Subgroups — C₃×#17984460 #27210534

Order 13260.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₁₀₅	C₂	1	1	yes	maximal, characteristic
2	#17984460	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#11725131	—	5	1	no	maximal, Hall
5	D₁₁₀₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₂₂₁	—	5	1	no	—
7	C₅×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×#66775	—	13	1	no	maximal, Hall
9	#11725131	—	5	1	no	Hall
10	C₃×#63121	—	17	1	no	maximal, Hall
11	C₃×C₁₃×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₈₅	—	13	1	no	—
13	D₂₂₁	—	5	1	no	—
14	C₃×D₆₅	—	17	1	no	—
15	#66775	—	13	1	no	Hall
16	#63121	—	17	1	no	Hall
17	C₃×C₅×C₁₇	#261	1	1	yes	characteristic, complemented, Hall
18	C₁₃×C₁₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
19	C₃×#595	—	65	1	no	Hall
20	C₃×C₅×C₁₃	#595	1	1	yes	characteristic, complemented, Hall
21	D₈₅	—	13	1	no	—
22	C₃×#261	—	85	1	no	Hall
23	D₆₅	—	17	1	no	—
24	C₃×D₁₇	—	65	1	no	—
25	C₅×C₁₇	C₃×#261	1	1	yes	characteristic, complemented, Hall
26	C₃×D₁₃	—	85	1	no	—
27	#595	—	65	1	no	Hall
28	C₅×C₁₃	C₃×#595	1	1	yes	characteristic, complemented, Hall
29	C₃×AGL(1,𝔽₅)	—	221	1	no	Hall
30	#261	—	85	1	no	Hall
31	C₃×C₁₇	#63121	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₃	#66775	1	1	yes	characteristic, complemented, Hall
33	D₁₇	—	65	1	no	—
34	C₃×D₅	—	221	1	no	—
35	D₁₃	—	85	1	no	—
36	AGL(1,𝔽₅)	—	221	1	no	Hall
37	C₁₇	C₃×#63121	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	#11725131	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₃×#66775	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	1105	1	no	Hall
41	D₅	—	221	1	no	—
42	C₂×C₃	—	1105	1	no	—
43	C₅	C₃×#11725131	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	1105	1	no	Sylow
45	C₃	#17984460	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	1105	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#17984460
commutator, hypocenter	C₅×C₁₃×C₁₇	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₇	C₄
prime radical	C₃×D₁₁₀₅	C₂
cosocle	D₁₁₀₅	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₁₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. #17984460	C₃	direct (N × H)
3. C₃×C₅×C₁₃×C₁₇	C₄	semidirect
7. C₅×C₁₃×C₁₇	C₃×C₄	semidirect
11. C₃×C₁₃×C₁₇	AGL(1,𝔽₅)	semidirect
17. C₃×C₅×C₁₇	#261	semidirect
18. C₁₃×C₁₇	C₃×AGL(1,𝔽₅)	semidirect
20. C₃×C₅×C₁₃	#595	semidirect
25. C₅×C₁₇	C₃×#261	semidirect
28. C₅×C₁₃	C₃×#595	semidirect
31. C₃×C₁₇	#63121	semidirect
32. C₃×C₁₃	#66775	semidirect
37. C₁₇	C₃×#63121	semidirect
38. C₃×C₅	#11725131	semidirect
39. C₁₃	C₃×#66775	semidirect
43. C₅	C₃×#11725131	semidirect
45. C₃	#17984460	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₁₁₀₅	2
#17984460	3
C₃×#11725131	5
C₃×#66775	13
C₃×#63121	17

Subgroups — C3×#17984460 #27210534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17984460 #27210534