Subgroups — C₃⋊#19153622 #31773308

Order 17340.

64 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	#19153622	—	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	C₅×C₁₇×D₁₇	D₃	1	1	yes	characteristic
6	C₃×C₁₇×D₁₇	D₅	1	1	yes	characteristic
7	C₅×C₁₇²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#11923885	—	15	1	no	Hall
9	C₃⋊#66772	—	17	1	no	maximal
10	Dic₂₅₅	—	17	1	no	maximal
11	C₃×C₁₇²	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₁₇×D₁₇	D₁₅	1	1	yes	characteristic
13	C₂×C₃×C₅×C₁₇	—	17	1	no	—
14	C₃×C₅×D₁₇	D₁₇	1	1	yes	characteristic
15	#66772	—	51	1	no	—
16	Dic₈₅	—	51	1	no	—
17	C₁₇²	Dic₁₅	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	C₂×C₅×C₁₇	—	17	1	no	—
24	C₅×D₁₇	D₅₁	1	1	yes	characteristic
25	C₂×C₃×C₁₇	—	17	1	no	—
26	C₃×D₁₇	D₈₅	1	1	yes	characteristic
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	Dic₁₅	—	289	1	no	Hall
33	C₃×C₁₇	—	4	4	no	—
34	C₃×C₁₇	Dic₈₅	1	1	yes	characteristic, complemented
35	C₃×C₁₇	#66772	1	1	yes	characteristic, complemented
36	C₂×C₁₇	—	17	1	no	—
37	D₁₇	D₂₅₅	1	1	yes	characteristic
38	C₂×C₃×C₅	—	17	1	no	—
39	Dic₅	—	867	1	no	Hall
40	C₁₇	—	4	4	no	—
41	C₁₇	Dic₂₅₅	1	1	yes	characteristic, complemented
42	C₁₇	C₃⋊#66772	1	1	yes	characteristic, complemented
43	C₃×C₅	#11923885	1	1	yes	characteristic, complemented, Hall
44	Dic₃	—	1445	1	no	Hall
45	C₂×C₅	—	17	1	no	—
46	C₂×C₃	—	17	1	no	—
47	C₅	C₃⋊#11923885	1	1	yes	characteristic, complemented, Sylow
48	C₄	—	4335	1	no	Sylow
49	C₃	#19153622	1	1	yes	characteristic, complemented, Sylow
50	C₂	—	17	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

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	Dic₅	semidirect
17. C₁₇²	Dic₁₅	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	Dic₈₅	semidirect
35. C₃×C₁₇	#66772	semidirect
41. C₁₇	Dic₂₅₅	semidirect
42. C₁₇	C₃⋊#66772	semidirect
43. C₃×C₅	#11923885	semidirect
47. C₅	C₃⋊#11923885	semidirect
49. C₃	#19153622	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₇×D₁₇	2
#19153622	3
C₃⋊#11923885	5
C₃⋊#66772	17
Dic₂₅₅	17

Subgroups — C3⋊#19153622 #31773308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#19153622 #31773308