Subgroups — D₁₉×D₁₅₁⋊C₃ #46806325

Order 34428.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₅₁⋊C₃)⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₉×C₁₅₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×D₁₅₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₁₅₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₉×C₁₅₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₈₆₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×D₁₅₁	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₉×C₁₅₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₉×C₁₅₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₁₅₁⋊C₃	—	19	1	no	maximal, Hall
11	C₂×C₁₅₁⋊C₃	—	19	1	no	—
12	D₁₅₁⋊C₃	—	19	1	no	—
13	D₁₅₁⋊C₃	D₁₉	1	1	yes	characteristic, direct product factor
14	C₂×D₁₅₁	—	19	1	no	Hall
15	C₁₅₁⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₅₁	—	19	1	no	—
17	D₁₅₁	—	19	1	no	—
18	D₁₅₁	C₃×D₁₉	1	1	yes	characteristic, complemented
19	C₂×C₃×D₁₉	—	151	1	no	maximal, Hall
20	C₁₅₁	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₉	—	151	1	no	—
22	C₃×D₁₉	—	151	1	no	—
23	C₃×D₁₉	—	151	1	no	—
24	C₂×D₁₉	—	151	1	no	Hall
25	C₃×C₁₉	—	151	1	no	Hall
26	C₂×C₁₉	—	151	1	no	—
27	D₁₉	—	151	1	no	—
28	D₁₉	D₁₅₁⋊C₃	1	1	yes	characteristic, direct product factor
29	C₁₉	C₂×D₁₅₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	2869	1	no	Hall
31	C₂×C₃	—	2869	1	no	—
32	C₂×C₃	—	2869	1	no	—
33	C₂×C₃	—	151	1	no	—
34	C₂²	—	2869	1	no	Sylow
35	C₃	—	151	1	no	Sylow
36	C₂	—	19	1	no	—
37	C₂	—	2869	1	no	—
38	C₂	—	151	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉×C₁₅₁	C₂²×C₃
LCS	G ▷ C₁₉×C₁₅₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. (C₁₅₁⋊C₃)⋊D₁₉	C₂	semidirect
2. D₁₉×C₁₅₁⋊C₃	C₂	semidirect
3. C₁₉×D₁₅₁⋊C₃	C₂	semidirect
4. D₁₉×D₁₅₁	C₃	semidirect
5. C₁₉×C₁₅₁⋊C₃	C₂²	semidirect
6. D₂₈₆₉	C₂×C₃	semidirect
7. C₁₉×D₁₅₁	C₂×C₃	semidirect
8. D₁₉×C₁₅₁	C₂×C₃	semidirect
9. C₁₉×C₁₅₁	C₂²×C₃	semidirect
13. D₁₅₁⋊C₃	D₁₉	direct (N × H)
15. C₁₅₁⋊C₃	C₂×D₁₉	semidirect
18. D₁₅₁	C₃×D₁₉	semidirect
20. C₁₅₁	C₂×C₃×D₁₉	semidirect
28. D₁₉	D₁₅₁⋊C₃	direct (N × H)
29. C₁₉	C₂×D₁₅₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
(C₁₅₁⋊C₃)⋊D₁₉	2
D₁₉×C₁₅₁⋊C₃	2
C₁₉×D₁₅₁⋊C₃	2
D₁₉×D₁₅₁	3
C₂×D₁₅₁⋊C₃	19
C₂×C₃×D₁₉	151

Subgroups — D19×D151⋊C3 #46806325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×D₁₅₁⋊C₃ #46806325