Subgroups — C₂×C₁₃²×D₁₉⋊C₃ #50310421

Order 38532.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃²×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃²×D₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₃²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃²×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃²×D₁₉	C₂×C₃	1	2	yes	complemented
6	C₂×C₁₃²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₃×D₁₉⋊C₃	C₁₃	1	14	yes	maximal, direct product factor
9	C₂²×C₃×C₁₃²	—	19	1	no	maximal, Hall
10	C₂×C₁₃×C₁₉⋊C₃	C₂×C₁₃	1	14	yes	complemented
11	C₁₃×D₁₉⋊C₃	C₂×C₁₃	1	28	yes	direct product factor
12	C₂×C₃×C₁₃²	—	19	2	no	—
13	C₂×C₃×C₁₃²	—	19	1	no	—
14	C₂×C₁₃×D₁₉	C₃×C₁₃	1	14	yes	complemented
15	C₁₃×C₁₉⋊C₃	C₂²×C₁₃	1	14	yes	complemented
16	C₂²×C₁₃²	—	19	1	no	Hall
17	C₃×C₁₃²	—	19	1	no	Hall
18	C₂×C₁₃×C₁₉	C₂×C₃×C₁₃	1	14	yes	complemented
19	C₁₃×D₁₉	C₂×C₃×C₁₃	1	28	yes	complemented
20	C₂×C₁₃²	—	19	2	no	—
21	C₂×C₁₃²	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
22	C₁₃×C₁₉	C₂²×C₃×C₁₃	1	14	yes	complemented
23	C₂×D₁₉⋊C₃	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
24	C₁₃²	C₂×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃×C₁₃	—	19	14	no	—
26	C₂×C₁₉⋊C₃	C₂×C₁₃²	1	1	yes	characteristic, complemented
27	D₁₉⋊C₃	C₂×C₁₃²	1	2	yes	direct product factor
28	C₂×C₃×C₁₃	—	19	28	no	—
29	C₂×C₃×C₁₃	—	19	14	no	—
30	C₂×D₁₉	C₃×C₁₃²	1	1	yes	characteristic, complemented, Hall
31	C₁₉⋊C₃	C₂²×C₁₃²	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₁₃	—	19	14	no	—
33	C₃×C₁₃	—	19	14	no	—
34	C₂×C₁₉	C₂×C₃×C₁₃²	1	1	yes	characteristic, complemented
35	D₁₉	C₂×C₃×C₁₃²	1	2	yes	complemented
36	C₂×C₁₃	—	19	28	no	—
37	C₂×C₁₃	C₁₃×D₁₉⋊C₃	1	14	yes	direct product factor
38	C₁₉	C₂²×C₃×C₁₃²	1	1	yes	characteristic, complemented, Sylow
39	C₁₃	C₂×C₁₃×D₁₉⋊C₃	1	14	yes	direct product factor
40	C₂²×C₃	—	19	1	no	Hall
41	C₂×C₃	—	19	2	no	—
42	C₂×C₃	—	19	1	no	—
43	C₂²	—	19	1	no	Sylow
44	C₃	—	19	1	no	Sylow
45	C₂	—	19	2	no	—
46	C₂	C₁₃²×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃²	D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃×C₁₃²
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²×C₁₉	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃²×C₁₉⋊C₃	C₂	semidirect
2. C₁₃²×D₁₉⋊C₃	C₂	direct (N × H)
3. C₂×C₁₃²×D₁₉	C₃	semidirect
4. C₁₃²×C₁₉⋊C₃	C₂²	semidirect
5. C₁₃²×D₁₉	C₂×C₃	semidirect
6. C₂×C₁₃²×C₁₉	C₂×C₃	semidirect
7. C₁₃²×C₁₉	C₂²×C₃	semidirect
8. C₂×C₁₃×D₁₉⋊C₃	C₁₃	direct (N × H)
10. C₂×C₁₃×C₁₉⋊C₃	C₂×C₁₃	semidirect
11. C₁₃×D₁₉⋊C₃	C₂×C₁₃	direct (N × H)
14. C₂×C₁₃×D₁₉	C₃×C₁₃	semidirect
15. C₁₃×C₁₉⋊C₃	C₂²×C₁₃	semidirect
18. C₂×C₁₃×C₁₉	C₂×C₃×C₁₃	semidirect
19. C₁₃×D₁₉	C₂×C₃×C₁₃	semidirect
21. C₂×C₁₃²	D₁₉⋊C₃	direct (N × H)
22. C₁₃×C₁₉	C₂²×C₃×C₁₃	semidirect
23. C₂×D₁₉⋊C₃	C₁₃²	direct (N × H)
24. C₁₃²	C₂×D₁₉⋊C₃	direct (N × H)
26. C₂×C₁₉⋊C₃	C₂×C₁₃²	semidirect
27. D₁₉⋊C₃	C₂×C₁₃²	direct (N × H)
30. C₂×D₁₉	C₃×C₁₃²	semidirect
31. C₁₉⋊C₃	C₂²×C₁₃²	semidirect
34. C₂×C₁₉	C₂×C₃×C₁₃²	semidirect
35. D₁₉	C₂×C₃×C₁₃²	semidirect
37. C₂×C₁₃	C₁₃×D₁₉⋊C₃	direct (N × H)
38. C₁₉	C₂²×C₃×C₁₃²	semidirect
39. C₁₃	C₂×C₁₃×D₁₉⋊C₃	direct (N × H)
46. C₂	C₁₃²×D₁₉⋊C₃	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×C₁₃²×C₁₉⋊C₃	2
C₁₃²×D₁₉⋊C₃	2
C₂×C₁₃²×D₁₉	3
C₂×C₁₃×D₁₉⋊C₃	13
C₂²×C₃×C₁₃²	19

Subgroups — C2×C132×D19⋊C3 #50310421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃²×D₁₉⋊C₃ #50310421