Subgroups — C₃⋊#19153616 #31773302

Order 17340.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₈₅	C₂	1	1	yes	maximal, characteristic
2	#19153616	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#11923885	—	5	1	no	maximal, Hall
5	C₁₇×D₈₅	D₃	1	1	yes	characteristic
6	C₃×C₁₇×D₁₇	—	5	1	no	—
7	C₅×C₁₇²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#11923885	—	15	1	no	Hall
9	C₃⋊#66774	—	17	1	no	maximal
10	C₃⋊#66776	—	17	1	no	maximal
11	C₃×C₁₇²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₁₇×D₁₇	—	5	1	no	—
13	C₃×D₈₅	D₁₇	1	1	yes	characteristic
14	C₃×D₅×C₁₇	—	17	1	no	—
15	#66776	—	51	1	no	—
16	#66774	—	51	1	no	—
17	C₁₇²	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₅×C₁₇	—	4	4	no	—
19	C₃×C₅×C₁₇	Dic₁₇	1	1	yes	characteristic, complemented
20	C₃×C₅×C₁₇	#595	1	1	yes	characteristic, complemented
21	C₃⋊#595	—	85	1	no	—
22	Dic₅₁	—	85	1	no	—
23	D₈₅	D₅₁	1	1	yes	characteristic
24	D₅×C₁₇	—	17	1	no	—
25	C₂×C₃×C₁₇	—	85	1	no	—
26	C₃×D₁₇	—	5	1	no	—
27	C₅×C₁₇	—	4	4	no	—
28	C₅×C₁₇	Dic₅₁	1	1	yes	characteristic, complemented
29	C₅×C₁₇	C₃⋊#595	1	1	yes	characteristic, complemented
30	#595	—	255	1	no	—
31	Dic₁₇	—	255	1	no	—
32	ΓL(1,𝔽₁₆)	—	289	1	no	Hall
33	C₃×C₁₇	—	4	4	no	—
34	C₃×C₁₇	#66774	1	1	yes	characteristic, complemented
35	C₃×C₁₇	#66776	1	1	yes	characteristic, complemented
36	C₂×C₁₇	—	85	1	no	—
37	D₁₇	—	5	1	no	—
38	C₃×D₅	—	17	1	no	—
39	AGL(1,𝔽₅)	—	867	1	no	Hall
40	C₁₇	—	4	4	no	—
41	C₁₇	C₃⋊#66776	1	1	yes	characteristic, complemented
42	C₁₇	C₃⋊#66774	1	1	yes	characteristic, complemented
43	C₃×C₅	#11923885	1	1	yes	characteristic, complemented, Hall
44	Dic₃	—	1445	1	no	Hall
45	D₅	—	17	1	no	—
46	C₂×C₃	—	85	1	no	—
47	C₅	C₃⋊#11923885	1	1	yes	characteristic, complemented, Sylow
48	C₄	—	4335	1	no	Sylow
49	C₃	#19153616	1	1	yes	characteristic, complemented, Sylow
50	C₂	—	85	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₁₇²	C₄
prime radical, cosocle	C₃×C₁₇×D₈₅	C₂
LCS	G ▷ C₃×C₅×C₁₇²
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₇²	C₄	semidirect
7. C₅×C₁₇²	Dic₃	semidirect
11. C₃×C₁₇²	AGL(1,𝔽₅)	semidirect
17. C₁₇²	ΓL(1,𝔽₁₆)	semidirect
19. C₃×C₅×C₁₇	Dic₁₇	semidirect
20. C₃×C₅×C₁₇	#595	semidirect
28. C₅×C₁₇	Dic₅₁	semidirect
29. C₅×C₁₇	C₃⋊#595	semidirect
34. C₃×C₁₇	#66774	semidirect
35. C₃×C₁₇	#66776	semidirect
41. C₁₇	C₃⋊#66776	semidirect
42. C₁₇	C₃⋊#66774	semidirect
43. C₃×C₅	#11923885	semidirect
47. C₅	C₃⋊#11923885	semidirect
49. C₃	#19153616	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₇×D₈₅	2
#19153616	3
C₃⋊#11923885	5
C₃⋊#66774	17
C₃⋊#66776	17

Subgroups — C3⋊#19153616 #31773302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#19153616 #31773302