Subgroups — C₃₇×C₇⋊#1039 #39905968

Order 25900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₇×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₇×Dic₃₅	—	5	6	no	maximal
4	C₃₇×#1039	—	7	1	no	maximal, Hall
5	C₂×C₅×C₇×C₃₇	D₅	1	6	yes	—
6	C₂×C₅²×C₃₇	D₇	1	1	yes	characteristic
7	C₅×C₇×C₃₇	Dic₅	1	6	yes	complemented
8	Dic₇×C₃₇	—	25	1	no	Hall
9	C₅²×C₃₇	Dic₇	1	1	yes	characteristic, complemented, Hall
10	Dic₅×C₃₇	—	35	6	no	—
11	C₇⋊#1039	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₇×C₃₇	C₅⋊D₅	1	1	yes	characteristic
13	C₂×C₅×C₃₇	D₃₅	1	6	yes	—
14	C₂×C₅²×C₇	C₂×C₃₇	1	1	yes	characteristic
15	C₇×C₃₇	#1039	1	1	yes	characteristic, complemented, Hall
16	C₅×C₃₇	Dic₃₅	1	6	yes	complemented
17	C₅²×C₇	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
18	C₄×C₃₇	—	175	1	no	Hall
19	Dic₃₅	—	5	6	no	—
20	#1039	—	7	1	no	Hall
21	C₂×C₃₇	C₅⋊D₃₅	1	1	yes	characteristic
22	C₂×C₅×C₇	D₅×C₃₇	1	6	yes	—
23	C₂×C₅²	D₇×C₃₇	1	1	yes	characteristic
24	C₃₇	C₇⋊#1039	1	1	yes	characteristic, direct product factor, Sylow
25	C₅×C₇	Dic₅×C₃₇	1	6	yes	complemented
26	Dic₇	—	25	1	no	Hall
27	C₅²	Dic₇×C₃₇	1	1	yes	characteristic, complemented, Sylow
28	Dic₅	—	35	6	no	—
29	C₂×C₇	C₃₇×C₅⋊D₅	1	1	yes	characteristic
30	C₂×C₅	C₃₇×D₃₅	1	6	yes	—
31	C₇	C₃₇×#1039	1	1	yes	characteristic, complemented, Sylow
32	C₅	C₃₇×Dic₃₅	1	6	yes	complemented
33	C₄	—	175	1	no	Sylow
34	C₂	C₃₇×C₅⋊D₃₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₇	C₅⋊D₃₅
commutator, hypocenter	C₅²×C₇	C₄×C₃₇
Frattini	C₂	C₃₇×C₅⋊D₃₅
Fitting, socle, prime radical	C₂×C₅²×C₇×C₃₇	C₂
cosocle	C₂×C₅²×C₇	C₂×C₃₇
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₂×C₃₇

Complements

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

N	H ≅ G/N	type
2. C₅²×C₇×C₃₇	C₄	semidirect
7. C₅×C₇×C₃₇	Dic₅	semidirect
9. C₅²×C₃₇	Dic₇	semidirect
11. C₇⋊#1039	C₃₇	direct (N × H)
15. C₇×C₃₇	#1039	semidirect
16. C₅×C₃₇	Dic₃₅	semidirect
17. C₅²×C₇	C₄×C₃₇	semidirect
24. C₃₇	C₇⋊#1039	direct (N × H)
25. C₅×C₇	Dic₅×C₃₇	semidirect
27. C₅²	Dic₇×C₃₇	semidirect
31. C₇	C₃₇×#1039	semidirect
32. C₅	C₃₇×Dic₃₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₇×C₃₇	2
C₃₇×Dic₃₅	5
C₃₇×#1039	7
C₇⋊#1039	37

Subgroups — C37×C7⋊#1039 #39905968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×C₇⋊#1039 #39905968