Subgroups — C₅×C₉⋊#66772 #29505795

Order 15300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊#66772	—	3	1	no	maximal
3	C₅²×C₉×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#66772	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₉⋊#595	—	5	1	no	maximal
6	C₃×C₅²×D₁₇	D₃	1	1	yes	characteristic
7	C₅×#66772	—	9	1	no	Hall
8	C₅×C₉×D₁₇	—	2	2	no	—
9	C₅×C₉×D₁₇	D₅	1	1	yes	characteristic
10	C₅×C₉×D₁₇	C₂×C₅	1	1	yes	characteristic
11	C₃×C₅²×C₁₇	Dic₃	1	1	yes	characteristic
12	C₃⋊#66772	—	3	1	no	—
13	C₅×C₃⋊#595	—	15	1	no	—
14	C₅×Dic₄₅	—	17	1	no	maximal, Hall
15	C₅²×D₁₇	D₉	1	1	yes	characteristic
16	C₅×C₉×C₁₇	—	2	2	no	—
17	C₅×C₉×C₁₇	Dic₅	1	1	yes	characteristic, complemented
18	C₅×C₉×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented
19	C₉⋊#595	—	5	1	no	Hall
20	C₃×C₅×D₁₇	—	2	2	no	—
21	C₃×C₅×D₁₇	C₅×D₃	1	1	yes	characteristic
22	C₃×C₅×D₁₇	D₁₅	1	1	yes	characteristic
23	C₂×C₅²×C₉	—	17	1	no	—
24	C₅²×C₁₇	Dic₉	1	1	yes	characteristic, complemented, Hall
25	#66772	—	9	1	no	—
26	C₅×#595	—	45	1	no	—
27	C₉×D₁₇	C₅×D₅	1	1	yes	characteristic
28	C₅×Dic₁₅	—	51	1	no	—
29	C₃×C₅×C₁₇	—	2	2	no	—
30	C₃×C₅×C₁₇	C₅×Dic₃	1	1	yes	characteristic
31	C₃×C₅×C₁₇	Dic₁₅	1	1	yes	characteristic
32	C₅²×C₉	#595	1	1	yes	characteristic, complemented, Hall
33	C₃⋊#595	—	15	1	no	—
34	Dic₄₅	—	17	1	no	—
35	C₅×Dic₉	—	85	1	no	—
36	C₅×D₁₇	—	2	2	no	—
37	C₅×D₁₇	C₅×D₉	1	1	yes	characteristic
38	C₅×D₁₇	D₄₅	1	1	yes	characteristic
39	C₉×C₁₇	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×C₅²	—	17	1	no	—
41	C₃×D₁₇	C₅×D₁₅	1	1	yes	characteristic
42	C₅×Dic₅	—	153	1	no	Hall
43	C₂×C₅×C₉	—	17	1	no	—
44	C₂×C₅×C₉	—	17	1	no	—
45	C₂×C₅×C₉	—	34	2	no	—
46	C₅×C₁₇	—	2	2	no	—
47	C₅×C₁₇	C₅×Dic₉	1	1	yes	characteristic, complemented
48	C₅×C₁₇	Dic₄₅	1	1	yes	characteristic, complemented
49	C₃×C₅²	C₃⋊#595	1	1	yes	characteristic
50	#595	—	45	1	no	Hall
51	Dic₁₅	—	51	1	no	—
52	C₅×Dic₃	—	255	1	no	—
53	C₃×C₁₇	C₅×Dic₁₅	1	1	yes	characteristic
54	C₂×C₅²	—	17	1	no	—
55	C₅×C₉	—	2	2	no	—
56	C₅×C₉	C₅×#595	1	1	yes	characteristic, complemented
57	C₅×C₉	#66772	1	1	yes	characteristic, complemented
58	Dic₉	—	85	1	no	Hall
59	D₁₇	C₅×D₄₅	1	1	yes	characteristic
60	C₂×C₃×C₅	—	17	1	no	—
61	C₂×C₃×C₅	—	17	1	no	—
62	C₂×C₃×C₅	—	34	2	no	—
63	C₅²	C₉⋊#595	1	1	yes	characteristic, complemented, Sylow
64	C₄×C₅	—	765	1	no	—
65	Dic₅	—	153	1	no	—
66	C₂×C₉	—	17	1	no	—
67	C₁₇	C₅×Dic₄₅	1	1	yes	characteristic, complemented, Sylow
68	C₃×C₅	—	2	2	no	—
69	C₃×C₅	C₅×C₃⋊#595	1	1	yes	characteristic
70	C₃×C₅	C₃⋊#66772	1	1	yes	characteristic
71	Dic₃	—	255	1	no	—
72	C₂×C₅	—	17	1	no	—
73	C₂×C₅	—	17	1	no	—
74	C₂×C₅	—	34	2	no	—
75	C₉	C₅×#66772	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	17	1	no	—
77	C₅	—	2	2	no	—
78	C₅	C₅×C₉⋊#595	1	1	yes	characteristic, complemented
79	C₅	C₉⋊#66772	1	1	yes	characteristic, direct product factor
80	C₄	—	765	1	no	Sylow
81	C₃	C₅×C₃⋊#66772	1	1	yes	characteristic
82	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₉⋊#66772
commutator, hypocenter	C₅×C₉×C₁₇	C₄×C₅
Frattini	C₃	C₅×C₃⋊#66772
Fitting	C₅²×C₉×C₁₇	C₄
socle	C₃×C₅²×C₁₇	Dic₃
prime radical	C₃×C₅²×D₁₇	D₃
cosocle	C₅×C₉×D₁₇	C₂×C₅
LCS	G ▷ C₅×C₉×C₁₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₁₇	C₄	semidirect
4. C₉⋊#66772	C₅	direct (N × H)
17. C₅×C₉×C₁₇	Dic₅	semidirect
18. C₅×C₉×C₁₇	C₄×C₅	semidirect
24. C₅²×C₁₇	Dic₉	semidirect
32. C₅²×C₉	#595	semidirect
39. C₉×C₁₇	C₅×Dic₅	semidirect
47. C₅×C₁₇	C₅×Dic₉	semidirect
48. C₅×C₁₇	Dic₄₅	semidirect
56. C₅×C₉	C₅×#595	semidirect
57. C₅×C₉	#66772	semidirect
63. C₅²	C₉⋊#595	semidirect
67. C₁₇	C₅×Dic₄₅	semidirect
75. C₉	C₅×#66772	semidirect
78. C₅	C₅×C₉⋊#595	semidirect
79. C₅	C₉⋊#66772	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₉×D₁₇	2
C₅×C₃⋊#66772	3
C₉⋊#66772	5
C₅×C₉⋊#595	5
C₅×Dic₄₅	17

Subgroups — C5×C9⋊#66772 #29505795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉⋊#66772 #29505795