₁₆₃	—	45	1	no	—
28	D₁₆₃	D₄₅	1	1	yes	characteristic, direct product factor
29	C₂×D₄₅	—	163	1	no	maximal, Hall
30	C₁₆₃	C₂×D₄₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅×C₉	—	163	1	no	—
32	D₄₅	—	163	1	no	—
33	D₄₅	D₁₆₃	1	1	yes	characteristic, direct product factor
34	C₂×D₁₅	—	489	1	no	—
35	C₅×C₉	C₂×D₁₆₃	1	1	yes	characteristic, complemented, Hall
36	C₂×D₉	—	815	1	no	Hall
37	C₂×C₃×C₅	—	163	1	no	—
38	D₁₅	—	3	1	no	—
39	D₁₅	—	489	1	no	—
40	C₂×D₅	—	1467	1	no	Hall
41	C₂×C₉	—	163	1	no	—
42	D₉	—	5	1	no	—
43	D₉	—	815	1	no	—
44	C₃×C₅	D₃×D₁₆₃	1	1	yes	characteristic
45	C₂×D₃	—	2445	1	no	—
46	C₂×C₅	—	163	1	no	—
47	D₅	—	9	1	no	—
48	D₅	—	1467	1	no	—
49	C₉	D₅×D₁₆₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	163	1	no	—
51	D₃	—	15	1	no	—
52	D₃	—	2445	1	no	—
53	C₅	D₉×D₁₆₃	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	7335	1	no	Sylow
55	C₃	D₁₅×D₁₆₃	1	1	yes	characteristic
56	C₂	—	45	1	no	—
57	C₂	—	163	1	no	—
58	C₂	—	7335	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₆₃	C₂²
Frattini	C₃	D₁₅×D₁₆₃
socle	C₃×C₅×C₁₆₃	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₆₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₇₃₃₅	C₂	semidirect
2. D₄₅×C₁₆₃	C₂	semidirect
3. C₅×C₉×D₁₆₃	C₂	semidirect
5. C₅×C₉×C₁₆₃	C₂²	semidirect
12. C₉×D₁₆₃	D₅	semidirect
17. C₅×D₁₆₃	D₉	semidirect
19. C₉×C₁₆₃	C₂×D₅	semidirect
23. C₅×C₁₆₃	C₂×D₉	semidirect
28. D₁₆₃	D₄₅	direct (N × H)
30. C₁₆₃	C₂×D₄₅	semidirect
33. D₄₅	D₁₆₃	direct (N × H)
35. C₅×C₉	C₂×D₁₆₃	semidirect
49. C₉	D₅×D₁₆₃	semidirect
53. C₅	D₉×D₁₆₃	semidirect

Maximal subgroups

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

subgroup	index
D₇₃₃₅	2
D₄₅×C₁₆₃	2
C₅×C₉×D₁₆₃	2
D₁₅×D₁₆₃	3
D₉×D₁₆₃	5
C₂×D₄₅	163

Subgroups — D45×D163 #44440010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₅×D₁₆₃ #44440010