Subgroups — C₃×D₃₉⋊D₅₃ #37613733

Order 24804.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₆₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₁₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉⋊D₅₃	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₁₃×D₅₃	—	3	1	no	maximal
6	C₃²×C₁₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₅₃×D₃₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×D₁₅₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₆₈₉	—	2	1	no	—
10	C₃×D₆₈₉	D₃	1	1	yes	characteristic, complemented
11	C₃×D₆₈₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×D₁₃×C₅₃	—	3	1	no	—
13	C₃×C₁₃×D₅₃	—	3	1	no	—
14	D₁₃×D₅₃	—	3	1	no	Hall
15	C₃×C₁₃×C₅₃	—	2	1	no	—
16	C₃×C₁₃×C₅₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₅₃	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₅₃	—	13	1	no	maximal, Hall
19	D₆₈₉	C₃×D₃	1	1	yes	characteristic, complemented
20	C₁₃×D₅₃	—	3	1	no	—
21	D₁₃×C₅₃	—	3	1	no	—
22	C₃×D₁₅₉	D₁₃	1	1	yes	characteristic, complemented
23	C₃×D₃×C₅₃	—	13	1	no	—
24	C₃²×D₅₃	—	13	1	no	—
25	C₁₃×C₅₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×D₅₃	—	39	1	no	—
27	D₃×D₅₃	—	13	1	no	—
28	C₃²×C₅₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₃×D₃×D₁₃	—	53	1	no	maximal, Hall
30	C₂×C₃×C₅₃	—	39	1	no	—
31	D₁₅₉	C₃×D₁₃	1	1	yes	characteristic, complemented
32	C₃×D₅₃	—	3	1	no	—
33	C₃×D₅₃	—	13	1	no	—
34	C₃×D₅₃	—	13	1	no	—
35	C₃×D₅₃	—	26	1	no	—
36	D₃×C₅₃	—	13	1	no	—
37	C₃×D₃₉	D₅₃	1	1	yes	characteristic, complemented
38	C₃×D₃×C₁₃	—	53	1	no	—
39	C₃²×D₁₃	—	53	1	no	—
40	C₂×D₅₃	—	39	1	no	Hall
41	C₃×C₅₃	—	2	1	no	—
42	C₃×C₅₃	D₃×D₁₃	1	1	yes	characteristic, complemented
43	C₃×C₅₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
44	C₂×C₃×D₁₃	—	159	1	no	—
45	D₃×D₁₃	—	53	1	no	—
46	C₃²×C₁₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
47	C₂×C₅₃	—	39	1	no	—
48	D₅₃	—	3	1	no	—
49	D₅₃	—	13	1	no	—
50	C₂×C₃×C₁₃	—	159	1	no	—
51	D₃₉	C₃×D₅₃	1	1	yes	characteristic, complemented
52	C₃×D₁₃	—	3	1	no	—
53	C₃×D₁₃	—	53	1	no	—
54	C₃×D₁₃	—	53	1	no	—
55	C₃×D₁₃	—	106	1	no	—
56	D₃×C₁₃	—	53	1	no	—
57	C₅₃	C₃×D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₁₃	—	159	1	no	Hall
59	C₃×C₁₃	—	2	1	no	—
60	C₃×C₁₃	D₃×D₅₃	1	1	yes	characteristic, complemented
61	C₃×C₁₃	C₂×C₃×D₅₃	1	1	yes	characteristic, complemented
62	C₂×C₃×D₃	—	689	1	no	Hall
63	C₂×C₁₃	—	159	1	no	—
64	D₁₃	—	3	1	no	—
65	D₁₃	—	53	1	no	—
66	C₂×C₃²	—	689	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	—	53	1	no	—
69	C₁₃	C₃×D₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	2067	1	no	—
71	C₂×D₃	—	689	1	no	—
72	C₃²	D₁₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	39	1	no	—
74	C₂×C₃	—	1378	1	no	—
75	C₂×C₃	—	159	1	no	—
76	C₂×C₃	—	689	1	no	—
77	C₂×C₃	—	689	1	no	—
78	D₃	—	13	1	no	—
79	D₃	—	53	1	no	—
80	C₂²	—	2067	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₁₃×D₅₃	1	1	yes	characteristic, complemented
83	C₃	D₃₉⋊D₅₃	1	1	yes	characteristic, direct product factor
84	C₂	—	39	1	no	—
85	C₂	—	159	1	no	—
86	C₂	—	689	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃₉⋊D₅₃
commutator, cosocle, hypocenter	C₃×C₁₃×C₅₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₅₃	C₂²
LCS	G ▷ C₃×C₁₃×C₅₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×D₆₈₉	C₂	semidirect
2. C₃×C₁₃×D₁₅₉	C₂	semidirect
3. C₃×C₅₃×D₃₉	C₂	semidirect
4. D₃₉⋊D₅₃	C₃	direct (N × H)
6. C₃²×C₁₃×C₅₃	C₂²	semidirect
7. C₅₃×D₃₉	C₂×C₃	semidirect
8. C₁₃×D₁₅₉	C₂×C₃	semidirect
10. C₃×D₆₈₉	D₃	semidirect
11. C₃×D₆₈₉	C₂×C₃	semidirect
16. C₃×C₁₃×C₅₃	C₂×D₃	semidirect
17. C₃×C₁₃×C₅₃	C₂²×C₃	semidirect
19. D₆₈₉	C₃×D₃	semidirect
22. C₃×D₁₅₉	D₁₃	semidirect
25. C₁₃×C₅₃	C₂×C₃×D₃	semidirect
28. C₃²×C₅₃	C₂×D₁₃	semidirect
31. D₁₅₉	C₃×D₁₃	semidirect
37. C₃×D₃₉	D₅₃	semidirect
42. C₃×C₅₃	D₃×D₁₃	semidirect
43. C₃×C₅₃	C₂×C₃×D₁₃	semidirect
46. C₃²×C₁₃	C₂×D₅₃	semidirect
51. D₃₉	C₃×D₅₃	semidirect
57. C₅₃	C₃×D₃×D₁₃	semidirect
60. C₃×C₁₃	D₃×D₅₃	semidirect
61. C₃×C₁₃	C₂×C₃×D₅₃	semidirect
69. C₁₃	C₃×D₃×D₅₃	semidirect
72. C₃²	D₁₃×D₅₃	semidirect
82. C₃	C₃×D₁₃×D₅₃	semidirect
83. C₃	D₃₉⋊D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₆₈₉	2
C₃×C₁₃×D₁₅₉	2
C₃×C₅₃×D₃₉	2
D₃₉⋊D₅₃	3
C₃×D₁₃×D₅₃	3
C₃×D₃×D₅₃	13
C₃×D₃×D₁₃	53

Subgroups — C3×D39⋊D53 #37613733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₉⋊D₅₃ #37613733