Subgroups — C₃₇×C₇⋊#1042 #39906002

Order 25900.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₅×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₇×C₇⋊AGL(1,𝔽₅)	—	5	1	no	maximal
4	C₃₇×Dic₃₅	—	5	1	no	maximal
5	C₃₇×#1042	—	7	1	no	maximal, Hall
6	C₇×D₅×C₃₇	D₅	1	1	yes	characteristic
7	C₂×C₅×C₇×C₃₇	—	5	1	no	—
8	C₅×D₅×C₃₇	D₇	1	1	yes	characteristic
9	C₅×C₇×C₃₇	—	4	1	no	—
10	C₅×C₇×C₃₇	Dic₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
12	Dic₇×C₃₇	—	25	1	no	Hall
13	C₅²×C₃₇	Dic₇	1	1	yes	characteristic, complemented, Hall
14	AGL(1,𝔽₅)×C₃₇	—	35	1	no	—
15	Dic₅×C₃₇	—	35	1	no	—
16	C₇⋊#1042	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₇×C₃₇	—	5	1	no	—
18	C₂×C₅×C₃₇	—	5	1	no	—
19	D₅×C₃₇	D₃₅	1	1	yes	characteristic
20	C₅×C₇×D₅	C₂×C₃₇	1	1	yes	characteristic
21	C₇×C₃₇	#1042	1	1	yes	characteristic, complemented, Hall
22	C₅×C₃₇	—	4	1	no	—
23	C₅×C₃₇	Dic₃₅	1	1	yes	characteristic, complemented
24	C₅×C₃₇	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
25	C₅²×C₇	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
26	C₄×C₃₇	—	175	1	no	Hall
27	C₇⋊AGL(1,𝔽₅)	—	5	1	no	—
28	Dic₃₅	—	5	1	no	—
29	#1042	—	7	1	no	Hall
30	C₂×C₃₇	—	5	1	no	—
31	C₂×C₅×C₇	—	5	1	no	—
32	C₇×D₅	D₅×C₃₇	1	1	yes	characteristic
33	C₅×D₅	D₇×C₃₇	1	1	yes	characteristic
34	C₃₇	C₇⋊#1042	1	1	yes	characteristic, direct product factor, Sylow
35	C₅×C₇	—	4	1	no	—
36	C₅×C₇	Dic₅×C₃₇	1	1	yes	characteristic, complemented
37	C₅×C₇	AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic, complemented
38	Dic₇	—	25	1	no	Hall
39	C₅²	Dic₇×C₃₇	1	1	yes	characteristic, complemented, Sylow
40	AGL(1,𝔽₅)	—	35	1	no	—
41	Dic₅	—	35	1	no	—
42	C₂×C₇	—	5	1	no	—
43	C₂×C₅	—	5	1	no	—
44	D₅	C₃₇×D₃₅	1	1	yes	characteristic
45	C₇	C₃₇×#1042	1	1	yes	characteristic, complemented, Sylow
46	C₅	—	4	1	no	—
47	C₅	C₃₇×Dic₃₅	1	1	yes	characteristic, complemented
48	C₅	C₃₇×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
49	C₄	—	175	1	no	Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	C₇⋊#1042
commutator, hypocenter	C₅²×C₇	C₄×C₃₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₃₇	C₄
prime radical	C₅×C₇×D₅×C₃₇	C₂
cosocle	C₅×C₇×D₅	C₂×C₃₇
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
2. C₅²×C₇×C₃₇	C₄	semidirect
10. C₅×C₇×C₃₇	Dic₅	semidirect
11. C₅×C₇×C₃₇	AGL(1,𝔽₅)	semidirect
13. C₅²×C₃₇	Dic₇	semidirect
16. C₇⋊#1042	C₃₇	direct (N × H)
21. C₇×C₃₇	#1042	semidirect
23. C₅×C₃₇	Dic₃₅	semidirect
24. C₅×C₃₇	C₇⋊AGL(1,𝔽₅)	semidirect
25. C₅²×C₇	C₄×C₃₇	semidirect
34. C₃₇	C₇⋊#1042	direct (N × H)
36. C₅×C₇	Dic₅×C₃₇	semidirect
37. C₅×C₇	AGL(1,𝔽₅)×C₃₇	semidirect
39. C₅²	Dic₇×C₃₇	semidirect
45. C₇	C₃₇×#1042	semidirect
47. C₅	C₃₇×Dic₃₅	semidirect
48. C₅	C₃₇×C₇⋊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×C₇×D₅×C₃₇	2
C₃₇×C₇⋊AGL(1,𝔽₅)	5
C₃₇×Dic₃₅	5
C₃₇×#1042	7
C₇⋊#1042	37

Subgroups — C37×C7⋊#1042 #39906002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×C₇⋊#1042 #39906002