Subgroups — C₅×Dic₉⋊C₄ #10623588

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	1	yes	maximal, characteristic
3	C₂×C₅×Dic₉	C₂	1	1	yes	maximal, characteristic
4	C₅×Dic₃⋊C₄	—	3	1	no	maximal
5	C₂²×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₄×C₅×C₉	—	2	1	no	—
7	C₅×Dic₉	—	2	1	no	—
8	C₅×Dic₉	C₄	1	2	yes	complemented
9	Dic₉⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₄×C₅	D₃	1	1	yes	characteristic
11	C₂×C₅×Dic₃	—	3	1	no	—
12	C₂×C₅×Dic₃	—	3	1	no	—
13	C₂×C₅×C₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₅×C₉	D₄	1	1	yes	characteristic
15	C₂×C₅×C₉	Q₈	1	1	yes	characteristic
16	C₅×C₄⋊C₄	—	9	1	no	Hall
17	C₂×C₄×C₉	C₂×C₅	1	1	yes	characteristic
18	C₂×Dic₉	C₂×C₅	1	1	yes	characteristic
19	C₂×Dic₉	C₂×C₅	1	1	yes	characteristic
20	C₂²×C₃×C₅	C₂×D₃	1	1	yes	characteristic
21	C₃×C₄×C₅	—	2	1	no	—
22	C₅×Dic₃	—	3	2	no	—
23	C₅×Dic₃	—	6	1	no	—
24	Dic₃⋊C₄	—	3	1	no	—
25	C₅×C₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
26	C₂×C₄×C₅	—	9	1	no	—
27	C₂×C₄×C₅	—	9	1	no	—
28	C₂×C₄×C₅	D₉	1	1	yes	characteristic
29	C₂²×C₉	C₂²×C₅	1	1	yes	characteristic
30	C₄×C₉	—	2	1	no	—
31	Dic₉	—	2	1	no	—
32	Dic₉	C₄×C₅	1	2	yes	complemented
33	C₂×C₃×C₅	Dic₆	1	1	yes	characteristic
34	C₂×C₃×C₅	C₄×D₃	1	1	yes	characteristic
35	C₂×C₃×C₅	#67	1	1	yes	characteristic
36	C₂×C₃×C₄	C₅×D₃	1	1	yes	characteristic
37	C₂×Dic₃	—	3	1	no	—
38	C₂×Dic₃	—	3	1	no	—
39	C₂²×C₅	C₂×D₉	1	1	yes	characteristic
40	C₄×C₅	—	2	1	no	—
41	C₄×C₅	—	9	2	no	—
42	C₄×C₅	—	18	1	no	—
43	C₂×C₉	C₂×C₄×C₅	1	1	yes	characteristic
44	C₂×C₉	C₅×D₄	1	1	yes	characteristic
45	C₂×C₉	C₅×Q₈	1	1	yes	characteristic
46	C₄⋊C₄	—	9	1	no	Sylow
47	C₃×C₅	Dic₃⋊C₄	1	1	yes	characteristic
48	C₂²×C₃	C₂×C₅×D₃	1	1	yes	characteristic
49	C₃×C₄	—	2	1	no	—
50	Dic₃	—	3	2	no	—
51	Dic₃	—	6	1	no	—
52	C₂×C₅	Dic₁₈	1	1	yes	characteristic
53	C₂×C₅	C₄×D₉	1	1	yes	characteristic
54	C₂×C₅	#611	1	1	yes	characteristic
55	C₉	C₅×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₄	—	9	1	no	—
57	C₂×C₄	—	9	1	no	—
58	C₂×C₄	C₅×D₉	1	1	yes	characteristic
59	C₂×C₃	C₅×Dic₆	1	1	yes	characteristic
60	C₂×C₃	C₄×C₅×D₃	1	1	yes	characteristic
61	C₂×C₃	C₅×#67	1	1	yes	characteristic
62	C₅	Dic₉⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
63	C₂²	C₂×C₅×D₉	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	9	2	no	—
66	C₄	—	18	1	no	—
67	C₃	C₅×Dic₃⋊C₄	1	1	yes	characteristic
68	C₂	C₅×Dic₁₈	1	1	yes	characteristic
69	C₂	C₄×C₅×D₉	1	1	yes	characteristic
70	C₂	C₅×#611	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
8. C₅×Dic₉	C₄	semidirect
9. Dic₉⋊C₄	C₅	direct (N × H)
25. C₅×C₉	C₄⋊C₄	semidirect
32. Dic₉	C₄×C₅	semidirect
55. C₉	C₅×C₄⋊C₄	semidirect
62. C₅	Dic₉⋊C₄	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×C₄×C₅×C₉	2
C₂×C₅×Dic₉	2
C₅×Dic₃⋊C₄	3
Dic₉⋊C₄	5

Subgroups — C5×Dic9⋊C4 #10623588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₉⋊C₄ #10623588