Subgroups — D₁₉⋊C₃×D₁₃₁ #44469331

Order 29868.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₉⋊C₃)⋊D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₉⋊C₃×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉⋊C₃×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₁₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₉⋊C₃×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₄₈₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×D₁₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₉×C₁₃₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₉×C₁₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×D₁₃₁	—	19	1	no	maximal, Hall
11	C₂×C₃×C₁₃₁	—	19	1	no	—
12	C₃×D₁₃₁	—	19	1	no	—
13	C₃×D₁₃₁	—	38	1	no	—
14	C₂×D₁₃₁	—	19	1	no	Hall
15	C₃×C₁₃₁	—	38	1	no	Hall
16	C₂×C₁₃₁	—	19	1	no	—
17	D₁₃₁	—	19	1	no	—
18	D₁₃₁	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
19	C₂×D₁₉⋊C₃	—	131	1	no	maximal, Hall
20	C₁₃₁	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₉⋊C₃	—	131	1	no	—
22	D₁₉⋊C₃	—	131	1	no	—
23	D₁₉⋊C₃	D₁₃₁	1	1	yes	characteristic, direct product factor
24	C₂×D₁₉	—	131	1	no	Hall
25	C₁₉⋊C₃	C₂×D₁₃₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₉	—	131	1	no	—
27	D₁₉	—	131	1	no	—
28	D₁₉	C₃×D₁₃₁	1	1	yes	characteristic, complemented
29	C₁₉	C₂×C₃×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	2489	1	no	Hall
31	C₂×C₃	—	19	1	no	—
32	C₂×C₃	—	2489	1	no	—
33	C₂×C₃	—	2489	1	no	—
34	C₂²	—	2489	1	no	Sylow
35	C₃	—	19	1	no	Sylow
36	C₂	—	19	1	no	—
37	C₂	—	131	1	no	—
38	C₂	—	2489	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. (C₁₉⋊C₃)⋊D₁₃₁	C₂	semidirect
2. D₁₉⋊C₃×C₁₃₁	C₂	semidirect
3. C₁₉⋊C₃×D₁₃₁	C₂	semidirect
4. D₁₉×D₁₃₁	C₃	semidirect
5. C₁₉⋊C₃×C₁₃₁	C₂²	semidirect
6. D₂₄₈₉	C₂×C₃	semidirect
7. C₁₉×D₁₃₁	C₂×C₃	semidirect
8. D₁₉×C₁₃₁	C₂×C₃	semidirect
9. C₁₉×C₁₃₁	C₂²×C₃	semidirect
18. D₁₃₁	D₁₉⋊C₃	direct (N × H)
20. C₁₃₁	C₂×D₁₉⋊C₃	semidirect
23. D₁₉⋊C₃	D₁₃₁	direct (N × H)
25. C₁₉⋊C₃	C₂×D₁₃₁	semidirect
28. D₁₉	C₃×D₁₃₁	semidirect
29. C₁₉	C₂×C₃×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
(C₁₉⋊C₃)⋊D₁₃₁	2
D₁₉⋊C₃×C₁₃₁	2
C₁₉⋊C₃×D₁₃₁	2
D₁₉×D₁₃₁	3
C₂×C₃×D₁₃₁	19
C₂×D₁₉⋊C₃	131

Subgroups — D19⋊C3×D131 #44469331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉⋊C₃×D₁₃₁ #44469331