Subgroups — C₂×C₄×C₇×C₁₃×C₁₉ #72192073

Order 13832.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₁₃×C₁₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×C₁₃×C₁₉	C₄	1	2	yes	direct product factor
4	C₂×C₇×C₁₃×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₃×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₃×C₁₉	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₄×C₇×C₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₁₃×C₁₉	C₂×C₇	1	1	yes	characteristic
9	C₄×C₁₃×C₁₉	C₂×C₇	1	2	yes	direct product factor
10	C₂×C₄×C₇×C₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₇×C₁₉	C₂×C₁₃	1	1	yes	characteristic
12	C₄×C₇×C₁₉	C₂×C₁₃	1	2	yes	direct product factor
13	C₂×C₁₃×C₁₉	C₄×C₇	1	2	yes	direct product factor
14	C₂×C₁₃×C₁₉	C₂²×C₇	1	1	yes	characteristic
15	C₂²×C₇×C₁₃	C₂×C₁₉	1	1	yes	characteristic
16	C₄×C₇×C₁₃	C₂×C₁₉	1	2	yes	direct product factor
17	C₂×C₇×C₁₉	C₄×C₁₃	1	2	yes	direct product factor
18	C₂×C₇×C₁₉	C₂²×C₁₃	1	1	yes	characteristic
19	C₁₃×C₁₉	C₂×C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₇×C₁₃	C₄×C₁₉	1	2	yes	direct product factor
21	C₂×C₇×C₁₃	C₂²×C₁₉	1	1	yes	characteristic
22	C₂×C₄×C₁₉	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₇×C₁₉	C₂×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₄×C₁₃	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
25	C₇×C₁₃	C₂×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₁₉	C₂×C₇×C₁₃	1	1	yes	characteristic
27	C₄×C₁₉	C₂×C₇×C₁₃	1	2	yes	direct product factor
28	C₂×C₄×C₇	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₁₃	C₂×C₇×C₁₉	1	1	yes	characteristic
30	C₄×C₁₃	C₂×C₇×C₁₉	1	2	yes	direct product factor
31	C₂×C₁₉	C₄×C₇×C₁₃	1	2	yes	direct product factor
32	C₂×C₁₉	C₂²×C₇×C₁₃	1	1	yes	characteristic
33	C₂²×C₇	C₂×C₁₃×C₁₉	1	1	yes	characteristic
34	C₄×C₇	C₂×C₁₃×C₁₉	1	2	yes	direct product factor
35	C₂×C₁₃	C₄×C₇×C₁₉	1	2	yes	direct product factor
36	C₂×C₁₃	C₂²×C₇×C₁₉	1	1	yes	characteristic
37	C₁₉	C₂×C₄×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₇	C₄×C₁₃×C₁₉	1	2	yes	direct product factor
39	C₂×C₇	C₂²×C₁₃×C₁₉	1	1	yes	characteristic
40	C₁₃	C₂×C₄×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₄	C₇×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂×C₄×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	C₂×C₇×C₁₃×C₁₉	1	1	yes	characteristic
44	C₄	C₂×C₇×C₁₃×C₁₉	1	2	yes	direct product factor
45	C₂	C₄×C₇×C₁₃×C₁₉	1	2	yes	direct product factor
46	C₂	C₂²×C₇×C₁₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₇×C₁₃×C₁₉
socle, prime radical	C₂²×C₇×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. C₄×C₇×C₁₃×C₁₉	C₂	direct (N × H)
3. C₂×C₇×C₁₃×C₁₉	C₄	direct (N × H)
5. C₂×C₄×C₁₃×C₁₉	C₇	direct (N × H)
6. C₇×C₁₃×C₁₉	C₂×C₄	direct (N × H)
7. C₂×C₄×C₇×C₁₉	C₁₃	direct (N × H)
9. C₄×C₁₃×C₁₉	C₂×C₇	direct (N × H)
10. C₂×C₄×C₇×C₁₃	C₁₉	direct (N × H)
12. C₄×C₇×C₁₉	C₂×C₁₃	direct (N × H)
13. C₂×C₁₃×C₁₉	C₄×C₇	direct (N × H)
16. C₄×C₇×C₁₃	C₂×C₁₉	direct (N × H)
17. C₂×C₇×C₁₉	C₄×C₁₃	direct (N × H)
19. C₁₃×C₁₉	C₂×C₄×C₇	direct (N × H)
20. C₂×C₇×C₁₃	C₄×C₁₉	direct (N × H)
22. C₂×C₄×C₁₉	C₇×C₁₃	direct (N × H)
23. C₇×C₁₉	C₂×C₄×C₁₃	direct (N × H)
24. C₂×C₄×C₁₃	C₇×C₁₉	direct (N × H)
25. C₇×C₁₃	C₂×C₄×C₁₉	direct (N × H)
27. C₄×C₁₉	C₂×C₇×C₁₃	direct (N × H)
28. C₂×C₄×C₇	C₁₃×C₁₉	direct (N × H)
30. C₄×C₁₃	C₂×C₇×C₁₉	direct (N × H)
31. C₂×C₁₉	C₄×C₇×C₁₃	direct (N × H)
34. C₄×C₇	C₂×C₁₃×C₁₉	direct (N × H)
35. C₂×C₁₃	C₄×C₇×C₁₉	direct (N × H)
37. C₁₉	C₂×C₄×C₇×C₁₃	direct (N × H)
38. C₂×C₇	C₄×C₁₃×C₁₉	direct (N × H)
40. C₁₃	C₂×C₄×C₇×C₁₉	direct (N × H)
41. C₂×C₄	C₇×C₁₃×C₁₉	direct (N × H)
42. C₇	C₂×C₄×C₁₃×C₁₉	direct (N × H)
44. C₄	C₂×C₇×C₁₃×C₁₉	direct (N × H)
45. C₂	C₄×C₇×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×C₇×C₁₃×C₁₉	2
C₄×C₇×C₁₃×C₁₉	2
C₂×C₄×C₁₃×C₁₉	7
C₂×C₄×C₇×C₁₉	13
C₂×C₄×C₇×C₁₃	19

Subgroups — C2×C4×C7×C13×C19 #72192073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₇×C₁₃×C₁₉ #72192073