Subgroups — C₂²×C₁₃⋊C₃×C₁₉⋊C₃ #22580306

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	3	yes	maximal, direct product factor
2	C₂²×#10625203	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×#10625202	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₁₃⋊C₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×#10625203	C₂×C₃	1	3	yes	complemented
8	C₂×#10625202	C₂×C₃	1	3	yes	complemented
9	C₂×C₁₉×C₁₃⋊C₃	C₂×C₃	1	3	yes	complemented
10	C₂×C₁₃×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
11	C₂²×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
12	#10625203	C₂²×C₃	1	1	yes	characteristic, complemented
13	#10625202	C₂²×C₃	1	1	yes	characteristic, complemented
14	C₁₃×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₁₉×C₁₃⋊C₃	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₁₉⋊C₃	—	13	1	no	maximal, Hall
17	C₂×C₁₃×C₁₉	C₂×C₃²	1	3	yes	complemented
18	C₂²×C₃×C₁₃⋊C₃	—	19	1	no	maximal, Hall
19	C₂×C₃×C₁₉⋊C₃	—	13	3	no	—
20	C₁₃×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃⋊C₃	—	19	3	no	—
22	C₂²×C₃×C₁₉	—	13	1	no	—
23	C₂²×C₁₉⋊C₃	—	13	1	no	—
24	C₂²×C₁₉⋊C₃	—	13	1	no	—
25	C₂²×C₁₉⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
26	C₃×C₁₉⋊C₃	—	13	1	no	Hall
27	C₂²×C₃×C₁₃	—	19	1	no	—
28	C₂²×C₁₃⋊C₃	—	19	1	no	—
29	C₂²×C₁₃⋊C₃	—	19	1	no	—
30	C₂²×C₁₃⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃×C₁₃⋊C₃	—	19	1	no	Hall
32	C₂×C₃×C₁₉	—	13	3	no	—
33	C₂×C₁₉⋊C₃	—	13	3	no	—
34	C₂×C₁₉⋊C₃	—	13	3	no	—
35	C₂×C₁₉⋊C₃	C₂×C₁₃⋊C₃	1	3	yes	direct product factor
36	C₂×C₃×C₁₃	—	19	3	no	—
37	C₂×C₁₃⋊C₃	—	19	3	no	—
38	C₂×C₁₃⋊C₃	—	19	3	no	—
39	C₂×C₁₃⋊C₃	C₂×C₁₉⋊C₃	1	3	yes	direct product factor
40	C₂²×C₁₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₉	—	13	1	no	—
42	C₁₉⋊C₃	—	13	1	no	—
43	C₁₉⋊C₃	—	13	1	no	—
44	C₁₉⋊C₃	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
45	C₂²×C₁₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
46	C₃×C₁₃	—	19	1	no	—
47	C₁₃⋊C₃	—	19	1	no	—
48	C₁₃⋊C₃	—	19	1	no	—
49	C₁₃⋊C₃	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
50	C₂×C₁₉	C₂×C₃×C₁₃⋊C₃	1	3	yes	complemented
51	C₂²×C₃²	—	247	1	no	Hall
52	C₂×C₁₃	C₂×C₃×C₁₉⋊C₃	1	3	yes	complemented
53	C₁₉	C₂²×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃²	—	247	3	no	—
55	C₁₃	C₂²×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₃	—	13	1	no	—
57	C₂²×C₃	—	19	1	no	—
58	C₂²×C₃	—	247	1	no	—
59	C₂²×C₃	—	247	1	no	—
60	C₃²	—	247	1	no	Sylow
61	C₂×C₃	—	13	3	no	—
62	C₂×C₃	—	19	3	no	—
63	C₂×C₃	—	247	3	no	—
64	C₂×C₃	—	247	3	no	—
65	C₂²	C₁₃⋊C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
66	C₃	—	13	1	no	—
67	C₃	—	19	1	no	—
68	C₃	—	247	1	no	—
69	C₃	—	247	1	no	—
70	C₂	C₂×C₁₃⋊C₃×C₁₉⋊C₃	1	3	yes	direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃⋊C₃×C₁₉⋊C₃	C₂	direct (N × H)
2. C₂²×#10625203	C₃	semidirect
3. C₂²×#10625202	C₃	semidirect
4. C₂²×C₁₉×C₁₃⋊C₃	C₃	semidirect
5. C₂²×C₁₃×C₁₉⋊C₃	C₃	semidirect
6. C₁₃⋊C₃×C₁₉⋊C₃	C₂²	direct (N × H)
7. C₂×#10625203	C₂×C₃	semidirect
8. C₂×#10625202	C₂×C₃	semidirect
9. C₂×C₁₉×C₁₃⋊C₃	C₂×C₃	semidirect
10. C₂×C₁₃×C₁₉⋊C₃	C₂×C₃	semidirect
11. C₂²×C₁₃×C₁₉	C₃²	semidirect
12. #10625203	C₂²×C₃	semidirect
13. #10625202	C₂²×C₃	semidirect
14. C₁₃×C₁₉⋊C₃	C₂²×C₃	semidirect
15. C₁₉×C₁₃⋊C₃	C₂²×C₃	semidirect
17. C₂×C₁₃×C₁₉	C₂×C₃²	semidirect
20. C₁₃×C₁₉	C₂²×C₃²	semidirect
25. C₂²×C₁₉⋊C₃	C₁₃⋊C₃	direct (N × H)
30. C₂²×C₁₃⋊C₃	C₁₉⋊C₃	direct (N × H)
35. C₂×C₁₉⋊C₃	C₂×C₁₃⋊C₃	direct (N × H)
39. C₂×C₁₃⋊C₃	C₂×C₁₉⋊C₃	direct (N × H)
40. C₂²×C₁₉	C₃×C₁₃⋊C₃	semidirect
44. C₁₉⋊C₃	C₂²×C₁₃⋊C₃	direct (N × H)
45. C₂²×C₁₃	C₃×C₁₉⋊C₃	semidirect
49. C₁₃⋊C₃	C₂²×C₁₉⋊C₃	direct (N × H)
50. C₂×C₁₉	C₂×C₃×C₁₃⋊C₃	semidirect
52. C₂×C₁₃	C₂×C₃×C₁₉⋊C₃	semidirect
53. C₁₉	C₂²×C₃×C₁₃⋊C₃	semidirect
55. C₁₃	C₂²×C₃×C₁₉⋊C₃	semidirect
65. C₂²	C₁₃⋊C₃×C₁₉⋊C₃	direct (N × H)
70. C₂	C₂×C₁₃⋊C₃×C₁₉⋊C₃	direct (N × H)

Subgroups — C22×C13⋊C3×C19⋊C3 #22580306

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₁₃⋊C₃×C₁₉⋊C₃ #22580306