Subgroups — #23778461

Order 10140.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#11759818	C₂	1	1	yes	maximal, characteristic
2	#16810005	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#92789	C₄	1	1	yes	characteristic, complemented, Hall
4	#14523149	—	5	1	no	maximal, Hall
5	C₁₃×D₆₅	C₂×C₃	1	1	yes	characteristic
6	#11759818	—	5	1	no	—
7	C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#63120⋊C₃	—	13	1	no	maximal
9	#63122⋊C₃	—	13	1	no	maximal
10	#10621730	—	5	1	no	Hall
11	#92789	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₅⋊(D₁₃⋊C₃)	—	13	1	no	—
13	D₅×C₁₃⋊C₃	—	13	1	no	—
14	C₁₃×D₁₃	—	5	1	no	—
15	#63122	—	13	1	no	—
16	#63120	—	13	1	no	—
17	C₅×C₁₃⋊C₃	—	13	1	no	—
18	C₅×C₁₃⋊C₃	—	13	1	no	—
19	C₁₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
20	AGL(1,𝔽₁₃)	—	65	1	no	—
21	Dic₁₃⋊C₃	—	65	1	no	—
22	D₆₅	D₁₃⋊C₃	1	1	yes	characteristic
23	D₅×C₁₃	—	13	1	no	—
24	C₂×C₁₃⋊C₃	—	65	1	no	—
25	D₁₃⋊C₃	—	65	1	no	—
26	C₅×C₁₃	—	12	1	no	—
27	C₅×C₁₃	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
28	C₅×C₁₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
29	C₃×AGL(1,𝔽₅)	—	169	1	no	Hall
30	#261	—	65	1	no	—
31	Dic₁₃	—	65	1	no	—
32	C₁₃⋊C₃	—	13	1	no	—
33	C₁₃⋊C₃	—	13	1	no	—
34	C₃×D₅	—	169	1	no	—
35	C₂×C₁₃	—	65	1	no	—
36	D₁₃	—	5	1	no	—
37	AGL(1,𝔽₅)	—	169	1	no	Hall
38	C₃×C₅	—	169	1	no	Hall
39	C₁₃	—	12	1	no	—
40	C₁₃	#63122⋊C₃	1	1	yes	characteristic, complemented
41	C₁₃	#63120⋊C₃	1	1	yes	characteristic, complemented
42	C₃×C₄	—	845	1	no	Hall
43	D₅	—	13	1	no	—
44	C₂×C₃	—	845	1	no	—
45	C₅	#14523149	1	1	yes	characteristic, complemented, Sylow
46	C₄	—	845	1	no	Sylow
47	C₃	—	169	1	no	Sylow
48	C₂	—	65	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃²	C₃×C₄
prime radical	C₅⋊#11759818	C₂
cosocle	C₁₃×D₆₅	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. #16810005	C₃	semidirect
3. C₅×#92789	C₄	semidirect
7. C₅×C₁₃²	C₃×C₄	semidirect
11. #92789	AGL(1,𝔽₅)	semidirect
19. C₁₃²	C₃×AGL(1,𝔽₅)	semidirect
27. C₅×C₁₃	Dic₁₃⋊C₃	semidirect
28. C₅×C₁₃	AGL(1,𝔽₁₃)	semidirect
40. C₁₃	#63122⋊C₃	semidirect
41. C₁₃	#63120⋊C₃	semidirect
45. C₅	#14523149	semidirect