Subgroups — C₃×D₃×C₁₃⋊D₁₃ #20258952

Order 6084.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊(C₁₃⋊D₁₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₁₃⋊D₁₃	—	3	1	no	maximal
5	D₃×C₁₃⋊D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₃²	—	3	1	no	—
8	C₃⋊(C₁₃⋊D₁₃)	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₁₃⋊D₁₃	—	2	1	no	—
11	C₃×C₁₃⋊D₁₃	—	3	1	no	—
12	C₃×C₁₃⋊D₁₃	D₃	1	1	yes	characteristic, direct product factor
13	C₃×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₁₃⋊D₁₃	—	3	1	no	Hall
15	C₃×C₁₃²	—	2	1	no	—
16	C₃×C₁₃²	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₁₃	—	13	14	no	maximal
19	C₂×C₁₃²	—	3	1	no	—
20	C₁₃⋊D₁₃	—	3	1	no	—
21	C₁₃⋊D₁₃	C₃×D₃	1	1	yes	characteristic, direct product factor
22	C₃×D₃₉	—	13	14	no	—
23	C₃×D₃×C₁₃	D₁₃	1	14	yes	complemented
24	C₃²×D₁₃	—	13	14	no	—
25	C₁₃²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×D₁₃	—	39	14	no	—
27	D₃×D₁₃	—	13	14	no	—
28	C₃²×C₁₃	C₂×D₁₃	1	14	yes	complemented
29	C₂×C₃×C₁₃	—	3	14	no	—
30	D₃₉	—	13	14	no	—
31	C₃×D₁₃	—	13	14	no	—
32	C₃×D₁₃	—	13	14	no	—
33	C₃×D₁₃	—	26	14	no	—
34	C₃×D₁₃	—	39	14	no	—
35	D₃×C₁₃	C₃×D₁₃	1	14	yes	complemented
36	C₂×D₁₃	—	39	14	no	—
37	C₃×C₁₃	—	2	14	no	—
38	C₃×C₁₃	D₃×D₁₃	1	14	yes	complemented
39	C₃×C₁₃	C₂×C₃×D₁₃	1	14	yes	complemented
40	C₂×C₃×D₃	—	169	1	no	Hall
41	C₂×C₁₃	—	3	14	no	—
42	D₁₃	—	13	14	no	—
43	D₁₃	—	39	14	no	—
44	C₂×C₃²	—	169	1	no	—
45	C₃×D₃	—	169	1	no	—
46	C₃×D₃	C₁₃⋊D₁₃	1	1	yes	characteristic, direct product factor
47	C₁₃	C₃×D₃×D₁₃	1	14	yes	complemented
48	C₂²×C₃	—	507	1	no	—
49	C₂×D₃	—	169	1	no	—
50	C₃²	C₂×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	3	1	no	—
52	C₂×C₃	—	338	1	no	—
53	C₂×C₃	—	169	1	no	—
54	C₂×C₃	—	169	1	no	—
55	C₂×C₃	—	507	1	no	—
56	D₃	—	169	1	no	—
57	D₃	C₃×C₁₃⋊D₁₃	1	1	yes	characteristic, direct product factor
58	C₂²	—	507	1	no	Sylow
59	C₃	—	2	1	no	—
60	C₃	D₃×C₁₃⋊D₁₃	1	1	yes	characteristic, direct product factor
61	C₃	C₂×C₃×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented
62	C₂	—	3	1	no	—
63	C₂	—	169	1	no	—
64	C₂	—	507	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃×C₁₃⋊D₁₃
commutator, hypocenter	C₃×C₁₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃²	C₂²
LCS	G ▷ C₃×C₁₃²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₃⋊(C₁₃⋊D₁₃)	C₂	semidirect
2. C₃×D₃×C₁₃²	C₂	semidirect
3. C₃²×C₁₃⋊D₁₃	C₂	semidirect
5. D₃×C₁₃⋊D₁₃	C₃	direct (N × H)
6. C₃²×C₁₃²	C₂²	semidirect
8. C₃⋊(C₁₃⋊D₁₃)	C₂×C₃	semidirect
9. D₃×C₁₃²	C₂×C₃	semidirect
12. C₃×C₁₃⋊D₁₃	D₃	direct (N × H)
13. C₃×C₁₃⋊D₁₃	C₂×C₃	semidirect
16. C₃×C₁₃²	C₂×D₃	semidirect
17. C₃×C₁₃²	C₂²×C₃	semidirect
21. C₁₃⋊D₁₃	C₃×D₃	direct (N × H)
23. C₃×D₃×C₁₃	D₁₃	semidirect
25. C₁₃²	C₂×C₃×D₃	semidirect
28. C₃²×C₁₃	C₂×D₁₃	semidirect
35. D₃×C₁₃	C₃×D₁₃	semidirect
38. C₃×C₁₃	D₃×D₁₃	semidirect
39. C₃×C₁₃	C₂×C₃×D₁₃	semidirect
46. C₃×D₃	C₁₃⋊D₁₃	direct (N × H)
47. C₁₃	C₃×D₃×D₁₃	semidirect
50. C₃²	C₂×C₁₃⋊D₁₃	semidirect
57. D₃	C₃×C₁₃⋊D₁₃	direct (N × H)
60. C₃	D₃×C₁₃⋊D₁₃	direct (N × H)
61. C₃	C₂×C₃×C₁₃⋊D₁₃	semidirect

Subgroups — C3×D3×C13⋊D13 #20258952

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₃×C₁₃⋊D₁₃ #20258952