Subgroups — C₅×C₃⋊#10621729 #23778564

Order 10140.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×#10621729	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#10621729	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₃⋊D₁₃	D₃	1	1	yes	characteristic
6	C₃×C₁₃⋊D₁₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₅×C₃⋊#261	—	13	2	no	maximal
9	#10621729	—	3	1	no	Hall
10	C₃×C₁₃²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×D₁₃	—	13	2	no	—
12	C₃×C₅×D₁₃	—	26	6	no	—
13	C₁₃⋊D₁₃	C₅×D₃	1	1	yes	characteristic
14	C₅×#261	—	39	2	no	—
15	C₃×C₅×C₁₃	—	2	6	no	—
16	C₃×C₅×C₁₃	#261	1	2	yes	complemented
17	C₁₃²	C₅×Dic₃	1	1	yes	characteristic, complemented, Sylow
18	C₃⋊#261	—	13	2	no	—
19	C₅×D₁₃	—	13	2	no	—
20	C₅×D₁₃	—	26	6	no	—
21	C₃×D₁₃	—	13	2	no	—
22	C₃×D₁₃	—	26	6	no	—
23	C₅×C₁₃	—	2	6	no	—
24	C₅×C₁₃	C₃⋊#261	1	2	yes	complemented
25	C₅×Dic₃	—	169	1	no	Hall
26	#261	—	39	2	no	—
27	C₃×C₁₃	—	2	6	no	—
28	C₃×C₁₃	C₅×#261	1	2	yes	complemented
29	C₂×C₃×C₅	—	169	1	no	—
30	D₁₃	—	13	2	no	—
31	D₁₃	—	26	6	no	—
32	C₄×C₅	—	507	1	no	Hall
33	C₃×C₅	#10621729	1	1	yes	characteristic, complemented, Hall
34	C₁₃	—	2	6	no	—
35	C₁₃	C₅×C₃⋊#261	1	2	yes	complemented
36	Dic₃	—	169	1	no	Hall
37	C₂×C₅	—	169	1	no	—
38	C₂×C₃	—	169	1	no	—
39	C₅	C₃⋊#10621729	1	1	yes	characteristic, direct product factor, Sylow
40	C₄	—	507	1	no	Sylow
41	C₃	C₅×#10621729	1	1	yes	characteristic, complemented, Sylow
42	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊#10621729
commutator, hypocenter	C₃×C₁₃²	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃²	C₄
prime radical	C₃×C₅×C₁₃⋊D₁₃	C₂
cosocle	C₃×C₁₃⋊D₁₃	C₂×C₅
LCS	G ▷ C₃×C₁₃²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₃²	C₄	semidirect
4. C₃⋊#10621729	C₅	direct (N × H)
7. C₅×C₁₃²	Dic₃	semidirect
10. C₃×C₁₃²	C₄×C₅	semidirect
16. C₃×C₅×C₁₃	#261	semidirect
17. C₁₃²	C₅×Dic₃	semidirect
24. C₅×C₁₃	C₃⋊#261	semidirect
28. C₃×C₁₃	C₅×#261	semidirect
33. C₃×C₅	#10621729	semidirect
35. C₁₃	C₅×C₃⋊#261	semidirect
39. C₅	C₃⋊#10621729	direct (N × H)
41. C₃	C₅×#10621729	semidirect

Subgroups — C5×C3⋊#10621729 #23778564

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₃⋊#10621729 #23778564