Subgroups — C₂×C₃×C₄×C₁₃×C₁₉ #72185141

Order 5928.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₃×C₁₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃×C₁₉	C₄	1	2	yes	direct product factor
5	C₂×C₃×C₁₃×C₁₉	C₂²	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₄×C₁₃×C₁₉	C₂×C₃	1	2	yes	direct product factor
8	C₃×C₁₃×C₁₉	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₃×C₁₉	C₃×C₄	1	2	yes	direct product factor
10	C₂×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic
11	C₂×C₃×C₄×C₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₄×C₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₃×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
14	C₂²×C₃×C₁₉	C₂×C₁₃	1	1	yes	characteristic
15	C₃×C₄×C₁₉	C₂×C₁₃	1	2	yes	direct product factor
16	C₂²×C₃×C₁₃	C₂×C₁₉	1	1	yes	characteristic
17	C₃×C₄×C₁₃	C₂×C₁₉	1	2	yes	direct product factor
18	C₂×C₄×C₁₉	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₁₉	C₄×C₁₃	1	2	yes	direct product factor
20	C₂×C₃×C₁₉	C₂²×C₁₃	1	1	yes	characteristic
21	C₂×C₄×C₁₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₁₃	C₄×C₁₉	1	2	yes	direct product factor
23	C₂×C₃×C₁₃	C₂²×C₁₉	1	1	yes	characteristic
24	C₂²×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic
25	C₄×C₁₉	C₂×C₃×C₁₃	1	2	yes	direct product factor
26	C₃×C₁₉	C₂×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂²×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic
28	C₄×C₁₃	C₂×C₃×C₁₉	1	2	yes	direct product factor
29	C₃×C₁₃	C₂×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₁₉	C₃×C₄×C₁₃	1	2	yes	direct product factor
31	C₂×C₁₉	C₂²×C₃×C₁₃	1	1	yes	characteristic
32	C₂×C₁₃	C₃×C₄×C₁₉	1	2	yes	direct product factor
33	C₂×C₁₃	C₂²×C₃×C₁₉	1	1	yes	characteristic
34	C₂×C₃×C₄	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
35	C₁₉	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₃	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₃	C₂×C₁₃×C₁₉	1	1	yes	characteristic
38	C₃×C₄	C₂×C₁₃×C₁₉	1	2	yes	direct product factor
39	C₂×C₄	C₃×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	C₄×C₁₃×C₁₉	1	2	yes	direct product factor
41	C₂×C₃	C₂²×C₁₃×C₁₉	1	1	yes	characteristic
42	C₂²	C₂×C₃×C₁₃×C₁₉	1	1	yes	characteristic
43	C₄	C₂×C₃×C₁₃×C₁₉	1	2	yes	direct product factor
44	C₃	C₂×C₄×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×C₄×C₁₃×C₁₉	1	2	yes	direct product factor
46	C₂	C₂²×C₃×C₁₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₁₃×C₁₉
socle, prime radical	C₂²×C₃×C₁₃×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₁₃×C₁₉	C₂	direct (N × H)
3. C₂×C₄×C₁₃×C₁₉	C₃	direct (N × H)
4. C₂×C₃×C₁₃×C₁₉	C₄	direct (N × H)
7. C₄×C₁₃×C₁₉	C₂×C₃	direct (N × H)
8. C₃×C₁₃×C₁₉	C₂×C₄	direct (N × H)
9. C₂×C₁₃×C₁₉	C₃×C₄	direct (N × H)
11. C₂×C₃×C₄×C₁₉	C₁₃	direct (N × H)
12. C₂×C₃×C₄×C₁₃	C₁₉	direct (N × H)
13. C₁₃×C₁₉	C₂×C₃×C₄	direct (N × H)
15. C₃×C₄×C₁₉	C₂×C₁₃	direct (N × H)
17. C₃×C₄×C₁₃	C₂×C₁₉	direct (N × H)
18. C₂×C₄×C₁₉	C₃×C₁₃	direct (N × H)
19. C₂×C₃×C₁₉	C₄×C₁₃	direct (N × H)
21. C₂×C₄×C₁₃	C₃×C₁₉	direct (N × H)
22. C₂×C₃×C₁₃	C₄×C₁₉	direct (N × H)
25. C₄×C₁₉	C₂×C₃×C₁₃	direct (N × H)
26. C₃×C₁₉	C₂×C₄×C₁₃	direct (N × H)
28. C₄×C₁₃	C₂×C₃×C₁₉	direct (N × H)
29. C₃×C₁₃	C₂×C₄×C₁₉	direct (N × H)
30. C₂×C₁₉	C₃×C₄×C₁₃	direct (N × H)
32. C₂×C₁₃	C₃×C₄×C₁₉	direct (N × H)
34. C₂×C₃×C₄	C₁₃×C₁₉	direct (N × H)
35. C₁₉	C₂×C₃×C₄×C₁₃	direct (N × H)
36. C₁₃	C₂×C₃×C₄×C₁₉	direct (N × H)
38. C₃×C₄	C₂×C₁₃×C₁₉	direct (N × H)
39. C₂×C₄	C₃×C₁₃×C₁₉	direct (N × H)
40. C₂×C₃	C₄×C₁₃×C₁₉	direct (N × H)
43. C₄	C₂×C₃×C₁₃×C₁₉	direct (N × H)
44. C₃	C₂×C₄×C₁₃×C₁₉	direct (N × H)
45. C₂	C₃×C₄×C₁₃×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
C₂²×C₃×C₁₃×C₁₉	2
C₃×C₄×C₁₃×C₁₉	2
C₂×C₄×C₁₃×C₁₉	3
C₂×C₃×C₄×C₁₉	13
C₂×C₃×C₄×C₁₃	19

Subgroups — C2×C3×C4×C13×C19 #72185141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₁₃×C₁₉ #72185141