Subgroups — C₁₉×D₂₁⋊D₁₃ #35209167

Order 20748.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₉×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×D₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₁₉×D₁₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₉₁	D₃	1	1	yes	characteristic, complemented
7	C₁₃×D₇×C₁₉	—	3	1	no	—
8	C₇×C₁₉×D₁₃	—	3	1	no	—
9	D₃×C₁₉×D₁₃	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×D₇×C₁₉	—	13	1	no	maximal, Hall
12	C₁₉×D₃₉	D₇	1	1	yes	characteristic, complemented
13	D₃×C₁₃×C₁₉	—	7	1	no	—
14	C₃×C₁₉×D₁₃	—	7	1	no	—
15	D₂₁⋊D₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₁₉×D₁₃	—	21	1	no	Hall
17	C₁₉×D₂₁	D₁₃	1	1	yes	characteristic, complemented
18	D₃×C₇×C₁₉	—	13	1	no	—
19	C₃×D₇×C₁₉	—	13	1	no	—
20	C₃×C₁₃×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₁₃×D₂₁	C₂×C₁₉	1	1	yes	characteristic, complemented
22	C₇×D₃₉	C₂×C₁₉	1	1	yes	characteristic, complemented
23	C₃×D₉₁	C₂×C₁₉	1	1	yes	characteristic, complemented
24	C₂×D₇×C₁₉	—	39	1	no	Hall
25	C₂×C₁₃×C₁₉	—	21	1	no	—
26	C₁₉×D₁₃	—	3	1	no	—
27	C₁₉×D₁₃	—	7	1	no	—
28	C₃×C₇×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	D₇×D₁₃	—	3	1	no	Hall
30	C₃×C₇×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇×C₁₉	—	39	1	no	—
32	D₇×C₁₉	—	3	1	no	—
33	D₇×C₁₉	—	13	1	no	—
34	C₁₃×C₁₉	D₃×D₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₃×C₁₉	—	91	1	no	Hall
36	D₉₁	D₃×C₁₉	1	1	yes	characteristic, complemented
37	C₇×D₁₃	—	3	1	no	—
38	C₁₃×D₇	—	3	1	no	—
39	D₃×D₁₃	—	7	1	no	Hall
40	C₇×C₁₉	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₁₉	—	91	1	no	—
42	D₃×C₁₉	—	7	1	no	—
43	D₃×C₁₉	—	13	1	no	—
44	C₇×C₁₃	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
45	D₃×D₇	—	13	1	no	Hall
46	D₃₉	D₇×C₁₉	1	1	yes	characteristic, complemented
47	C₃×D₁₃	—	7	1	no	—
48	D₃×C₁₃	—	7	1	no	—
49	C₂²×C₁₉	—	273	1	no	Hall
50	C₃×C₁₉	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	21	1	no	Hall
52	D₂₁	C₁₉×D₁₃	1	1	yes	characteristic, complemented
53	C₃×D₇	—	13	1	no	—
54	D₃×C₇	—	13	1	no	—
55	C₃×C₁₃	C₂×D₇×C₁₉	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₉	—	21	1	no	—
57	C₂×C₁₉	—	39	1	no	—
58	C₂×C₁₉	—	91	1	no	—
59	C₂×D₇	—	39	1	no	Hall
60	C₂×C₁₃	—	21	1	no	—
61	D₁₃	—	3	1	no	—
62	D₁₃	—	7	1	no	—
63	C₃×C₇	C₂×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Hall
64	C₁₉	D₂₁⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₇	—	39	1	no	—
66	D₇	—	3	1	no	—
67	D₇	—	13	1	no	—
68	C₁₃	D₃×D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	91	1	no	Hall
70	C₇	D₃×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	91	1	no	—
72	D₃	—	7	1	no	—
73	D₃	—	13	1	no	—
74	C₂²	—	273	1	no	Sylow
75	C₃	D₇×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	21	1	no	—
77	C₂	—	39	1	no	—
78	C₂	—	91	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₂₁⋊D₁₃
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×D₂₁	C₂	semidirect
2. C₇×C₁₉×D₃₉	C₂	semidirect
3. C₃×C₁₉×D₉₁	C₂	semidirect
5. C₃×C₇×C₁₃×C₁₉	C₂²	semidirect
6. C₁₉×D₉₁	D₃	semidirect
10. C₇×C₁₃×C₁₉	C₂×D₃	semidirect
12. C₁₉×D₃₉	D₇	semidirect
15. D₂₁⋊D₁₃	C₁₉	direct (N × H)
17. C₁₉×D₂₁	D₁₃	semidirect
20. C₃×C₁₃×C₁₉	C₂×D₇	semidirect
21. C₁₃×D₂₁	C₂×C₁₉	semidirect
22. C₇×D₃₉	C₂×C₁₉	semidirect
23. C₃×D₉₁	C₂×C₁₉	semidirect
28. C₃×C₇×C₁₉	C₂×D₁₃	semidirect
30. C₃×C₇×C₁₃	C₂²×C₁₉	semidirect
34. C₁₃×C₁₉	D₃×D₇	semidirect
36. D₉₁	D₃×C₁₉	semidirect
40. C₇×C₁₉	D₃×D₁₃	semidirect
44. C₇×C₁₃	C₂×D₃×C₁₉	semidirect
46. D₃₉	D₇×C₁₉	semidirect
50. C₃×C₁₉	D₇×D₁₃	semidirect
52. D₂₁	C₁₉×D₁₃	semidirect
55. C₃×C₁₃	C₂×D₇×C₁₉	semidirect
63. C₃×C₇	C₂×C₁₉×D₁₃	semidirect
64. C₁₉	D₂₁⋊D₁₃	direct (N × H)
68. C₁₃	D₃×D₇×C₁₉	semidirect
70. C₇	D₃×C₁₉×D₁₃	semidirect
75. C₃	D₇×C₁₉×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×D₂₁	2
C₇×C₁₉×D₃₉	2
C₃×C₁₉×D₉₁	2
D₇×C₁₉×D₁₃	3
D₃×C₁₉×D₁₃	7
D₃×D₇×C₁₉	13
D₂₁⋊D₁₃	19

Subgroups — C19×D21⋊D13 #35209167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₂₁⋊D₁₃ #35209167