Subgroups — C₉×C₃₇×#1035 #45685752

Order 33300.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₇×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₇×#1035	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×AGL(1,𝔽₅)×C₃₇	—	5	1	no	maximal
5	C₃×C₃₇×D₂₅	C₂×C₃	1	1	yes	characteristic
6	C₃₇×#1035	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×D₅×C₃₇	—	5	1	no	—
8	C₃×C₂₅×C₃₇	C₃×C₄	1	1	yes	characteristic
9	C₃×AGL(1,𝔽₅)×C₃₇	—	5	1	no	—
10	C₃₇×D₂₅	C₂×C₉	1	1	yes	characteristic
11	C₅×C₉×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic
12	C₄×C₉×C₃₇	—	25	1	no	Hall
13	C₃×D₅×C₃₇	—	5	1	no	—
14	C₂₅×C₃₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
15	C₉×#1035	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	AGL(1,𝔽₅)×C₃₇	—	5	1	no	—
17	C₂×C₉×C₃₇	—	25	1	no	—
18	C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
19	C₉×D₂₅	C₂×C₃₇	1	1	yes	characteristic
20	C₃×C₄×C₃₇	—	25	1	no	—
21	D₅×C₃₇	—	5	1	no	—
22	C₉×C₃₇	#1035	1	1	yes	characteristic, direct product factor, Hall
23	C₃×#1035	C₃×C₃₇	1	1	yes	characteristic
24	C₉×C₂₅	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₃₇	—	25	1	no	—
26	C₅×C₃₇	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₉×AGL(1,𝔽₅)	—	5	1	no	—
28	C₃×D₂₅	C₂×C₃×C₃₇	1	1	yes	characteristic
29	C₄×C₃₇	—	25	1	no	Hall
30	C₃×C₃₇	C₃×#1035	1	1	yes	characteristic
31	#1035	C₉×C₃₇	1	1	yes	characteristic, direct product factor, Hall
32	C₉×D₅	—	5	1	no	—
33	C₃×C₂₅	C₃×C₄×C₃₇	1	1	yes	characteristic
34	C₂×C₃₇	—	25	1	no	—
35	C₃×AGL(1,𝔽₅)	—	5	1	no	—
36	D₂₅	C₂×C₉×C₃₇	1	1	yes	characteristic
37	C₅×C₉	AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic
38	C₃₇	C₉×#1035	1	1	yes	characteristic, direct product factor, Sylow
39	C₄×C₉	—	25	1	no	Hall
40	C₃×D₅	—	5	1	no	—
41	C₂₅	C₄×C₉×C₃₇	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,𝔽₅)	—	5	1	no	—
43	C₂×C₉	—	25	1	no	—
44	C₃×C₅	C₃×AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic
45	C₃×C₄	—	25	1	no	—
46	D₅	—	5	1	no	—
47	C₉	C₃₇×#1035	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₃	—	25	1	no	—
49	C₅	C₉×AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic
50	C₄	—	25	1	no	Sylow
51	C₃	C₃×C₃₇×#1035	1	1	yes	characteristic
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₃₇	#1035
commutator, hypocenter	C₂₅	C₄×C₉×C₃₇
Frattini	C₃×C₅	C₃×AGL(1,𝔽₅)×C₃₇
Fitting	C₉×C₂₅×C₃₇	C₄
socle	C₃×C₅×C₃₇	C₃×AGL(1,𝔽₅)
prime radical	C₃×C₃₇×D₂₅	C₂×C₃
cosocle	C₃×D₂₅	C₂×C₃×C₃₇
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₉×C₃₇

Complements

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

N	H ≅ G/N	type
3. C₉×C₂₅×C₃₇	C₄	semidirect
6. C₃₇×#1035	C₉	direct (N × H)
14. C₂₅×C₃₇	C₄×C₉	semidirect
15. C₉×#1035	C₃₇	direct (N × H)
22. C₉×C₃₇	#1035	direct (N × H)
24. C₉×C₂₅	C₄×C₃₇	semidirect
31. #1035	C₉×C₃₇	direct (N × H)
38. C₃₇	C₉×#1035	direct (N × H)
41. C₂₅	C₄×C₉×C₃₇	semidirect
47. C₉	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
C₉×C₃₇×D₂₅	2
C₃×C₃₇×#1035	3
C₉×AGL(1,𝔽₅)×C₃₇	5
C₉×#1035	37

Subgroups — C9×C37×#1035 #45685752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₃₇×#1035 #45685752