Subgroups — #29505749

Order 15300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊#66772	—	3	1	no	maximal
3	C₁₇×C₅²⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅²×D₁₇	D₃	1	1	yes	characteristic
5	C₅×#66772	—	9	1	no	Hall
6	C₃×C₅²×C₁₇	Dic₃	1	1	yes	characteristic
7	C₃⋊#66772	—	3	1	no	—
8	C₅×C₃⋊#595	—	15	1	no	—
9	#11744607	—	17	1	no	maximal, Hall
10	C₅²×D₁₇	D₉	1	1	yes	characteristic
11	C₉⋊#595	—	25	1	no	maximal, Hall
12	C₃×C₅×D₁₇	—	3	1	no	—
13	C₃×C₅×D₁₇	—	6	1	no	—
14	C₂×C₅²⋊C₉	—	17	1	no	—
15	C₅²×C₁₇	Dic₉	1	1	yes	characteristic, complemented, Hall
16	#66772	—	9	1	no	—
17	C₅×#595	—	45	1	no	—
18	C₉×D₁₇	—	50	1	no	—
19	C₅×Dic₁₅	—	51	1	no	—
20	C₃×C₅×C₁₇	—	3	1	no	—
21	C₃×C₅×C₁₇	—	6	1	no	—
22	C₅²⋊C₉	#595	1	1	yes	characteristic, complemented, Hall
23	C₃⋊#595	—	15	1	no	—
24	C₅×D₁₇	—	3	1	no	—
25	C₅×D₁₇	—	6	1	no	—
26	C₉×C₁₇	—	50	1	no	Hall
27	C₂×C₃×C₅²	—	17	1	no	—
28	C₃×D₁₇	#3874	1	1	yes	characteristic
29	C₅×Dic₅	—	153	1	no	Hall
30	C₅×C₁₇	—	3	1	no	—
31	C₅×C₁₇	—	6	1	no	—
32	C₃×C₅²	C₃⋊#595	1	1	yes	characteristic
33	#595	—	45	1	no	Hall
34	Dic₁₅	—	51	1	no	—
35	C₅×Dic₃	—	255	1	no	—
36	C₃×C₁₇	#64470	1	1	yes	characteristic
37	C₂×C₅²	—	17	1	no	—
38	Dic₉	—	425	1	no	Hall
39	D₁₇	#90646	1	1	yes	characteristic
40	C₂×C₃×C₅	—	102	1	no	—
41	C₂×C₃×C₅	—	102	1	no	—
42	C₅²	C₉⋊#595	1	1	yes	characteristic, complemented, Sylow
43	C₄×C₅	—	765	1	no	—
44	Dic₅	—	153	1	no	—
45	C₂×C₉	—	850	1	no	—
46	C₁₇	#11744607	1	1	yes	characteristic, complemented, Sylow
47	C₃×C₅	—	6	1	no	—
48	C₃×C₅	—	6	1	no	—
49	Dic₃	—	255	1	no	—
50	C₂×C₅	—	51	1	no	—
51	C₂×C₅	—	102	1	no	—
52	C₉	—	50	1	no	Sylow
53	C₂×C₃	—	17	1	no	—
54	C₅	—	3	1	no	—
55	C₅	—	6	1	no	—
56	C₄	—	765	1	no	Sylow
57	C₃	#19099756	1	1	yes	characteristic
58	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₁₇×C₅²⋊C₉	C₄
Frattini	C₃	#19099756
Fitting, socle	C₃×C₅²×C₁₇	Dic₃
prime radical	C₃×C₅²×D₁₇	D₃
cosocle	D₁₇×C₅²⋊C₉	C₂
LCS	G ▷ C₁₇×C₅²⋊C₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₁₇×C₅²⋊C₉	C₄	semidirect
15. C₅²×C₁₇	Dic₉	semidirect
22. C₅²⋊C₉	#595	semidirect
42. C₅²	C₉⋊#595	semidirect
46. C₁₇	#11744607	semidirect

Maximal subgroups

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

subgroup	index
D₁₇×C₅²⋊C₉	2
C₅×C₃⋊#66772	3
#11744607	17
C₉⋊#595	25