Subgroups — C₁₃×D₂₁⋊D₁₉ #35209158

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×C₁₃×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₁₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×D₇×D₁₉	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₁₃₃	D₃	1	1	yes	characteristic, complemented
7	C₁₃×D₇×C₁₉	—	3	1	no	—
8	C₇×C₁₃×D₁₉	—	3	1	no	—
9	D₃×C₁₃×D₁₉	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₂₁⋊D₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₃×D₅₇	D₇	1	1	yes	characteristic, complemented
13	D₃×C₁₃×C₁₉	—	7	1	no	—
14	C₃×C₁₃×D₁₉	—	7	1	no	—
15	D₃×C₁₃×D₇	—	19	1	no	maximal, Hall
16	C₂×C₁₃×D₁₉	—	21	1	no	Hall
17	C₁₉×D₂₁	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₇×D₅₇	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₃×D₁₃₃	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₃×C₁₃×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₁₃×D₂₁	D₁₉	1	1	yes	characteristic, complemented
22	D₃×C₇×C₁₃	—	19	1	no	—
23	C₃×C₁₃×D₇	—	19	1	no	—
24	D₇×D₁₉	—	3	1	no	Hall
25	C₂×C₁₃×C₁₉	—	21	1	no	—
26	C₁₃×D₁₉	—	3	1	no	—
27	C₁₃×D₁₉	—	7	1	no	—
28	C₃×C₇×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₁₃×D₇	—	57	1	no	Hall
30	C₃×C₇×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	D₁₃₃	D₃×C₁₃	1	1	yes	characteristic, complemented
32	C₇×D₁₉	—	3	1	no	—
33	D₇×C₁₉	—	3	1	no	—
34	C₁₃×C₁₉	D₃×D₇	1	1	yes	characteristic, complemented, Hall
35	D₃×D₁₉	—	7	1	no	Hall
36	C₂×C₇×C₁₃	—	57	1	no	—
37	C₁₃×D₇	—	3	1	no	—
38	C₁₃×D₇	—	19	1	no	—
39	C₂×D₃×C₁₃	—	133	1	no	Hall
40	C₇×C₁₉	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
41	D₅₇	C₁₃×D₇	1	1	yes	characteristic, complemented
42	C₃×D₁₉	—	7	1	no	—
43	D₃×C₁₉	—	7	1	no	—
44	C₇×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented, Hall
45	D₃×D₇	—	19	1	no	Hall
46	C₂×C₃×C₁₃	—	133	1	no	—
47	D₃×C₁₃	—	7	1	no	—
48	D₃×C₁₃	—	19	1	no	—
49	C₂×D₁₉	—	21	1	no	Hall
50	C₃×C₁₉	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
51	C₂²×C₁₃	—	399	1	no	Hall
52	D₂₁	C₁₃×D₁₉	1	1	yes	characteristic, complemented
53	C₃×D₇	—	19	1	no	—
54	D₃×C₇	—	19	1	no	—
55	C₃×C₁₃	D₇×D₁₉	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₉	—	21	1	no	—
57	D₁₉	—	3	1	no	—
58	D₁₉	—	7	1	no	—
59	C₂×D₇	—	57	1	no	Hall
60	C₂×C₁₃	—	21	1	no	—
61	C₂×C₁₃	—	57	1	no	—
62	C₂×C₁₃	—	133	1	no	—
63	C₃×C₇	C₂×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
64	C₁₉	D₃×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₇	—	57	1	no	—
66	D₇	—	3	1	no	—
67	D₇	—	19	1	no	—
68	C₁₃	D₂₁⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×D₃	—	133	1	no	Hall
70	C₇	D₃×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	133	1	no	—
72	D₃	—	7	1	no	—
73	D₃	—	19	1	no	—
74	C₂²	—	399	1	no	Sylow
75	C₃	C₁₃×D₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	21	1	no	—
77	C₂	—	57	1	no	—
78	C₂	—	133	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₂₁⋊D₁₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₇×C₁₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×D₂₁	C₂	semidirect
2. C₇×C₁₃×D₅₇	C₂	semidirect
3. C₃×C₁₃×D₁₃₃	C₂	semidirect
5. C₃×C₇×C₁₃×C₁₉	C₂²	semidirect
6. C₁₃×D₁₃₃	D₃	semidirect
10. C₇×C₁₃×C₁₉	C₂×D₃	semidirect
11. D₂₁⋊D₁₉	C₁₃	direct (N × H)
12. C₁₃×D₅₇	D₇	semidirect
17. C₁₉×D₂₁	C₂×C₁₃	semidirect
18. C₇×D₅₇	C₂×C₁₃	semidirect
19. C₃×D₁₃₃	C₂×C₁₃	semidirect
20. C₃×C₁₃×C₁₉	C₂×D₇	semidirect
21. C₁₃×D₂₁	D₁₉	semidirect
28. C₃×C₇×C₁₉	C₂²×C₁₃	semidirect
30. C₃×C₇×C₁₃	C₂×D₁₉	semidirect
31. D₁₃₃	D₃×C₁₃	semidirect
34. C₁₃×C₁₉	D₃×D₇	semidirect
40. C₇×C₁₉	C₂×D₃×C₁₃	semidirect
41. D₅₇	C₁₃×D₇	semidirect
44. C₇×C₁₃	D₃×D₁₉	semidirect
50. C₃×C₁₉	C₂×C₁₃×D₇	semidirect
52. D₂₁	C₁₃×D₁₉	semidirect
55. C₃×C₁₃	D₇×D₁₉	semidirect
63. C₃×C₇	C₂×C₁₃×D₁₉	semidirect
64. C₁₉	D₃×C₁₃×D₇	semidirect
68. C₁₃	D₂₁⋊D₁₉	direct (N × H)
70. C₇	D₃×C₁₃×D₁₉	semidirect
75. C₃	C₁₃×D₇×D₁₉	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×C₁₃×D₅₇	2
C₃×C₁₃×D₁₃₃	2
C₁₃×D₇×D₁₉	3
D₃×C₁₃×D₁₉	7
D₂₁⋊D₁₉	13
D₃×C₁₃×D₇	19

Subgroups — C13×D21⋊D19 #35209158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₂₁⋊D₁₉ #35209158