Subgroups — C₅×C₄⋊Dic₉ #10623589

Order 720.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₉	C₂	1	2	yes	maximal
3	C₅×C₄⋊Dic₃	—	3	1	no	maximal
4	C₂²×C₅×C₉	C₂²	1	1	yes	characteristic
5	C₄×C₅×C₉	C₄	1	2	yes	complemented
6	C₅×Dic₉	—	2	2	no	—
7	C₄⋊Dic₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₄×C₅	D₃	1	1	yes	characteristic
9	C₂×C₅×Dic₃	—	3	2	no	—
10	C₂×C₅×C₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₅×C₉	D₄	1	1	yes	characteristic
12	C₂×C₅×C₉	Q₈	1	1	yes	characteristic
13	C₅×C₄⋊C₄	—	9	1	no	Hall
14	C₂×C₄×C₉	C₂×C₅	1	1	yes	characteristic
15	C₂×Dic₉	C₂×C₅	1	2	yes	—
16	C₂²×C₃×C₅	C₂×D₃	1	1	yes	characteristic
17	C₃×C₄×C₅	Dic₃	1	2	yes	—
18	C₅×Dic₃	—	6	2	no	—
19	C₄⋊Dic₃	—	3	1	no	—
20	C₅×C₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
21	C₂×C₄×C₅	—	9	2	no	—
22	C₂×C₄×C₅	D₉	1	1	yes	characteristic
23	C₂²×C₉	C₂²×C₅	1	1	yes	characteristic
24	C₄×C₉	C₄×C₅	1	2	yes	complemented
25	Dic₉	—	2	2	no	—
26	C₂×C₃×C₅	Dic₆	1	1	yes	characteristic
27	C₂×C₃×C₅	D₁₂	1	1	yes	characteristic
28	C₂×C₃×C₅	C₂×Dic₃	1	1	yes	characteristic
29	C₂×C₃×C₄	C₅×D₃	1	1	yes	characteristic
30	C₂×Dic₃	—	3	2	no	—
31	C₂²×C₅	C₂×D₉	1	1	yes	characteristic
32	C₄×C₅	—	18	2	no	—
33	C₄×C₅	Dic₉	1	2	yes	complemented
34	C₂×C₉	C₂×C₄×C₅	1	1	yes	characteristic
35	C₂×C₉	C₅×D₄	1	1	yes	characteristic
36	C₂×C₉	C₅×Q₈	1	1	yes	characteristic
37	C₄⋊C₄	—	9	1	no	Sylow
38	C₃×C₅	C₄⋊Dic₃	1	1	yes	characteristic
39	C₂²×C₃	C₂×C₅×D₃	1	1	yes	characteristic
40	C₃×C₄	C₅×Dic₃	1	2	yes	—
41	Dic₃	—	6	2	no	—
42	C₂×C₅	Dic₁₈	1	1	yes	characteristic
43	C₂×C₅	D₃₆	1	1	yes	characteristic
44	C₂×C₅	C₂×Dic₉	1	1	yes	characteristic
45	C₉	C₅×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₄	—	9	2	no	—
47	C₂×C₄	C₅×D₉	1	1	yes	characteristic
48	C₂×C₃	C₅×Dic₆	1	1	yes	characteristic
49	C₂×C₃	C₅×D₁₂	1	1	yes	characteristic
50	C₂×C₃	C₂×C₅×Dic₃	1	1	yes	characteristic
51	C₅	C₄⋊Dic₉	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²	C₂×C₅×D₉	1	1	yes	characteristic
53	C₄	—	18	2	no	—
54	C₄	C₅×Dic₉	1	2	yes	complemented
55	C₃	C₅×C₄⋊Dic₃	1	1	yes	characteristic
56	C₂	C₅×Dic₁₈	1	1	yes	characteristic
57	C₂	C₅×D₃₆	1	1	yes	characteristic
58	C₂	C₂×C₅×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₉
commutator	C₂×C₉	C₂×C₄×C₅
Frattini	C₂²×C₃	C₂×C₅×D₃
Fitting	C₂×C₄×C₅×C₉	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×D₃
cosocle	C₂²×C₉	C₂²×C₅
hypercenter	C₂×C₄×C₅	D₉
hypocenter	C₉	C₅×C₄⋊C₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
5. C₄×C₅×C₉	C₄	semidirect
7. C₄⋊Dic₉	C₅	direct (N × H)
20. C₅×C₉	C₄⋊C₄	semidirect
24. C₄×C₉	C₄×C₅	semidirect
33. C₄×C₅	Dic₉	semidirect
45. C₉	C₅×C₄⋊C₄	semidirect
51. C₅	C₄⋊Dic₉	direct (N × H)
54. C₄	C₅×Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₉	2
C₂×C₅×Dic₉	2
C₅×C₄⋊Dic₃	3
C₄⋊Dic₉	5

Subgroups — C5×C4⋊Dic9 #10623589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄⋊Dic₉ #10623589