Subgroups — C₃×C₅×C₁₃×#595 #27210518

Order 13260.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×#595	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×#595	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₃×D₁₇	C₂×C₃	1	1	yes	characteristic
6	C₃×C₁₃×D₁₇	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×#595	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₃×#595	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₄×C₅×C₁₃	—	17	1	no	maximal, Hall
11	C₃×C₁₃×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×D₁₇	C₂×C₁₃	1	1	yes	characteristic
13	C₁₃×D₁₇	C₂×C₃×C₅	1	1	yes	characteristic
14	C₂×C₃×C₅×C₁₃	—	17	1	no	—
15	C₅×#595	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₄×C₅×C₁₃	—	17	1	no	Hall
17	C₃×C₅×C₁₇	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
18	C₁₃×C₁₇	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
19	C₃×#595	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₅×C₁₃	#595	1	1	yes	characteristic, direct product factor, Hall
21	C₅×D₁₇	C₂×C₃×C₁₃	1	1	yes	characteristic
22	C₃×C₄×C₁₃	—	17	1	no	Hall
23	C₂×C₅×C₁₃	—	17	1	no	—
24	C₃×D₁₇	C₂×C₅×C₁₃	1	1	yes	characteristic
25	C₅×C₁₇	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₃	—	17	1	no	—
27	#595	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₅×C₁₃	C₃×#595	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₄×C₅	—	17	1	no	Hall
30	C₄×C₁₃	—	17	1	no	Hall
31	C₃×C₁₇	C₄×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₃	C₅×#595	1	1	yes	characteristic, direct product factor, Hall
33	D₁₇	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic
34	C₂×C₃×C₅	—	17	1	no	—
35	C₂×C₁₃	—	17	1	no	—
36	C₄×C₅	—	17	1	no	Hall
37	C₁₇	C₃×C₄×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	C₁₃×#595	1	1	yes	characteristic, direct product factor, Hall
39	C₁₃	C₃×C₅×#595	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₄	—	17	1	no	Hall
41	C₂×C₅	—	17	1	no	—
42	C₂×C₃	—	17	1	no	—
43	C₅	C₃×C₁₃×#595	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	17	1	no	Sylow
45	C₃	C₅×C₁₃×#595	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₃	#595
commutator, hypocenter	C₁₇	C₃×C₄×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₇	C₄
prime radical	C₃×C₅×C₁₃×D₁₇	C₂
cosocle	D₁₇	C₂×C₃×C₅×C₁₃
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₃×#595	C₃	direct (N × H)
3. C₃×C₅×C₁₃×C₁₇	C₄	semidirect
4. C₃×C₁₃×#595	C₅	direct (N × H)
7. C₅×C₁₃×C₁₇	C₃×C₄	semidirect
8. C₃×C₅×#595	C₁₃	direct (N × H)
9. C₁₃×#595	C₃×C₅	direct (N × H)
11. C₃×C₁₃×C₁₇	C₄×C₅	semidirect
15. C₅×#595	C₃×C₁₃	direct (N × H)
17. C₃×C₅×C₁₇	C₄×C₁₃	semidirect
18. C₁₃×C₁₇	C₃×C₄×C₅	semidirect
19. C₃×#595	C₅×C₁₃	direct (N × H)
20. C₃×C₅×C₁₃	#595	direct (N × H)
25. C₅×C₁₇	C₃×C₄×C₁₃	semidirect
27. #595	C₃×C₅×C₁₃	direct (N × H)
28. C₅×C₁₃	C₃×#595	direct (N × H)
31. C₃×C₁₇	C₄×C₅×C₁₃	semidirect
32. C₃×C₁₃	C₅×#595	direct (N × H)
37. C₁₇	C₃×C₄×C₅×C₁₃	semidirect
38. C₃×C₅	C₁₃×#595	direct (N × H)
39. C₁₃	C₃×C₅×#595	direct (N × H)
43. C₅	C₃×C₁₃×#595	direct (N × H)
45. C₃	C₅×C₁₃×#595	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₃×D₁₇	2
C₅×C₁₃×#595	3
C₃×C₁₃×#595	5
C₃×C₅×#595	13
C₃×C₄×C₅×C₁₃	17

Subgroups — C3×C5×C13×#595 #27210518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₃×#595 #27210518