Subgroups — C₃₇×C₉⋊#1042 #45686038

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	C₃₇×C₃⋊#1042	—	3	1	no	maximal
3	C₅²×C₉×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₇×C₉⋊AGL(1,𝔽₅)	—	5	1	no	maximal
5	C₃₇×Dic₄₅	—	5	1	no	maximal
6	C₃×C₅×D₅×C₃₇	D₃	1	1	yes	characteristic
7	C₃₇×#1042	—	9	1	no	Hall
8	C₉×D₅×C₃₇	D₅	1	1	yes	characteristic
9	C₂×C₅×C₉×C₃₇	—	5	1	no	—
10	C₃×C₅²×C₃₇	Dic₃	1	1	yes	characteristic
11	C₃₇×ΓL(1,𝔽₁₆)	—	15	1	no	—
12	C₃₇×Dic₁₅	—	15	1	no	—
13	C₅×D₅×C₃₇	D₉	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	Dic₉×C₃₇	—	25	1	no	Hall
18	C₂×C₃×C₅×C₃₇	—	5	1	no	—
19	C₃×D₅×C₃₇	D₁₅	1	1	yes	characteristic
20	C₅²×C₃₇	Dic₉	1	1	yes	characteristic, complemented, Hall
21	C₉⋊#1042	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
22	AGL(1,𝔽₅)×C₃₇	—	45	1	no	—
23	Dic₅×C₃₇	—	45	1	no	—
24	C₂×C₉×C₃₇	—	5	1	no	—
25	C₃×C₅×C₃₇	—	4	1	no	—
26	C₃×C₅×C₃₇	Dic₁₅	1	1	yes	characteristic
27	C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
28	C₅×C₉×D₅	C₂×C₃₇	1	1	yes	characteristic
29	Dic₃×C₃₇	—	75	1	no	—
30	C₂×C₅×C₃₇	—	5	1	no	—
31	D₅×C₃₇	D₄₅	1	1	yes	characteristic
32	C₉×C₃₇	#1042	1	1	yes	characteristic, complemented, Hall
33	C₃⋊#1042	—	3	1	no	—
34	C₅²×C₉	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₃₇	—	5	1	no	—
36	C₅×C₃₇	—	4	1	no	—
37	C₅×C₃₇	Dic₄₅	1	1	yes	characteristic, complemented
38	C₅×C₃₇	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
39	C₉⋊AGL(1,𝔽₅)	—	5	1	no	—
40	Dic₄₅	—	5	1	no	—
41	C₃×C₅×D₅	D₃×C₃₇	1	1	yes	characteristic
42	C₄×C₃₇	—	225	1	no	Hall
43	C₃×C₃₇	C₃⋊#1042	1	1	yes	characteristic
44	#1042	—	9	1	no	Hall
45	C₂×C₅×C₉	—	5	1	no	—
46	C₉×D₅	D₅×C₃₇	1	1	yes	characteristic
47	C₃×C₅²	Dic₃×C₃₇	1	1	yes	characteristic
48	C₂×C₃₇	—	5	1	no	—
49	ΓL(1,𝔽₁₆)	—	15	1	no	—
50	Dic₁₅	—	15	1	no	—
51	C₅×D₅	D₉×C₃₇	1	1	yes	characteristic
52	C₅×C₉	—	4	1	no	—
53	C₅×C₉	Dic₅×C₃₇	1	1	yes	characteristic, complemented
54	C₅×C₉	AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic, complemented
55	C₃₇	C₉⋊#1042	1	1	yes	characteristic, direct product factor, Sylow
56	Dic₉	—	25	1	no	Hall
57	C₂×C₃×C₅	—	5	1	no	—
58	C₃×D₅	D₁₅×C₃₇	1	1	yes	characteristic
59	C₅²	Dic₉×C₃₇	1	1	yes	characteristic, complemented, Sylow
60	AGL(1,𝔽₅)	—	45	1	no	—
61	Dic₅	—	45	1	no	—
62	C₂×C₉	—	5	1	no	—
63	C₃×C₅	—	4	1	no	—
64	C₃×C₅	C₃₇×Dic₁₅	1	1	yes	characteristic
65	C₃×C₅	C₃₇×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
66	Dic₃	—	75	1	no	—
67	C₂×C₅	—	5	1	no	—
68	D₅	C₃₇×D₄₅	1	1	yes	characteristic
69	C₉	C₃₇×#1042	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	5	1	no	—
71	C₅	—	4	1	no	—
72	C₅	C₃₇×Dic₄₅	1	1	yes	characteristic, complemented
73	C₅	C₃₇×C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
74	C₄	—	225	1	no	Sylow
75	C₃	C₃₇×C₃⋊#1042	1	1	yes	characteristic
76	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	C₉⋊#1042
commutator, hypocenter	C₅²×C₉	C₄×C₃₇
Frattini	C₃	C₃₇×C₃⋊#1042
Fitting	C₅²×C₉×C₃₇	C₄
socle	C₃×C₅²×C₃₇	Dic₃
prime radical	C₃×C₅×D₅×C₃₇	D₃
cosocle	C₅×C₉×D₅	C₂×C₃₇
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₃₇	C₄	semidirect
15. C₅×C₉×C₃₇	Dic₅	semidirect
16. C₅×C₉×C₃₇	AGL(1,𝔽₅)	semidirect
20. C₅²×C₃₇	Dic₉	semidirect
21. C₉⋊#1042	C₃₇	direct (N × H)
32. C₉×C₃₇	#1042	semidirect
34. C₅²×C₉	C₄×C₃₇	semidirect
37. C₅×C₃₇	Dic₄₅	semidirect
38. C₅×C₃₇	C₉⋊AGL(1,𝔽₅)	semidirect
53. C₅×C₉	Dic₅×C₃₇	semidirect
54. C₅×C₉	AGL(1,𝔽₅)×C₃₇	semidirect
55. C₃₇	C₉⋊#1042	direct (N × H)
59. C₅²	Dic₉×C₃₇	semidirect
69. C₉	C₃₇×#1042	semidirect
72. C₅	C₃₇×Dic₄₅	semidirect
73. C₅	C₃₇×C₉⋊AGL(1,𝔽₅)	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
C₃₇×C₃⋊#1042	3
C₃₇×C₉⋊AGL(1,𝔽₅)	5
C₃₇×Dic₄₅	5
C₉⋊#1042	37

Subgroups — C37×C9⋊#1042 #45686038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×C₉⋊#1042 #45686038