Subgroups — D₃₉×D₁₃₁ #35205455

Order 20436.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₉×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₃₁	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₇₀₃	—	3	1	no	—
7	C₁₃×D₁₃₁	D₃	1	1	yes	characteristic, complemented
8	D₁₃×C₁₃₁	—	3	1	no	—
9	C₁₃×C₁₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₁₃₁	—	13	1	no	maximal, Hall
11	D₃₉₃	—	13	1	no	—
12	C₃×D₁₃₁	D₁₃	1	1	yes	characteristic, complemented
13	D₃×C₁₃₁	—	13	1	no	—
14	C₂×D₁₃₁	—	39	1	no	Hall
15	C₃×C₁₃₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃₁	—	39	1	no	—
17	D₁₃₁	—	39	1	no	—
18	D₁₃₁	D₃₉	1	1	yes	characteristic, direct product factor
19	C₂×D₃₉	—	131	1	no	maximal, Hall
20	C₁₃₁	C₂×D₃₉	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₃	—	131	1	no	—
22	D₃₉	—	131	1	no	—
23	D₃₉	D₁₃₁	1	1	yes	characteristic, direct product factor
24	C₂×D₁₃	—	393	1	no	Hall
25	C₃×C₁₃	C₂×D₁₃₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	131	1	no	—
27	D₁₃	—	3	1	no	—
28	D₁₃	—	393	1	no	—
29	C₁₃	D₃×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	1703	1	no	Hall
31	C₂×C₃	—	131	1	no	—
32	D₃	—	13	1	no	—
33	D₃	—	1703	1	no	—
34	C₂²	—	5109	1	no	Sylow
35	C₃	D₁₃×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	39	1	no	—
37	C₂	—	131	1	no	—
38	C₂	—	5109	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₁₃₁	C₂²
LCS	G ▷ C₃×C₁₃×C₁₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₁₀₉	C₂	semidirect
2. D₃₉×C₁₃₁	C₂	semidirect
3. C₃×C₁₃×D₁₃₁	C₂	semidirect
5. C₃×C₁₃×C₁₃₁	C₂²	semidirect
7. C₁₃×D₁₃₁	D₃	semidirect
9. C₁₃×C₁₃₁	C₂×D₃	semidirect
12. C₃×D₁₃₁	D₁₃	semidirect
15. C₃×C₁₃₁	C₂×D₁₃	semidirect
18. D₁₃₁	D₃₉	direct (N × H)
20. C₁₃₁	C₂×D₃₉	semidirect
23. D₃₉	D₁₃₁	direct (N × H)
25. C₃×C₁₃	C₂×D₁₃₁	semidirect
29. C₁₃	D₃×D₁₃₁	semidirect
35. C₃	D₁₃×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
D₅₁₀₉	2
D₃₉×C₁₃₁	2
C₃×C₁₃×D₁₃₁	2
D₁₃×D₁₃₁	3
D₃×D₁₃₁	13
C₂×D₃₉	131

Subgroups — D39×D131 #35205455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₉×D₁₃₁ #35205455