Subgroups — C₂×C₃×(C₁₃⋊C₃)⋊D₁₉ #22580324

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×(C₁₃⋊C₃)⋊D₁₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₂₄₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₁₃⋊C₃)⋊D₁₉	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₁₉×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₂₄₇	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₉×C₁₃⋊C₃	C₂×C₃	1	3	yes	complemented
9	(C₁₃⋊C₃)⋊D₁₉	C₂×C₃	1	6	yes	direct product factor
10	C₂×D₂₄₇	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
12	C₁₉×C₁₃⋊C₃	C₂²×C₃	1	3	yes	complemented
13	C₂×C₃²×D₁₉	—	13	1	no	maximal, Hall
14	C₂×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
15	D₂₄₇	C₂×C₃²	1	2	yes	complemented
16	C₂×C₃×D₁₃⋊C₃	—	19	1	no	maximal, Hall
17	C₂×C₃²×C₁₉	—	13	1	no	—
18	C₃²×D₁₉	—	13	2	no	—
19	C₁₃×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₃⋊C₃	D₁₉	1	1	yes	characteristic, complemented
21	C₃×D₁₃⋊C₃	—	19	2	no	—
22	C₂×C₃×D₁₉	—	13	3	no	—
23	C₂×C₃×D₁₉	—	13	1	no	—
24	C₃²×C₁₉	—	13	1	no	Hall
25	C₂×C₃×D₁₃	—	19	1	no	—
26	C₂×D₁₃⋊C₃	—	19	3	no	—
27	C₃×C₁₃⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₉	—	13	3	no	—
29	C₂×C₃×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
30	C₃×D₁₉	—	13	6	no	—
31	C₃×D₁₉	—	13	2	no	—
32	C₂×C₃×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
33	C₃×D₁₃	—	19	2	no	—
34	C₂×C₁₃⋊C₃	C₃×D₁₉	1	3	yes	complemented
35	D₁₃⋊C₃	—	19	6	no	—
36	C₂×D₁₉	—	13	1	no	Hall
37	C₃×C₁₉	—	13	3	no	—
38	C₃×C₁₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
39	C₂×D₁₃	—	19	1	no	Hall
40	C₃×C₁₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
41	C₁₃⋊C₃	C₂×C₃×D₁₉	1	3	yes	complemented
42	C₂×C₁₉	C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented
43	D₁₉	—	13	2	no	—
44	C₂²×C₃²	—	247	1	no	Hall
45	C₂×C₁₃	C₃²×D₁₉	1	1	yes	characteristic, complemented
46	D₁₃	—	19	2	no	—
47	C₁₉	C₂×C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃²	—	13	1	no	—
49	C₂×C₃²	—	247	2	no	—
50	C₁₃	C₂×C₃²×D₁₉	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₃	—	247	3	no	—
52	C₂²×C₃	—	247	1	no	—
53	C₃²	—	13	1	no	Sylow
54	C₂×C₃	—	13	3	no	—
55	C₂×C₃	—	247	6	no	—
56	C₂×C₃	—	247	2	no	—
57	C₂×C₃	(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor
58	C₂²	—	247	1	no	Sylow
59	C₃	—	13	3	no	—
60	C₃	C₂×(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor
61	C₂	—	247	2	no	—
62	C₂	C₃×(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₁₃⋊C₃)⋊D₁₉
commutator, hypocenter	C₁₃×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₉×C₁₃⋊C₃	C₂	semidirect
2. C₃×(C₁₃⋊C₃)⋊D₁₉	C₂	direct (N × H)
3. C₂×C₃×D₂₄₇	C₃	semidirect
4. C₂×(C₁₃⋊C₃)⋊D₁₉	C₃	direct (N × H)
5. C₃×C₁₉×C₁₃⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₃×D₂₄₇	C₂×C₃	semidirect
8. C₂×C₁₉×C₁₃⋊C₃	C₂×C₃	semidirect
9. (C₁₃⋊C₃)⋊D₁₉	C₂×C₃	direct (N × H)
10. C₂×D₂₄₇	C₃²	semidirect
11. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
12. C₁₉×C₁₃⋊C₃	C₂²×C₃	semidirect
14. C₂×C₁₃×C₁₉	C₂×C₃²	semidirect
15. D₂₄₇	C₂×C₃²	semidirect
19. C₁₃×C₁₉	C₂²×C₃²	semidirect
20. C₂×C₃×C₁₃⋊C₃	D₁₉	semidirect
27. C₃×C₁₃⋊C₃	C₂×D₁₉	semidirect
29. C₂×C₃×C₁₉	D₁₃⋊C₃	semidirect
32. C₂×C₃×C₁₃	C₃×D₁₉	semidirect
34. C₂×C₁₃⋊C₃	C₃×D₁₉	semidirect
38. C₃×C₁₉	C₂×D₁₃⋊C₃	semidirect
40. C₃×C₁₃	C₂×C₃×D₁₉	semidirect
41. C₁₃⋊C₃	C₂×C₃×D₁₉	semidirect
42. C₂×C₁₉	C₃×D₁₃⋊C₃	semidirect
45. C₂×C₁₃	C₃²×D₁₉	semidirect
47. C₁₉	C₂×C₃×D₁₃⋊C₃	semidirect
50. C₁₃	C₂×C₃²×D₁₉	semidirect
57. C₂×C₃	(C₁₃⋊C₃)⋊D₁₉	direct (N × H)
60. C₃	C₂×(C₁₃⋊C₃)⋊D₁₉	direct (N × H)
62. C₂	C₃×(C₁₃⋊C₃)⋊D₁₉	direct (N × H)

Subgroups — C2×C3×(C13⋊C3)⋊D19 #22580324

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×(C₁₃⋊C₃)⋊D₁₉ #22580324