Subgroups — C₂×D₁₉⋊C₃×C₁₃₁ #44469332

Order 29868.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₉⋊C₃×C₁₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₉⋊C₃×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₉×C₁₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉⋊C₃×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₁₃₁	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₉×C₁₃₁	C₂×C₃	1	2	yes	complemented
7	C₁₉×C₁₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₃×C₁₃₁	—	19	1	no	maximal, Hall
9	C₂×C₃×C₁₃₁	—	19	2	no	—
10	C₂×C₃×C₁₃₁	—	19	1	no	—
11	C₂²×C₁₃₁	—	19	1	no	Hall
12	C₃×C₁₃₁	—	19	1	no	Hall
13	C₂×C₁₃₁	—	19	2	no	—
14	C₂×C₁₃₁	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
15	C₂×D₁₉⋊C₃	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₃₁	C₂×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₁₉⋊C₃	C₂×C₁₃₁	1	1	yes	characteristic, complemented
18	D₁₉⋊C₃	C₂×C₁₃₁	1	2	yes	direct product factor
19	C₂×D₁₉	C₃×C₁₃₁	1	1	yes	characteristic, complemented, Hall
20	C₁₉⋊C₃	C₂²×C₁₃₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₉	C₂×C₃×C₁₃₁	1	1	yes	characteristic, complemented
22	D₁₉	C₂×C₃×C₁₃₁	1	2	yes	complemented
23	C₁₉	C₂²×C₃×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	19	1	no	Hall
25	C₂×C₃	—	19	2	no	—
26	C₂×C₃	—	19	1	no	—
27	C₂²	—	19	1	no	Sylow
28	C₃	—	19	1	no	Sylow
29	C₂	—	19	2	no	—
30	C₂	D₁₉⋊C₃×C₁₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃₁	D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃×C₁₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₁₃₁	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₃₁

Complements

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

N	H ≅ G/N	type
1. D₁₉⋊C₃×C₁₃₁	C₂	direct (N × H)
2. C₂×C₁₉⋊C₃×C₁₃₁	C₂	semidirect
3. C₂×D₁₉×C₁₃₁	C₃	semidirect
4. C₁₉⋊C₃×C₁₃₁	C₂²	semidirect
5. C₂×C₁₉×C₁₃₁	C₂×C₃	semidirect
6. D₁₉×C₁₃₁	C₂×C₃	semidirect
7. C₁₉×C₁₃₁	C₂²×C₃	semidirect
14. C₂×C₁₃₁	D₁₉⋊C₃	direct (N × H)
15. C₂×D₁₉⋊C₃	C₁₃₁	direct (N × H)
16. C₁₃₁	C₂×D₁₉⋊C₃	direct (N × H)
17. C₂×C₁₉⋊C₃	C₂×C₁₃₁	semidirect
18. D₁₉⋊C₃	C₂×C₁₃₁	direct (N × H)
19. C₂×D₁₉	C₃×C₁₃₁	semidirect
20. C₁₉⋊C₃	C₂²×C₁₃₁	semidirect
21. C₂×C₁₉	C₂×C₃×C₁₃₁	semidirect
22. D₁₉	C₂×C₃×C₁₃₁	semidirect
23. C₁₉	C₂²×C₃×C₁₃₁	semidirect
30. C₂	D₁₉⋊C₃×C₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₉⋊C₃×C₁₃₁	2
C₂×C₁₉⋊C₃×C₁₃₁	2
C₂×D₁₉×C₁₃₁	3
C₂²×C₃×C₁₃₁	19
C₂×D₁₉⋊C₃	131

Subgroups — C2×D19⋊C3×C131 #44469332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₉⋊C₃×C₁₃₁ #44469332