Subgroups — C₂×C₇×C₁₃⋊C₃×C₁₉⋊C₃ #44527796

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃⋊C₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×#10625203	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#10625202	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×C₁₉×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×C₁₃×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₇×#10625203	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×#10625202	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₁₉×C₁₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₁₃⋊C₃×C₁₉⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₇×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₇×C₁₉⋊C₃	—	13	1	no	maximal, Hall
13	C₁₃⋊C₃×C₁₉⋊C₃	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₇×C₁₃⋊C₃	—	19	1	no	maximal, Hall
16	C₂×#10625203	C₃×C₇	1	1	yes	characteristic, complemented
17	C₂×#10625202	C₃×C₇	1	1	yes	characteristic, complemented
18	C₂×C₁₉×C₁₃⋊C₃	C₃×C₇	1	1	yes	characteristic, complemented
19	C₂×C₁₃×C₁₉⋊C₃	C₃×C₇	1	1	yes	characteristic, complemented
20	C₃×C₇×C₁₉⋊C₃	—	13	1	no	Hall
21	C₃×C₇×C₁₃⋊C₃	—	19	1	no	Hall
22	C₂×C₃×C₇×C₁₉	—	13	1	no	—
23	C₂×C₇×C₁₉⋊C₃	—	13	1	no	—
24	C₂×C₇×C₁₉⋊C₃	—	13	1	no	—
25	C₂×C₇×C₁₉⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
26	#10625203	C₂×C₃×C₇	1	1	yes	characteristic, complemented
27	#10625202	C₂×C₃×C₇	1	1	yes	characteristic, complemented
28	C₁₃×C₁₉⋊C₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
29	C₁₉×C₁₃⋊C₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
30	C₂×C₃×C₇×C₁₃	—	19	1	no	—
31	C₂×C₇×C₁₃⋊C₃	—	19	1	no	—
32	C₂×C₇×C₁₃⋊C₃	—	19	1	no	—
33	C₂×C₇×C₁₃⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
34	C₂×C₁₃×C₁₉	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
35	C₃×C₇×C₁₉	—	13	1	no	—
36	C₇×C₁₉⋊C₃	—	13	1	no	—
37	C₇×C₁₉⋊C₃	—	13	1	no	—
38	C₇×C₁₉⋊C₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
39	C₂×C₃×C₁₉⋊C₃	—	13	1	no	Hall
40	C₃×C₇×C₁₃	—	19	1	no	—
41	C₇×C₁₃⋊C₃	—	19	1	no	—
42	C₇×C₁₃⋊C₃	—	19	1	no	—
43	C₇×C₁₃⋊C₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
44	C₂×C₇×C₁₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
45	C₁₃×C₁₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₁₃⋊C₃	—	19	1	no	Hall
47	C₂×C₇×C₁₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
48	C₃×C₁₉⋊C₃	—	13	1	no	Hall
49	C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃²×C₇	—	247	1	no	Hall
51	C₃×C₁₃⋊C₃	—	19	1	no	Hall
52	C₂×C₃×C₁₉	—	13	1	no	—
53	C₂×C₁₉⋊C₃	—	13	1	no	—
54	C₂×C₁₉⋊C₃	—	13	1	no	—
55	C₂×C₁₉⋊C₃	C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
56	C₇×C₁₃	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃×C₁₃	—	19	1	no	—
58	C₂×C₁₃⋊C₃	—	19	1	no	—
59	C₂×C₁₃⋊C₃	—	19	1	no	—
60	C₂×C₁₃⋊C₃	C₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
61	C₃²×C₇	—	247	1	no	Hall
62	C₃×C₁₉	—	13	1	no	—
63	C₁₉⋊C₃	—	13	1	no	—
64	C₁₉⋊C₃	—	13	1	no	—
65	C₁₉⋊C₃	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
66	C₂×C₃×C₇	—	13	1	no	—
67	C₂×C₃×C₇	—	19	1	no	—
68	C₂×C₃×C₇	—	247	1	no	—
69	C₂×C₃×C₇	—	247	1	no	—
70	C₃×C₁₃	—	19	1	no	—
71	C₁₃⋊C₃	—	19	1	no	—
72	C₁₃⋊C₃	—	19	1	no	—
73	C₁₃⋊C₃	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
74	C₂×C₁₉	C₃×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
75	C₂×C₁₃	C₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
76	C₃×C₇	—	13	1	no	—
77	C₃×C₇	—	19	1	no	—
78	C₃×C₇	—	247	1	no	—
79	C₃×C₇	—	247	1	no	—
80	C₁₉	C₂×C₃×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃²	—	247	1	no	Hall
82	C₂×C₇	C₁₃⋊C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
83	C₁₃	C₂×C₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
84	C₃²	—	247	1	no	Sylow
85	C₇	C₂×C₁₃⋊C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×C₃	—	13	1	no	—
87	C₂×C₃	—	19	1	no	—
88	C₂×C₃	—	247	1	no	—
89	C₂×C₃	—	247	1	no	—
90	C₃	—	13	1	no	—
91	C₃	—	19	1	no	—
92	C₃	—	247	1	no	—
93	C₃	—	247	1	no	—
94	C₂	C₇×C₁₃⋊C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃⋊C₃×C₁₉⋊C₃	C₂	direct (N × H)
2. C₂×C₇×#10625203	C₃	semidirect
3. C₂×C₇×#10625202	C₃	semidirect
4. C₂×C₇×C₁₉×C₁₃⋊C₃	C₃	semidirect
5. C₂×C₇×C₁₃×C₁₉⋊C₃	C₃	semidirect
6. C₇×#10625203	C₂×C₃	semidirect
7. C₇×#10625202	C₂×C₃	semidirect
8. C₇×C₁₉×C₁₃⋊C₃	C₂×C₃	semidirect
9. C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	semidirect
10. C₂×C₁₃⋊C₃×C₁₉⋊C₃	C₇	direct (N × H)
11. C₂×C₇×C₁₃×C₁₉	C₃²	semidirect
13. C₁₃⋊C₃×C₁₉⋊C₃	C₂×C₇	direct (N × H)
14. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
16. C₂×#10625203	C₃×C₇	semidirect
17. C₂×#10625202	C₃×C₇	semidirect
18. C₂×C₁₉×C₁₃⋊C₃	C₃×C₇	semidirect
19. C₂×C₁₃×C₁₉⋊C₃	C₃×C₇	semidirect
25. C₂×C₇×C₁₉⋊C₃	C₁₃⋊C₃	direct (N × H)
26. #10625203	C₂×C₃×C₇	semidirect
27. #10625202	C₂×C₃×C₇	semidirect
28. C₁₃×C₁₉⋊C₃	C₂×C₃×C₇	semidirect
29. C₁₉×C₁₃⋊C₃	C₂×C₃×C₇	semidirect
33. C₂×C₇×C₁₃⋊C₃	C₁₉⋊C₃	direct (N × H)
34. C₂×C₁₃×C₁₉	C₃²×C₇	semidirect
38. C₇×C₁₉⋊C₃	C₂×C₁₃⋊C₃	direct (N × H)
43. C₇×C₁₃⋊C₃	C₂×C₁₉⋊C₃	direct (N × H)
44. C₂×C₇×C₁₉	C₃×C₁₃⋊C₃	semidirect
45. C₁₃×C₁₉	C₂×C₃²×C₇	semidirect
47. C₂×C₇×C₁₃	C₃×C₁₉⋊C₃	semidirect
49. C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	semidirect
55. C₂×C₁₉⋊C₃	C₇×C₁₃⋊C₃	direct (N × H)
56. C₇×C₁₃	C₂×C₃×C₁₉⋊C₃	semidirect
60. C₂×C₁₃⋊C₃	C₇×C₁₉⋊C₃	direct (N × H)
65. C₁₉⋊C₃	C₂×C₇×C₁₃⋊C₃	direct (N × H)
73. C₁₃⋊C₃	C₂×C₇×C₁₉⋊C₃	direct (N × H)
74. C₂×C₁₉	C₃×C₇×C₁₃⋊C₃	semidirect
75. C₂×C₁₃	C₃×C₇×C₁₉⋊C₃	semidirect
80. C₁₉	C₂×C₃×C₇×C₁₃⋊C₃	semidirect
82. C₂×C₇	C₁₃⋊C₃×C₁₉⋊C₃	direct (N × H)
83. C₁₃	C₂×C₃×C₇×C₁₉⋊C₃	semidirect
85. C₇	C₂×C₁₃⋊C₃×C₁₉⋊C₃	direct (N × H)
94. C₂	C₇×C₁₃⋊C₃×C₁₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₃⋊C₃×C₁₉⋊C₃	2
C₂×C₇×#10625203	3
C₂×C₇×#10625202	3
C₂×C₇×C₁₉×C₁₃⋊C₃	3
C₂×C₇×C₁₃×C₁₉⋊C₃	3
C₂×C₁₃⋊C₃×C₁₉⋊C₃	7
C₂×C₃×C₇×C₁₉⋊C₃	13
C₂×C₃×C₇×C₁₃⋊C₃	19

Subgroups — C2×C7×C13⋊C3×C19⋊C3 #44527796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₁₃⋊C₃×C₁₉⋊C₃ #44527796