Subgroups — C₃×C₅×C₃⋊#6923 #24926813

Order 10980.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊#6923	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×#6923	—	3	1	no	maximal
4	C₃²×C₅×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃⋊#6923	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×D₆₁	—	2	1	no	—
7	C₃×C₅×D₆₁	D₃	1	1	yes	characteristic
8	C₃×C₅×D₆₁	C₂×C₃	1	1	yes	characteristic
9	C₅×#6923	—	3	1	no	Hall
10	C₃²×D₆₁	C₂×C₅	1	1	yes	characteristic
11	C₃×C₅×C₆₁	—	2	1	no	—
12	C₃×C₅×C₆₁	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃⋊#6923	C₃×C₅	1	1	yes	characteristic, direct product factor
15	C₃×#6923	—	3	1	no	—
16	C₅×D₆₁	C₃×D₃	1	1	yes	characteristic
17	C₃²×C₆₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
18	C₃×D₆₁	—	2	1	no	—
19	C₃×D₆₁	C₅×D₃	1	1	yes	characteristic
20	C₃×D₆₁	C₂×C₃×C₅	1	1	yes	characteristic
21	C₅×C₆₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
22	#6923	—	3	1	no	Hall
23	C₃×C₆₁	—	2	1	no	—
24	C₃×C₆₁	C₅×Dic₃	1	1	yes	characteristic, complemented
25	C₃×C₆₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented
26	C₃×C₅×Dic₃	—	61	1	no	maximal, Hall
27	D₆₁	C₃×C₅×D₃	1	1	yes	characteristic
28	C₂×C₃²×C₅	—	61	1	no	—
29	C₆₁	C₃×C₅×Dic₃	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₄×C₅	—	183	1	no	—
31	C₅×Dic₃	—	61	1	no	—
32	C₃²×C₅	#6923	1	1	yes	characteristic, complemented, Hall
33	C₃×Dic₃	—	61	1	no	Hall
34	C₂×C₃×C₅	—	61	1	no	—
35	C₂×C₃×C₅	—	61	1	no	—
36	C₂×C₃×C₅	—	122	1	no	—
37	C₄×C₅	—	183	1	no	Hall
38	C₂×C₃²	—	61	1	no	—
39	C₃×C₅	—	2	1	no	—
40	C₃×C₅	C₃×#6923	1	1	yes	characteristic, complemented
41	C₃×C₅	C₃⋊#6923	1	1	yes	characteristic, direct product factor
42	C₃×C₄	—	183	1	no	—
43	Dic₃	—	61	1	no	—
44	C₂×C₅	—	61	1	no	—
45	C₃²	C₅×#6923	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	61	1	no	—
47	C₂×C₃	—	61	1	no	—
48	C₂×C₃	—	122	1	no	—
49	C₅	C₃×C₃⋊#6923	1	1	yes	characteristic, direct product factor, Sylow
50	C₄	—	183	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₅×#6923	1	1	yes	characteristic, complemented
53	C₃	C₅×C₃⋊#6923	1	1	yes	characteristic, direct product factor
54	C₂	—	61	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	C₃⋊#6923
commutator, hypocenter	C₃×C₆₁	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₆₁	C₄
prime radical	C₃²×C₅×D₆₁	C₂
cosocle	C₃×D₆₁	C₂×C₃×C₅
LCS	G ▷ C₃×C₆₁
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₃⋊#6923	C₃	direct (N × H)
4. C₃²×C₅×C₆₁	C₄	semidirect
5. C₃×C₃⋊#6923	C₅	direct (N × H)
12. C₃×C₅×C₆₁	Dic₃	semidirect
13. C₃×C₅×C₆₁	C₃×C₄	semidirect
14. C₃⋊#6923	C₃×C₅	direct (N × H)
17. C₃²×C₆₁	C₄×C₅	semidirect
21. C₅×C₆₁	C₃×Dic₃	semidirect
24. C₃×C₆₁	C₅×Dic₃	semidirect
25. C₃×C₆₁	C₃×C₄×C₅	semidirect
29. C₆₁	C₃×C₅×Dic₃	semidirect
32. C₃²×C₅	#6923	semidirect
40. C₃×C₅	C₃×#6923	semidirect
41. C₃×C₅	C₃⋊#6923	direct (N × H)
45. C₃²	C₅×#6923	semidirect
49. C₅	C₃×C₃⋊#6923	direct (N × H)
52. C₃	C₃×C₅×#6923	semidirect
53. C₃	C₅×C₃⋊#6923	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×D₆₁	2
C₅×C₃⋊#6923	3
C₃×C₅×#6923	3
C₃×C₃⋊#6923	5
C₃×C₅×Dic₃	61

Subgroups — C3×C5×C3⋊#6923 #24926813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₃⋊#6923 #24926813