Subgroups — C₂×C₁₃⋊C₃×D₁₃₁ #35205448

Order 20436.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×D₁₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃⋊C₃×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₁₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃⋊C₃×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₃₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₃×D₁₃₁	C₂×C₃	1	2	yes	complemented
7	C₁₃×C₁₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₁₃₁	—	13	1	no	maximal, Hall
9	C₂×C₃×C₁₃₁	—	13	1	no	—
10	C₃×D₁₃₁	—	13	2	no	—
11	C₂×D₁₃₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₁₃₁	—	13	1	no	Hall
13	C₂×C₁₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
14	D₁₃₁	C₂×C₁₃⋊C₃	1	2	yes	direct product factor
15	C₂²×C₁₃⋊C₃	—	131	1	no	maximal, Hall
16	C₁₃₁	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₃⋊C₃	—	131	2	no	—
18	C₂×C₁₃⋊C₃	D₁₃₁	1	1	yes	characteristic, direct product factor
19	C₂²×C₁₃	—	131	1	no	Hall
20	C₁₃⋊C₃	C₂×D₁₃₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₃	—	131	2	no	—
22	C₂×C₁₃	C₃×D₁₃₁	1	1	yes	characteristic, complemented
23	C₁₃	C₂×C₃×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	1703	1	no	Hall
25	C₂×C₃	—	13	1	no	—
26	C₂×C₃	—	1703	2	no	—
27	C₂²	—	131	1	no	Sylow
28	C₃	—	13	1	no	Sylow
29	C₂	—	131	2	no	—
30	C₂	C₁₃⋊C₃×D₁₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₃⋊C₃×D₁₃₁
commutator, cosocle, hypocenter	C₁₃×C₁₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₁₃₁	C₂×C₃
LCS	G ▷ C₁₃×C₁₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₃×D₁₃₁	C₂	direct (N × H)
2. C₂×C₁₃⋊C₃×C₁₃₁	C₂	semidirect
3. C₂×C₁₃×D₁₃₁	C₃	semidirect
4. C₁₃⋊C₃×C₁₃₁	C₂²	semidirect
5. C₂×C₁₃×C₁₃₁	C₂×C₃	semidirect
6. C₁₃×D₁₃₁	C₂×C₃	semidirect
7. C₁₃×C₁₃₁	C₂²×C₃	semidirect
11. C₂×D₁₃₁	C₁₃⋊C₃	direct (N × H)
13. C₂×C₁₃₁	C₂×C₁₃⋊C₃	semidirect
14. D₁₃₁	C₂×C₁₃⋊C₃	direct (N × H)
16. C₁₃₁	C₂²×C₁₃⋊C₃	semidirect
18. C₂×C₁₃⋊C₃	D₁₃₁	direct (N × H)
20. C₁₃⋊C₃	C₂×D₁₃₁	direct (N × H)
22. C₂×C₁₃	C₃×D₁₃₁	semidirect
23. C₁₃	C₂×C₃×D₁₃₁	semidirect
30. C₂	C₁₃⋊C₃×D₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃⋊C₃×D₁₃₁	2
C₂×C₁₃⋊C₃×C₁₃₁	2
C₂×C₁₃×D₁₃₁	3
C₂×C₃×D₁₃₁	13
C₂²×C₁₃⋊C₃	131

Subgroups — C2×C13⋊C3×D131 #35205448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃⋊C₃×D₁₃₁ #35205448