Subgroups — C₃²×C₃₇×#1035 #45685873

Order 33300.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₇×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₇×#1035	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₂₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×AGL(1,𝔽₅)×C₃₇	—	5	1	no	maximal
5	C₃×C₃₇×D₂₅	C₂×C₃	1	4	yes	—
6	C₃₇×#1035	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×D₅×C₃₇	—	5	1	no	—
8	C₃×C₂₅×C₃₇	C₃×C₄	1	4	yes	complemented
9	C₃×AGL(1,𝔽₅)×C₃₇	—	5	4	no	—
10	C₃₇×D₂₅	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₅×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic
12	C₃²×C₄×C₃₇	—	25	1	no	Hall
13	C₃×D₅×C₃₇	—	5	4	no	—
14	C₂₅×C₃₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₃²×#1035	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	AGL(1,𝔽₅)×C₃₇	—	5	1	no	—
17	C₂×C₃²×C₃₇	—	25	1	no	—
18	C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)	1	4	yes	—
19	C₃²×D₂₅	C₂×C₃₇	1	1	yes	characteristic
20	C₃×C₄×C₃₇	—	25	4	no	—
21	D₅×C₃₇	—	5	1	no	—
22	C₃²×C₃₇	#1035	1	1	yes	characteristic, direct product factor, Hall
23	C₃×#1035	C₃×C₃₇	1	4	yes	direct product factor
24	C₃²×C₂₅	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₃₇	—	25	4	no	—
26	C₅×C₃₇	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₃²×AGL(1,𝔽₅)	—	5	1	no	—
28	C₃×D₂₅	C₂×C₃×C₃₇	1	4	yes	—
29	C₄×C₃₇	—	25	1	no	Hall
30	C₃×C₃₇	C₃×#1035	1	4	yes	direct product factor
31	#1035	C₃²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
32	C₃²×D₅	—	5	1	no	—
33	C₃×C₂₅	C₃×C₄×C₃₇	1	4	yes	complemented
34	C₂×C₃₇	—	25	1	no	—
35	C₃×AGL(1,𝔽₅)	—	5	4	no	—
36	D₂₅	C₂×C₃²×C₃₇	1	1	yes	characteristic
37	C₃²×C₅	AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic
38	C₃₇	C₃²×#1035	1	1	yes	characteristic, direct product factor, Sylow
39	C₃²×C₄	—	25	1	no	Hall
40	C₃×D₅	—	5	4	no	—
41	C₂₅	C₃²×C₄×C₃₇	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,𝔽₅)	—	5	1	no	—
43	C₂×C₃²	—	25	1	no	—
44	C₃×C₅	C₃×AGL(1,𝔽₅)×C₃₇	1	4	yes	—
45	C₃×C₄	—	25	4	no	—
46	D₅	—	5	1	no	—
47	C₃²	C₃₇×#1035	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₃	—	25	4	no	—
49	C₅	C₃²×AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic
50	C₄	—	25	1	no	Sylow
51	C₃	C₃×C₃₇×#1035	1	4	yes	direct product factor
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₃₇	#1035
commutator, hypocenter	C₂₅	C₃²×C₄×C₃₇
Frattini	C₅	C₃²×AGL(1,𝔽₅)×C₃₇
Fitting	C₃²×C₂₅×C₃₇	C₄
socle	C₃²×C₅×C₃₇	AGL(1,𝔽₅)
prime radical	C₃²×C₃₇×D₂₅	C₂
cosocle	D₂₅	C₂×C₃²×C₃₇
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃²×C₃₇

Complements

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

N	H ≅ G/N	type
2. C₃×C₃₇×#1035	C₃	direct (N × H)
3. C₃²×C₂₅×C₃₇	C₄	semidirect
6. C₃₇×#1035	C₃²	direct (N × H)
8. C₃×C₂₅×C₃₇	C₃×C₄	semidirect
14. C₂₅×C₃₇	C₃²×C₄	semidirect
15. C₃²×#1035	C₃₇	direct (N × H)
22. C₃²×C₃₇	#1035	direct (N × H)
23. C₃×#1035	C₃×C₃₇	direct (N × H)
24. C₃²×C₂₅	C₄×C₃₇	semidirect
30. C₃×C₃₇	C₃×#1035	direct (N × H)
31. #1035	C₃²×C₃₇	direct (N × H)
33. C₃×C₂₅	C₃×C₄×C₃₇	semidirect
38. C₃₇	C₃²×#1035	direct (N × H)
41. C₂₅	C₃²×C₄×C₃₇	semidirect
47. C₃²	C₃₇×#1035	direct (N × H)
51. C₃	C₃×C₃₇×#1035	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₃₇×D₂₅	2
C₃×C₃₇×#1035	3
C₃²×AGL(1,𝔽₅)×C₃₇	5
C₃²×#1035	37

Subgroups — C32×C37×#1035 #45685873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₃₇×#1035 #45685873