Subgroups — C₁₉×C₁₃⋊C₃×D₂₁ #44528002

Order 31122.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₁₉×C₁₃⋊C₃	—	3	1	no	maximal
3	C₁₃×C₁₉×D₂₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₉×C₁₃⋊C₃	—	2	1	no	—
5	C₇×C₁₉×C₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×C₁₉×C₁₃⋊C₃	—	7	1	no	maximal, Hall
8	C₁₃×D₇×C₁₉	—	3	1	no	Hall
9	C₃×C₁₉×D₂₁	—	13	1	no	maximal, Hall
10	C₃×C₁₉×C₁₃⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃⋊C₃×D₂₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	D₃×C₁₃×C₁₉	—	7	1	no	—
14	C₂×C₁₉×C₁₃⋊C₃	—	21	1	no	—
15	C₃²×C₇×C₁₉	—	13	1	no	Hall
16	C₃×C₇×C₁₃⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₁₉×D₂₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
18	C₃×D₇×C₁₉	—	39	1	no	—
19	C₃×C₁₃×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
20	C₁₉×C₁₃⋊C₃	—	2	1	no	—
21	C₁₉×C₁₃⋊C₃	D₂₁	1	1	yes	characteristic, direct product factor
22	C₁₃×D₂₁	C₃×C₁₉	1	1	yes	characteristic, complemented
23	D₇×C₁₃⋊C₃	—	3	1	no	—
24	C₂×C₁₃×C₁₉	—	21	1	no	Hall
25	C₃×C₇×C₁₉	—	13	1	no	—
26	C₃×C₇×C₁₉	—	26	1	no	—
27	C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
28	C₃×D₃×C₁₉	—	91	1	no	Hall
29	C₃×C₇×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
30	C₇×C₁₃⋊C₃	—	2	1	no	—
31	C₇×C₁₃⋊C₃	D₃×C₁₉	1	1	yes	characteristic, complemented
32	D₇×C₁₉	—	3	1	no	Hall
33	C₁₃×C₁₉	C₃×D₂₁	1	1	yes	characteristic, complemented, Hall
34	D₃×C₁₃⋊C₃	—	7	1	no	Hall
35	C₁₃×D₇	—	3	1	no	Hall
36	C₃²×C₁₉	—	13	1	no	Hall
37	C₇×C₁₉	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
38	C₃×D₂₁	—	13	1	no	Hall
39	C₃×C₁₃⋊C₃	D₇×C₁₉	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×C₁₉	—	273	1	no	—
41	D₃×C₁₉	—	7	1	no	—
42	C₇×C₁₃	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
43	D₃×C₁₃	—	7	1	no	—
44	C₂×C₁₃⋊C₃	—	21	1	no	—
45	C₃²×C₇	—	13	1	no	Hall
46	C₃×C₁₉	—	13	1	no	—
47	C₃×C₁₉	—	26	1	no	—
48	C₃×C₁₉	D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
49	D₂₁	C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
50	C₃×D₇	—	39	1	no	—
51	C₃×C₁₃	C₃×D₇×C₁₉	1	1	yes	characteristic, complemented
52	C₁₃⋊C₃	—	2	1	no	—
53	C₁₃⋊C₃	C₁₉×D₂₁	1	1	yes	characteristic, direct product factor
54	C₂×C₁₉	—	21	1	no	Hall
55	C₂×C₁₃	—	21	1	no	Hall
56	C₃×C₇	—	13	1	no	—
57	C₃×C₇	—	26	1	no	—
58	C₃×C₇	C₂×C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented
59	C₁₉	C₁₃⋊C₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
60	C₃×D₃	—	91	1	no	Hall
61	D₇	—	3	1	no	Hall
62	C₁₃	C₃×C₁₉×D₂₁	1	1	yes	characteristic, complemented, Sylow
63	C₃²	—	13	1	no	Sylow
64	C₇	D₃×C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	273	1	no	—
66	D₃	—	7	1	no	—
67	C₃	—	13	1	no	—
68	C₃	—	26	1	no	—
69	C₃	D₇×C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented
70	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₁₃⋊C₃×D₂₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
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. C₃×C₇×C₁₉×C₁₃⋊C₃	C₂	semidirect
3. C₁₃×C₁₉×D₂₁	C₃	semidirect
5. C₇×C₁₉×C₁₃⋊C₃	D₃	semidirect
6. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
10. C₃×C₁₉×C₁₃⋊C₃	D₇	semidirect
11. C₇×C₁₃×C₁₉	C₃×D₃	semidirect
12. C₁₃⋊C₃×D₂₁	C₁₉	direct (N × H)
16. C₃×C₇×C₁₃⋊C₃	C₂×C₁₉	semidirect
17. C₁₉×D₂₁	C₁₃⋊C₃	direct (N × H)
19. C₃×C₁₃×C₁₉	C₃×D₇	semidirect
21. C₁₉×C₁₃⋊C₃	D₂₁	direct (N × H)
22. C₁₃×D₂₁	C₃×C₁₉	semidirect
27. C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	semidirect
29. C₃×C₇×C₁₃	C₂×C₃×C₁₉	semidirect
31. C₇×C₁₃⋊C₃	D₃×C₁₉	semidirect
33. C₁₃×C₁₉	C₃×D₂₁	semidirect
37. C₇×C₁₉	D₃×C₁₃⋊C₃	semidirect
39. C₃×C₁₃⋊C₃	D₇×C₁₉	semidirect
42. C₇×C₁₃	C₃×D₃×C₁₉	semidirect
48. C₃×C₁₉	D₇×C₁₃⋊C₃	semidirect
49. D₂₁	C₁₉×C₁₃⋊C₃	direct (N × H)
51. C₃×C₁₃	C₃×D₇×C₁₉	semidirect
53. C₁₃⋊C₃	C₁₉×D₂₁	direct (N × H)
58. C₃×C₇	C₂×C₁₉×C₁₃⋊C₃	semidirect
59. C₁₉	C₁₃⋊C₃×D₂₁	direct (N × H)
62. C₁₃	C₃×C₁₉×D₂₁	semidirect
64. C₇	D₃×C₁₉×C₁₃⋊C₃	semidirect
69. C₃	D₇×C₁₉×C₁₃⋊C₃	semidirect

Maximal subgroups

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

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

Subgroups — C19×C13⋊C3×D21 #44528002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₁₃⋊C₃×D₂₁ #44528002