Subgroups — C₂×C₃²×C₁₉×C₁₀₁ #46828811

Order 34542.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₁₀₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₉×C₁₀₁	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₁₉×C₁₀₁	C₂×C₃	1	4	yes	direct product factor
4	C₂×C₁₉×C₁₀₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₁₉×C₁₀₁	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃²×C₁₀₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃²×C₁₀₁	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₁₀₁	C₃×C₁₉	1	4	yes	direct product factor
9	C₂×C₃²×C₁₉	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₀₁	C₂×C₃×C₁₉	1	4	yes	direct product factor
11	C₂×C₁₀₁	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
12	C₃²×C₁₉	C₂×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₉	C₃×C₁₀₁	1	4	yes	direct product factor
14	C₁₀₁	C₂×C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₉	C₂×C₃×C₁₀₁	1	4	yes	direct product factor
16	C₂×C₁₉	C₃²×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
17	C₁₉	C₂×C₃²×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃²	C₁₉×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
19	C₃²	C₂×C₁₉×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₁₉×C₁₀₁	1	4	yes	direct product factor
21	C₃	C₂×C₃×C₁₉×C₁₀₁	1	4	yes	direct product factor
22	C₂	C₃²×C₁₉×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₉×C₁₀₁	C₂	direct (N × H)
2. C₂×C₃×C₁₉×C₁₀₁	C₃	direct (N × H)
3. C₃×C₁₉×C₁₀₁	C₂×C₃	direct (N × H)
4. C₂×C₁₉×C₁₀₁	C₃²	direct (N × H)
5. C₁₉×C₁₀₁	C₂×C₃²	direct (N × H)
6. C₂×C₃²×C₁₀₁	C₁₉	direct (N × H)
7. C₃²×C₁₀₁	C₂×C₁₉	direct (N × H)
8. C₂×C₃×C₁₀₁	C₃×C₁₉	direct (N × H)
9. C₂×C₃²×C₁₉	C₁₀₁	direct (N × H)
10. C₃×C₁₀₁	C₂×C₃×C₁₉	direct (N × H)
11. C₂×C₁₀₁	C₃²×C₁₉	direct (N × H)
12. C₃²×C₁₉	C₂×C₁₀₁	direct (N × H)
13. C₂×C₃×C₁₉	C₃×C₁₀₁	direct (N × H)
14. C₁₀₁	C₂×C₃²×C₁₉	direct (N × H)
15. C₃×C₁₉	C₂×C₃×C₁₀₁	direct (N × H)
16. C₂×C₁₉	C₃²×C₁₀₁	direct (N × H)
17. C₁₉	C₂×C₃²×C₁₀₁	direct (N × H)
18. C₂×C₃²	C₁₉×C₁₀₁	direct (N × H)
19. C₃²	C₂×C₁₉×C₁₀₁	direct (N × H)
20. C₂×C₃	C₃×C₁₉×C₁₀₁	direct (N × H)
21. C₃	C₂×C₃×C₁₉×C₁₀₁	direct (N × H)
22. C₂	C₃²×C₁₉×C₁₀₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₉×C₁₀₁	2
C₂×C₃×C₁₉×C₁₀₁	3
C₂×C₃²×C₁₀₁	19
C₂×C₃²×C₁₉	101

Subgroups — C2×C32×C19×C101 #46828811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₉×C₁₀₁ #46828811