Subgroups — C₂×C₁₉⋊C₃×D₁₃⋊C₃ #22580253

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊C₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉⋊C₃×D₁₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₁₃×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#13093365	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×#13093364	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×D₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
7	C₁₃⋊C₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
8	C₂×#10625203	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×#10625202	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₁₉×C₁₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
12	#13093365	C₂×C₃	1	2	yes	complemented
13	#13093364	C₂×C₃	1	2	yes	complemented
14	C₁₉×D₁₃⋊C₃	C₂×C₃	1	2	yes	complemented
15	D₁₃×C₁₉⋊C₃	C₂×C₃	1	2	yes	complemented
16	C₂×C₁₉×D₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
17	#10625203	C₂²×C₃	1	1	yes	characteristic, complemented
18	#10625202	C₂²×C₃	1	1	yes	characteristic, complemented
19	C₁₃×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic, complemented
20	C₁₉×C₁₃⋊C₃	C₂²×C₃	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₁₉⋊C₃	—	13	1	no	maximal, Hall
22	C₂×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
23	C₁₉×D₁₃	C₂×C₃²	1	2	yes	complemented
24	C₂×C₃×D₁₃⋊C₃	—	19	1	no	maximal, Hall
25	C₂×C₃×C₁₉⋊C₃	—	13	2	no	—
26	C₂×C₃×C₁₉⋊C₃	—	13	1	no	—
27	C₁₃×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₃⋊C₃	—	19	1	no	—
29	C₃×D₁₃⋊C₃	—	19	2	no	—
30	C₂²×C₃×C₁₉	—	13	1	no	—
31	C₂²×C₁₉⋊C₃	—	13	1	no	—
32	C₂²×C₁₉⋊C₃	—	13	1	no	—
33	C₂²×C₁₉⋊C₃	—	13	1	no	—
34	C₃×C₁₉⋊C₃	—	13	1	no	Hall
35	C₂×C₃×D₁₃	—	19	1	no	—
36	C₂×D₁₃⋊C₃	—	19	1	no	—
37	C₂×D₁₃⋊C₃	—	19	1	no	—
38	C₂×D₁₃⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
39	C₃×C₁₃⋊C₃	—	19	1	no	Hall
40	C₂×C₃×C₁₉	—	13	2	no	—
41	C₂×C₃×C₁₉	—	13	1	no	—
42	C₂×C₁₉⋊C₃	—	13	2	no	—
43	C₂×C₁₉⋊C₃	—	13	2	no	—
44	C₂×C₁₉⋊C₃	—	13	1	no	—
45	C₂×C₁₉⋊C₃	—	13	1	no	—
46	C₂×C₁₉⋊C₃	—	13	2	no	—
47	C₂×C₁₉⋊C₃	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
48	C₂×C₃×C₁₃	—	19	1	no	—
49	C₃×D₁₃	—	19	2	no	—
50	C₂×C₁₃⋊C₃	—	19	1	no	—
51	C₂×C₁₃⋊C₃	—	19	1	no	—
52	C₂×C₁₃⋊C₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
53	D₁₃⋊C₃	—	19	2	no	—
54	D₁₃⋊C₃	—	19	2	no	—
55	D₁₃⋊C₃	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
56	C₂²×C₁₉	—	13	1	no	Hall
57	C₃×C₁₉	—	13	1	no	—
58	C₁₉⋊C₃	—	13	1	no	—
59	C₁₉⋊C₃	—	13	1	no	—
60	C₁₉⋊C₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
61	C₂×D₁₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
62	C₃×C₁₃	—	19	1	no	—
63	C₁₃⋊C₃	—	19	1	no	—
64	C₁₃⋊C₃	—	19	1	no	—
65	C₁₃⋊C₃	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
66	C₂×C₁₉	—	13	2	no	—
67	C₂×C₁₉	C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented
68	C₂²×C₃²	—	247	1	no	Hall
69	C₂×C₁₃	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
70	D₁₃	C₂×C₃×C₁₉⋊C₃	1	2	yes	complemented
71	C₁₉	C₂×C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃²	—	247	1	no	—
73	C₂×C₃²	—	247	2	no	—
74	C₁₃	C₂²×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₃	—	13	1	no	—
76	C₂²×C₃	—	247	1	no	—
77	C₂²×C₃	—	247	1	no	—
78	C₂²×C₃	—	247	1	no	—
79	C₃²	—	247	1	no	Sylow
80	C₂×C₃	—	13	2	no	—
81	C₂×C₃	—	13	1	no	—
82	C₂×C₃	—	19	1	no	—
83	C₂×C₃	—	247	2	no	—
84	C₂×C₃	—	247	2	no	—
85	C₂×C₃	—	247	2	no	—
86	C₂×C₃	—	247	1	no	—
87	C₂×C₃	—	247	1	no	—
88	C₂²	—	13	1	no	Sylow
89	C₃	—	13	1	no	—
90	C₃	—	19	1	no	—
91	C₃	—	247	1	no	—
92	C₃	—	247	1	no	—
93	C₂	—	13	2	no	—
94	C₂	C₁₉⋊C₃×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₉⋊C₃×D₁₃⋊C₃
commutator, hypocenter	C₁₃×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₁₉	C₂×C₃²
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃⋊C₃×C₁₉⋊C₃	C₂	semidirect
2. C₁₉⋊C₃×D₁₃⋊C₃	C₂	direct (N × H)
3. C₂×D₁₃×C₁₉⋊C₃	C₃	semidirect
4. C₂×#13093365	C₃	semidirect
5. C₂×#13093364	C₃	semidirect
6. C₂×C₁₉×D₁₃⋊C₃	C₃	semidirect
7. C₁₃⋊C₃×C₁₉⋊C₃	C₂²	semidirect
8. C₂×#10625203	C₂×C₃	semidirect
9. C₂×#10625202	C₂×C₃	semidirect
10. C₂×C₁₉×C₁₃⋊C₃	C₂×C₃	semidirect
11. C₂×C₁₃×C₁₉⋊C₃	C₂×C₃	semidirect
12. #13093365	C₂×C₃	semidirect
13. #13093364	C₂×C₃	semidirect
14. C₁₉×D₁₃⋊C₃	C₂×C₃	semidirect
15. D₁₃×C₁₉⋊C₃	C₂×C₃	semidirect
16. C₂×C₁₉×D₁₃	C₃²	semidirect
17. #10625203	C₂²×C₃	semidirect
18. #10625202	C₂²×C₃	semidirect
19. C₁₃×C₁₉⋊C₃	C₂²×C₃	semidirect
20. C₁₉×C₁₃⋊C₃	C₂²×C₃	semidirect
22. C₂×C₁₃×C₁₉	C₂×C₃²	semidirect
23. C₁₉×D₁₃	C₂×C₃²	semidirect
27. C₁₃×C₁₉	C₂²×C₃²	semidirect
38. C₂×D₁₃⋊C₃	C₁₉⋊C₃	direct (N × H)
47. C₂×C₁₉⋊C₃	D₁₃⋊C₃	direct (N × H)
52. C₂×C₁₃⋊C₃	C₂×C₁₉⋊C₃	semidirect
55. D₁₃⋊C₃	C₂×C₁₉⋊C₃	direct (N × H)
60. C₁₉⋊C₃	C₂×D₁₃⋊C₃	direct (N × H)
61. C₂×D₁₃	C₃×C₁₉⋊C₃	semidirect
65. C₁₃⋊C₃	C₂²×C₁₉⋊C₃	semidirect
67. C₂×C₁₉	C₃×D₁₃⋊C₃	semidirect
69. C₂×C₁₃	C₂×C₃×C₁₉⋊C₃	semidirect
70. D₁₃	C₂×C₃×C₁₉⋊C₃	semidirect
71. C₁₉	C₂×C₃×D₁₃⋊C₃	semidirect
74. C₁₃	C₂²×C₃×C₁₉⋊C₃	semidirect
94. C₂	C₁₉⋊C₃×D₁₃⋊C₃	direct (N × H)

Subgroups — C2×C19⋊C3×D13⋊C3 #22580253

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₉⋊C₃×D₁₃⋊C₃ #22580253