Subgroups — C₃×C₅×C₇×C₁₃×D₇ #34062206

Order 19110.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×C₁₃×D₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₃×D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₃×D₇	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×C₅×C₇×C₁₃	—	7	1	no	maximal
7	C₃×C₇²×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×C₇×D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×C₇×C₁₃	—	2	3	no	—
10	C₃×C₅×C₇×C₁₃	D₇	1	1	yes	characteristic, direct product factor
11	C₃×C₅×C₇×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
12	C₇×C₁₃×D₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅×C₇×C₁₃	—	7	1	no	—
14	C₅×C₁₃×D₇	C₃×C₇	1	1	yes	characteristic, direct product factor
15	C₃×C₅×C₇²	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₇²×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇×C₁₃	—	7	1	no	—
18	C₃×C₁₃×D₇	C₅×C₇	1	1	yes	characteristic, direct product factor
19	C₅×C₇×D₇	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₇×C₁₃	—	2	3	no	—
21	C₅×C₇×C₁₃	C₃×D₇	1	1	yes	characteristic, direct product factor
22	C₅×C₇×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×C₁₃	—	7	1	no	Hall
24	C₃×C₇×D₇	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₇×C₁₃	—	2	3	no	—
26	C₃×C₇×C₁₃	C₅×D₇	1	1	yes	characteristic, direct product factor
27	C₃×C₇×C₁₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
28	C₅×C₇²	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₅×C₇	—	7	1	no	—
30	C₃×C₅×D₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor
31	C₃×C₅×C₁₃	C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₇×C₁₃	—	7	1	no	—
33	C₁₃×D₇	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor
34	C₃×C₇²	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₅×C₁₃	—	7	1	no	Hall
36	C₃×C₅×C₇	—	2	3	no	—
37	C₃×C₅×C₇	C₁₃×D₇	1	1	yes	characteristic, direct product factor
38	C₃×C₅×C₇	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
39	C₇×D₇	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
40	C₇×C₁₃	—	2	3	no	—
41	C₇×C₁₃	C₃×C₅×D₇	1	1	yes	characteristic, direct product factor
42	C₇×C₁₃	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented
43	C₂×C₃×C₁₃	—	7	1	no	Hall
44	C₂×C₅×C₇	—	7	1	no	—
45	C₅×D₇	C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor
46	C₅×C₁₃	C₃×C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
47	C₇²	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₇	—	7	1	no	—
49	C₃×D₇	C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor
50	C₃×C₁₃	C₅×C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
51	C₅×C₇	—	2	3	no	—
52	C₅×C₇	C₃×C₁₃×D₇	1	1	yes	characteristic, direct product factor
53	C₅×C₇	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅	—	7	1	no	Hall
55	C₂×C₁₃	—	7	1	no	Hall
56	C₃×C₇	—	2	3	no	—
57	C₃×C₇	C₅×C₁₃×D₇	1	1	yes	characteristic, direct product factor
58	C₃×C₇	C₂×C₅×C₇×C₁₃	1	1	yes	characteristic, complemented
59	C₃×C₅	C₇×C₁₃×D₇	1	1	yes	characteristic, direct product factor, Hall
60	C₂×C₇	—	7	1	no	—
61	D₇	C₃×C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor
62	C₁₃	C₃×C₅×C₇×D₇	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₅	—	7	1	no	Hall
64	C₇	—	2	3	no	—
65	C₇	C₂×C₃×C₅×C₇×C₁₃	1	1	yes	characteristic, complemented
66	C₇	C₃×C₅×C₁₃×D₇	1	1	yes	characteristic, direct product factor
67	C₂×C₃	—	7	1	no	Hall
68	C₅	C₃×C₇×C₁₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
69	C₃	C₅×C₇×C₁₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₇×C₁₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₅×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₅×C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇²×C₁₃	C₂	semidirect
2. C₅×C₇×C₁₃×D₇	C₃	direct (N × H)
3. C₃×C₇×C₁₃×D₇	C₅	direct (N × H)
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
5. C₃×C₅×C₁₃×D₇	C₇	direct (N × H)
7. C₃×C₇²×C₁₃	C₂×C₅	semidirect
8. C₃×C₅×C₇×D₇	C₁₃	direct (N × H)
10. C₃×C₅×C₇×C₁₃	D₇	direct (N × H)
11. C₃×C₅×C₇×C₁₃	C₂×C₇	semidirect
12. C₇×C₁₃×D₇	C₃×C₅	direct (N × H)
14. C₅×C₁₃×D₇	C₃×C₇	direct (N × H)
15. C₃×C₅×C₇²	C₂×C₁₃	semidirect
16. C₇²×C₁₃	C₂×C₃×C₅	semidirect
18. C₃×C₁₃×D₇	C₅×C₇	direct (N × H)
19. C₅×C₇×D₇	C₃×C₁₃	direct (N × H)
21. C₅×C₇×C₁₃	C₃×D₇	direct (N × H)
22. C₅×C₇×C₁₃	C₂×C₃×C₇	semidirect
24. C₃×C₇×D₇	C₅×C₁₃	direct (N × H)
26. C₃×C₇×C₁₃	C₅×D₇	direct (N × H)
27. C₃×C₇×C₁₃	C₂×C₅×C₇	semidirect
28. C₅×C₇²	C₂×C₃×C₁₃	semidirect
30. C₃×C₅×D₇	C₇×C₁₃	direct (N × H)
31. C₃×C₅×C₁₃	C₇×D₇	direct (N × H)
33. C₁₃×D₇	C₃×C₅×C₇	direct (N × H)
34. C₃×C₇²	C₂×C₅×C₁₃	semidirect
37. C₃×C₅×C₇	C₁₃×D₇	direct (N × H)
38. C₃×C₅×C₇	C₂×C₇×C₁₃	semidirect
39. C₇×D₇	C₃×C₅×C₁₃	direct (N × H)
41. C₇×C₁₃	C₃×C₅×D₇	direct (N × H)
42. C₇×C₁₃	C₂×C₃×C₅×C₇	semidirect
45. C₅×D₇	C₃×C₇×C₁₃	direct (N × H)
46. C₅×C₁₃	C₃×C₇×D₇	direct (N × H)
47. C₇²	C₂×C₃×C₅×C₁₃	semidirect
49. C₃×D₇	C₅×C₇×C₁₃	direct (N × H)
50. C₃×C₁₃	C₅×C₇×D₇	direct (N × H)
52. C₅×C₇	C₃×C₁₃×D₇	direct (N × H)
53. C₅×C₇	C₂×C₃×C₇×C₁₃	semidirect
57. C₃×C₇	C₅×C₁₃×D₇	direct (N × H)
58. C₃×C₇	C₂×C₅×C₇×C₁₃	semidirect
59. C₃×C₅	C₇×C₁₃×D₇	direct (N × H)
61. D₇	C₃×C₅×C₇×C₁₃	direct (N × H)
62. C₁₃	C₃×C₅×C₇×D₇	direct (N × H)
65. C₇	C₂×C₃×C₅×C₇×C₁₃	semidirect
66. C₇	C₃×C₅×C₁₃×D₇	direct (N × H)
68. C₅	C₃×C₇×C₁₃×D₇	direct (N × H)
69. C₃	C₅×C₇×C₁₃×D₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇²×C₁₃	2
C₅×C₇×C₁₃×D₇	3
C₃×C₇×C₁₃×D₇	5
C₃×C₅×C₁₃×D₇	7
C₂×C₃×C₅×C₇×C₁₃	7
C₃×C₅×C₇×D₇	13

Subgroups — C3×C5×C7×C13×D7 #34062206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₇×C₁₃×D₇ #34062206