Subgroups — C₃×C₇×(C₁₃⋊C₃)⋊D₁₉ #44527821

Order 31122.

96 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	C₇×(C₁₃⋊C₃)⋊D₁₉	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×D₂₄₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₉×C₁₃⋊C₃	C₂×C₃	1	3	yes	complemented
5	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×(C₁₃⋊C₃)⋊D₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×D₂₄₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₇×D₁₉	—	13	1	no	maximal, Hall
9	C₃×C₁₉×C₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×D₁₃⋊C₃	—	19	1	no	maximal, Hall
12	C₃×D₂₄₇	C₃×C₇	1	1	yes	characteristic, complemented
13	(C₁₃⋊C₃)⋊D₁₉	C₃×C₇	1	3	yes	direct product factor
14	C₃²×C₇×C₁₉	—	13	1	no	Hall
15	C₃×C₇×C₁₃⋊C₃	D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×D₁₉	—	13	3	no	—
17	C₃×C₇×D₁₉	—	13	1	no	—
18	C₃×C₁₃×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
19	C₁₉×C₁₃⋊C₃	C₂×C₃×C₇	1	3	yes	complemented
20	C₃×C₇×D₁₃	—	19	1	no	—
21	C₇×D₁₃⋊C₃	—	19	3	no	—
22	D₂₄₇	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₉	—	13	3	no	—
24	C₃×C₇×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
25	C₃²×D₁₉	—	13	1	no	Hall
26	C₃×C₇×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
27	C₇×C₁₃⋊C₃	C₃×D₁₉	1	3	yes	complemented
28	C₇×D₁₉	—	13	1	no	Hall
29	C₁₃×C₁₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₃⋊C₃	—	19	1	no	Hall
31	C₇×D₁₃	—	19	1	no	Hall
32	C₃²×C₁₉	—	13	1	no	Hall
33	C₇×C₁₉	C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃²×C₇	—	247	1	no	Hall
35	C₃×C₁₃⋊C₃	C₇×D₁₉	1	1	yes	characteristic, complemented, Hall
36	C₃×D₁₉	—	13	3	no	—
37	C₃×D₁₉	—	13	1	no	—
38	C₇×C₁₃	C₃²×D₁₉	1	1	yes	characteristic, complemented, Hall
39	C₃×D₁₃	—	19	1	no	—
40	D₁₃⋊C₃	—	19	3	no	—
41	C₃²×C₇	—	13	1	no	Hall
42	C₃×C₁₉	—	13	3	no	—
43	C₃×C₁₉	C₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
44	C₂×C₃×C₇	—	247	3	no	—
45	C₂×C₃×C₇	—	247	1	no	—
46	C₃×C₁₃	C₃×C₇×D₁₉	1	1	yes	characteristic, complemented
47	C₁₃⋊C₃	C₃×C₇×D₁₉	1	3	yes	complemented
48	D₁₉	—	13	1	no	Hall
49	D₁₃	—	19	1	no	Hall
50	C₃×C₇	—	13	3	no	—
51	C₃×C₇	(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor
52	C₁₉	C₃×C₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃²	—	247	1	no	Hall
54	C₂×C₇	—	247	1	no	Hall
55	C₁₃	C₃²×C₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
56	C₃²	—	13	1	no	Sylow
57	C₇	C₃×(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₃	—	247	3	no	—
59	C₂×C₃	—	247	1	no	—
60	C₃	—	13	3	no	—
61	C₃	C₇×(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor
62	C₂	—	247	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	(C₁₃⋊C₃)⋊D₁₉
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₉×C₁₃⋊C₃	C₂	semidirect
2. C₇×(C₁₃⋊C₃)⋊D₁₉	C₃	direct (N × H)
3. C₃×C₇×D₂₄₇	C₃	semidirect
4. C₇×C₁₉×C₁₃⋊C₃	C₂×C₃	semidirect
5. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
6. C₃×(C₁₃⋊C₃)⋊D₁₉	C₇	direct (N × H)
7. C₇×D₂₄₇	C₃²	semidirect
9. C₃×C₁₉×C₁₃⋊C₃	C₂×C₇	semidirect
10. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
12. C₃×D₂₄₇	C₃×C₇	semidirect
13. (C₁₃⋊C₃)⋊D₁₉	C₃×C₇	direct (N × H)
15. C₃×C₇×C₁₃⋊C₃	D₁₉	semidirect
18. C₃×C₁₃×C₁₉	C₂×C₃×C₇	semidirect
19. C₁₉×C₁₃⋊C₃	C₂×C₃×C₇	semidirect
22. D₂₄₇	C₃²×C₇	semidirect
24. C₃×C₇×C₁₉	D₁₃⋊C₃	semidirect
26. C₃×C₇×C₁₃	C₃×D₁₉	semidirect
27. C₇×C₁₃⋊C₃	C₃×D₁₉	semidirect
29. C₁₃×C₁₉	C₂×C₃²×C₇	semidirect
33. C₇×C₁₉	C₃×D₁₃⋊C₃	semidirect
35. C₃×C₁₃⋊C₃	C₇×D₁₉	semidirect
38. C₇×C₁₃	C₃²×D₁₉	semidirect
43. C₃×C₁₉	C₇×D₁₃⋊C₃	semidirect
46. C₃×C₁₃	C₃×C₇×D₁₉	semidirect
47. C₁₃⋊C₃	C₃×C₇×D₁₉	semidirect
51. C₃×C₇	(C₁₃⋊C₃)⋊D₁₉	direct (N × H)
52. C₁₉	C₃×C₇×D₁₃⋊C₃	semidirect
55. C₁₃	C₃²×C₇×D₁₉	semidirect
57. C₇	C₃×(C₁₃⋊C₃)⋊D₁₉	direct (N × H)
61. C₃	C₇×(C₁₃⋊C₃)⋊D₁₉	direct (N × H)

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
C₇×(C₁₃⋊C₃)⋊D₁₉	3
C₃×C₇×D₂₄₇	3
C₃×(C₁₃⋊C₃)⋊D₁₉	7
C₃²×C₇×D₁₉	13
C₃×C₇×D₁₃⋊C₃	19

Subgroups — C3×C7×(C13⋊C3)⋊D19 #44527821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×(C₁₃⋊C₃)⋊D₁₉ #44527821