Subgroups — C₁₃×C₃⋊#63122 #23778570

Order 10140.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#63122	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×C₃⋊#261	—	5	1	no	maximal, Hall
5	C₁₃×D₆₅	D₃	1	1	yes	characteristic
6	C₃×C₁₃×D₁₃	—	5	1	no	—
7	C₅×C₁₃²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₃⋊#63122	C₁₃	1	1	yes	maximal, characteristic, direct product factor
9	C₁₃×ΓL(1,𝔽₁₆)	—	13	1	no	maximal
10	C₁₃×#261	—	15	1	no	Hall
11	C₃×C₁₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₆₅	C₂×C₁₃	1	1	yes	characteristic
13	C₃×D₅×C₁₃	—	13	1	no	—
14	C₁₃×D₁₃	—	5	1	no	—
15	#63122	—	3	1	no	—
16	C₁₃×AGL(1,𝔽₅)	—	39	1	no	—
17	C₃×C₅×C₁₃	—	4	3	no	—
18	C₃×C₅×C₁₃	C₄×C₁₃	1	1	yes	characteristic, complemented
19	C₃×C₅×C₁₃	#261	1	1	yes	characteristic, complemented
20	C₁₃²	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
21	C₃⋊#261	—	5	1	no	—
22	Dic₃×C₁₃	—	65	1	no	—
23	D₆₅	D₃×C₁₃	1	1	yes	characteristic
24	D₅×C₁₃	—	13	1	no	—
25	C₂×C₃×C₁₃	—	65	1	no	—
26	C₃×D₁₃	—	5	1	no	—
27	C₅×C₁₃	—	4	3	no	—
28	C₅×C₁₃	Dic₃×C₁₃	1	1	yes	characteristic, complemented
29	C₅×C₁₃	C₃⋊#261	1	1	yes	characteristic, complemented
30	ΓL(1,𝔽₁₆)	—	13	1	no	Hall
31	#261	—	15	1	no	—
32	C₄×C₁₃	—	195	1	no	—
33	C₃×C₁₃	—	4	3	no	—
34	C₃×C₁₃	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
35	C₃×C₁₃	#63122	1	1	yes	characteristic, complemented
36	C₃×D₅	—	13	1	no	—
37	C₂×C₁₃	—	65	1	no	—
38	D₁₃	—	5	1	no	—
39	AGL(1,𝔽₅)	—	39	1	no	Hall
40	C₃×C₅	C₁₃×#261	1	1	yes	characteristic, complemented, Hall
41	C₁₃	—	4	3	no	—
42	C₁₃	C₁₃×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
43	C₁₃	C₃⋊#63122	1	1	yes	characteristic, direct product factor
44	Dic₃	—	65	1	no	Hall
45	D₅	—	13	1	no	—
46	C₂×C₃	—	65	1	no	—
47	C₅	C₁₃×C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
48	C₄	—	195	1	no	Sylow
49	C₃	C₁₃×#63122	1	1	yes	characteristic, complemented, Sylow
50	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊#63122
commutator, hypocenter	C₃×C₅×C₁₃	C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃²	C₄
prime radical	C₃×C₁₃×D₆₅	C₂
cosocle	C₃×D₆₅	C₂×C₁₃
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₃²	C₄	semidirect
7. C₅×C₁₃²	Dic₃	semidirect
8. C₃⋊#63122	C₁₃	direct (N × H)
11. C₃×C₁₃²	AGL(1,𝔽₅)	semidirect
18. C₃×C₅×C₁₃	C₄×C₁₃	semidirect
19. C₃×C₅×C₁₃	#261	semidirect
20. C₁₃²	ΓL(1,𝔽₁₆)	semidirect
28. C₅×C₁₃	Dic₃×C₁₃	semidirect
29. C₅×C₁₃	C₃⋊#261	semidirect
34. C₃×C₁₃	C₁₃×AGL(1,𝔽₅)	semidirect
35. C₃×C₁₃	#63122	semidirect
40. C₃×C₅	C₁₃×#261	semidirect
42. C₁₃	C₁₃×ΓL(1,𝔽₁₆)	semidirect
43. C₁₃	C₃⋊#63122	direct (N × H)
47. C₅	C₁₃×C₃⋊#261	semidirect
49. C₃	C₁₃×#63122	semidirect

Subgroups — C13×C3⋊#63122 #23778570

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×C₃⋊#63122 #23778570