Subgroups — C₅×C₃⋊#10596816 #22576462

Order 8700.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×#10596816	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#10596816	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×Dic₈₇	—	5	1	no	maximal
6	C₅×D₅×C₂₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₅×C₂₉	—	5	1	no	—
8	C₃×D₅×C₂₉	C₂×C₅	1	1	yes	characteristic
9	C₅²×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
10	#10596816	—	3	1	no	—
11	C₅×Dic₂₉	—	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	Dic₈₇	—	5	1	no	Hall
16	C₅×ΓL(1,𝔽₁₆)	—	29	1	no	maximal, Hall
17	C₂×C₅×C₂₉	—	5	1	no	—
18	D₅×C₂₉	C₅×D₃	1	1	yes	characteristic
19	C₂×C₃×C₂₉	—	5	1	no	—
20	C₃×C₅×D₅	D₂₉	1	1	yes	characteristic
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	Dic₂₉	—	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	Dic₂₉	1	1	yes	characteristic, complemented, Hall
28	ΓL(1,𝔽₁₆)	—	29	1	no	—
29	C₅×Dic₃	—	145	1	no	—
30	C₂×C₂₉	—	5	1	no	—
31	C₅×D₅	D₈₇	1	1	yes	characteristic
32	C₂×C₃×C₅	—	5	1	no	—
33	C₃×D₅	C₅×D₂₉	1	1	yes	characteristic
34	C₂₉	C₅×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
35	C₅²	Dic₈₇	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×Dic₂₉	1	1	yes	characteristic, complemented
40	C₃×C₅	#10596816	1	1	yes	characteristic, complemented
41	Dic₃	—	145	1	no	Hall
42	C₂×C₅	—	5	1	no	—
43	D₅	C₅×D₈₇	1	1	yes	characteristic
44	C₂×C₃	—	5	1	no	—
45	C₅	—	4	1	no	—
46	C₅	C₅×Dic₈₇	1	1	yes	characteristic, complemented
47	C₅	C₃⋊#10596816	1	1	yes	characteristic, direct product factor
48	C₄	—	435	1	no	Sylow
49	C₃	C₅×#10596816	1	1	yes	characteristic, complemented, Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊#10596816
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⋊#10596816	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	Dic₂₉	semidirect
34. C₂₉	C₅×ΓL(1,𝔽₁₆)	semidirect
35. C₅²	Dic₈₇	semidirect
39. C₃×C₅	C₅×Dic₂₉	semidirect
40. C₃×C₅	#10596816	semidirect
46. C₅	C₅×Dic₈₇	semidirect
47. C₅	C₃⋊#10596816	direct (N × H)
49. C₃	C₅×#10596816	semidirect

Subgroups — C5×C3⋊#10596816 #22576462

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₃⋊#10596816 #22576462