Subgroups — C₃⋊#19153613 #31773299

Order 17340.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊(C₁₇⋊D₁₇)	C₂	1	1	yes	maximal, characteristic
2	#19153613	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#11923883	—	5	1	no	maximal, Hall
5	C₅⋊(C₁₇⋊D₁₇)	D₃	1	1	yes	characteristic
6	C₃×C₁₇⋊D₁₇	—	5	1	no	—
7	C₅×C₁₇²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#11923883	—	15	1	no	Hall
9	C₃⋊#66776	—	17	18	no	maximal
10	C₃×C₁₇²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₁₇⋊D₁₇	—	5	1	no	—
12	C₃×D₈₅	—	17	18	no	—
13	#66776	—	51	18	no	—
14	C₁₇²	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₅×C₁₇	#595	1	18	yes	complemented
16	C₃⋊#595	—	85	18	no	—
17	D₈₅	—	17	18	no	—
18	C₃×D₁₇	—	85	18	no	—
19	C₅×C₁₇	C₃⋊#595	1	18	yes	complemented
20	#595	—	255	18	no	—
21	ΓL(1,𝔽₁₆)	—	289	1	no	Hall
22	C₃×C₁₇	#66776	1	18	yes	complemented
23	D₁₇	—	85	18	no	—
24	C₃×D₅	—	289	1	no	—
25	AGL(1,𝔽₅)	—	867	1	no	Hall
26	C₁₇	C₃⋊#66776	1	18	yes	complemented
27	C₃×C₅	#11923883	1	1	yes	characteristic, complemented, Hall
28	Dic₃	—	1445	1	no	Hall
29	D₅	—	289	1	no	—
30	C₂×C₃	—	1445	1	no	—
31	C₅	C₃⋊#11923883	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	4335	1	no	Sylow
33	C₃	#19153613	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	1445	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₁₇²	C₄
prime radical, cosocle	C₃×C₅⋊(C₁₇⋊D₁₇)	C₂
LCS	G ▷ C₃×C₅×C₁₇²
UCS	C₁

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

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