Subgroups — C₁₃×D₇×D₂₁ #21439769

Order 7644.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₃×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×D₇²	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×C₇⋊D₇	—	3	1	no	—
7	C₇×C₁₃×D₇	—	3	1	no	—
8	C₇×C₁₃×D₇	D₃	1	1	yes	characteristic, complemented
9	C₂×C₁₃×D₂₁	—	7	1	no	maximal
10	D₃×C₁₃×D₇	—	7	1	no	maximal
11	C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₇×D₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₇×C₁₃	—	7	1	no	—
14	C₁₃×D₂₁	—	7	1	no	—
15	C₁₃×D₂₁	—	7	1	no	—
16	C₁₃×D₂₁	—	14	3	no	—
17	C₁₃×D₂₁	D₇	1	1	yes	characteristic, direct product factor
18	D₃×C₇×C₁₃	—	7	1	no	—
19	C₃×C₁₃×D₇	D₇	1	1	yes	characteristic, complemented
20	C₂×C₁₃×D₇	—	21	1	no	—
21	C₂×C₁₃×D₇	—	21	1	no	—
22	C₃⋊(C₇⋊D₇)	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₇×D₂₁	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₃×C₇×D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₃×C₇×C₁₃	—	2	3	no	—
26	C₃×C₇×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented
27	C₃×C₇×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented
28	D₇²	—	3	1	no	Hall
29	C₂×C₇×C₁₃	—	7	1	no	—
30	C₂×C₇×C₁₃	—	21	1	no	—
31	C₁₃×D₇	—	3	1	no	—
32	C₁₃×D₇	—	21	1	no	—
33	C₁₃×D₇	—	21	1	no	—
34	C₁₃×D₇	—	42	3	no	—
35	C₁₃×D₇	D₂₁	1	1	yes	characteristic, direct product factor
36	C₂×D₃×C₁₃	—	49	1	no	Hall
37	C₃×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
38	C₇⋊D₇	—	3	1	no	—
39	C₇×D₇	—	3	1	no	—
40	C₇×D₇	D₃×C₁₃	1	1	yes	characteristic, complemented
41	C₇×C₁₃	—	2	3	no	—
42	C₇×C₁₃	D₃×D₇	1	1	yes	characteristic, complemented
43	C₇×C₁₃	C₂×D₂₁	1	1	yes	characteristic, complemented
44	C₂×D₂₁	—	7	1	no	—
45	D₃×D₇	—	7	1	no	—
46	C₂×C₃×C₁₃	—	7	1	no	—
47	D₃×C₁₃	—	7	1	no	—
48	D₃×C₁₃	—	49	1	no	—
49	C₂²×C₁₃	—	147	1	no	Hall
50	C₇²	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃×C₇	—	7	1	no	—
52	D₂₁	—	7	1	no	—
53	D₂₁	—	7	1	no	—
54	D₂₁	—	14	3	no	—
55	D₂₁	C₁₃×D₇	1	1	yes	characteristic, direct product factor
56	C₃×D₇	C₁₃×D₇	1	1	yes	characteristic, complemented
57	D₃×C₇	—	7	1	no	—
58	C₃×C₁₃	D₇²	1	1	yes	characteristic, complemented, Hall
59	C₂×D₇	—	21	1	no	—
60	C₂×D₇	—	21	1	no	—
61	C₂×C₁₃	—	7	1	no	—
62	C₂×C₁₃	—	21	1	no	—
63	C₂×C₁₃	—	147	1	no	—
64	C₃×C₇	—	2	3	no	—
65	C₃×C₇	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented
66	C₃×C₇	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented
67	C₂×C₇	—	7	1	no	—
68	C₂×C₇	—	21	1	no	—
69	D₇	—	3	1	no	—
70	D₇	—	21	1	no	—
71	D₇	—	21	1	no	—
72	D₇	—	42	3	no	—
73	D₇	C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
74	C₁₃	D₇×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×D₃	—	49	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₃×C₁₃×D₇	1	1	yes	characteristic, complemented
78	C₇	C₂×C₁₃×D₂₁	1	1	yes	characteristic, complemented
79	C₂×C₃	—	7	1	no	—
80	D₃	—	7	1	no	—
81	D₃	—	49	1	no	—
82	C₂²	—	147	1	no	Sylow
83	C₃	C₁₃×D₇²	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	7	1	no	—
85	C₂	—	21	1	no	—
86	C₂	—	147	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₇×D₂₁
commutator, hypocenter	C₃×C₇²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂²
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊(C₇⋊D₇)	C₂	semidirect
2. C₇×C₁₃×D₂₁	C₂	semidirect
3. C₃×C₇×C₁₃×D₇	C₂	semidirect
5. C₃×C₇²×C₁₃	C₂²	semidirect
8. C₇×C₁₃×D₇	D₃	semidirect
11. C₇²×C₁₃	C₂×D₃	semidirect
12. D₇×D₂₁	C₁₃	direct (N × H)
17. C₁₃×D₂₁	D₇	direct (N × H)
19. C₃×C₁₃×D₇	D₇	semidirect
22. C₃⋊(C₇⋊D₇)	C₂×C₁₃	semidirect
23. C₇×D₂₁	C₂×C₁₃	semidirect
24. C₃×C₇×D₇	C₂×C₁₃	semidirect
26. C₃×C₇×C₁₃	C₂×D₇	semidirect
27. C₃×C₇×C₁₃	C₂×D₇	semidirect
35. C₁₃×D₇	D₂₁	direct (N × H)
37. C₃×C₇²	C₂²×C₁₃	semidirect
40. C₇×D₇	D₃×C₁₃	semidirect
42. C₇×C₁₃	D₃×D₇	semidirect
43. C₇×C₁₃	C₂×D₂₁	semidirect
50. C₇²	C₂×D₃×C₁₃	semidirect
55. D₂₁	C₁₃×D₇	direct (N × H)
56. C₃×D₇	C₁₃×D₇	semidirect
58. C₃×C₁₃	D₇²	semidirect
65. C₃×C₇	C₂×C₁₃×D₇	semidirect
66. C₃×C₇	C₂×C₁₃×D₇	semidirect
73. D₇	C₁₃×D₂₁	direct (N × H)
74. C₁₃	D₇×D₂₁	direct (N × H)
77. C₇	D₃×C₁₃×D₇	semidirect
78. C₇	C₂×C₁₃×D₂₁	semidirect
83. C₃	C₁₃×D₇²	semidirect

Subgroups — C13×D7×D21 #21439769

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×D₇×D₂₁ #21439769