Subgroups — C₃×D₁₃×D₁₉⋊C₃ #22580270

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃	D₁₃×D₁₉⋊C₃
commutator, hypocenter	C₁₃×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₃×C₁₉⋊C₃	C₂	semidirect
2. C₃×(C₁₉⋊C₃)⋊D₁₃	C₂	semidirect
3. C₃×C₁₃×D₁₉⋊C₃	C₂	semidirect
4. C₃×D₁₃×D₁₉	C₃	semidirect
5. D₁₃×D₁₉⋊C₃	C₃	direct (N × H)
6. C₃×C₁₃×C₁₉⋊C₃	C₂²	semidirect
7. C₃×D₂₄₇	C₂×C₃	semidirect
8. C₃×C₁₉×D₁₃	C₂×C₃	semidirect
9. C₃×C₁₃×D₁₉	C₂×C₃	semidirect
10. (C₁₉⋊C₃)⋊D₁₃	C₂×C₃	semidirect
11. D₁₃×C₁₉⋊C₃	C₂×C₃	semidirect
12. C₁₃×D₁₉⋊C₃	C₂×C₃	semidirect
13. D₁₃×D₁₉	C₃²	semidirect
14. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
15. C₁₃×C₁₉⋊C₃	C₂²×C₃	semidirect
17. D₂₄₇	C₂×C₃²	semidirect
18. C₁₃×D₁₉	C₂×C₃²	semidirect
19. C₁₉×D₁₃	C₂×C₃²	semidirect
23. C₃×D₁₉⋊C₃	D₁₃	direct (N × H)
24. C₁₃×C₁₉	C₂²×C₃²	semidirect
30. C₃×C₁₉⋊C₃	C₂×D₁₃	semidirect
36. C₃×D₁₉	C₃×D₁₃	semidirect
39. D₁₉⋊C₃	C₃×D₁₃	direct (N × H)
45. C₃×D₁₃	D₁₉⋊C₃	direct (N × H)
47. C₃×C₁₉	C₂×C₃×D₁₃	semidirect
48. C₁₉⋊C₃	C₂×C₃×D₁₃	semidirect
51. C₃×C₁₃	C₂×D₁₉⋊C₃	semidirect
54. D₁₉	C₃²×D₁₃	semidirect
58. D₁₃	C₃×D₁₉⋊C₃	direct (N × H)
59. C₁₉	C₂×C₃²×D₁₃	semidirect
63. C₁₃	C₂×C₃×D₁₉⋊C₃	semidirect
75. C₃	D₁₃×D₁₉⋊C₃	direct (N × H)

Subgroups — C3×D13×D19⋊C3 #22580270

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₃×D₁₉⋊C₃ #22580270