Subgroups — C₉×#16814886 #45686013

Order 33300.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×D₅×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃×#16814886	C₃	1	1	yes	maximal, characteristic
3	C₅²×C₉×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×#10625193	—	5	1	no	maximal
5	C₉×Dic₁₈₅	—	5	1	no	maximal
6	C₃×C₅×D₅×C₃₇	C₂×C₃	1	1	yes	characteristic
7	#16814886	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₉×D₅×C₃₇	D₅	1	1	yes	characteristic
9	C₂×C₅×C₉×C₃₇	—	5	1	no	—
10	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic
11	C₃×#10625193	—	5	1	no	—
12	C₃×Dic₁₈₅	—	5	1	no	—
13	C₅×D₅×C₃₇	C₂×C₉	1	1	yes	characteristic
14	C₅×C₉×C₃₇	—	4	1	no	—
15	C₅×C₉×C₃₇	Dic₅	1	1	yes	characteristic, complemented
16	C₅×C₉×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
17	C₉×Dic₃₇	—	25	1	no	Hall
18	C₂×C₃×C₅×C₃₇	—	5	1	no	—
19	C₃×D₅×C₃₇	C₃×D₅	1	1	yes	characteristic
20	C₅²×C₃₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
21	C₉×#1042	—	37	1	no	maximal, Hall
22	#10625193	—	5	1	no	—
23	Dic₁₈₅	—	5	1	no	—
24	C₂×C₉×C₃₇	—	5	1	no	—
25	C₃×C₅×C₃₇	—	4	1	no	—
26	C₃×C₅×C₃₇	C₃×Dic₅	1	1	yes	characteristic
27	C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₅×C₉×D₅	D₃₇	1	1	yes	characteristic
29	C₃×Dic₃₇	—	25	1	no	—
30	C₂×C₅×C₃₇	—	5	1	no	—
31	D₅×C₃₇	C₉×D₅	1	1	yes	characteristic
32	C₉×C₃₇	#1042	1	1	yes	characteristic, complemented, Hall
33	C₃×#1042	—	37	1	no	—
34	C₅²×C₉	Dic₃₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₃₇	—	5	1	no	—
36	C₅×C₃₇	—	4	1	no	—
37	C₅×C₃₇	C₉×Dic₅	1	1	yes	characteristic, complemented
38	C₅×C₃₇	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
39	C₉×AGL(1,𝔽₅)	—	185	1	no	—
40	C₉×Dic₅	—	185	1	no	—
41	C₃×C₅×D₅	C₃×D₃₇	1	1	yes	characteristic
42	Dic₃₇	—	25	1	no	Hall
43	C₃×C₃₇	C₃×#1042	1	1	yes	characteristic
44	#1042	—	37	1	no	Hall
45	C₂×C₅×C₉	—	5	1	no	—
46	C₉×D₅	D₁₈₅	1	1	yes	characteristic
47	C₃×C₅²	C₃×Dic₃₇	1	1	yes	characteristic
48	C₂×C₃₇	—	5	1	no	—
49	C₃×AGL(1,𝔽₅)	—	185	1	no	—
50	C₃×Dic₅	—	185	1	no	—
51	C₅×D₅	C₉×D₃₇	1	1	yes	characteristic
52	C₅×C₉	—	4	1	no	—
53	C₅×C₉	Dic₁₈₅	1	1	yes	characteristic, complemented
54	C₅×C₉	#10625193	1	1	yes	characteristic, complemented
55	C₃₇	C₉×#1042	1	1	yes	characteristic, complemented, Sylow
56	C₄×C₉	—	925	1	no	Hall
57	C₂×C₃×C₅	—	5	1	no	—
58	C₃×D₅	C₃×D₁₈₅	1	1	yes	characteristic
59	C₅²	C₉×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
60	AGL(1,𝔽₅)	—	185	1	no	—
61	Dic₅	—	185	1	no	—
62	C₂×C₉	—	5	1	no	—
63	C₃×C₅	—	4	1	no	—
64	C₃×C₅	C₃×Dic₁₈₅	1	1	yes	characteristic
65	C₃×C₅	C₃×#10625193	1	1	yes	characteristic
66	C₃×C₄	—	925	1	no	—
67	C₂×C₅	—	5	1	no	—
68	D₅	C₉×D₁₈₅	1	1	yes	characteristic
69	C₉	#16814886	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	5	1	no	—
71	C₅	—	4	1	no	—
72	C₅	C₉×Dic₁₈₅	1	1	yes	characteristic, complemented
73	C₅	C₉×#10625193	1	1	yes	characteristic, complemented
74	C₄	—	925	1	no	Sylow
75	C₃	C₃×#16814886	1	1	yes	characteristic
76	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₉	#16814886
commutator, hypocenter	C₅²×C₃₇	C₄×C₉
Frattini	C₃	C₃×#16814886
Fitting	C₅²×C₉×C₃₇	C₄
socle	C₃×C₅²×C₃₇	C₃×C₄
prime radical, cosocle	C₃×C₅×D₅×C₃₇	C₂×C₃
LCS	G ▷ C₅²×C₃₇
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₃₇	C₄	semidirect
7. #16814886	C₉	direct (N × H)
15. C₅×C₉×C₃₇	Dic₅	semidirect
16. C₅×C₉×C₃₇	AGL(1,𝔽₅)	semidirect
20. C₅²×C₃₇	C₄×C₉	semidirect
32. C₉×C₃₇	#1042	semidirect
34. C₅²×C₉	Dic₃₇	semidirect
37. C₅×C₃₇	C₉×Dic₅	semidirect
38. C₅×C₃₇	C₉×AGL(1,𝔽₅)	semidirect
53. C₅×C₉	Dic₁₈₅	semidirect
54. C₅×C₉	#10625193	semidirect
55. C₃₇	C₉×#1042	semidirect
59. C₅²	C₉×Dic₃₇	semidirect
69. C₉	#16814886	direct (N × H)
72. C₅	C₉×Dic₁₈₅	semidirect
73. C₅	C₉×#10625193	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×D₅×C₃₇	2
C₃×#16814886	3
C₉×#10625193	5
C₉×Dic₁₈₅	5
C₉×#1042	37

Subgroups — C9×#16814886 #45686013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#16814886 #45686013