Subgroups — D₇×C₁₉×D₁₃⋊C₃ #35209015

Order 20748.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×(C₁₃⋊C₃)⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₉×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₁₉×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×C₁₉×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₉₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₁₉×D₁₃⋊C₃	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₇×C₁₉	—	13	1	no	maximal, Hall
12	C₂×C₁₉×C₁₃⋊C₃	—	7	1	no	—
13	C₁₉×D₁₃⋊C₃	—	7	1	no	—
14	C₁₉×D₁₃⋊C₃	D₇	1	1	yes	characteristic, direct product factor
15	D₇×D₁₃⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₁₉×D₁₃	—	7	1	no	Hall
17	C₂×C₃×C₇×C₁₉	—	13	1	no	—
18	C₃×D₇×C₁₉	—	13	1	no	—
19	C₃×D₇×C₁₉	—	13	1	no	—
20	C₁₉×C₁₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	(C₁₃⋊C₃)⋊D₇	C₂×C₁₉	1	1	yes	characteristic, complemented
22	D₇×C₁₃⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented
23	C₇×D₁₃⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented
24	C₂×D₇×C₁₉	—	13	1	no	Hall
25	C₂×C₁₃×C₁₉	—	7	1	no	—
26	C₁₉×D₁₃	—	7	1	no	—
27	C₁₉×D₁₃	C₃×D₇	1	1	yes	characteristic, complemented
28	C₃×C₇×C₁₉	—	13	1	no	Hall
29	D₇×D₁₃	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₇×C₁₃⋊C₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇×C₁₉	—	13	1	no	—
32	D₇×C₁₉	—	13	1	no	—
33	D₇×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
34	C₁₃×C₁₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₃×C₁₉	—	91	1	no	Hall
36	D₉₁	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
37	C₇×D₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
38	C₁₃×D₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
39	C₂×D₁₃⋊C₃	—	7	1	no	Hall
40	C₇×C₁₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₁₉	—	13	1	no	—
42	C₂×C₃×C₁₉	—	91	1	no	—
43	C₂×C₃×C₁₉	—	91	1	no	—
44	C₇×C₁₃	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×D₇	—	13	1	no	Hall
46	C₂×C₁₃⋊C₃	—	7	1	no	—
47	D₁₃⋊C₃	—	7	1	no	—
48	D₁₃⋊C₃	D₇×C₁₉	1	1	yes	characteristic, direct product factor
49	C₂²×C₁₉	—	91	1	no	Hall
50	C₃×C₁₉	—	13	1	no	Hall
51	C₂×D₁₃	—	7	1	no	Hall
52	C₂×C₃×C₇	—	13	1	no	—
53	C₃×D₇	—	13	1	no	—
54	C₃×D₇	—	13	1	no	—
55	C₁₃⋊C₃	C₂×D₇×C₁₉	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₉	—	7	1	no	—
57	C₂×C₁₉	—	13	1	no	—
58	C₂×C₁₉	—	91	1	no	—
59	C₂×D₇	—	13	1	no	Hall
60	C₂×C₁₃	—	7	1	no	—
61	D₁₃	—	7	1	no	—
62	D₁₃	C₃×D₇×C₁₉	1	1	yes	characteristic, complemented
63	C₃×C₇	—	13	1	no	Hall
64	C₁₉	D₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₇	—	13	1	no	—
66	D₇	—	13	1	no	—
67	D₇	C₁₉×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
68	C₁₃	C₂×C₃×D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₃	—	91	1	no	Hall
70	C₇	C₂×C₁₉×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	13	1	no	—
72	C₂×C₃	—	91	1	no	—
73	C₂×C₃	—	91	1	no	—
74	C₂²	—	91	1	no	Sylow
75	C₃	—	13	1	no	Sylow
76	C₂	—	7	1	no	—
77	C₂	—	13	1	no	—
78	C₂	—	91	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₇×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×(C₁₃⋊C₃)⋊D₇	C₂	semidirect
2. D₇×C₁₉×C₁₃⋊C₃	C₂	semidirect
3. C₇×C₁₉×D₁₃⋊C₃	C₂	semidirect
4. D₇×C₁₉×D₁₃	C₃	semidirect
5. C₇×C₁₉×C₁₃⋊C₃	C₂²	semidirect
6. C₁₉×D₉₁	C₂×C₃	semidirect
7. C₁₃×D₇×C₁₉	C₂×C₃	semidirect
8. C₇×C₁₉×D₁₃	C₂×C₃	semidirect
10. C₇×C₁₃×C₁₉	C₂²×C₃	semidirect
14. C₁₉×D₁₃⋊C₃	D₇	direct (N × H)
15. D₇×D₁₃⋊C₃	C₁₉	direct (N × H)
20. C₁₉×C₁₃⋊C₃	C₂×D₇	semidirect
21. (C₁₃⋊C₃)⋊D₇	C₂×C₁₉	semidirect
22. D₇×C₁₃⋊C₃	C₂×C₁₉	semidirect
23. C₇×D₁₃⋊C₃	C₂×C₁₉	semidirect
27. C₁₉×D₁₃	C₃×D₇	semidirect
29. D₇×D₁₃	C₃×C₁₉	semidirect
30. C₇×C₁₃⋊C₃	C₂²×C₁₉	semidirect
33. D₇×C₁₉	D₁₃⋊C₃	direct (N × H)
34. C₁₃×C₁₉	C₂×C₃×D₇	semidirect
36. D₉₁	C₂×C₃×C₁₉	semidirect
37. C₇×D₁₃	C₂×C₃×C₁₉	semidirect
38. C₁₃×D₇	C₂×C₃×C₁₉	semidirect
40. C₇×C₁₉	C₂×D₁₃⋊C₃	semidirect
44. C₇×C₁₃	C₂²×C₃×C₁₉	semidirect
48. D₁₃⋊C₃	D₇×C₁₉	direct (N × H)
55. C₁₃⋊C₃	C₂×D₇×C₁₉	semidirect
62. D₁₃	C₃×D₇×C₁₉	semidirect
64. C₁₉	D₇×D₁₃⋊C₃	direct (N × H)
67. D₇	C₁₉×D₁₃⋊C₃	direct (N × H)
68. C₁₃	C₂×C₃×D₇×C₁₉	semidirect
70. C₇	C₂×C₁₉×D₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×(C₁₃⋊C₃)⋊D₇	2
D₇×C₁₉×C₁₃⋊C₃	2
C₇×C₁₉×D₁₃⋊C₃	2
D₇×C₁₉×D₁₃	3
C₂×C₁₉×D₁₃⋊C₃	7
C₂×C₃×D₇×C₁₉	13
D₇×D₁₃⋊C₃	19

Subgroups — D7×C19×D13⋊C3 #35209015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₁₉×D₁₃⋊C₃ #35209015