Subgroups — D₅×D₇×C₁₃₇ #34062811

Order 19180.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₅×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₅×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₇×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₇×C₁₃₇	—	5	1	no	maximal, Hall
6	C₂×D₅×C₁₃₇	—	7	1	no	maximal, Hall
7	C₂×C₇×C₁₃₇	—	5	1	no	—
8	D₇×C₁₃₇	—	5	1	no	—
9	D₇×C₁₃₇	D₅	1	1	yes	characteristic, direct product factor
10	C₂×C₅×C₁₃₇	—	7	1	no	—
11	D₅×C₁₃₇	—	7	1	no	—
12	D₅×C₁₃₇	D₇	1	1	yes	characteristic, direct product factor
13	C₇×C₁₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₃₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₁₃₇	—	35	1	no	Hall
16	C₂×C₁₃₇	—	5	1	no	—
17	C₂×C₁₃₇	—	7	1	no	—
18	C₂×C₁₃₇	—	35	1	no	—
19	D₅×D₇	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₁₃₇	D₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
21	D₃₅	C₂×C₁₃₇	1	1	yes	characteristic, complemented
22	C₅×D₇	C₂×C₁₃₇	1	1	yes	characteristic, complemented
23	C₇×D₅	C₂×C₁₃₇	1	1	yes	characteristic, complemented
24	C₅×C₇	C₂²×C₁₃₇	1	1	yes	characteristic, complemented, Hall
25	C₂×D₇	—	5	1	no	Hall
26	C₂×D₅	—	7	1	no	Hall
27	C₂×C₇	—	5	1	no	—
28	D₇	—	5	1	no	—
29	D₇	D₅×C₁₃₇	1	1	yes	characteristic, direct product factor
30	C₂×C₅	—	7	1	no	—
31	D₅	—	7	1	no	—
32	D₅	D₇×C₁₃₇	1	1	yes	characteristic, direct product factor
33	C₇	C₂×D₅×C₁₃₇	1	1	yes	characteristic, complemented, Sylow
34	C₅	C₂×D₇×C₁₃₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	35	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	7	1	no	—
38	C₂	—	35	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃₇	D₅×D₇
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₁₃₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃₇	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₁₃₇

Complements

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

N	H ≅ G/N	type
1. D₃₅×C₁₃₇	C₂	semidirect
2. C₇×D₅×C₁₃₇	C₂	semidirect
3. C₅×D₇×C₁₃₇	C₂	semidirect
4. C₅×C₇×C₁₃₇	C₂²	semidirect
9. D₇×C₁₃₇	D₅	direct (N × H)
12. D₅×C₁₃₇	D₇	direct (N × H)
13. C₇×C₁₃₇	C₂×D₅	semidirect
14. C₅×C₁₃₇	C₂×D₇	semidirect
19. D₅×D₇	C₁₃₇	direct (N × H)
20. C₁₃₇	D₅×D₇	direct (N × H)
21. D₃₅	C₂×C₁₃₇	semidirect
22. C₅×D₇	C₂×C₁₃₇	semidirect
23. C₇×D₅	C₂×C₁₃₇	semidirect
24. C₅×C₇	C₂²×C₁₃₇	semidirect
29. D₇	D₅×C₁₃₇	direct (N × H)
32. D₅	D₇×C₁₃₇	direct (N × H)
33. C₇	C₂×D₅×C₁₃₇	semidirect
34. C₅	C₂×D₇×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
D₃₅×C₁₃₇	2
C₇×D₅×C₁₃₇	2
C₅×D₇×C₁₃₇	2
C₂×D₇×C₁₃₇	5
C₂×D₅×C₁₃₇	7
D₅×D₇	137

Subgroups — D5×D7×C137 #34062811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₇×C₁₃₇ #34062811