Subgroups — C₂×D₇×#10625203 #35209124

Order 20748.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇×#10625203	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×#10625203	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₇×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×#10625203	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₇×C₁₉	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×#10625203	—	7	1	no	maximal, Hall
8	C₇×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×D₇×C₁₉⋊C₃	—	13	1	no	maximal, Hall
10	C₂×#10625203	—	7	2	no	—
11	C₂×#10625203	D₇	1	1	yes	characteristic, direct product factor
12	C₂×D₇×C₁₃⋊C₃	—	19	1	no	maximal, Hall
13	C₂²×C₁₃×C₁₉	—	7	1	no	Hall
14	C₂×C₇×C₁₉⋊C₃	—	13	1	no	—
15	D₇×C₁₉⋊C₃	—	13	2	no	—
16	#10625203	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₇×C₁₃⋊C₃	—	19	1	no	—
18	D₇×C₁₃⋊C₃	—	19	2	no	—
19	C₂×D₇×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₃×C₁₉	—	7	2	no	—
21	C₂×C₁₃×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
22	C₇×C₁₉⋊C₃	—	13	1	no	Hall
23	C₂×C₁₃×D₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
24	C₇×C₁₃⋊C₃	—	19	1	no	Hall
25	C₂×C₇×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
26	D₇×C₁₉	C₂×C₁₃⋊C₃	1	2	yes	complemented
27	C₁₃×C₁₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₉⋊C₃	—	91	1	no	Hall
29	C₂×C₇×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
30	C₁₃×D₇	C₂×C₁₉⋊C₃	1	2	yes	complemented
31	C₂²×C₁₃⋊C₃	—	133	1	no	Hall
32	C₇×C₁₉	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₉⋊C₃	—	13	1	no	—
34	C₂×C₁₉⋊C₃	—	91	2	no	—
35	C₇×C₁₃	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×D₇	—	247	1	no	Hall
37	C₂×C₁₃⋊C₃	—	19	1	no	—
38	C₂×C₁₃⋊C₃	—	133	2	no	—
39	C₂²×C₁₉	—	7	1	no	Hall
40	C₁₉⋊C₃	—	13	1	no	Hall
41	C₂²×C₁₃	—	7	1	no	Hall
42	C₂×C₃×C₇	—	247	1	no	—
43	C₃×D₇	—	247	2	no	—
44	C₁₃⋊C₃	—	19	1	no	Hall
45	C₂×C₁₉	—	7	2	no	—
46	C₂×C₁₉	D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
47	C₂×D₇	#10625203	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₁₃	—	7	2	no	—
49	C₂×C₁₃	D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
50	C₃×C₇	—	247	1	no	Hall
51	C₁₉	C₂×D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₇	C₂×#10625203	1	1	yes	characteristic, complemented
53	D₇	C₂×#10625203	1	2	yes	direct product factor
54	C₁₃	C₂×D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	1729	1	no	Hall
56	C₇	C₂²×#10625203	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	1729	2	no	—
58	C₂×C₃	—	247	1	no	—
59	C₂²	—	7	1	no	Sylow
60	C₃	—	247	1	no	Sylow
61	C₂	—	7	2	no	—
62	C₂	D₇×#10625203	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇×#10625203
commutator, cosocle, hypocenter	C₇×C₁₃×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₇×#10625203	C₂	direct (N × H)
2. C₂×C₇×#10625203	C₂	semidirect
3. C₂×C₁₃×D₇×C₁₉	C₃	semidirect
4. C₇×#10625203	C₂²	semidirect
5. C₁₃×D₇×C₁₉	C₂×C₃	semidirect
6. C₂×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
8. C₇×C₁₃×C₁₉	C₂²×C₃	semidirect
11. C₂×#10625203	D₇	direct (N × H)
16. #10625203	C₂×D₇	direct (N × H)
19. C₂×D₇×C₁₉	C₁₃⋊C₃	semidirect
21. C₂×C₁₃×C₁₉	C₃×D₇	semidirect
23. C₂×C₁₃×D₇	C₁₉⋊C₃	semidirect
25. C₂×C₇×C₁₉	C₂×C₁₃⋊C₃	semidirect
26. D₇×C₁₉	C₂×C₁₃⋊C₃	semidirect
27. C₁₃×C₁₉	C₂×C₃×D₇	semidirect
29. C₂×C₇×C₁₃	C₂×C₁₉⋊C₃	semidirect
30. C₁₃×D₇	C₂×C₁₉⋊C₃	semidirect
32. C₇×C₁₉	C₂²×C₁₃⋊C₃	semidirect
35. C₇×C₁₃	C₂²×C₁₉⋊C₃	semidirect
46. C₂×C₁₉	D₇×C₁₃⋊C₃	semidirect
47. C₂×D₇	#10625203	direct (N × H)
49. C₂×C₁₃	D₇×C₁₉⋊C₃	semidirect
51. C₁₉	C₂×D₇×C₁₃⋊C₃	semidirect
52. C₂×C₇	C₂×#10625203	semidirect
53. D₇	C₂×#10625203	direct (N × H)
54. C₁₃	C₂×D₇×C₁₉⋊C₃	semidirect
56. C₇	C₂²×#10625203	semidirect
62. C₂	D₇×#10625203	direct (N × H)

Maximal subgroups

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

subgroup	index
D₇×#10625203	2
C₂×C₇×#10625203	2
C₂×C₁₃×D₇×C₁₉	3
C₂²×#10625203	7
C₂×D₇×C₁₉⋊C₃	13
C₂×D₇×C₁₃⋊C₃	19

Subgroups — C2×D7×#10625203 #35209124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇×#10625203 #35209124