Subgroups — C₉⋊#16814881 #45686036

Order 33300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₅⋊D₁₈₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16814881	—	3	1	no	maximal
3	C₅²×C₉×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10625192	—	5	1	no	maximal
5	C₉⋊#10625191	—	5	1	no	maximal
6	C₃×C₅⋊D₁₈₅	D₃	1	1	yes	characteristic
7	#16814881	—	9	1	no	Hall
8	C₉×D₁₈₅	—	5	1	no	—
9	C₉×D₁₈₅	—	5	1	no	—
10	C₉×D₁₈₅	—	10	2	no	—
11	C₃×C₅²×C₃₇	Dic₃	1	1	yes	characteristic
12	C₃⋊#10625192	—	15	1	no	—
13	C₃⋊#10625191	—	15	1	no	—
14	C₅⋊D₁₈₅	D₉	1	1	yes	characteristic
15	C₅×C₉×C₃₇	—	2	2	no	—
16	C₅×C₉×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
17	C₅×C₉×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
18	C₉⋊#3866	—	25	1	no	Hall
19	C₃×D₁₈₅	—	5	1	no	—
20	C₃×D₁₈₅	—	5	1	no	—
21	C₃×D₁₈₅	—	10	2	no	—
22	C₅²×C₃₇	Dic₉	1	1	yes	characteristic, complemented, Hall
23	C₉⋊#1044	—	37	1	no	maximal, Hall
24	#10625192	—	45	1	no	—
25	#10625191	—	45	1	no	—
26	C₉×D₃₇	—	25	1	no	—
27	C₃×C₅×C₃₇	—	2	2	no	—
28	C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
29	C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
30	C₉×C₅⋊D₅	—	37	1	no	—
31	C₃⋊#3866	—	75	1	no	—
32	D₁₈₅	—	5	1	no	—
33	D₁₈₅	—	5	1	no	—
34	D₁₈₅	—	10	2	no	—
35	C₉×C₃₇	#1044	1	1	yes	characteristic, complemented, Hall
36	C₃⋊#1044	—	111	1	no	—
37	C₅²×C₉	#3866	1	1	yes	characteristic, complemented, Hall
38	C₃×D₃₇	—	25	1	no	—
39	C₅×C₃₇	—	2	2	no	—
40	C₅×C₃₇	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
41	C₅×C₃₇	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
42	C₉⋊AGL(1,𝔽₅)	—	185	1	no	—
43	C₉⋊AGL(1,𝔽₅)	—	185	1	no	—
44	C₃×C₅⋊D₅	—	37	1	no	—
45	#3866	—	225	1	no	Hall
46	C₃×C₃₇	C₃⋊#1044	1	1	yes	characteristic
47	#1044	—	333	1	no	Hall
48	C₉×D₅	—	370	2	no	—
49	C₉×D₅	—	185	1	no	—
50	C₉×D₅	—	185	1	no	—
51	C₃×C₅²	C₃⋊#3866	1	1	yes	characteristic
52	D₃₇	—	25	1	no	—
53	ΓL(1,𝔽₁₆)	—	555	1	no	—
54	ΓL(1,𝔽₁₆)	—	555	1	no	—
55	C₅⋊D₅	—	37	1	no	—
56	C₅×C₉	—	2	2	no	—
57	C₅×C₉	#10625191	1	1	yes	characteristic, complemented
58	C₅×C₉	#10625192	1	1	yes	characteristic, complemented
59	C₃₇	C₉⋊#1044	1	1	yes	characteristic, complemented, Sylow
60	Dic₉	—	925	1	no	Hall
61	C₃×D₅	—	370	2	no	—
62	C₃×D₅	—	185	1	no	—
63	C₃×D₅	—	185	1	no	—
64	C₅²	C₉⋊#3866	1	1	yes	characteristic, complemented, Sylow
65	AGL(1,𝔽₅)	—	1665	1	no	—
66	AGL(1,𝔽₅)	—	1665	1	no	—
67	C₂×C₉	—	925	1	no	—
68	C₃×C₅	—	2	2	no	—
69	C₃×C₅	C₃⋊#10625191	1	1	yes	characteristic
70	C₃×C₅	C₃⋊#10625192	1	1	yes	characteristic
71	Dic₃	—	2775	1	no	—
72	D₅	—	370	2	no	—
73	D₅	—	185	1	no	—
74	D₅	—	185	1	no	—
75	C₉	#16814881	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	925	1	no	—
77	C₅	—	2	2	no	—
78	C₅	C₉⋊#10625191	1	1	yes	characteristic, complemented
79	C₅	C₉⋊#10625192	1	1	yes	characteristic, complemented
80	C₄	—	8325	1	no	Sylow
81	C₃	C₃⋊#16814881	1	1	yes	characteristic
82	C₂	—	925	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₉×C₃₇	C₄
Frattini	C₃	C₃⋊#16814881
socle	C₃×C₅²×C₃₇	Dic₃
prime radical	C₃×C₅⋊D₁₈₅	D₃
cosocle	C₉×C₅⋊D₁₈₅	C₂
LCS	G ▷ C₅²×C₉×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₃₇	C₄	semidirect
16. C₅×C₉×C₃₇	AGL(1,𝔽₅)	semidirect
17. C₅×C₉×C₃₇	AGL(1,𝔽₅)	semidirect
22. C₅²×C₃₇	Dic₉	semidirect
35. C₉×C₃₇	#1044	semidirect
37. C₅²×C₉	#3866	semidirect
40. C₅×C₃₇	C₉⋊AGL(1,𝔽₅)	semidirect
41. C₅×C₃₇	C₉⋊AGL(1,𝔽₅)	semidirect
57. C₅×C₉	#10625191	semidirect
58. C₅×C₉	#10625192	semidirect
59. C₃₇	C₉⋊#1044	semidirect
64. C₅²	C₉⋊#3866	semidirect
75. C₉	#16814881	semidirect
78. C₅	C₉⋊#10625191	semidirect
79. C₅	C₉⋊#10625192	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₅⋊D₁₈₅	2
C₃⋊#16814881	3
C₉⋊#10625192	5
C₉⋊#10625191	5
C₉⋊#1044	37

Subgroups — C9⋊#16814881 #45686036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#16814881 #45686036