Subgroups — C₂×C₁₉×C₁₁⋊(D₁₃⋊C₃) #45656758

Order 32604.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₁₁⋊(D₁₃⋊C₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×D₁₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×C₁₉×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₉×D₁₄₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₁₁×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₁₉×D₁₃⋊C₃	—	11	1	no	maximal, Hall
8	C₁₁×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₉×D₁₁	—	13	1	no	maximal, Hall
10	C₂×C₁₁⋊(D₁₃⋊C₃)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₉×C₁₃⋊C₃	D₁₁	1	1	yes	characteristic, complemented
12	C₁₉×D₁₃⋊C₃	—	11	2	no	—
13	C₂×C₃×C₁₁×C₁₉	—	13	1	no	—
14	C₃×C₁₉×D₁₁	—	13	2	no	—
15	C₂×C₁₉×D₁₃	—	11	1	no	Hall
16	C₂×C₁₁×C₁₃⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented
17	C₁₁⋊(D₁₃⋊C₃)	C₂×C₁₉	1	2	yes	direct product factor
18	C₂×C₁₉×D₁₁	—	13	1	no	Hall
19	C₁₉×C₁₃⋊C₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₁×C₁₉	—	13	1	no	Hall
21	C₂×D₁₄₃	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃×C₁₉	C₃×D₁₁	1	1	yes	characteristic, complemented
23	C₁₉×D₁₃	—	11	2	no	—
24	C₁₁×C₁₃⋊C₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₁×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₁₉×D₁₁	—	13	2	no	—
27	C₂×C₁₁×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
28	D₁₄₃	C₂×C₃×C₁₉	1	2	yes	complemented
29	C₁₃×C₁₉	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃×C₁₉	—	143	1	no	Hall
31	C₁₁×C₁₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
32	C₂×D₁₃⋊C₃	—	11	1	no	Hall
33	C₁₁×C₁₃	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×D₁₁	—	13	1	no	Hall
35	C₂×C₃×C₁₉	—	13	1	no	—
36	C₂×C₃×C₁₉	—	143	2	no	—
37	C₂×C₁₃⋊C₃	C₁₉×D₁₁	1	1	yes	characteristic, complemented
38	D₁₃⋊C₃	—	11	2	no	—
39	C₂²×C₁₉	—	143	1	no	Hall
40	C₂×C₃×C₁₁	—	13	1	no	—
41	C₃×D₁₁	—	13	2	no	—
42	C₃×C₁₉	—	13	1	no	Hall
43	C₂×D₁₃	—	11	1	no	Hall
44	C₂×D₁₁	—	13	1	no	Hall
45	C₁₃⋊C₃	C₂×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Hall
46	C₂×C₁₉	—	143	2	no	—
47	C₂×C₁₉	C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
48	C₃×C₁₁	—	13	1	no	Hall
49	C₂×C₁₃	C₃×C₁₉×D₁₁	1	1	yes	characteristic, complemented
50	D₁₃	—	11	2	no	—
51	C₂×C₁₁	C₁₉×D₁₃⋊C₃	1	1	yes	characteristic, complemented
52	D₁₁	—	13	2	no	—
53	C₁₉	C₂×C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
54	C₁₃	C₂×C₃×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	143	1	no	Hall
56	C₁₁	C₂×C₁₉×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	13	1	no	—
58	C₂×C₃	—	143	2	no	—
59	C₂²	—	143	1	no	Sylow
60	C₃	—	13	1	no	Sylow
61	C₂	—	143	2	no	—
62	C₂	C₁₉×C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₁₁⋊(D₁₃⋊C₃)
commutator, cosocle, hypocenter	C₁₁×C₁₃	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₁₁⋊(D₁₃⋊C₃)	C₂	direct (N × H)
2. C₂×C₁₁×C₁₉×C₁₃⋊C₃	C₂	semidirect
3. C₂×C₁₉×D₁₄₃	C₃	semidirect
4. C₁₁×C₁₉×C₁₃⋊C₃	C₂²	semidirect
5. C₁₉×D₁₄₃	C₂×C₃	semidirect
6. C₂×C₁₁×C₁₃×C₁₉	C₂×C₃	semidirect
8. C₁₁×C₁₃×C₁₉	C₂²×C₃	semidirect
10. C₂×C₁₁⋊(D₁₃⋊C₃)	C₁₉	direct (N × H)
11. C₂×C₁₉×C₁₃⋊C₃	D₁₁	semidirect
16. C₂×C₁₁×C₁₃⋊C₃	C₂×C₁₉	semidirect
17. C₁₁⋊(D₁₃⋊C₃)	C₂×C₁₉	direct (N × H)
19. C₁₉×C₁₃⋊C₃	C₂×D₁₁	semidirect
21. C₂×D₁₄₃	C₃×C₁₉	semidirect
22. C₂×C₁₃×C₁₉	C₃×D₁₁	semidirect
24. C₁₁×C₁₃⋊C₃	C₂²×C₁₉	semidirect
25. C₂×C₁₁×C₁₉	D₁₃⋊C₃	semidirect
27. C₂×C₁₁×C₁₃	C₂×C₃×C₁₉	semidirect
28. D₁₄₃	C₂×C₃×C₁₉	semidirect
29. C₁₃×C₁₉	C₂×C₃×D₁₁	semidirect
31. C₁₁×C₁₉	C₂×D₁₃⋊C₃	semidirect
33. C₁₁×C₁₃	C₂²×C₃×C₁₉	semidirect
37. C₂×C₁₃⋊C₃	C₁₉×D₁₁	semidirect
45. C₁₃⋊C₃	C₂×C₁₉×D₁₁	semidirect
47. C₂×C₁₉	C₁₁⋊(D₁₃⋊C₃)	direct (N × H)
49. C₂×C₁₃	C₃×C₁₉×D₁₁	semidirect
51. C₂×C₁₁	C₁₉×D₁₃⋊C₃	semidirect
53. C₁₉	C₂×C₁₁⋊(D₁₃⋊C₃)	direct (N × H)
54. C₁₃	C₂×C₃×C₁₉×D₁₁	semidirect
56. C₁₁	C₂×C₁₉×D₁₃⋊C₃	semidirect
62. C₂	C₁₉×C₁₁⋊(D₁₃⋊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
C₁₉×C₁₁⋊(D₁₃⋊C₃)	2
C₂×C₁₁×C₁₉×C₁₃⋊C₃	2
C₂×C₁₉×D₁₄₃	3
C₂×C₁₉×D₁₃⋊C₃	11
C₂×C₃×C₁₉×D₁₁	13
C₂×C₁₁⋊(D₁₃⋊C₃)	19

Subgroups — C2×C19×C11⋊(D13⋊C3) #45656758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×C₁₁⋊(D₁₃⋊C₃) #45656758