Subgroups — C₂×C₃⁴×C₇×C₁₉ #72199055

Order 21546.

1696 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃³×C₇×C₁₉	C₃	1	40	yes	maximal, direct product factor
3	C₃³×C₇×C₁₉	C₂×C₃	1	40	yes	direct product factor
4	C₂×C₃⁴×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃²×C₇×C₁₉	C₃²	1	130	yes	direct product factor
6	C₃⁴×C₁₉	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇×C₁₉	C₂×C₃²	1	130	yes	direct product factor
8	C₂×C₃⁴×C₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃³×C₁₉	C₃×C₇	1	40	yes	direct product factor
10	C₂×C₃×C₇×C₁₉	C₃³	1	40	yes	direct product factor
11	C₃⁴×C₇	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
12	C₃³×C₁₉	C₂×C₃×C₇	1	40	yes	direct product factor
13	C₃×C₇×C₁₉	C₂×C₃³	1	40	yes	direct product factor
14	C₂×C₃³×C₇	C₃×C₁₉	1	40	yes	direct product factor
15	C₂×C₃²×C₁₉	C₃²×C₇	1	130	yes	direct product factor
16	C₂×C₇×C₁₉	C₃⁴	1	1	yes	characteristic, direct product factor, Hall
17	C₃³×C₇	C₂×C₃×C₁₉	1	40	yes	direct product factor
18	C₃²×C₁₉	C₂×C₃²×C₇	1	130	yes	direct product factor
19	C₂×C₃⁴	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
20	C₇×C₁₉	C₂×C₃⁴	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃²×C₇	C₃²×C₁₉	1	130	yes	direct product factor
22	C₂×C₃×C₁₉	C₃³×C₇	1	40	yes	direct product factor
23	C₃⁴	C₂×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₃²×C₇	C₂×C₃²×C₁₉	1	130	yes	direct product factor
25	C₃×C₁₉	C₂×C₃³×C₇	1	40	yes	direct product factor
26	C₂×C₃³	C₃×C₇×C₁₉	1	40	yes	direct product factor
27	C₂×C₃×C₇	C₃³×C₁₉	1	40	yes	direct product factor
28	C₂×C₁₉	C₃⁴×C₇	1	1	yes	characteristic, direct product factor, Hall
29	C₃³	C₂×C₃×C₇×C₁₉	1	40	yes	direct product factor
30	C₃×C₇	C₂×C₃³×C₁₉	1	40	yes	direct product factor
31	C₁₉	C₂×C₃⁴×C₇	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃²	C₃²×C₇×C₁₉	1	130	yes	direct product factor
33	C₂×C₇	C₃⁴×C₁₉	1	1	yes	characteristic, direct product factor, Hall
34	C₃²	C₂×C₃²×C₇×C₁₉	1	130	yes	direct product factor
35	C₇	C₂×C₃⁴×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃	C₃³×C₇×C₁₉	1	40	yes	direct product factor
37	C₃	C₂×C₃³×C₇×C₁₉	1	40	yes	direct product factor
38	C₂	C₃⁴×C₇×C₁₉	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. C₃⁴×C₇×C₁₉	C₂	direct (N × H)
2. C₂×C₃³×C₇×C₁₉	C₃	direct (N × H)
3. C₃³×C₇×C₁₉	C₂×C₃	direct (N × H)
4. C₂×C₃⁴×C₁₉	C₇	direct (N × H)
5. C₂×C₃²×C₇×C₁₉	C₃²	direct (N × H)
6. C₃⁴×C₁₉	C₂×C₇	direct (N × H)
7. C₃²×C₇×C₁₉	C₂×C₃²	direct (N × H)
8. C₂×C₃⁴×C₇	C₁₉	direct (N × H)
9. C₂×C₃³×C₁₉	C₃×C₇	direct (N × H)
10. C₂×C₃×C₇×C₁₉	C₃³	direct (N × H)
11. C₃⁴×C₇	C₂×C₁₉	direct (N × H)
12. C₃³×C₁₉	C₂×C₃×C₇	direct (N × H)
13. C₃×C₇×C₁₉	C₂×C₃³	direct (N × H)
14. C₂×C₃³×C₇	C₃×C₁₉	direct (N × H)
15. C₂×C₃²×C₁₉	C₃²×C₇	direct (N × H)
16. C₂×C₇×C₁₉	C₃⁴	direct (N × H)
17. C₃³×C₇	C₂×C₃×C₁₉	direct (N × H)
18. C₃²×C₁₉	C₂×C₃²×C₇	direct (N × H)
19. C₂×C₃⁴	C₇×C₁₉	direct (N × H)
20. C₇×C₁₉	C₂×C₃⁴	direct (N × H)
21. C₂×C₃²×C₇	C₃²×C₁₉	direct (N × H)
22. C₂×C₃×C₁₉	C₃³×C₇	direct (N × H)
23. C₃⁴	C₂×C₇×C₁₉	direct (N × H)
24. C₃²×C₇	C₂×C₃²×C₁₉	direct (N × H)
25. C₃×C₁₉	C₂×C₃³×C₇	direct (N × H)
26. C₂×C₃³	C₃×C₇×C₁₉	direct (N × H)
27. C₂×C₃×C₇	C₃³×C₁₉	direct (N × H)
28. C₂×C₁₉	C₃⁴×C₇	direct (N × H)
29. C₃³	C₂×C₃×C₇×C₁₉	direct (N × H)
30. C₃×C₇	C₂×C₃³×C₁₉	direct (N × H)
31. C₁₉	C₂×C₃⁴×C₇	direct (N × H)
32. C₂×C₃²	C₃²×C₇×C₁₉	direct (N × H)
33. C₂×C₇	C₃⁴×C₁₉	direct (N × H)
34. C₃²	C₂×C₃²×C₇×C₁₉	direct (N × H)
35. C₇	C₂×C₃⁴×C₁₉	direct (N × H)
36. C₂×C₃	C₃³×C₇×C₁₉	direct (N × H)
37. C₃	C₂×C₃³×C₇×C₁₉	direct (N × H)
38. C₂	C₃⁴×C₇×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
C₃⁴×C₇×C₁₉	2
C₂×C₃³×C₇×C₁₉	3
C₂×C₃⁴×C₁₉	7
C₂×C₃⁴×C₇	19

Subgroups — C2×C34×C7×C19 #72199055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⁴×C₇×C₁₉ #72199055