Subgroups — #23778495

Order 10140.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×(C₁₃⋊C₃)⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	#16810010	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#14523150	—	5	1	no	maximal, Hall
5	C₅×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic
6	(C₁₃⋊C₃)⋊D₁₃	D₅	1	1	yes	characteristic
7	C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×#63118	—	13	1	no	maximal
9	#63118⋊C₃	—	13	1	no	maximal
10	#10621728	—	5	1	no	Hall
11	C₁₃×C₁₃⋊C₃	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×D₁₃	—	13	1	no	—
13	C₅×D₁₃⋊C₃	—	13	1	no	—
14	C₁₃⋊D₁₃	C₃×D₅	1	1	yes	characteristic
15	#63118	—	13	1	no	—
16	#63118	—	13	1	no	—
17	#63118	—	39	4	no	—
18	C₃×C₅×C₁₃	—	13	1	no	—
19	C₅×C₁₃⋊C₃	#261	1	1	yes	characteristic, complemented
20	C₁₃²	C₃×Dic₅	1	1	yes	characteristic, complemented, Sylow
21	C₃×#261	—	65	1	no	—
22	AGL(1,𝔽₁₃)	—	65	1	no	—
23	C₅×D₁₃	—	13	1	no	—
24	C₅×D₁₃	—	13	1	no	—
25	C₅×D₁₃	—	39	4	no	—
26	C₃×D₁₃	—	13	1	no	—
27	D₁₃⋊C₃	—	13	1	no	—
28	C₅×C₁₃	—	3	4	no	—
29	C₅×C₁₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
30	C₅×C₁₃	C₃×#261	1	1	yes	characteristic, complemented
31	C₃×Dic₅	—	169	1	no	Hall
32	#261	—	65	1	no	—
33	#261	—	65	1	no	—
34	#261	—	195	4	no	—
35	C₃×C₁₃	—	13	1	no	—
36	C₁₃⋊C₃	#63118	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅	—	169	1	no	—
38	D₁₃	—	13	1	no	—
39	D₁₃	—	13	1	no	—
40	D₁₃	—	39	4	no	—
41	Dic₅	—	169	1	no	Hall
42	C₃×C₅	—	13	1	no	Hall
43	C₁₃	—	3	4	no	—
44	C₁₃	#63118⋊C₃	1	1	yes	characteristic, complemented
45	C₁₃	C₃×#63118	1	1	yes	characteristic, complemented
46	C₃×C₄	—	845	1	no	Hall
47	C₂×C₅	—	169	1	no	—
48	C₂×C₃	—	169	1	no	—
49	C₅	#14523150	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	845	1	no	Sylow
51	C₃	—	13	1	no	Sylow
52	C₂	—	169	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃²	C₃×C₄
prime radical	C₅×(C₁₃⋊C₃)⋊D₁₃	C₂
cosocle	C₅×C₁₃⋊D₁₃	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #16810010	C₃	semidirect
3. C₅×C₁₃×C₁₃⋊C₃	C₄	semidirect
7. C₅×C₁₃²	C₃×C₄	semidirect
11. C₁₃×C₁₃⋊C₃	Dic₅	semidirect
19. C₅×C₁₃⋊C₃	#261	semidirect
20. C₁₃²	C₃×Dic₅	semidirect
29. C₅×C₁₃	AGL(1,𝔽₁₃)	semidirect
30. C₅×C₁₃	C₃×#261	semidirect
36. C₁₃⋊C₃	#63118	semidirect
44. C₁₃	#63118⋊C₃	semidirect
45. C₁₃	C₃×#63118	semidirect
49. C₅	#14523150	semidirect