Subgroups — C₃×C₁₃×#170 #13095607

Order 1560.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#170	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅×C₁₃	C₄	1	1	yes	characteristic
4	C₃×C₈×C₁₃	—	5	1	no	maximal, Hall
5	C₁₃×Dic₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅×C₁₃	C₈	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₁₃	—	5	1	no	—
8	C₂×C₅×C₁₃	C₃×C₄	1	1	yes	characteristic
9	C₃×#170	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₈×C₁₃	—	5	1	no	Hall
11	C₂×C₃×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic
12	C₅×C₁₃	C₃×C₈	1	1	yes	characteristic, complemented, Hall
13	C₃×Dic₅	C₂×C₁₃	1	1	yes	characteristic
14	C₄×C₁₃	—	5	1	no	—
15	#170	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₃	#170	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₅	C₄×C₁₃	1	1	yes	characteristic
18	C₂×C₁₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
19	C₃×C₈	—	5	1	no	Hall
20	Dic₅	C₂×C₃×C₁₃	1	1	yes	characteristic
21	C₃×C₅	C₈×C₁₃	1	1	yes	characteristic, complemented, Hall
22	C₁₃	C₃×#170	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₄	—	5	1	no	—
24	C₂×C₅	C₃×C₄×C₁₃	1	1	yes	characteristic
25	C₈	—	5	1	no	Sylow
26	C₂×C₃	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₅	C₃×C₈×C₁₃	1	1	yes	characteristic, complemented, Sylow
28	C₄	—	5	1	no	—
29	C₃	C₁₃×#170	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₃×C₈×C₁₃
Frattini	C₂	C₃×C₁₃×AGL(1,𝔽₅)
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₃	C₄
cosocle	Dic₅	C₂×C₃×C₁₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₁₃×#170	C₃	direct (N × H)
6. C₃×C₅×C₁₃	C₈	semidirect
9. C₃×#170	C₁₃	direct (N × H)
12. C₅×C₁₃	C₃×C₈	semidirect
15. #170	C₃×C₁₃	direct (N × H)
16. C₃×C₁₃	#170	direct (N × H)
21. C₃×C₅	C₈×C₁₃	semidirect
22. C₁₃	C₃×#170	direct (N × H)
27. C₅	C₃×C₈×C₁₃	semidirect
29. C₃	C₁₃×#170	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×C₁₃×Dic₅	2
C₁₃×#170	3
C₃×C₈×C₁₃	5
C₃×#170	13

Subgroups — C3×C13×#170 #13095607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×#170 #13095607