Subgroups — C₅×C₃⋊#10596815 #22576461

Order 8700.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₁₄₅	C₂	1	1	yes	maximal, characteristic
2	C₅×#10596815	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#10596815	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₃⋊#1181	—	5	1	no	maximal
6	C₅×D₁₄₅	D₃	1	1	yes	characteristic
7	C₃×D₁₄₅	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×D₂₉	—	5	1	no	—
9	C₅²×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
10	#10596815	—	3	1	no	—
11	C₅×#1181	—	15	1	no	—
12	C₃×C₅×C₂₉	—	4	1	no	—
13	C₃×C₅×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	C₃⋊#1181	—	5	1	no	Hall
16	C₅×ΓL(1,𝔽₁₆)	—	29	1	no	maximal, Hall
17	D₁₄₅	C₅×D₃	1	1	yes	characteristic
18	C₅×D₂₉	—	5	1	no	—
19	C₃×D₂₉	—	5	1	no	—
20	C₃×C₅×D₅	—	29	1	no	—
21	C₅×C₂₉	—	4	1	no	—
22	C₅×C₂₉	C₅×Dic₃	1	1	yes	characteristic, complemented
23	C₅×C₂₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
24	#1181	—	15	1	no	Hall
25	C₅×AGL(1,𝔽₅)	—	87	1	no	Hall
26	C₃×C₂₉	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
27	C₃×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
28	ΓL(1,𝔽₁₆)	—	29	1	no	—
29	C₅×Dic₃	—	145	1	no	—
30	D₂₉	—	5	1	no	—
31	C₅×D₅	—	29	1	no	—
32	C₂×C₃×C₅	—	145	1	no	—
33	C₃×D₅	—	29	1	no	—
34	C₂₉	C₅×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
35	C₅²	C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	87	1	no	—
37	C₄×C₅	—	435	1	no	—
38	C₃×C₅	—	4	1	no	—
39	C₃×C₅	C₅×#1181	1	1	yes	characteristic, complemented
40	C₃×C₅	#10596815	1	1	yes	characteristic, complemented
41	Dic₃	—	145	1	no	Hall
42	C₂×C₅	—	145	1	no	—
43	D₅	—	29	1	no	—
44	C₂×C₃	—	145	1	no	—
45	C₅	—	4	1	no	—
46	C₅	C₅×C₃⋊#1181	1	1	yes	characteristic, complemented
47	C₅	C₃⋊#10596815	1	1	yes	characteristic, direct product factor
48	C₄	—	435	1	no	Sylow
49	C₃	C₅×#10596815	1	1	yes	characteristic, complemented, Sylow
50	C₂	—	145	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊#10596815
commutator, hypocenter	C₃×C₅×C₂₉	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₄
LCS	G ▷ C₃×C₅×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₂₉	C₄	semidirect
4. C₃⋊#10596815	C₅	direct (N × H)
9. C₅²×C₂₉	Dic₃	semidirect
13. C₃×C₅×C₂₉	C₄×C₅	semidirect
14. C₃×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
22. C₅×C₂₉	C₅×Dic₃	semidirect
23. C₅×C₂₉	ΓL(1,𝔽₁₆)	semidirect
26. C₃×C₂₉	C₅×AGL(1,𝔽₅)	semidirect
27. C₃×C₅²	#1181	semidirect
34. C₂₉	C₅×ΓL(1,𝔽₁₆)	semidirect
35. C₅²	C₃⋊#1181	semidirect
39. C₃×C₅	C₅×#1181	semidirect
40. C₃×C₅	#10596815	semidirect
46. C₅	C₅×C₃⋊#1181	semidirect
47. C₅	C₃⋊#10596815	direct (N × H)
49. C₃	C₅×#10596815	semidirect

Subgroups — C5×C3⋊#10596815 #22576461

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₃⋊#10596815 #22576461