Subgroups — D₁₉×D₄₅₃ #46806342

Order 34428.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₆₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₄₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₉×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₁₅₁	—	3	1	no	maximal, Hall
5	C₃×C₁₉×C₁₅₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₈₆₉	—	3	1	no	—
7	C₁₉×D₁₅₁	—	3	1	no	—
8	D₁₉×C₁₅₁	D₃	1	1	yes	characteristic, complemented
9	C₁₉×C₁₅₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₄₅₃	—	19	1	no	maximal, Hall
11	C₂×C₃×C₁₅₁	—	19	1	no	—
12	D₄₅₃	—	19	1	no	—
13	D₄₅₃	D₁₉	1	1	yes	characteristic, direct product factor
14	C₂×D₁₅₁	—	57	1	no	Hall
15	C₃×C₁₅₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₅₁	—	19	1	no	—
17	D₁₅₁	—	3	1	no	—
18	D₁₅₁	—	57	1	no	—
19	D₃×D₁₉	—	151	1	no	maximal, Hall
20	C₁₅₁	D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
21	D₅₇	—	151	1	no	—
22	C₃×D₁₉	D₁₅₁	1	1	yes	characteristic, complemented
23	D₃×C₁₉	—	151	1	no	—
24	C₂×D₁₉	—	453	1	no	Hall
25	C₃×C₁₉	C₂×D₁₅₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₉	—	453	1	no	—
27	D₁₉	—	453	1	no	—
28	D₁₉	D₄₅₃	1	1	yes	characteristic, direct product factor
29	C₁₉	C₂×D₄₅₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2869	1	no	Hall
31	C₂×C₃	—	19	1	no	—
32	D₃	—	2869	1	no	—
33	D₃	—	151	1	no	—
34	C₂²	—	8607	1	no	Sylow
35	C₃	D₁₉×D₁₅₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	19	1	no	—
37	C₂	—	8607	1	no	—
38	C₂	—	453	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₈₆₀₇	C₂	semidirect
2. C₁₉×D₄₅₃	C₂	semidirect
3. C₃×D₁₉×C₁₅₁	C₂	semidirect
5. C₃×C₁₉×C₁₅₁	C₂²	semidirect
8. D₁₉×C₁₅₁	D₃	semidirect
9. C₁₉×C₁₅₁	C₂×D₃	semidirect
13. D₄₅₃	D₁₉	direct (N × H)
15. C₃×C₁₅₁	C₂×D₁₉	semidirect
20. C₁₅₁	D₃×D₁₉	semidirect
22. C₃×D₁₉	D₁₅₁	semidirect
25. C₃×C₁₉	C₂×D₁₅₁	semidirect
28. D₁₉	D₄₅₃	direct (N × H)
29. C₁₉	C₂×D₄₅₃	semidirect
35. C₃	D₁₉×D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
D₈₆₀₇	2
C₁₉×D₄₅₃	2
C₃×D₁₉×C₁₅₁	2
D₁₉×D₁₅₁	3
C₂×D₄₅₃	19
D₃×D₁₉	151

Subgroups — D19×D453 #46806342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×D₄₅₃ #46806342