Subgroups — C₃×#16814882⋊C₃ #45686241

Order 33300.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#16814882	C₃	1	1	yes	maximal, characteristic, complemented
3	#16814882⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅²×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×#10625193⋊C₃	—	5	2	no	maximal
6	C₃×C₃₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
7	C₅⋊D₅×C₃₇⋊C₃	C₂×C₃	1	3	yes	—
8	#16814882	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅×C₃₇⋊C₃	—	5	2	no	—
10	C₃×D₅×C₃₇⋊C₃	—	10	2	no	—
11	C₅²×C₃₇⋊C₃	C₃×C₄	1	3	yes	complemented
12	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented
13	C₃×#10625193	—	5	2	no	—
14	#10625193⋊C₃	—	5	6	no	—
15	C₃₇×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
16	C₃×C₅×C₃₇⋊C₃	—	2	2	no	—
17	C₃×C₅×C₃₇⋊C₃	AGL(1,𝔽₅)	1	2	yes	complemented
18	C₃×Dic₃₇⋊C₃	—	25	1	no	Hall
19	C₃×D₅×C₃₇	—	5	2	no	—
20	C₃×D₅×C₃₇	—	10	2	no	—
21	D₅×C₃₇⋊C₃	—	5	6	no	—
22	D₅×C₃₇⋊C₃	—	10	6	no	—
23	C₅²×C₃₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
24	C₃²×#1044	—	37	1	no	maximal, Hall
25	#10625193	—	5	2	no	—
26	C₂×C₃×C₃₇⋊C₃	—	25	1	no	—
27	C₃×C₅×C₃₇	—	2	2	no	—
28	C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
29	C₅×C₃₇⋊C₃	—	2	6	no	—
30	C₅×C₃₇⋊C₃	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
31	C₃²×C₅⋊D₅	—	37	1	no	—
32	C₃×Dic₃₇	—	25	1	no	—
33	Dic₃₇⋊C₃	—	25	3	no	—
34	D₅×C₃₇	—	5	2	no	—
35	D₅×C₃₇	—	10	2	no	—
36	C₃×C₃₇⋊C₃	#1044	1	1	yes	characteristic, complemented, Hall
37	C₃×#1044	—	37	3	no	—
38	C₃×#1044	—	37	1	no	—
39	C₃²×C₅²	—	37	1	no	Hall
40	C₂×C₃×C₃₇	—	25	1	no	—
41	C₂×C₃₇⋊C₃	—	25	3	no	—
42	C₅×C₃₇	—	2	2	no	—
43	C₅×C₃₇	C₃²×AGL(1,𝔽₅)	1	2	yes	complemented
44	C₃²×AGL(1,𝔽₅)	—	185	2	no	—
45	C₃×C₅⋊D₅	—	37	3	no	—
46	C₃×C₅⋊D₅	D₃₇⋊C₃	1	1	yes	characteristic
47	Dic₃₇	—	25	1	no	Hall
48	C₃×C₃₇	C₃×#1044	1	1	yes	characteristic, complemented
49	C₃₇⋊C₃	C₃×#1044	1	3	yes	complemented
50	#1044	—	37	1	no	Hall
51	C₃²×D₅	—	370	2	no	—
52	C₃²×D₅	—	185	2	no	—
53	C₃×C₅²	—	37	3	no	—
54	C₃×C₅²	Dic₃₇⋊C₃	1	1	yes	characteristic, complemented
55	C₂×C₃₇	—	25	1	no	—
56	C₃×AGL(1,𝔽₅)	—	185	2	no	—
57	C₃×AGL(1,𝔽₅)	—	185	6	no	—
58	C₅⋊D₅	C₃×D₃₇⋊C₃	1	1	yes	characteristic
59	C₃²×C₅	—	37	2	no	—
60	C₃²×C₅	—	74	2	no	—
61	C₃₇	C₃²×#1044	1	1	yes	characteristic, complemented, Sylow
62	C₃²×C₄	—	925	1	no	Hall
63	C₃×D₅	—	5	2	no	—
64	C₃×D₅	—	10	2	no	—
65	C₃×D₅	—	370	6	no	—
66	C₃×D₅	—	185	6	no	—
67	C₅²	C₃×Dic₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
68	AGL(1,𝔽₅)	—	185	2	no	—
69	C₂×C₃²	—	925	1	no	—
70	C₃×C₅	—	2	2	no	—
71	C₃×C₅	—	37	6	no	—
72	C₃×C₅	—	74	6	no	—
73	C₃×C₅	#10625193⋊C₃	1	2	yes	complemented
74	C₃×C₄	—	925	1	no	—
75	C₃×C₄	—	925	3	no	—
76	D₅	—	5	2	no	—
77	D₅	—	10	2	no	—
78	C₃²	—	37	1	no	Sylow
79	C₂×C₃	—	25	1	no	—
80	C₂×C₃	—	925	3	no	—
81	C₅	—	2	2	no	—
82	C₅	C₃×#10625193⋊C₃	1	2	yes	complemented
83	C₄	—	925	1	no	Sylow
84	C₃	—	37	3	no	—
85	C₃	#16814882⋊C₃	1	1	yes	characteristic, direct product factor
86	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#16814882⋊C₃
commutator, hypocenter	C₅²×C₃₇	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₇	C₃×C₄
prime radical	C₃×C₅⋊D₅×C₃₇⋊C₃	C₂
cosocle	C₃₇×C₅⋊D₅	C₂×C₃²
LCS	G ▷ C₅²×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×#16814882	C₃	semidirect
3. #16814882⋊C₃	C₃	direct (N × H)
4. C₃×C₅²×C₃₇⋊C₃	C₄	semidirect
8. #16814882	C₃²	semidirect
11. C₅²×C₃₇⋊C₃	C₃×C₄	semidirect
12. C₃×C₅²×C₃₇	C₃×C₄	semidirect
17. C₃×C₅×C₃₇⋊C₃	AGL(1,𝔽₅)	semidirect
23. C₅²×C₃₇	C₃²×C₄	semidirect
28. C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)	semidirect
30. C₅×C₃₇⋊C₃	C₃×AGL(1,𝔽₅)	semidirect
36. C₃×C₃₇⋊C₃	#1044	semidirect
43. C₅×C₃₇	C₃²×AGL(1,𝔽₅)	semidirect
48. C₃×C₃₇	C₃×#1044	semidirect
49. C₃₇⋊C₃	C₃×#1044	semidirect
54. C₃×C₅²	Dic₃₇⋊C₃	semidirect
61. C₃₇	C₃²×#1044	semidirect
67. C₅²	C₃×Dic₃₇⋊C₃	semidirect
73. C₃×C₅	#10625193⋊C₃	semidirect
82. C₅	C₃×#10625193⋊C₃	semidirect
85. C₃	#16814882⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅⋊D₅×C₃₇⋊C₃	2
C₃×#16814882	3
#16814882⋊C₃	3
C₃×#10625193⋊C₃	5
C₃²×#1044	37

Subgroups — C3×#16814882⋊C3 #45686241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#16814882⋊C₃ #45686241