Subgroups — C₂×D₃×C₁₃₁⋊C₁₃ #35205441

Order 20436.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₃₁⋊C₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃₁⋊C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃₁⋊C₁₃	—	3	1	no	maximal, Hall
4	C₃×C₁₃₁⋊C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃₁⋊C₁₃	—	3	2	no	—
6	C₂×C₁₃₁⋊C₁₃	D₃	1	1	yes	characteristic, direct product factor
7	C₁₃₁⋊C₁₃	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×D₃×C₁₃₁	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
9	C₂×C₃×C₁₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented
10	D₃×C₁₃₁	C₂×C₁₃	1	2	yes	complemented
11	C₂²×C₁₃₁	—	3	1	no	Hall
12	C₃×C₁₃₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₃₁	—	3	2	no	—
14	C₂×C₁₃₁	D₃×C₁₃	1	1	yes	characteristic, complemented
15	C₂×D₃×C₁₃	—	131	1	no	maximal, Hall
16	C₁₃₁	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₁₃	—	131	1	no	—
18	D₃×C₁₃	—	131	2	no	—
19	C₂²×C₁₃	—	393	1	no	Hall
20	C₃×C₁₃	—	131	1	no	Hall
21	C₂×C₁₃	—	131	1	no	—
22	C₂×C₁₃	—	393	2	no	—
23	C₁₃	—	131	1	no	Sylow
24	C₂×D₃	C₁₃₁⋊C₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃	C₂×C₁₃₁⋊C₁₃	1	1	yes	characteristic, complemented
26	D₃	C₂×C₁₃₁⋊C₁₃	1	2	yes	direct product factor
27	C₂²	—	3	1	no	Sylow
28	C₃	C₂²×C₁₃₁⋊C₁₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	D₃×C₁₃₁⋊C₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×C₁₃₁⋊C₁₃
commutator, cosocle, hypocenter	C₃×C₁₃₁	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃₁	C₂×C₁₃
LCS	G ▷ C₃×C₁₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₃×C₁₃₁⋊C₁₃	C₂	direct (N × H)
2. C₂×C₃×C₁₃₁⋊C₁₃	C₂	semidirect
4. C₃×C₁₃₁⋊C₁₃	C₂²	semidirect
6. C₂×C₁₃₁⋊C₁₃	D₃	direct (N × H)
7. C₁₃₁⋊C₁₃	C₂×D₃	direct (N × H)
8. C₂×D₃×C₁₃₁	C₁₃	semidirect
9. C₂×C₃×C₁₃₁	C₂×C₁₃	semidirect
10. D₃×C₁₃₁	C₂×C₁₃	semidirect
12. C₃×C₁₃₁	C₂²×C₁₃	semidirect
14. C₂×C₁₃₁	D₃×C₁₃	semidirect
16. C₁₃₁	C₂×D₃×C₁₃	semidirect
24. C₂×D₃	C₁₃₁⋊C₁₃	direct (N × H)
25. C₂×C₃	C₂×C₁₃₁⋊C₁₃	semidirect
26. D₃	C₂×C₁₃₁⋊C₁₃	direct (N × H)
28. C₃	C₂²×C₁₃₁⋊C₁₃	semidirect
30. C₂	D₃×C₁₃₁⋊C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃×C₁₃₁⋊C₁₃	2
C₂×C₃×C₁₃₁⋊C₁₃	2
C₂²×C₁₃₁⋊C₁₃	3
C₂×D₃×C₁₃₁	13
C₂×D₃×C₁₃	131

Subgroups — C2×D3×C131⋊C13 #35205441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₁₃₁⋊C₁₃ #35205441