Subgroups — C₃×C₁₃×ΓL(1,𝔽₈)⋊D₁₉ #44527832

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₁₉×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×ΓL(1,𝔽₈)⋊D₁₉	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₃×D₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×C₁₉×ΓL(1,𝔽₈)	C₂×C₃	1	3	yes	complemented
5	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃²×C₁₃×D₁₉	—	7	1	no	maximal, Hall
7	C₁₃×D₁₃₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×ΓL(1,𝔽₈)⋊D₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃²×C₁₃×C₁₉	—	7	1	no	Hall
10	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₃×AGL(1,𝔽₇)	—	19	1	no	maximal, Hall
12	C₃×C₁₃×D₁₉	—	7	3	no	—
13	C₃×C₁₃×D₁₉	—	7	1	no	—
14	C₃×C₁₉×ΓL(1,𝔽₈)	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₃×ΓL(1,𝔽₈)	D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₃×D₁₃₃	C₃×C₁₃	1	1	yes	characteristic, complemented
17	ΓL(1,𝔽₈)⋊D₁₉	C₃×C₁₃	1	3	yes	direct product factor
18	C₃×C₁₃×C₁₉	—	7	3	no	—
19	C₃×C₁₃×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
20	C₃×C₁₃×D₇	—	19	1	no	—
21	C₁₃×AGL(1,𝔽₇)	—	19	3	no	—
22	C₁₃×D₁₉	—	7	1	no	Hall
23	C₃×C₇×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
24	C₁₉×ΓL(1,𝔽₈)	C₂×C₃×C₁₃	1	3	yes	complemented
25	C₃²×D₁₉	—	7	1	no	Hall
26	C₃×C₇×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
27	C₁₃×ΓL(1,𝔽₈)	C₃×D₁₉	1	3	yes	complemented
28	D₁₃₃	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₁₃×C₁₉	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃²×C₁₃	—	133	1	no	Hall
31	C₁₃×D₇	—	19	1	no	Hall
32	C₃²×C₁₉	—	7	1	no	Hall
33	C₇×C₁₉	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
34	C₃×AGL(1,𝔽₇)	—	19	1	no	Hall
35	C₃²×C₁₃	—	7	1	no	Hall
36	C₃×D₁₉	—	7	3	no	—
37	C₃×D₁₉	—	7	1	no	—
38	C₇×C₁₃	C₃²×D₁₉	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃×C₁₃	—	133	3	no	—
40	C₂×C₃×C₁₃	—	133	1	no	—
41	C₃×ΓL(1,𝔽₈)	C₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₉	—	7	3	no	—
43	C₃×C₁₉	C₁₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
44	C₃×D₇	—	19	1	no	—
45	AGL(1,𝔽₇)	—	19	3	no	—
46	C₃×C₁₃	—	7	3	no	—
47	C₃×C₁₃	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, direct product factor
48	D₁₉	—	7	1	no	Hall
49	C₂×C₁₃	—	133	1	no	Hall
50	C₃×C₇	C₃×C₁₃×D₁₉	1	1	yes	characteristic, complemented
51	ΓL(1,𝔽₈)	C₃×C₁₃×D₁₉	1	3	yes	complemented
52	C₁₉	C₃×C₁₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃²	—	133	1	no	Hall
54	D₇	—	19	1	no	Hall
55	C₁₃	C₃×ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₃²	—	7	1	no	Sylow
57	C₇	C₃²×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃	—	133	3	no	—
59	C₂×C₃	—	133	1	no	—
60	C₃	—	7	3	no	—
61	C₃	C₁₃×ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, direct product factor
62	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	ΓL(1,𝔽₈)⋊D₁₉
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₁₉×ΓL(1,𝔽₈)	C₂	semidirect
2. C₁₃×ΓL(1,𝔽₈)⋊D₁₉	C₃	direct (N × H)
3. C₃×C₁₃×D₁₃₃	C₃	semidirect
4. C₁₃×C₁₉×ΓL(1,𝔽₈)	C₂×C₃	semidirect
5. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₁₃×D₁₃₃	C₃²	semidirect
8. C₃×ΓL(1,𝔽₈)⋊D₁₉	C₁₃	direct (N × H)
10. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
14. C₃×C₁₉×ΓL(1,𝔽₈)	C₂×C₁₃	semidirect
15. C₃×C₁₃×ΓL(1,𝔽₈)	D₁₉	semidirect
16. C₃×D₁₃₃	C₃×C₁₃	semidirect
17. ΓL(1,𝔽₈)⋊D₁₉	C₃×C₁₃	direct (N × H)
19. C₃×C₁₃×C₁₉	AGL(1,𝔽₇)	semidirect
23. C₃×C₇×C₁₉	C₂×C₃×C₁₃	semidirect
24. C₁₉×ΓL(1,𝔽₈)	C₂×C₃×C₁₃	semidirect
26. C₃×C₇×C₁₃	C₃×D₁₉	semidirect
27. C₁₃×ΓL(1,𝔽₈)	C₃×D₁₉	semidirect
28. D₁₃₃	C₃²×C₁₃	semidirect
29. C₁₃×C₁₉	C₃×AGL(1,𝔽₇)	semidirect
33. C₇×C₁₉	C₂×C₃²×C₁₃	semidirect
38. C₇×C₁₃	C₃²×D₁₉	semidirect
41. C₃×ΓL(1,𝔽₈)	C₁₃×D₁₉	semidirect
43. C₃×C₁₉	C₁₃×AGL(1,𝔽₇)	semidirect
47. C₃×C₁₃	ΓL(1,𝔽₈)⋊D₁₉	direct (N × H)
50. C₃×C₇	C₃×C₁₃×D₁₉	semidirect
51. ΓL(1,𝔽₈)	C₃×C₁₃×D₁₉	semidirect
52. C₁₉	C₃×C₁₃×AGL(1,𝔽₇)	semidirect
55. C₁₃	C₃×ΓL(1,𝔽₈)⋊D₁₉	direct (N × H)
57. C₇	C₃²×C₁₃×D₁₉	semidirect
61. C₃	C₁₃×ΓL(1,𝔽₈)⋊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×C₁₃×C₁₉×ΓL(1,𝔽₈)	2
C₁₃×ΓL(1,𝔽₈)⋊D₁₉	3
C₃×C₁₃×D₁₃₃	3
C₃²×C₁₃×D₁₉	7
C₃×ΓL(1,𝔽₈)⋊D₁₉	13
C₃×C₁₃×AGL(1,𝔽₇)	19

Subgroups — C3×C13×ΓL(1,𝔽8)⋊D19 #44527832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×ΓL(1,𝔽₈)⋊D₁₉ #44527832