Subgroups — C₃⋊#15668532 #22576477

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	#15668532	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#10596817	—	5	1	no	maximal
5	C₃⋊#10596814	—	5	1	no	maximal
6	C₅×D₁₄₅	D₃	1	1	yes	characteristic
7	C₃×D₁₄₅	D₅	1	1	yes	characteristic
8	C₃×C₅×D₂₉	—	5	1	no	—
9	C₅²×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
10	#10596817	—	15	1	no	—
11	#10596814	—	15	1	no	—
12	C₃×C₅×C₂₉	—	4	1	no	—
13	C₃×C₅×C₂₉	Dic₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	C₃⋊#1181	—	25	1	no	Hall
16	C₃⋊#1042	—	29	1	no	maximal, Hall
17	D₁₄₅	D₁₅	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	Dic₁₅	1	1	yes	characteristic, complemented
23	C₅×C₂₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
24	#1181	—	75	1	no	Hall
25	#1042	—	87	1	no	Hall
26	C₃×C₂₉	#1042	1	1	yes	characteristic, complemented, Hall
27	C₃×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
28	ΓL(1,𝔽₁₆)	—	145	1	no	—
29	Dic₁₅	—	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	C₃⋊#1042	1	1	yes	characteristic, complemented, Sylow
35	C₅²	C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	435	1	no	—
37	Dic₅	—	435	1	no	—
38	C₃×C₅	—	4	1	no	—
39	C₃×C₅	#10596814	1	1	yes	characteristic, complemented
40	C₃×C₅	#10596817	1	1	yes	characteristic, complemented
41	Dic₃	—	725	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	C₃⋊#10596814	1	1	yes	characteristic, complemented
47	C₅	C₃⋊#10596817	1	1	yes	characteristic, complemented
48	C₄	—	2175	1	no	Sylow
49	C₃	#15668532	1	1	yes	characteristic, complemented, Sylow
50	C₂	—	145	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₂₉	C₄	semidirect
9. C₅²×C₂₉	Dic₃	semidirect
13. C₃×C₅×C₂₉	Dic₅	semidirect
14. C₃×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
22. C₅×C₂₉	Dic₁₅	semidirect
23. C₅×C₂₉	ΓL(1,𝔽₁₆)	semidirect
26. C₃×C₂₉	#1042	semidirect
27. C₃×C₅²	#1181	semidirect
34. C₂₉	C₃⋊#1042	semidirect
35. C₅²	C₃⋊#1181	semidirect
39. C₃×C₅	#10596814	semidirect
40. C₃×C₅	#10596817	semidirect
46. C₅	C₃⋊#10596814	semidirect
47. C₅	C₃⋊#10596817	semidirect
49. C₃	#15668532	semidirect

Subgroups — C3⋊#15668532 #22576477

Conjugacy classes of subgroups

Complements

Subgroups — C₃⋊#15668532 #22576477