Subgroups — C₂×C₃×D₇×C₁₉ #13097635

Order 1596.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₇×C₁₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₇×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	D₇×C₁₉	C₂×C₃	1	2	yes	direct product factor
7	C₂²×C₃×C₁₉	—	7	1	no	maximal, Hall
8	C₇×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₉	—	7	2	no	—
10	C₂×C₃×C₁₉	D₇	1	1	yes	characteristic, direct product factor
11	C₂×C₃×D₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₁₉	—	7	1	no	Hall
13	C₃×C₁₉	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇	C₂×C₁₉	1	1	yes	characteristic, complemented
15	C₃×D₇	C₂×C₁₉	1	2	yes	direct product factor
16	C₂×C₁₉	—	7	2	no	—
17	C₂×C₁₉	C₃×D₇	1	1	yes	characteristic, direct product factor
18	C₂×D₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
20	C₁₉	C₂×C₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
22	D₇	C₂×C₃×C₁₉	1	2	yes	direct product factor
23	C₂²×C₃	—	7	1	no	Hall
24	C₇	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	7	2	no	—
26	C₂×C₃	D₇×C₁₉	1	1	yes	characteristic, direct product factor
27	C₂²	—	7	1	no	Sylow
28	C₃	C₂×D₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	7	2	no	—
30	C₂	C₃×D₇×C₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₇×C₁₉	C₂	semidirect
2. C₃×D₇×C₁₉	C₂	direct (N × H)
3. C₂×D₇×C₁₉	C₃	direct (N × H)
4. C₃×C₇×C₁₉	C₂²	semidirect
5. C₂×C₇×C₁₉	C₂×C₃	semidirect
6. D₇×C₁₉	C₂×C₃	direct (N × H)
8. C₇×C₁₉	C₂²×C₃	semidirect
10. C₂×C₃×C₁₉	D₇	direct (N × H)
11. C₂×C₃×D₇	C₁₉	direct (N × H)
13. C₃×C₁₉	C₂×D₇	direct (N × H)
14. C₂×C₃×C₇	C₂×C₁₉	semidirect
15. C₃×D₇	C₂×C₁₉	direct (N × H)
17. C₂×C₁₉	C₃×D₇	direct (N × H)
18. C₂×D₇	C₃×C₁₉	direct (N × H)
19. C₃×C₇	C₂²×C₁₉	semidirect
20. C₁₉	C₂×C₃×D₇	direct (N × H)
21. C₂×C₇	C₂×C₃×C₁₉	semidirect
22. D₇	C₂×C₃×C₁₉	direct (N × H)
24. C₇	C₂²×C₃×C₁₉	semidirect
26. C₂×C₃	D₇×C₁₉	direct (N × H)
28. C₃	C₂×D₇×C₁₉	direct (N × H)
30. C₂	C₃×D₇×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₉	2
C₃×D₇×C₁₉	2
C₂×D₇×C₁₉	3
C₂²×C₃×C₁₉	7
C₂×C₃×D₇	19

Subgroups — C2×C3×D7×C19 #13097635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₇×C₁₉ #13097635