Subgroups — C₁₃×D₂₁⋊D₇ #21439773

Order 7644.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×D₂₁	C₂	1	2	yes	maximal, complemented
2	C₃×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₇²	—	3	1	no	maximal, Hall
4	C₃×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₇⋊D₇	D₃	1	1	yes	characteristic, complemented
6	C₇×C₁₃×D₇	—	3	2	no	—
7	D₃×C₁₃×D₇	—	7	2	no	maximal
8	C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	D₂₁⋊D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₃×D₂₁	D₇	1	2	yes	complemented
11	D₃×C₇×C₁₃	—	7	2	no	—
12	C₃×C₁₃×D₇	—	7	2	no	—
13	C₃×C₁₃×D₇	—	14	3	no	—
14	C₂×C₁₃×D₇	—	21	2	no	—
15	C₇×D₂₁	C₂×C₁₃	1	2	yes	complemented
16	C₃×C₇⋊D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₃×C₇×C₁₃	—	2	3	no	—
18	C₃×C₇×C₁₃	C₂×D₇	1	2	yes	complemented
19	D₇²	—	3	1	no	Hall
20	C₂×C₇×C₁₃	—	21	2	no	—
21	C₁₃×D₇	—	3	2	no	—
22	C₁₃×D₇	—	7	2	no	—
23	C₁₃×D₇	—	14	3	no	—
24	C₂×D₃×C₁₃	—	49	1	no	Hall
25	C₃×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₇⋊D₇	D₃×C₁₃	1	1	yes	characteristic, complemented
27	C₇×D₇	—	3	2	no	—
28	C₇×C₁₃	—	2	3	no	—
29	C₇×C₁₃	D₃×D₇	1	2	yes	complemented
30	D₃×D₇	—	7	2	no	—
31	C₂×C₃×C₁₃	—	49	1	no	—
32	D₃×C₁₃	—	7	2	no	—
33	C₂²×C₁₃	—	147	1	no	Hall
34	C₇²	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
35	D₂₁	C₁₃×D₇	1	2	yes	complemented
36	C₃×D₇	—	7	2	no	—
37	C₃×D₇	—	14	3	no	—
38	D₃×C₇	—	7	2	no	—
39	C₃×C₁₃	D₇²	1	1	yes	characteristic, complemented, Hall
40	C₂×D₇	—	21	2	no	—
41	C₂×C₁₃	—	21	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	—	21	2	no	—
46	D₇	—	3	2	no	—
47	D₇	—	7	2	no	—
48	D₇	—	14	3	no	—
49	C₁₃	D₂₁⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×D₃	—	49	1	no	Hall
51	C₇	—	2	3	no	—
52	C₇	D₃×C₁₃×D₇	1	2	yes	complemented
53	C₂×C₃	—	49	1	no	—
54	D₃	—	7	2	no	—
55	C₂²	—	147	1	no	Sylow
56	C₃	C₁₃×D₇²	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	21	2	no	—
58	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₂₁⋊D₇
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. C₇×C₁₃×D₂₁	C₂	semidirect
2. C₃×C₁₃×C₇⋊D₇	C₂	semidirect
4. C₃×C₇²×C₁₃	C₂²	semidirect
5. C₁₃×C₇⋊D₇	D₃	semidirect
8. C₇²×C₁₃	C₂×D₃	semidirect
9. D₂₁⋊D₇	C₁₃	direct (N × H)
10. C₁₃×D₂₁	D₇	semidirect
15. C₇×D₂₁	C₂×C₁₃	semidirect
16. C₃×C₇⋊D₇	C₂×C₁₃	semidirect
18. C₃×C₇×C₁₃	C₂×D₇	semidirect
25. C₃×C₇²	C₂²×C₁₃	semidirect
26. C₇⋊D₇	D₃×C₁₃	semidirect
29. C₇×C₁₃	D₃×D₇	semidirect
34. C₇²	C₂×D₃×C₁₃	semidirect
35. D₂₁	C₁₃×D₇	semidirect
39. C₃×C₁₃	D₇²	semidirect
44. C₃×C₇	C₂×C₁₃×D₇	semidirect
49. C₁₃	D₂₁⋊D₇	direct (N × H)
52. C₇	D₃×C₁₃×D₇	semidirect
56. C₃	C₁₃×D₇²	semidirect

Subgroups — C13×D21⋊D7 #21439773

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×D₂₁⋊D₇ #21439773