Subgroups — D₃×C₁₃×C₁₇×D₁₃ #46828342

Order 34476.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₁₇×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₁₇×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×C₁₇×D₁₃	—	3	1	no	maximal, Hall
5	C₃×C₁₃²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×C₁₇×D₁₃	—	3	1	no	—
7	C₁₃×C₁₇×D₁₃	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₁₃²×C₁₇	—	3	1	no	—
9	C₁₃²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃×C₁₃×C₁₇	—	13	1	no	maximal
11	D₃×C₁₇×D₁₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
12	D₃×C₁₃×D₁₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₁₃×C₁₇	—	13	1	no	—
14	C₁₇×D₃₉	C₂×C₁₃	1	1	yes	characteristic, complemented
15	D₃×C₁₃×C₁₇	—	2	6	no	—
16	D₃×C₁₃×C₁₇	—	13	1	no	—
17	D₃×C₁₃×C₁₇	D₁₃	1	1	yes	characteristic, direct product factor
18	D₃×C₁₃×C₁₇	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₃×C₁₇×D₁₃	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₁₃×D₃₉	C₂×C₁₇	1	1	yes	characteristic, complemented
21	D₃×C₁₃²	C₂×C₁₇	1	1	yes	characteristic, complemented
22	C₃×C₁₃×D₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented
23	C₂²×C₁₃×C₁₇	—	39	1	no	—
24	C₂×C₁₇×D₁₃	—	3	1	no	—
25	C₂×C₁₃×D₁₃	—	3	1	no	Hall
26	C₃×C₁₃×C₁₇	—	2	6	no	—
27	C₃×C₁₃×C₁₇	C₂×D₁₃	1	1	yes	characteristic, complemented
28	C₃×C₁₃×C₁₇	C₂²×C₁₃	1	1	yes	characteristic, complemented
29	C₃×C₁₃²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₃×C₁₇	—	3	1	no	—
31	C₂×C₁₃×C₁₇	—	3	1	no	—
32	C₂×C₁₃×C₁₇	—	6	6	no	—
33	C₂×C₁₃×C₁₇	—	13	1	no	—
34	C₂×C₁₃×C₁₇	—	39	1	no	—
35	C₁₇×D₁₃	—	3	1	no	—
36	C₁₇×D₁₃	D₃×C₁₃	1	1	yes	characteristic, direct product factor
37	C₂×C₁₃²	—	3	1	no	—
38	C₁₃×D₁₃	—	3	1	no	—
39	C₁₃×D₁₃	D₃×C₁₇	1	1	yes	characteristic, direct product factor
40	C₁₃×C₁₇	—	2	6	no	—
41	C₁₃×C₁₇	D₃×D₁₃	1	1	yes	characteristic, direct product factor
42	C₁₃×C₁₇	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented
43	C₂×D₃×C₁₇	—	13	1	no	Hall
44	C₁₃²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₃×C₁₃	—	13	1	no	—
46	D₃×D₁₃	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor
47	C₂×C₃×C₁₇	—	13	1	no	—
48	D₃×C₁₇	—	13	1	no	—
49	D₃×C₁₇	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor
50	C₂×C₃×C₁₃	—	13	1	no	—
51	D₃₉	C₂×C₁₃×C₁₇	1	1	yes	characteristic, complemented
52	C₃×D₁₃	C₂×C₁₃×C₁₇	1	1	yes	characteristic, complemented
53	D₃×C₁₃	—	2	6	no	—
54	D₃×C₁₃	—	13	1	no	—
55	D₃×C₁₃	C₁₇×D₁₃	1	1	yes	characteristic, direct product factor
56	D₃×C₁₃	C₂×C₁₃×C₁₇	1	1	yes	characteristic, complemented
57	C₂²×C₁₇	—	39	1	no	Hall
58	C₂²×C₁₃	—	39	1	no	—
59	C₂×D₁₃	—	3	1	no	—
60	C₃×C₁₇	C₂×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Hall
61	C₃×C₁₃	—	2	6	no	—
62	C₃×C₁₃	C₂×C₁₇×D₁₃	1	1	yes	characteristic, complemented
63	C₃×C₁₃	C₂²×C₁₃×C₁₇	1	1	yes	characteristic, complemented
64	C₂×C₁₇	—	3	1	no	—
65	C₂×C₁₇	—	13	1	no	—
66	C₂×C₁₇	—	39	1	no	—
67	C₂×C₁₃	—	3	1	no	—
68	C₂×C₁₃	—	3	1	no	—
69	C₂×C₁₃	—	6	6	no	—
70	C₂×C₁₃	—	13	1	no	—
71	C₂×C₁₃	—	39	1	no	—
72	D₁₃	—	3	1	no	—
73	D₁₃	D₃×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor
74	C₁₇	D₃×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
75	C₁₃	—	2	6	no	—
76	C₁₃	D₃×C₁₇×D₁₃	1	1	yes	characteristic, direct product factor
77	C₁₃	C₂×D₃×C₁₃×C₁₇	1	1	yes	characteristic, complemented
78	C₂×D₃	—	13	1	no	Hall
79	C₂×C₃	—	13	1	no	—
80	D₃	—	13	1	no	—
81	D₃	C₁₃×C₁₇×D₁₃	1	1	yes	characteristic, direct product factor
82	C₂²	—	39	1	no	Sylow
83	C₃	C₂×C₁₃×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	3	1	no	—
85	C₂	—	13	1	no	—
86	C₂	—	39	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃×C₁₇	D₃×D₁₃
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₁₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₁₇	C₂²
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₁₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₁₇×D₁₃	C₂	semidirect
2. D₃×C₁₃²×C₁₇	C₂	semidirect
3. C₁₃×C₁₇×D₃₉	C₂	semidirect
5. C₃×C₁₃²×C₁₇	C₂²	semidirect
7. C₁₃×C₁₇×D₁₃	D₃	direct (N × H)
9. C₁₃²×C₁₇	C₂×D₃	semidirect
11. D₃×C₁₇×D₁₃	C₁₃	direct (N × H)
12. D₃×C₁₃×D₁₃	C₁₇	direct (N × H)
14. C₁₇×D₃₉	C₂×C₁₃	semidirect
17. D₃×C₁₃×C₁₇	D₁₃	direct (N × H)
18. D₃×C₁₃×C₁₇	C₂×C₁₃	semidirect
19. C₃×C₁₇×D₁₃	C₂×C₁₃	semidirect
20. C₁₃×D₃₉	C₂×C₁₇	semidirect
21. D₃×C₁₃²	C₂×C₁₇	semidirect
22. C₃×C₁₃×D₁₃	C₂×C₁₇	semidirect
27. C₃×C₁₃×C₁₇	C₂×D₁₃	semidirect
28. C₃×C₁₃×C₁₇	C₂²×C₁₃	semidirect
29. C₃×C₁₃²	C₂²×C₁₇	semidirect
36. C₁₇×D₁₃	D₃×C₁₃	direct (N × H)
39. C₁₃×D₁₃	D₃×C₁₇	direct (N × H)
41. C₁₃×C₁₇	D₃×D₁₃	direct (N × H)
42. C₁₃×C₁₇	C₂×D₃×C₁₃	semidirect
44. C₁₃²	C₂×D₃×C₁₇	semidirect
46. D₃×D₁₃	C₁₃×C₁₇	direct (N × H)
49. D₃×C₁₇	C₁₃×D₁₃	direct (N × H)
51. D₃₉	C₂×C₁₃×C₁₇	semidirect
52. C₃×D₁₃	C₂×C₁₃×C₁₇	semidirect
55. D₃×C₁₃	C₁₇×D₁₃	direct (N × H)
56. D₃×C₁₃	C₂×C₁₃×C₁₇	semidirect
60. C₃×C₁₇	C₂×C₁₃×D₁₃	semidirect
62. C₃×C₁₃	C₂×C₁₇×D₁₃	semidirect
63. C₃×C₁₃	C₂²×C₁₃×C₁₇	semidirect
73. D₁₃	D₃×C₁₃×C₁₇	direct (N × H)
74. C₁₇	D₃×C₁₃×D₁₃	direct (N × H)
76. C₁₃	D₃×C₁₇×D₁₃	direct (N × H)
77. C₁₃	C₂×D₃×C₁₃×C₁₇	semidirect
81. D₃	C₁₃×C₁₇×D₁₃	direct (N × H)
83. C₃	C₂×C₁₃×C₁₇×D₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₁₃×C₁₇×D₁₃	2
D₃×C₁₃²×C₁₇	2
C₁₃×C₁₇×D₃₉	2
C₂×C₁₃×C₁₇×D₁₃	3
C₂×D₃×C₁₃×C₁₇	13
D₃×C₁₇×D₁₃	13
D₃×C₁₃×D₁₃	17

Subgroups — D3×C13×C17×D13 #46828342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₃×C₁₇×D₁₃ #46828342