Subgroups — C₁₃×D₁₃×D₅₁ #46828343

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	C₁₃²×D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₆₆₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×D₁₃×D₁₇	—	3	1	no	maximal, Hall
5	C₃×C₁₃²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₂₂₁	—	3	1	no	—
7	C₁₃×C₁₇×D₁₃	D₃	1	1	yes	characteristic, complemented
8	C₁₃²×D₁₇	—	3	1	no	—
9	C₁₃²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃×D₅₁	—	13	1	no	maximal
11	D₁₃×D₅₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor
12	D₃×C₁₃×D₁₃	—	17	1	no	maximal, Hall
13	C₂×C₃×C₁₃×C₁₇	—	13	1	no	—
14	D₆₆₃	C₂×C₁₃	1	1	yes	characteristic, complemented
15	C₁₃×D₅₁	—	2	6	no	—
16	C₁₃×D₅₁	—	13	1	no	—
17	C₁₃×D₅₁	D₁₃	1	1	yes	characteristic, direct product factor
18	C₁₃×D₅₁	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₃×C₁₇×D₁₃	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₁₃×D₃₉	—	17	1	no	—
21	D₃×C₁₃²	—	17	1	no	—
22	C₃×C₁₃×D₁₃	D₁₇	1	1	yes	characteristic, complemented
23	C₂×C₁₃×D₁₇	—	39	1	no	—
24	D₁₃×D₁₇	—	3	1	no	—
25	C₂×C₁₃×D₁₃	—	51	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	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₃×C₁₇	—	13	1	no	—
31	D₂₂₁	—	3	1	no	—
32	C₁₃×D₁₇	—	3	1	no	—
33	C₁₃×D₁₇	—	3	1	no	—
34	C₁₃×D₁₇	—	6	6	no	—
35	C₁₃×D₁₇	—	39	1	no	—
36	C₁₇×D₁₃	D₃×C₁₃	1	1	yes	characteristic, complemented
37	C₂×C₁₃²	—	51	1	no	—
38	C₁₃×D₁₃	—	51	1	no	—
39	C₁₃×D₁₃	D₅₁	1	1	yes	characteristic, direct product factor
40	C₁₃×C₁₇	—	2	6	no	—
41	C₁₃×C₁₇	D₃×D₁₃	1	1	yes	characteristic, complemented
42	C₁₃×C₁₇	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented
43	C₂×D₅₁	—	13	1	no	Hall
44	C₁₃²	C₂×D₅₁	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₃×C₁₃	—	221	1	no	—
46	D₃×D₁₃	—	17	1	no	—
47	C₂×C₃×C₁₇	—	13	1	no	—
48	D₅₁	—	13	1	no	—
49	D₅₁	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor
50	C₂×C₃×C₁₃	—	13	1	no	—
51	D₃₉	—	17	1	no	—
52	C₃×D₁₃	C₁₃×D₁₇	1	1	yes	characteristic, complemented
53	D₃×C₁₃	—	17	1	no	—
54	D₃×C₁₃	—	17	1	no	—
55	D₃×C₁₃	—	34	6	no	—
56	D₃×C₁₃	—	221	1	no	—
57	C₂×D₁₇	—	39	1	no	Hall
58	C₂²×C₁₃	—	663	1	no	—
59	C₂×D₁₃	—	51	1	no	—
60	C₃×C₁₇	C₂×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Hall
61	C₃×C₁₃	—	2	6	no	—
62	C₃×C₁₃	D₁₃×D₁₇	1	1	yes	characteristic, complemented
63	C₃×C₁₃	C₂×C₁₃×D₁₇	1	1	yes	characteristic, complemented
64	C₂×C₁₇	—	13	1	no	—
65	D₁₇	—	3	1	no	—
66	D₁₇	—	39	1	no	—
67	C₂×C₁₃	—	13	1	no	—
68	C₂×C₁₃	—	51	1	no	—
69	C₂×C₁₃	—	51	1	no	—
70	C₂×C₁₃	—	102	6	no	—
71	C₂×C₁₃	—	663	1	no	—
72	D₁₃	—	51	1	no	—
73	D₁₃	C₁₃×D₅₁	1	1	yes	characteristic, direct product factor
74	C₁₇	D₃×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
75	C₁₃	—	2	6	no	—
76	C₁₃	D₁₃×D₅₁	1	1	yes	characteristic, direct product factor
77	C₁₃	C₂×C₁₃×D₅₁	1	1	yes	characteristic, complemented
78	C₂×D₃	—	221	1	no	Hall
79	C₂×C₃	—	13	1	no	—
80	D₃	—	17	1	no	—
81	D₃	—	221	1	no	—
82	C₂²	—	663	1	no	Sylow
83	C₃	C₁₃×D₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	13	1	no	—
85	C₂	—	51	1	no	—
86	C₂	—	663	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₁₃×D₅₁
commutator, cosocle, hypocenter	C₃×C₁₃×C₁₇	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₁₇	C₂²
LCS	G ▷ C₃×C₁₃×C₁₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₁₇×D₁₃	C₂	semidirect
2. C₁₃²×D₅₁	C₂	semidirect
3. C₁₃×D₆₆₃	C₂	semidirect
5. C₃×C₁₃²×C₁₇	C₂²	semidirect
7. C₁₃×C₁₇×D₁₃	D₃	semidirect
9. C₁₃²×C₁₇	C₂×D₃	semidirect
11. D₁₃×D₅₁	C₁₃	direct (N × H)
14. D₆₆₃	C₂×C₁₃	semidirect
17. C₁₃×D₅₁	D₁₃	direct (N × H)
18. C₁₃×D₅₁	C₂×C₁₃	semidirect
19. C₃×C₁₇×D₁₃	C₂×C₁₃	semidirect
22. C₃×C₁₃×D₁₃	D₁₇	semidirect
27. C₃×C₁₃×C₁₇	C₂×D₁₃	semidirect
28. C₃×C₁₃×C₁₇	C₂²×C₁₃	semidirect
29. C₃×C₁₃²	C₂×D₁₇	semidirect
36. C₁₇×D₁₃	D₃×C₁₃	semidirect
39. C₁₃×D₁₃	D₅₁	direct (N × H)
41. C₁₃×C₁₇	D₃×D₁₃	semidirect
42. C₁₃×C₁₇	C₂×D₃×C₁₃	semidirect
44. C₁₃²	C₂×D₅₁	semidirect
49. D₅₁	C₁₃×D₁₃	direct (N × H)
52. C₃×D₁₃	C₁₃×D₁₇	semidirect
60. C₃×C₁₇	C₂×C₁₃×D₁₃	semidirect
62. C₃×C₁₃	D₁₃×D₁₇	semidirect
63. C₃×C₁₃	C₂×C₁₃×D₁₇	semidirect
73. D₁₃	C₁₃×D₅₁	direct (N × H)
74. C₁₇	D₃×C₁₃×D₁₃	semidirect
76. C₁₃	D₁₃×D₅₁	direct (N × H)
77. C₁₃	C₂×C₁₃×D₅₁	semidirect
83. C₃	C₁₃×D₁₃×D₁₇	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
C₁₃²×D₅₁	2
C₁₃×D₆₆₃	2
C₁₃×D₁₃×D₁₇	3
C₂×C₁₃×D₅₁	13
D₁₃×D₅₁	13
D₃×C₁₃×D₁₃	17

Subgroups — C13×D13×D51 #46828343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₁₃×D₅₁ #46828343