Subgroups — C₃×C₅×#13181892 #39907232

Order 26010.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₇×D₁₇	—	3	1	no	maximal
3	C₅×#13181892	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×#13181892	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₇²⋊C₃	—	2	1	no	—
6	C₅×C₁₇²⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₇²	D₃	1	1	yes	characteristic, complemented
8	C₅×C₁₇×D₁₇	—	3	1	no	Hall
9	C₃×C₁₇²⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₇×D₁₇	—	3	1	no	—
11	#13181892	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₅×C₁₇²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₇²	C₅×D₃	1	1	yes	characteristic, complemented
14	C₁₇²⋊C₃	—	2	1	no	—
15	C₁₇²⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	C₁₇×D₁₇	—	3	1	no	Hall
17	C₂×C₃×C₅×C₁₇	—	51	1	no	—
18	C₃×C₅×D₁₇	—	3	1	no	—
19	C₁₇²	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₅×C₁₇	—	3	1	no	—
21	C₃×C₅×C₁₇	—	3	1	no	—
22	C₃×C₅×C₁₇	—	6	2	no	—
23	C₂×C₅×C₁₇	—	51	1	no	—
24	C₅×D₁₇	—	3	1	no	—
25	C₂×C₃×C₁₇	—	51	1	no	—
26	C₃×D₁₇	—	3	1	no	—
27	C₃×C₅×D₃	—	289	1	no	maximal, Hall
28	C₅×C₁₇	—	3	1	no	—
29	C₅×C₁₇	—	3	1	no	—
30	C₅×C₁₇	—	6	2	no	—
31	C₃×C₁₇	—	3	1	no	—
32	C₃×C₁₇	—	3	1	no	—
33	C₃×C₁₇	—	6	2	no	—
34	C₃²×C₅	—	289	1	no	Hall
35	C₂×C₁₇	—	51	1	no	—
36	D₁₇	—	3	1	no	—
37	C₂×C₃×C₅	—	51	1	no	—
38	C₅×D₃	—	289	1	no	—
39	C₃×D₃	—	289	1	no	Hall
40	C₁₇	—	3	1	no	—
41	C₁₇	—	3	1	no	—
42	C₁₇	—	6	2	no	—
43	C₃×C₅	—	289	1	no	—
44	C₃×C₅	—	578	1	no	—
45	C₃×C₅	#13181892	1	1	yes	characteristic, direct product factor
46	C₂×C₅	—	51	1	no	Hall
47	C₃²	—	289	1	no	Sylow
48	C₂×C₃	—	51	1	no	—
49	D₃	—	289	1	no	—
50	C₅	C₃×#13181892	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	—	289	1	no	—
52	C₃	—	578	1	no	—
53	C₃	C₅×#13181892	1	1	yes	characteristic, direct product factor
54	C₂	—	51	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	#13181892
commutator, cosocle, hypocenter	C₁₇²⋊C₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇²	D₃
LCS	G ▷ C₁₇²⋊C₃
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇²⋊C₃	C₂	semidirect
3. C₅×#13181892	C₃	direct (N × H)
4. C₃×#13181892	C₅	direct (N × H)
6. C₅×C₁₇²⋊C₃	C₂×C₃	semidirect
7. C₃×C₅×C₁₇²	D₃	semidirect
9. C₃×C₁₇²⋊C₃	C₂×C₅	semidirect
11. #13181892	C₃×C₅	direct (N × H)
12. C₅×C₁₇²	C₃×D₃	semidirect
13. C₃×C₁₇²	C₅×D₃	semidirect
15. C₁₇²⋊C₃	C₂×C₃×C₅	semidirect
19. C₁₇²	C₃×C₅×D₃	semidirect
45. C₃×C₅	#13181892	direct (N × H)
50. C₅	C₃×#13181892	direct (N × H)
53. C₃	C₅×#13181892	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×C₅×C₁₇²⋊C₃	2
C₃×C₅×C₁₇×D₁₇	3
C₅×#13181892	3
C₃×#13181892	5
C₃×C₅×D₃	289

Subgroups — C3×C5×#13181892 #39907232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#13181892 #39907232