Subgroups — C₅×C₉×#106 #13083892

Order 1440.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₉×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₃×C₅×#106	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₉	—	2	2	no	—
5	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₅×C₈×C₉	C₄	1	2	yes	complemented
7	C₉×#106	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅×C₈	C₂×C₃	1	1	yes	characteristic
9	C₃×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
10	C₂²×C₅×C₉	D₄	1	1	yes	characteristic
11	C₄×C₅×C₉	—	4	2	no	—
12	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
13	C₄×C₅×C₉	Q₈	1	1	yes	characteristic
14	C₅×#106	C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₈×C₉	C₂×C₅	1	1	yes	characteristic
16	C₉×C₄⋊C₄	C₂×C₅	1	2	yes	—
17	C₂×C₃×C₄×C₅	—	2	2	no	—
18	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
19	C₃×C₅×C₈	C₃×C₄	1	2	yes	—
20	C₃×#106	C₃×C₅	1	1	yes	characteristic
21	C₂×C₅×C₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₅×C₉	SD₁₆	1	2	yes	—
23	C₂×C₅×C₈	C₂×C₉	1	1	yes	characteristic
24	C₅×C₄⋊C₄	C₂×C₉	1	2	yes	—
25	C₂×C₄×C₉	—	2	2	no	—
26	C₂×C₄×C₉	C₂²×C₅	1	1	yes	characteristic
27	C₈×C₉	C₄×C₅	1	2	yes	complemented
28	C₂²×C₃×C₅	C₃×D₄	1	1	yes	characteristic
29	C₃×C₄×C₅	—	4	2	no	—
30	C₃×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
31	C₃×C₄×C₅	C₃×Q₈	1	1	yes	characteristic
32	C₂×C₃×C₈	C₂×C₃×C₅	1	1	yes	characteristic
33	C₃×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
34	C₅×C₉	#106	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₄×C₅	—	2	2	no	—
36	C₂×C₄×C₅	C₂²×C₉	1	1	yes	characteristic
37	C₅×C₈	C₄×C₉	1	2	yes	complemented
38	C₂²×C₉	C₅×D₄	1	1	yes	characteristic
39	C₄×C₉	—	4	2	no	—
40	C₄×C₉	C₂×C₄×C₅	1	1	yes	characteristic
41	C₄×C₉	C₅×Q₈	1	1	yes	characteristic
42	#106	C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₃×C₅	C₃×SD₁₆	1	2	yes	—
45	C₂×C₃×C₄	—	2	2	no	—
46	C₂×C₃×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
47	C₃×C₈	C₃×C₄×C₅	1	2	yes	—
48	C₂²×C₅	D₄×C₉	1	1	yes	characteristic
49	C₄×C₅	—	4	2	no	—
50	C₄×C₅	C₂×C₄×C₉	1	1	yes	characteristic
51	C₄×C₅	Q₈×C₉	1	1	yes	characteristic
52	C₂×C₉	C₅×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₉	C₅×SD₁₆	1	2	yes	—
54	C₂×C₈	C₂×C₅×C₉	1	1	yes	characteristic
55	C₄⋊C₄	C₂×C₅×C₉	1	2	yes	—
56	C₃×C₅	C₃×#106	1	1	yes	characteristic
57	C₂²×C₃	C₃×C₅×D₄	1	1	yes	characteristic
58	C₃×C₄	—	4	2	no	—
59	C₃×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
60	C₃×C₄	C₃×C₅×Q₈	1	1	yes	characteristic
61	C₂×C₅	C₉×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₅	C₉×SD₁₆	1	2	yes	—
63	C₉	C₅×#106	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	C₂²×C₅×C₉	1	1	yes	characteristic
66	C₈	C₄×C₅×C₉	1	2	yes	complemented
67	C₂×C₃	C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₃	C₃×C₅×SD₁₆	1	2	yes	—
69	C₅	C₉×#106	1	1	yes	characteristic, direct product factor, Sylow
70	C₂²	C₅×D₄×C₉	1	1	yes	characteristic
71	C₄	—	4	2	no	—
72	C₄	C₂×C₄×C₅×C₉	1	1	yes	characteristic
73	C₄	C₅×Q₈×C₉	1	1	yes	characteristic
74	C₃	C₃×C₅×#106	1	1	yes	characteristic
75	C₂	C₅×C₉×C₄⋊C₄	1	1	yes	characteristic
76	C₂	C₅×C₉×SD₁₆	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
6. C₅×C₈×C₉	C₄	semidirect
7. C₉×#106	C₅	direct (N × H)
14. C₅×#106	C₉	direct (N × H)
27. C₈×C₉	C₄×C₅	semidirect
34. C₅×C₉	#106	direct (N × H)
37. C₅×C₈	C₄×C₉	semidirect
42. #106	C₅×C₉	direct (N × H)
63. C₉	C₅×#106	direct (N × H)
66. C₈	C₄×C₅×C₉	semidirect
69. C₅	C₉×#106	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×C₅×C₈×C₉	2
C₅×C₉×C₄⋊C₄	2
C₃×C₅×#106	3
C₉×#106	5

Subgroups — C5×C9×#106 #13083892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×#106 #13083892