Subgroups — C₁₃×C₃⋊D₃×D₁₉ #22580357

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₃×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₃×D₁₉	—	3	4	no	maximal
5	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₅₇	—	3	4	no	—
7	D₃×C₁₃×C₁₉	—	3	4	no	—
8	C₃×C₁₃×D₁₉	D₃	1	4	yes	complemented
9	C₂×C₁₃×D₁₉	—	9	1	no	Hall
10	C₃×C₁₃×C₁₉	C₂×D₃	1	4	yes	complemented
11	C₃⋊D₃×D₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₁₃×C₁₉	—	9	1	no	—
13	C₁₃×D₁₉	—	9	1	no	—
14	C₁₃×D₁₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₁₃×C₃⋊D₃	—	19	1	no	maximal, Hall
16	C₃⋊D₅₇	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₃⋊D₃×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₃²×D₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₁₃×C₁₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃²×C₁₃	—	19	1	no	—
21	C₁₃×C₃⋊D₃	—	19	1	no	—
22	C₁₃×C₃⋊D₃	D₁₉	1	1	yes	characteristic, direct product factor
23	D₃×D₁₉	—	3	4	no	—
24	C₃²×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃×C₁₃	—	57	4	no	—
26	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
27	D₅₇	—	3	4	no	—
28	C₃×D₁₉	D₃×C₁₃	1	4	yes	complemented
29	D₃×C₁₉	—	3	4	no	—
30	C₂×C₃×C₁₃	—	19	4	no	—
31	D₃×C₁₃	—	3	4	no	—
32	D₃×C₁₃	—	57	4	no	—
33	C₂×D₁₉	—	9	1	no	Hall
34	C₃×C₁₉	C₂×D₃×C₁₃	1	4	yes	complemented
35	C₂²×C₁₃	—	171	1	no	Hall
36	C₃×C₁₃	D₃×D₁₉	1	4	yes	complemented
37	C₂×C₁₉	—	9	1	no	—
38	D₁₉	—	9	1	no	—
39	D₁₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃⋊D₃	—	19	1	no	Hall
41	C₂×C₁₃	—	9	1	no	—
42	C₂×C₁₃	—	19	1	no	—
43	C₂×C₁₃	—	171	1	no	—
44	C₁₉	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃²	—	19	1	no	—
46	C₃⋊D₃	—	19	1	no	—
47	C₃⋊D₃	C₁₃×D₁₉	1	1	yes	characteristic, direct product factor
48	C₁₃	C₃⋊D₃×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×D₃	—	57	4	no	—
50	C₃²	C₂×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	19	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	57	4	no	—
54	C₂²	—	171	1	no	Sylow
55	C₃	D₃×C₁₃×D₁₉	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	19	1	no	—
58	C₂	—	171	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊D₃×D₁₉
commutator, hypocenter	C₃²×C₁₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₅₇	C₂	semidirect
2. C₁₃×C₃⋊D₃×C₁₉	C₂	semidirect
3. C₃²×C₁₃×D₁₉	C₂	semidirect
5. C₃²×C₁₃×C₁₉	C₂²	semidirect
8. C₃×C₁₃×D₁₉	D₃	semidirect
10. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
11. C₃⋊D₃×D₁₉	C₁₃	direct (N × H)
14. C₁₃×D₁₉	C₃⋊D₃	direct (N × H)
16. C₃⋊D₅₇	C₂×C₁₃	semidirect
17. C₃⋊D₃×C₁₉	C₂×C₁₃	semidirect
18. C₃²×D₁₉	C₂×C₁₃	semidirect
19. C₁₃×C₁₉	C₂×C₃⋊D₃	semidirect
22. C₁₃×C₃⋊D₃	D₁₉	direct (N × H)
24. C₃²×C₁₉	C₂²×C₁₃	semidirect
26. C₃²×C₁₃	C₂×D₁₉	semidirect
28. C₃×D₁₉	D₃×C₁₃	semidirect
34. C₃×C₁₉	C₂×D₃×C₁₃	semidirect
36. C₃×C₁₃	D₃×D₁₉	semidirect
39. D₁₉	C₁₃×C₃⋊D₃	direct (N × H)
44. C₁₉	C₂×C₁₃×C₃⋊D₃	semidirect
47. C₃⋊D₃	C₁₃×D₁₉	direct (N × H)
48. C₁₃	C₃⋊D₃×D₁₉	direct (N × H)
50. C₃²	C₂×C₁₃×D₁₉	semidirect
55. C₃	D₃×C₁₃×D₁₉	semidirect

Subgroups — C13×C3⋊D3×D19 #22580357

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×C₃⋊D₃×D₁₉ #22580357