Subgroups — C₂×C₃×C₄×C₁₉×C₄₃ #72197300

Order 19608.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₉×C₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂²×C₃×C₁₉×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₁₉×C₄₃	C₂	1	2	yes	maximal, direct product factor
4	C₂×C₃×C₁₉×C₄₃	C₄	1	2	yes	direct product factor
5	C₂×C₃×C₁₉×C₄₃	C₂²	1	1	yes	characteristic
6	C₂²×C₁₉×C₄₃	C₂×C₃	1	1	yes	characteristic
7	C₄×C₁₉×C₄₃	C₂×C₃	1	2	yes	direct product factor
8	C₃×C₁₉×C₄₃	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₉×C₄₃	C₃×C₄	1	2	yes	direct product factor
10	C₂×C₁₉×C₄₃	C₂²×C₃	1	1	yes	characteristic
11	C₂×C₃×C₄×C₄₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₉×C₄₃	C₂×C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₃×C₄₃	C₂×C₁₉	1	1	yes	characteristic
14	C₃×C₄×C₄₃	C₂×C₁₉	1	2	yes	direct product factor
15	C₂×C₃×C₄×C₁₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₄×C₄₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₄₃	C₄×C₁₉	1	2	yes	direct product factor
18	C₂×C₃×C₄₃	C₂²×C₁₉	1	1	yes	characteristic
19	C₂²×C₃×C₁₉	C₂×C₄₃	1	1	yes	characteristic
20	C₃×C₄×C₁₉	C₂×C₄₃	1	2	yes	direct product factor
21	C₂²×C₄₃	C₂×C₃×C₁₉	1	1	yes	characteristic
22	C₄×C₄₃	C₂×C₃×C₁₉	1	2	yes	direct product factor
23	C₂×C₄×C₁₉	C₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₄₃	C₂×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₁₉	C₄×C₄₃	1	2	yes	direct product factor
26	C₂×C₃×C₁₉	C₂²×C₄₃	1	1	yes	characteristic
27	C₂×C₄₃	C₃×C₄×C₁₉	1	2	yes	direct product factor
28	C₂×C₄₃	C₂²×C₃×C₁₉	1	1	yes	characteristic
29	C₂²×C₁₉	C₂×C₃×C₄₃	1	1	yes	characteristic
30	C₄×C₁₉	C₂×C₃×C₄₃	1	2	yes	direct product factor
31	C₃×C₁₉	C₂×C₄×C₄₃	1	1	yes	characteristic, direct product factor, Hall
32	C₄₃	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₁₉	C₃×C₄×C₄₃	1	2	yes	direct product factor
34	C₂×C₁₉	C₂²×C₃×C₄₃	1	1	yes	characteristic
35	C₂×C₃×C₄	C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
36	C₁₉	C₂×C₃×C₄×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₃	C₂×C₁₉×C₄₃	1	1	yes	characteristic
38	C₃×C₄	C₂×C₁₉×C₄₃	1	2	yes	direct product factor
39	C₂×C₄	C₃×C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	C₄×C₁₉×C₄₃	1	2	yes	direct product factor
41	C₂×C₃	C₂²×C₁₉×C₄₃	1	1	yes	characteristic
42	C₂²	C₂×C₃×C₁₉×C₄₃	1	1	yes	characteristic
43	C₄	C₂×C₃×C₁₉×C₄₃	1	2	yes	direct product factor
44	C₃	C₂×C₄×C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×C₄×C₁₉×C₄₃	1	2	yes	direct product factor
46	C₂	C₂²×C₃×C₁₉×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₁₉×C₄₃
socle, prime radical	C₂²×C₃×C₁₉×C₄₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₉×C₄₃	C₃	direct (N × H)
3. C₃×C₄×C₁₉×C₄₃	C₂	direct (N × H)
4. C₂×C₃×C₁₉×C₄₃	C₄	direct (N × H)
7. C₄×C₁₉×C₄₃	C₂×C₃	direct (N × H)
8. C₃×C₁₉×C₄₃	C₂×C₄	direct (N × H)
9. C₂×C₁₉×C₄₃	C₃×C₄	direct (N × H)
11. C₂×C₃×C₄×C₄₃	C₁₉	direct (N × H)
12. C₁₉×C₄₃	C₂×C₃×C₄	direct (N × H)
14. C₃×C₄×C₄₃	C₂×C₁₉	direct (N × H)
15. C₂×C₃×C₄×C₁₉	C₄₃	direct (N × H)
16. C₂×C₄×C₄₃	C₃×C₁₉	direct (N × H)
17. C₂×C₃×C₄₃	C₄×C₁₉	direct (N × H)
20. C₃×C₄×C₁₉	C₂×C₄₃	direct (N × H)
22. C₄×C₄₃	C₂×C₃×C₁₉	direct (N × H)
23. C₂×C₄×C₁₉	C₃×C₄₃	direct (N × H)
24. C₃×C₄₃	C₂×C₄×C₁₉	direct (N × H)
25. C₂×C₃×C₁₉	C₄×C₄₃	direct (N × H)
27. C₂×C₄₃	C₃×C₄×C₁₉	direct (N × H)
30. C₄×C₁₉	C₂×C₃×C₄₃	direct (N × H)
31. C₃×C₁₉	C₂×C₄×C₄₃	direct (N × H)
32. C₄₃	C₂×C₃×C₄×C₁₉	direct (N × H)
33. C₂×C₁₉	C₃×C₄×C₄₃	direct (N × H)
35. C₂×C₃×C₄	C₁₉×C₄₃	direct (N × H)
36. C₁₉	C₂×C₃×C₄×C₄₃	direct (N × H)
38. C₃×C₄	C₂×C₁₉×C₄₃	direct (N × H)
39. C₂×C₄	C₃×C₁₉×C₄₃	direct (N × H)
40. C₂×C₃	C₄×C₁₉×C₄₃	direct (N × H)
43. C₄	C₂×C₃×C₁₉×C₄₃	direct (N × H)
44. C₃	C₂×C₄×C₁₉×C₄₃	direct (N × H)
45. C₂	C₃×C₄×C₁₉×C₄₃	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×C₄×C₁₉×C₄₃	3
C₂²×C₃×C₁₉×C₄₃	2
C₃×C₄×C₁₉×C₄₃	2
C₂×C₃×C₄×C₄₃	19
C₂×C₃×C₄×C₁₉	43

Subgroups — C2×C3×C4×C19×C43 #72197300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₁₉×C₄₃ #72197300