Subgroups — C₃×D₁₃×D₁₃⋊C₃ #20258880

Order 6084.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×(C₁₃⋊C₃)⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₃²	C₃	1	1	yes	maximal, characteristic, complemented
5	D₁₃×D₁₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
6	C₃×C₁₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₁₃×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₁₃×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
10	D₁₃×C₁₃⋊C₃	C₂×C₃	1	3	yes	complemented
11	(C₁₃⋊C₃)⋊D₁₃	C₂×C₃	1	3	yes	complemented
12	C₁₃×D₁₃⋊C₃	C₂×C₃	1	3	yes	complemented
13	D₁₃²	C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₁₃⋊C₃	C₂²×C₃	1	3	yes	complemented
16	C₂×C₃²×D₁₃	—	13	1	no	maximal
17	C₂×C₃×D₁₃⋊C₃	—	13	1	no	maximal
18	C₁₃⋊D₁₃	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₁₃×D₁₃	C₂×C₃²	1	1	yes	characteristic, complemented
20	C₁₃×D₁₃	C₂×C₃²	1	1	yes	characteristic, complemented
21	C₂×C₃²×C₁₃	—	13	1	no	—
22	C₃²×D₁₃	—	13	1	no	—
23	C₃²×D₁₃	—	13	1	no	—
24	C₂×C₃×C₁₃⋊C₃	—	13	1	no	—
25	C₃×D₁₃⋊C₃	—	13	1	no	—
26	C₃×D₁₃⋊C₃	D₁₃	1	1	yes	characteristic, direct product factor
27	C₁₃²	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃×D₁₃	—	13	3	no	—
29	C₂×C₃×D₁₃	—	13	1	no	—
30	C₂×C₃×D₁₃	—	13	1	no	—
31	C₂×D₁₃⋊C₃	—	13	3	no	—
32	C₃²×C₁₃	—	13	1	no	—
33	C₃×C₁₃⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₁₃	—	13	3	no	—
35	C₂×C₃×C₁₃	—	13	1	no	—
36	C₂×C₃×C₁₃	—	13	1	no	—
37	C₃×D₁₃	—	13	3	no	—
38	C₃×D₁₃	—	13	1	no	—
39	C₃×D₁₃	—	13	1	no	—
40	C₃×D₁₃	—	13	3	no	—
41	C₃×D₁₃	—	78	2	no	—
42	C₃×D₁₃	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
43	C₃×D₁₃	C₃×D₁₃	1	1	yes	characteristic, complemented
44	C₂×C₁₃⋊C₃	—	13	3	no	—
45	D₁₃⋊C₃	—	13	3	no	—
46	D₁₃⋊C₃	C₃×D₁₃	1	3	yes	direct product factor
47	C₂×D₁₃	—	13	1	no	—
48	C₂×D₁₃	—	13	1	no	—
49	C₃×C₁₃	—	6	2	no	—
50	C₃×C₁₃	—	13	3	no	—
51	C₃×C₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
52	C₃×C₁₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
53	C₁₃⋊C₃	C₂×C₃×D₁₃	1	3	yes	complemented
54	C₂²×C₃²	—	169	1	no	Hall
55	C₂×C₁₃	—	13	1	no	—
56	C₂×C₁₃	—	13	1	no	—
57	D₁₃	—	13	1	no	—
58	D₁₃	—	13	1	no	—
59	D₁₃	—	78	2	no	—
60	D₁₃	C₃×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
61	D₁₃	C₃²×D₁₃	1	1	yes	characteristic, complemented
62	C₂×C₃²	—	13	1	no	—
63	C₂×C₃²	—	169	1	no	—
64	C₂×C₃²	—	169	1	no	—
65	C₁₃	—	6	2	no	—
66	C₁₃	C₂×C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented
67	C₁₃	C₂×C₃²×D₁₃	1	1	yes	characteristic, complemented
68	C₂²×C₃	—	169	1	no	—
69	C₂²×C₃	—	169	3	no	—
70	C₃²	—	13	1	no	Sylow
71	C₂×C₃	—	13	3	no	—
72	C₂×C₃	—	13	1	no	—
73	C₂×C₃	—	13	1	no	—
74	C₂×C₃	—	169	3	no	—
75	C₂×C₃	—	169	3	no	—
76	C₂×C₃	—	169	1	no	—
77	C₂²	—	169	1	no	Sylow
78	C₃	—	13	3	no	—
79	C₃	D₁₃×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
80	C₂	—	13	1	no	—
81	C₂	—	13	1	no	—
82	C₂	—	169	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₃×C₁₃⋊C₃	C₂	semidirect
2. C₃×(C₁₃⋊C₃)⋊D₁₃	C₂	semidirect
3. C₃×C₁₃×D₁₃⋊C₃	C₂	semidirect
4. C₃×D₁₃²	C₃	semidirect
5. D₁₃×D₁₃⋊C₃	C₃	direct (N × H)
6. C₃×C₁₃×C₁₃⋊C₃	C₂²	semidirect
7. C₃×C₁₃⋊D₁₃	C₂×C₃	semidirect
8. C₃×C₁₃×D₁₃	C₂×C₃	semidirect
9. C₃×C₁₃×D₁₃	C₂×C₃	semidirect
10. D₁₃×C₁₃⋊C₃	C₂×C₃	semidirect
11. (C₁₃⋊C₃)⋊D₁₃	C₂×C₃	semidirect
12. C₁₃×D₁₃⋊C₃	C₂×C₃	semidirect
13. D₁₃²	C₃²	semidirect
14. C₃×C₁₃²	C₂²×C₃	semidirect
15. C₁₃×C₁₃⋊C₃	C₂²×C₃	semidirect
18. C₁₃⋊D₁₃	C₂×C₃²	semidirect
19. C₁₃×D₁₃	C₂×C₃²	semidirect
20. C₁₃×D₁₃	C₂×C₃²	semidirect
26. C₃×D₁₃⋊C₃	D₁₃	direct (N × H)
27. C₁₃²	C₂²×C₃²	semidirect
33. C₃×C₁₃⋊C₃	C₂×D₁₃	semidirect
42. C₃×D₁₃	D₁₃⋊C₃	direct (N × H)
43. C₃×D₁₃	C₃×D₁₃	semidirect
46. D₁₃⋊C₃	C₃×D₁₃	direct (N × H)
51. C₃×C₁₃	C₂×D₁₃⋊C₃	semidirect
52. C₃×C₁₃	C₂×C₃×D₁₃	semidirect
53. C₁₃⋊C₃	C₂×C₃×D₁₃	semidirect
60. D₁₃	C₃×D₁₃⋊C₃	direct (N × H)
61. D₁₃	C₃²×D₁₃	semidirect
66. C₁₃	C₂×C₃×D₁₃⋊C₃	semidirect
67. C₁₃	C₂×C₃²×D₁₃	semidirect
79. C₃	D₁₃×D₁₃⋊C₃	direct (N × H)

Subgroups — C3×D13×D13⋊C3 #20258880

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₃×D₁₃⋊C₃ #20258880