Subgroups — C₂×C₃×C₇×#10625203 #44528013

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#10625203	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×#10625203	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₇×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×#10625203	C₂×C₃	1	3	yes	direct product factor
5	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×C₃×#10625203	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₇×C₁₉⋊C₃	—	13	1	no	maximal, Hall
9	C₃×#10625203	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇×C₁₃⋊C₃	—	19	1	no	maximal, Hall
12	C₂×C₃×C₁₃×C₁₉	C₃×C₇	1	1	yes	characteristic, complemented
13	C₂×#10625203	C₃×C₇	1	3	yes	direct product factor
14	C₃×C₇×C₁₉⋊C₃	—	13	1	no	Hall
15	C₃×C₇×C₁₃⋊C₃	—	19	1	no	Hall
16	C₂×C₃×C₇×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
17	C₂×C₇×C₁₉⋊C₃	—	13	3	no	—
18	C₃×C₁₃×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
19	#10625203	C₂×C₃×C₇	1	3	yes	direct product factor
20	C₂×C₃×C₇×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented
21	C₂×C₇×C₁₃⋊C₃	—	19	3	no	—
22	C₂×C₁₃×C₁₉	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
24	C₇×C₁₉⋊C₃	—	13	3	no	—
25	C₂×C₃×C₁₉⋊C₃	—	13	1	no	Hall
26	C₃×C₇×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
27	C₇×C₁₃⋊C₃	—	19	3	no	—
28	C₂×C₇×C₁₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₁₃×C₁₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃⋊C₃	—	19	1	no	Hall
31	C₂×C₇×C₁₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₉⋊C₃	—	13	1	no	Hall
33	C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃²×C₇	—	247	1	no	Hall
35	C₃×C₁₃⋊C₃	—	19	1	no	Hall
36	C₂×C₃×C₁₉	C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
37	C₂×C₁₉⋊C₃	—	13	3	no	—
38	C₇×C₁₃	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃×C₁₃	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
40	C₂×C₁₃⋊C₃	—	19	3	no	—
41	C₃²×C₇	—	247	1	no	Hall
42	C₃×C₁₉	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
43	C₁₉⋊C₃	—	13	3	no	—
44	C₂×C₃×C₇	—	247	3	no	—
45	C₂×C₃×C₇	#10625203	1	1	yes	characteristic, direct product factor
46	C₃×C₁₃	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
47	C₁₃⋊C₃	—	19	3	no	—
48	C₂×C₁₉	C₃×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
49	C₂×C₁₃	C₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
50	C₃×C₇	—	247	3	no	—
51	C₃×C₇	C₂×#10625203	1	1	yes	characteristic, direct product factor
52	C₁₉	C₂×C₃×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃²	—	247	1	no	Hall
54	C₂×C₇	C₃×#10625203	1	1	yes	characteristic, direct product factor, Hall
55	C₁₃	C₂×C₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₃²	—	247	1	no	Sylow
57	C₇	C₂×C₃×#10625203	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₃	—	247	3	no	—
59	C₂×C₃	C₇×#10625203	1	1	yes	characteristic, direct product factor
60	C₃	—	247	3	no	—
61	C₃	C₂×C₇×#10625203	1	1	yes	characteristic, direct product factor
62	C₂	C₃×C₇×#10625203	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	#10625203
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₁₉	C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×#10625203	C₂	direct (N × H)
2. C₂×C₇×#10625203	C₃	direct (N × H)
3. C₂×C₃×C₇×C₁₃×C₁₉	C₃	semidirect
4. C₇×#10625203	C₂×C₃	direct (N × H)
5. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
6. C₂×C₃×#10625203	C₇	direct (N × H)
7. C₂×C₇×C₁₃×C₁₉	C₃²	semidirect
9. C₃×#10625203	C₂×C₇	direct (N × H)
10. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
12. C₂×C₃×C₁₃×C₁₉	C₃×C₇	semidirect
13. C₂×#10625203	C₃×C₇	direct (N × H)
16. C₂×C₃×C₇×C₁₉	C₁₃⋊C₃	semidirect
18. C₃×C₁₃×C₁₉	C₂×C₃×C₇	semidirect
19. #10625203	C₂×C₃×C₇	direct (N × H)
20. C₂×C₃×C₇×C₁₃	C₁₉⋊C₃	semidirect
22. C₂×C₁₃×C₁₉	C₃²×C₇	semidirect
23. C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	semidirect
26. C₃×C₇×C₁₃	C₂×C₁₉⋊C₃	semidirect
28. C₂×C₇×C₁₉	C₃×C₁₃⋊C₃	semidirect
29. C₁₃×C₁₉	C₂×C₃²×C₇	semidirect
31. C₂×C₇×C₁₃	C₃×C₁₉⋊C₃	semidirect
33. C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	semidirect
36. C₂×C₃×C₁₉	C₇×C₁₃⋊C₃	semidirect
38. C₇×C₁₃	C₂×C₃×C₁₉⋊C₃	semidirect
39. C₂×C₃×C₁₃	C₇×C₁₉⋊C₃	semidirect
42. C₃×C₁₉	C₂×C₇×C₁₃⋊C₃	semidirect
45. C₂×C₃×C₇	#10625203	direct (N × H)
46. C₃×C₁₃	C₂×C₇×C₁₉⋊C₃	semidirect
48. C₂×C₁₉	C₃×C₇×C₁₃⋊C₃	semidirect
49. C₂×C₁₃	C₃×C₇×C₁₉⋊C₃	semidirect
51. C₃×C₇	C₂×#10625203	direct (N × H)
52. C₁₉	C₂×C₃×C₇×C₁₃⋊C₃	semidirect
54. C₂×C₇	C₃×#10625203	direct (N × H)
55. C₁₃	C₂×C₃×C₇×C₁₉⋊C₃	semidirect
57. C₇	C₂×C₃×#10625203	direct (N × H)
59. C₂×C₃	C₇×#10625203	direct (N × H)
61. C₃	C₂×C₇×#10625203	direct (N × H)
62. C₂	C₃×C₇×#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
C₃×C₇×#10625203	2
C₂×C₇×#10625203	3
C₂×C₃×C₇×C₁₃×C₁₉	3
C₂×C₃×#10625203	7
C₂×C₃×C₇×C₁₉⋊C₃	13
C₂×C₃×C₇×C₁₃⋊C₃	19

Subgroups — C2×C3×C7×#10625203 #44528013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×#10625203 #44528013