Subgroups — C₃²×C₇×C₁₉×D₁₃ #44528024

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×C₁₉×D₁₃	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	4	yes	complemented
4	C₃²×C₁₉×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₉×D₁₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃²×C₇×C₁₉	—	13	1	no	maximal, Hall
7	C₃²×C₁₃×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₇×D₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₉×D₁₃	C₃×C₇	1	4	yes	direct product factor
11	C₃²×C₇×C₁₉	D₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃²×C₇×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇×C₁₉	—	13	4	no	—
14	C₃×C₁₃×C₁₉	C₂×C₃×C₇	1	4	yes	complemented
15	C₃×C₇×D₁₃	C₃×C₁₉	1	4	yes	direct product factor
16	C₁₉×D₁₃	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇×C₁₉	C₃×D₁₃	1	4	yes	direct product factor
18	C₂×C₃²×C₁₉	—	13	1	no	Hall
19	C₃×C₇×C₁₃	C₂×C₃×C₁₉	1	4	yes	complemented
20	C₂×C₇×C₁₉	—	13	1	no	Hall
21	C₁₃×C₁₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₃²×D₁₃	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
23	C₇×D₁₃	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃²×C₁₉	C₇×D₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₇×C₁₉	C₃²×D₁₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₃²×C₇	—	13	1	no	Hall
27	C₃²×C₁₃	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₉	—	13	4	no	—
29	C₇×C₁₃	C₂×C₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₃	C₃×C₇×C₁₉	1	4	yes	direct product factor
31	C₃²×C₇	C₁₉×D₁₃	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₉	C₃×C₇×D₁₃	1	4	yes	direct product factor
33	C₂×C₃×C₇	—	13	4	no	—
34	C₃×C₁₃	C₂×C₃×C₇×C₁₉	1	4	yes	complemented
35	C₂×C₁₉	—	13	1	no	Hall
36	D₁₃	C₃²×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₇	C₃×C₁₉×D₁₃	1	4	yes	direct product factor
38	C₁₉	C₃²×C₇×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₃²	—	13	1	no	Hall
40	C₂×C₇	—	13	1	no	Hall
41	C₁₃	C₂×C₃²×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
42	C₃²	C₇×C₁₉×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₇	C₃²×C₁₉×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃	—	13	4	no	—
45	C₃	C₃×C₇×C₁₉×D₁₃	1	4	yes	direct product factor
46	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇×C₁₉	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃²×C₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₃×C₁₉	C₂	semidirect
2. C₃×C₇×C₁₉×D₁₃	C₃	direct (N × H)
3. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
4. C₃²×C₁₉×D₁₃	C₇	direct (N × H)
5. C₇×C₁₉×D₁₃	C₃²	direct (N × H)
7. C₃²×C₁₃×C₁₉	C₂×C₇	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
9. C₃²×C₇×D₁₃	C₁₉	direct (N × H)
10. C₃×C₁₉×D₁₃	C₃×C₇	direct (N × H)
11. C₃²×C₇×C₁₉	D₁₃	direct (N × H)
12. C₃²×C₇×C₁₃	C₂×C₁₉	semidirect
14. C₃×C₁₃×C₁₉	C₂×C₃×C₇	semidirect
15. C₃×C₇×D₁₃	C₃×C₁₉	direct (N × H)
16. C₁₉×D₁₃	C₃²×C₇	direct (N × H)
17. C₃×C₇×C₁₉	C₃×D₁₃	direct (N × H)
19. C₃×C₇×C₁₃	C₂×C₃×C₁₉	semidirect
21. C₁₃×C₁₉	C₂×C₃²×C₇	semidirect
22. C₃²×D₁₃	C₇×C₁₉	direct (N × H)
23. C₇×D₁₃	C₃²×C₁₉	direct (N × H)
24. C₃²×C₁₉	C₇×D₁₃	direct (N × H)
25. C₇×C₁₉	C₃²×D₁₃	direct (N × H)
27. C₃²×C₁₃	C₂×C₇×C₁₉	semidirect
29. C₇×C₁₃	C₂×C₃²×C₁₉	semidirect
30. C₃×D₁₃	C₃×C₇×C₁₉	direct (N × H)
31. C₃²×C₇	C₁₉×D₁₃	direct (N × H)
32. C₃×C₁₉	C₃×C₇×D₁₃	direct (N × H)
34. C₃×C₁₃	C₂×C₃×C₇×C₁₉	semidirect
36. D₁₃	C₃²×C₇×C₁₉	direct (N × H)
37. C₃×C₇	C₃×C₁₉×D₁₃	direct (N × H)
38. C₁₉	C₃²×C₇×D₁₃	direct (N × H)
41. C₁₃	C₂×C₃²×C₇×C₁₉	semidirect
42. C₃²	C₇×C₁₉×D₁₃	direct (N × H)
43. C₇	C₃²×C₁₉×D₁₃	direct (N × H)
45. C₃	C₃×C₇×C₁₉×D₁₃	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×C₇×C₁₃×C₁₉	2
C₃×C₇×C₁₉×D₁₃	3
C₃²×C₁₉×D₁₃	7
C₂×C₃²×C₇×C₁₉	13
C₃²×C₇×D₁₃	19

Subgroups — C32×C7×C19×D13 #44528024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×C₁₉×D₁₃ #44528024