Subgroups — C₃×C₁₃×D₇² #21439749

Order 7644.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×C₁₃×D₇	C₂	1	2	yes	maximal, complemented
3	C₁₃×D₇²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×C₁₃×D₇	C₂×C₃	1	2	yes	complemented
7	C₂×C₃×C₁₃×D₇	—	7	2	no	maximal
8	C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₇²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₇×C₁₃	—	7	2	no	—
11	C₃×C₁₃×D₇	—	7	2	no	—
12	C₃×C₁₃×D₇	—	14	3	no	—
13	C₃×C₁₃×D₇	D₇	1	2	yes	direct product factor
14	C₂×C₁₃×D₇	—	7	2	no	—
15	C₃×C₇⋊D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
16	C₃×C₇×D₇	C₂×C₁₃	1	2	yes	complemented
17	C₃×C₇×C₁₃	—	2	3	no	—
18	C₃×C₇×C₁₃	C₂×D₇	1	2	yes	complemented
19	D₇²	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₇×C₁₃	—	7	2	no	—
21	C₁₃×D₇	—	7	2	no	—
22	C₁₃×D₇	—	14	3	no	—
23	C₁₃×D₇	C₃×D₇	1	2	yes	direct product factor
24	C₂²×C₃×C₁₃	—	49	1	no	Hall
25	C₃×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₇⋊D₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
27	C₇×D₇	C₂×C₃×C₁₃	1	2	yes	complemented
28	C₇×C₁₃	—	2	3	no	—
29	C₇×C₁₃	C₂×C₃×D₇	1	2	yes	complemented
30	C₂×C₃×D₇	—	7	2	no	—
31	C₂×C₃×C₁₃	—	7	2	no	—
32	C₂×C₃×C₁₃	—	49	1	no	—
33	C₂²×C₁₃	—	49	1	no	Hall
34	C₇²	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₇	—	7	2	no	—
36	C₃×D₇	—	7	2	no	—
37	C₃×D₇	—	14	3	no	—
38	C₃×D₇	C₁₃×D₇	1	2	yes	direct product factor
39	C₃×C₁₃	D₇²	1	1	yes	characteristic, direct product factor, Hall
40	C₂×D₇	—	7	2	no	—
41	C₂×C₁₃	—	7	2	no	—
42	C₂×C₁₃	—	49	1	no	—
43	C₃×C₇	—	2	3	no	—
44	C₃×C₇	C₂×C₁₃×D₇	1	2	yes	complemented
45	C₂×C₇	—	7	2	no	—
46	D₇	—	7	2	no	—
47	D₇	—	14	3	no	—
48	D₇	C₃×C₁₃×D₇	1	2	yes	direct product factor
49	C₁₃	C₃×D₇²	1	1	yes	characteristic, direct product factor, Sylow
50	C₂²×C₃	—	49	1	no	Hall
51	C₇	—	2	3	no	—
52	C₇	C₂×C₃×C₁₃×D₇	1	2	yes	complemented
53	C₂×C₃	—	7	2	no	—
54	C₂×C₃	—	49	1	no	—
55	C₂²	—	49	1	no	Sylow
56	C₃	C₁₃×D₇²	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	7	2	no	—
58	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₇²
commutator, hypocenter	C₇²	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₇⋊D₇	C₂	semidirect
2. C₃×C₇×C₁₃×D₇	C₂	semidirect
3. C₁₃×D₇²	C₃	direct (N × H)
4. C₃×C₇²×C₁₃	C₂²	semidirect
5. C₁₃×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×C₁₃×D₇	C₂×C₃	semidirect
8. C₇²×C₁₃	C₂²×C₃	semidirect
9. C₃×D₇²	C₁₃	direct (N × H)
13. C₃×C₁₃×D₇	D₇	direct (N × H)
15. C₃×C₇⋊D₇	C₂×C₁₃	semidirect
16. C₃×C₇×D₇	C₂×C₁₃	semidirect
18. C₃×C₇×C₁₃	C₂×D₇	semidirect
19. D₇²	C₃×C₁₃	direct (N × H)
23. C₁₃×D₇	C₃×D₇	direct (N × H)
25. C₃×C₇²	C₂²×C₁₃	semidirect
26. C₇⋊D₇	C₂×C₃×C₁₃	semidirect
27. C₇×D₇	C₂×C₃×C₁₃	semidirect
29. C₇×C₁₃	C₂×C₃×D₇	semidirect
34. C₇²	C₂²×C₃×C₁₃	semidirect
38. C₃×D₇	C₁₃×D₇	direct (N × H)
39. C₃×C₁₃	D₇²	direct (N × H)
44. C₃×C₇	C₂×C₁₃×D₇	semidirect
48. D₇	C₃×C₁₃×D₇	direct (N × H)
49. C₁₃	C₃×D₇²	direct (N × H)
52. C₇	C₂×C₃×C₁₃×D₇	semidirect
56. C₃	C₁₃×D₇²	direct (N × H)

Subgroups — C3×C13×D72 #21439749

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×D₇² #21439749