Subgroups — C₇×C₃⋊D₃×D₂₉ #20300654

Order 7308.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊D₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₇×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₇×D₂₉	—	3	4	no	maximal
5	C₃²×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₈₇	—	3	4	no	—
7	D₃×C₇×C₂₉	—	3	4	no	—
8	C₃×C₇×D₂₉	D₃	1	4	yes	complemented
9	C₃⋊D₃×D₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×D₂₉	—	9	1	no	Hall
11	C₃×C₇×C₂₉	C₂×D₃	1	4	yes	complemented
12	C₃⋊D₈₇	C₂×C₇	1	1	yes	characteristic, complemented
13	C₃⋊D₃×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃²×D₂₉	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×C₇×C₂₉	—	9	1	no	—
16	C₇×D₂₉	—	9	1	no	—
17	C₇×D₂₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
18	D₃×D₂₉	—	3	4	no	—
19	C₃²×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₇×C₃⋊D₃	—	29	1	no	maximal, Hall
21	C₇×C₂₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
22	D₈₇	—	3	4	no	—
23	C₃×D₂₉	D₃×C₇	1	4	yes	complemented
24	D₃×C₂₉	—	3	4	no	—
25	C₂×C₃²×C₇	—	29	1	no	—
26	C₇×C₃⋊D₃	—	29	1	no	—
27	C₇×C₃⋊D₃	D₂₉	1	1	yes	characteristic, direct product factor
28	C₂×D₂₉	—	9	1	no	Hall
29	C₃×C₂₉	C₂×D₃×C₇	1	4	yes	complemented
30	C₂×D₃×C₇	—	87	4	no	—
31	C₃²×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₂₉	—	9	1	no	—
33	D₂₉	—	9	1	no	—
34	D₂₉	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
35	C₂×C₃×C₇	—	29	4	no	—
36	D₃×C₇	—	3	4	no	—
37	D₃×C₇	—	87	4	no	—
38	C₂×C₃⋊D₃	—	29	1	no	Hall
39	C₂₉	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₇	—	261	1	no	Hall
41	C₃×C₇	D₃×D₂₉	1	4	yes	complemented
42	C₂×C₃²	—	29	1	no	—
43	C₃⋊D₃	—	29	1	no	—
44	C₃⋊D₃	C₇×D₂₉	1	1	yes	characteristic, direct product factor
45	C₂×C₇	—	261	1	no	—
46	C₂×C₇	—	9	1	no	—
47	C₂×C₇	—	29	1	no	—
48	C₂×D₃	—	87	4	no	—
49	C₃²	C₂×C₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
50	C₇	C₃⋊D₃×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	29	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	87	4	no	—
54	C₂²	—	261	1	no	Sylow
55	C₃	D₃×C₇×D₂₉	1	4	yes	complemented
56	C₂	—	261	1	no	—
57	C₂	—	9	1	no	—
58	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₃×D₂₉
commutator, hypocenter	C₃²×C₂₉	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₂²
LCS	G ▷ C₃²×C₂₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃⋊D₈₇	C₂	semidirect
2. C₇×C₃⋊D₃×C₂₉	C₂	semidirect
3. C₃²×C₇×D₂₉	C₂	semidirect
5. C₃²×C₇×C₂₉	C₂²	semidirect
8. C₃×C₇×D₂₉	D₃	semidirect
9. C₃⋊D₃×D₂₉	C₇	direct (N × H)
11. C₃×C₇×C₂₉	C₂×D₃	semidirect
12. C₃⋊D₈₇	C₂×C₇	semidirect
13. C₃⋊D₃×C₂₉	C₂×C₇	semidirect
14. C₃²×D₂₉	C₂×C₇	semidirect
17. C₇×D₂₉	C₃⋊D₃	direct (N × H)
19. C₃²×C₂₉	C₂²×C₇	semidirect
21. C₇×C₂₉	C₂×C₃⋊D₃	semidirect
23. C₃×D₂₉	D₃×C₇	semidirect
27. C₇×C₃⋊D₃	D₂₉	direct (N × H)
29. C₃×C₂₉	C₂×D₃×C₇	semidirect
31. C₃²×C₇	C₂×D₂₉	semidirect
34. D₂₉	C₇×C₃⋊D₃	direct (N × H)
39. C₂₉	C₂×C₇×C₃⋊D₃	semidirect
41. C₃×C₇	D₃×D₂₉	semidirect
44. C₃⋊D₃	C₇×D₂₉	direct (N × H)
49. C₃²	C₂×C₇×D₂₉	semidirect
50. C₇	C₃⋊D₃×D₂₉	direct (N × H)
55. C₃	D₃×C₇×D₂₉	semidirect

Subgroups — C7×C3⋊D3×D29 #20300654

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₃⋊D₃×D₂₉ #20300654