Subgroups — C₃×C₃₇×#1043⋊C₃ #45686209

Order 33300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₇×#1043	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#1043⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₃₇×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₃₇×(C₅⋊D₅)⋊C₃	C₂×C₃	1	3	yes	—
7	C₃₇×#1043	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃₇×C₅²⋊C₃	C₃×C₄	1	3	yes	complemented
9	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented
10	C₃×AGL(1,𝔽₅)×C₃₇	—	15	2	no	—
11	C₃₇×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
12	C₃²×C₄×C₃₇	—	25	1	no	maximal, Hall
13	C₃×D₅×C₃₇	—	15	2	no	—
14	C₅²×C₃₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₃×#1043⋊C₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	AGL(1,𝔽₅)×C₃₇	—	15	2	no	—
17	C₂×C₃²×C₃₇	—	25	1	no	—
18	C₃×C₅×C₃₇	—	3	2	no	—
19	C₃×(C₅⋊D₅)⋊C₃	C₂×C₃₇	1	1	yes	characteristic
20	C₃×C₄×C₃₇	—	25	1	no	—
21	C₃×C₄×C₃₇	—	25	3	no	—
22	D₅×C₃₇	—	15	2	no	—
23	C₃²×C₃₇	—	25	1	no	Hall
24	C₃×#1043	C₃×C₃₇	1	1	yes	characteristic, complemented
25	#1043⋊C₃	C₃×C₃₇	1	3	yes	direct product factor
26	C₃×C₅²⋊C₃	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₃₇	—	25	3	no	—
28	C₂×C₃×C₃₇	—	25	1	no	—
29	C₅×C₃₇	—	3	2	no	—
30	C₃×C₅⋊D₅	C₂×C₃×C₃₇	1	1	yes	characteristic
31	(C₅⋊D₅)⋊C₃	C₂×C₃×C₃₇	1	3	yes	—
32	C₄×C₃₇	—	25	1	no	Hall
33	C₃×C₃₇	—	25	3	no	—
34	C₃×C₃₇	#1043⋊C₃	1	1	yes	characteristic, direct product factor
35	#1043	C₃²×C₃₇	1	1	yes	characteristic, complemented, Hall
36	C₃×C₅²	C₃×C₄×C₃₇	1	1	yes	characteristic, complemented
37	C₅²⋊C₃	C₃×C₄×C₃₇	1	3	yes	complemented
38	C₂×C₃₇	—	25	1	no	—
39	C₃×AGL(1,𝔽₅)	—	15	2	no	—
40	C₅⋊D₅	C₂×C₃²×C₃₇	1	1	yes	characteristic
41	C₃₇	C₃×#1043⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₃²×C₄	—	25	1	no	Hall
43	C₃×D₅	—	15	2	no	—
44	C₅²	C₃²×C₄×C₃₇	1	1	yes	characteristic, complemented, Sylow
45	AGL(1,𝔽₅)	—	15	2	no	—
46	C₂×C₃²	—	25	1	no	—
47	C₃×C₅	—	3	2	no	—
48	C₃×C₄	—	25	1	no	—
49	C₃×C₄	—	25	3	no	—
50	D₅	—	15	2	no	—
51	C₃²	—	25	1	no	Sylow
52	C₂×C₃	—	25	3	no	—
53	C₂×C₃	—	25	1	no	—
54	C₅	—	3	2	no	—
55	C₄	—	25	1	no	Sylow
56	C₃	—	25	3	no	—
57	C₃	C₃₇×#1043⋊C₃	1	1	yes	characteristic, direct product factor
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₃₇	#1043⋊C₃
commutator, hypocenter	C₅²	C₃²×C₄×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₇	C₃×C₄
prime radical	C₃×C₃₇×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₅⋊D₅	C₂×C₃²×C₃₇
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₃₇

Complements

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

N	H ≅ G/N	type
2. C₃×C₃₇×#1043	C₃	semidirect
3. C₃₇×#1043⋊C₃	C₃	direct (N × H)
4. C₃×C₃₇×C₅²⋊C₃	C₄	semidirect
7. C₃₇×#1043	C₃²	semidirect
8. C₃₇×C₅²⋊C₃	C₃×C₄	semidirect
9. C₃×C₅²×C₃₇	C₃×C₄	semidirect
14. C₅²×C₃₇	C₃²×C₄	semidirect
15. C₃×#1043⋊C₃	C₃₇	direct (N × H)
24. C₃×#1043	C₃×C₃₇	semidirect
25. #1043⋊C₃	C₃×C₃₇	direct (N × H)
26. C₃×C₅²⋊C₃	C₄×C₃₇	semidirect
34. C₃×C₃₇	#1043⋊C₃	direct (N × H)
35. #1043	C₃²×C₃₇	semidirect
36. C₃×C₅²	C₃×C₄×C₃₇	semidirect
37. C₅²⋊C₃	C₃×C₄×C₃₇	semidirect
41. C₃₇	C₃×#1043⋊C₃	direct (N × H)
44. C₅²	C₃²×C₄×C₃₇	semidirect
57. C₃	C₃₇×#1043⋊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×C₃₇×(C₅⋊D₅)⋊C₃	2
C₃×C₃₇×#1043	3
C₃₇×#1043⋊C₃	3
C₃²×C₄×C₃₇	25
C₃×#1043⋊C₃	37

Subgroups — C3×C37×#1043⋊C3 #45686209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₇×#1043⋊C₃ #45686209