Subgroups — C₅×C₉×SD₁₆ #10623618

Order 720.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₄×C₉	C₂	1	1	yes	maximal, characteristic
3	C₅×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×SD₁₆	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₅×C₉	—	2	1	no	—
6	C₄×C₅×C₉	—	2	1	no	—
7	C₄×C₅×C₉	C₂²	1	1	yes	characteristic
8	C₉×SD₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
10	C₃×C₅×D₄	C₂×C₃	1	1	yes	characteristic
11	C₃×C₅×C₈	C₂×C₃	1	1	yes	characteristic
12	C₂×C₅×C₉	—	4	1	no	—
13	C₂×C₅×C₉	D₄	1	1	yes	characteristic
14	C₅×SD₁₆	C₉	1	1	yes	characteristic, direct product factor, Hall
15	Q₈×C₉	C₂×C₅	1	1	yes	characteristic, complemented
16	D₄×C₉	C₂×C₅	1	1	yes	characteristic
17	C₈×C₉	C₂×C₅	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₅	—	2	1	no	—
19	C₃×C₄×C₅	—	2	1	no	—
20	C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
21	C₃×SD₁₆	C₃×C₅	1	1	yes	characteristic
22	C₅×C₉	SD₁₆	1	1	yes	characteristic, direct product factor, Hall
23	C₅×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
24	C₅×D₄	C₂×C₉	1	1	yes	characteristic
25	C₅×C₈	C₂×C₉	1	1	yes	characteristic, complemented
26	C₂²×C₉	—	2	1	no	—
27	C₄×C₉	—	2	1	no	—
28	C₄×C₉	C₂²×C₅	1	1	yes	characteristic
29	C₂×C₃×C₅	—	4	1	no	—
30	C₂×C₃×C₅	C₃×D₄	1	1	yes	characteristic
31	C₃×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
32	C₃×D₄	C₂×C₃×C₅	1	1	yes	characteristic
33	C₃×C₈	C₂×C₃×C₅	1	1	yes	characteristic
34	C₂²×C₅	—	2	1	no	—
35	C₄×C₅	—	2	1	no	—
36	C₄×C₅	C₂²×C₉	1	1	yes	characteristic
37	C₂×C₉	—	4	1	no	—
38	C₂×C₉	C₅×D₄	1	1	yes	characteristic
39	SD₁₆	C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₅	C₃×SD₁₆	1	1	yes	characteristic
41	C₂²×C₃	—	2	1	no	—
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
44	C₂×C₅	—	4	1	no	—
45	C₂×C₅	D₄×C₉	1	1	yes	characteristic
46	C₉	C₅×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
47	Q₈	C₂×C₅×C₉	1	1	yes	characteristic, complemented
48	D₄	C₂×C₅×C₉	1	1	yes	characteristic
49	C₈	C₂×C₅×C₉	1	1	yes	characteristic, complemented
50	C₂×C₃	—	4	1	no	—
51	C₂×C₃	C₃×C₅×D₄	1	1	yes	characteristic
52	C₅	C₉×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²	—	2	1	no	—
54	C₄	—	2	1	no	—
55	C₄	C₂²×C₅×C₉	1	1	yes	characteristic
56	C₃	C₃×C₅×SD₁₆	1	1	yes	characteristic
57	C₂	—	4	1	no	—
58	C₂	C₅×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₉	D₄
commutator	C₄	C₂²×C₅×C₉
Frattini, cosocle	C₃×C₄	C₂²×C₃×C₅
socle	C₂×C₃×C₅	C₃×D₄
prime radical	C₃×C₅×D₄	C₂×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₉ ◁ C₄×C₅×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×Q₈×C₉	C₂	semidirect
3. C₅×C₈×C₉	C₂	semidirect
8. C₉×SD₁₆	C₅	direct (N × H)
14. C₅×SD₁₆	C₉	direct (N × H)
15. Q₈×C₉	C₂×C₅	semidirect
17. C₈×C₉	C₂×C₅	semidirect
22. C₅×C₉	SD₁₆	direct (N × H)
23. C₅×Q₈	C₂×C₉	semidirect
25. C₅×C₈	C₂×C₉	semidirect
39. SD₁₆	C₅×C₉	direct (N × H)
46. C₉	C₅×SD₁₆	direct (N × H)
47. Q₈	C₂×C₅×C₉	semidirect
49. C₈	C₂×C₅×C₉	semidirect
52. C₅	C₉×SD₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×Q₈×C₉	2
C₅×D₄×C₉	2
C₅×C₈×C₉	2
C₃×C₅×SD₁₆	3
C₉×SD₁₆	5

Subgroups — C5×C9×SD16 #10623618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×SD₁₆ #10623618