Subgroups — C₃²×C₁₁×C₁₉⋊AGL(1,𝔽₅) #49178659

Order 37620.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₁×C₁₉⋊AGL(1,𝔽₅)	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₁₁×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×C₁₁×Dic₁₉	—	5	1	no	maximal, Hall
5	C₃×D₅×C₁₁×C₁₉	C₂×C₃	1	4	yes	—
6	C₁₁×C₁₉⋊AGL(1,𝔽₅)	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₁₁×C₁₉	—	5	1	no	—
8	C₃²×C₁₉⋊AGL(1,𝔽₅)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×C₁₁×C₁₉	C₃×C₄	1	4	yes	complemented
10	C₃×C₁₁×Dic₁₉	—	5	4	no	—
11	D₅×C₁₁×C₁₉	C₂×C₃²	1	1	yes	characteristic
12	C₃²×C₁₁×AGL(1,𝔽₅)	—	19	1	no	maximal, Hall
13	C₃²×C₁₁×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
14	C₃²×D₅×C₁₉	C₂×C₁₁	1	1	yes	characteristic
15	C₂×C₃×C₁₁×C₁₉	—	5	4	no	—
16	C₃×C₁₉⋊AGL(1,𝔽₅)	C₃×C₁₁	1	4	yes	direct product factor
17	C₅×C₁₁×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
18	C₃²×D₅×C₁₁	D₁₉	1	1	yes	characteristic
19	C₃²×C₅×C₁₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₁₁×Dic₁₉	—	5	1	no	Hall
21	C₃²×Dic₁₉	—	5	1	no	Hall
22	C₃×C₁₁×AGL(1,𝔽₅)	—	19	4	no	—
23	C₃×C₁₁×C₁₉	C₃×AGL(1,𝔽₅)	1	4	yes	complemented
24	C₃×D₅×C₁₉	C₂×C₃×C₁₁	1	4	yes	—
25	C₃²×C₅×C₁₁	Dic₁₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁×C₁₉	—	5	1	no	—
27	C₃²×C₄×C₁₁	—	95	1	no	Hall
28	C₁₉⋊AGL(1,𝔽₅)	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃²×C₁₉	—	5	1	no	—
30	C₃×D₅×C₁₁	C₃×D₁₉	1	4	yes	—
31	C₃×C₅×C₁₉	C₃×C₄×C₁₁	1	4	yes	complemented
32	C₃×Dic₁₉	—	5	4	no	—
33	C₁₁×AGL(1,𝔽₅)	—	19	1	no	Hall
34	C₁₁×C₁₉	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃²×C₁₁	—	5	1	no	—
36	D₅×C₁₉	C₂×C₃²×C₁₁	1	1	yes	characteristic
37	C₃²×AGL(1,𝔽₅)	—	19	1	no	Hall
38	C₃²×C₁₉	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₁	C₃×Dic₁₉	1	4	yes	complemented
40	C₃×C₄×C₁₁	—	95	4	no	—
41	C₂×C₃×C₁₉	—	5	4	no	—
42	D₅×C₁₁	C₃²×D₁₉	1	1	yes	characteristic
43	C₃²×C₁₁	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
44	C₅×C₁₉	C₃²×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
45	C₃²×D₅	C₁₁×D₁₉	1	1	yes	characteristic
46	Dic₁₉	—	5	1	no	Hall
47	C₂×C₃×C₁₁	—	5	4	no	—
48	C₃×AGL(1,𝔽₅)	—	19	4	no	—
49	C₃×C₁₉	C₃×C₁₁×AGL(1,𝔽₅)	1	4	yes	complemented
50	C₅×C₁₁	C₃²×Dic₁₉	1	1	yes	characteristic, complemented, Hall
51	C₃²×C₅	C₁₁×Dic₁₉	1	1	yes	characteristic, complemented, Hall
52	C₄×C₁₁	—	95	1	no	Hall
53	C₂×C₁₉	—	5	1	no	—
54	C₃²×C₄	—	95	1	no	Hall
55	C₃×C₁₁	C₃×C₁₉⋊AGL(1,𝔽₅)	1	4	yes	direct product factor
56	C₃×D₅	C₃×C₁₁×D₁₉	1	4	yes	—
57	C₂×C₁₁	—	5	1	no	—
58	AGL(1,𝔽₅)	—	19	1	no	Hall
59	C₁₉	C₃²×C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃²	—	5	1	no	—
61	C₃×C₅	C₃×C₁₁×Dic₁₉	1	4	yes	complemented
62	C₃×C₄	—	95	4	no	—
63	C₁₁	C₃²×C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
64	D₅	C₃²×C₁₁×D₁₉	1	1	yes	characteristic
65	C₃²	C₁₁×C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₃	—	5	4	no	—
67	C₅	C₃²×C₁₁×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	95	1	no	Sylow
69	C₃	C₃×C₁₁×C₁₉⋊AGL(1,𝔽₅)	1	4	yes	direct product factor
70	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₁₁	C₁₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₁₉	C₃²×C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₁₉	C₄
prime radical	C₃²×D₅×C₁₁×C₁₉	C₂
cosocle	D₅×C₁₉	C₂×C₃²×C₁₁
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃²×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₁×C₁₉⋊AGL(1,𝔽₅)	C₃	direct (N × H)
3. C₃²×C₅×C₁₁×C₁₉	C₄	semidirect
6. C₁₁×C₁₉⋊AGL(1,𝔽₅)	C₃²	direct (N × H)
8. C₃²×C₁₉⋊AGL(1,𝔽₅)	C₁₁	direct (N × H)
9. C₃×C₅×C₁₁×C₁₉	C₃×C₄	semidirect
13. C₃²×C₁₁×C₁₉	AGL(1,𝔽₅)	semidirect
16. C₃×C₁₉⋊AGL(1,𝔽₅)	C₃×C₁₁	direct (N × H)
17. C₅×C₁₁×C₁₉	C₃²×C₄	semidirect
19. C₃²×C₅×C₁₉	C₄×C₁₁	semidirect
23. C₃×C₁₁×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
25. C₃²×C₅×C₁₁	Dic₁₉	semidirect
28. C₁₉⋊AGL(1,𝔽₅)	C₃²×C₁₁	direct (N × H)
31. C₃×C₅×C₁₉	C₃×C₄×C₁₁	semidirect
34. C₁₁×C₁₉	C₃²×AGL(1,𝔽₅)	semidirect
38. C₃²×C₁₉	C₁₁×AGL(1,𝔽₅)	semidirect
39. C₃×C₅×C₁₁	C₃×Dic₁₉	semidirect
43. C₃²×C₁₁	C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
44. C₅×C₁₉	C₃²×C₄×C₁₁	semidirect
49. C₃×C₁₉	C₃×C₁₁×AGL(1,𝔽₅)	semidirect
50. C₅×C₁₁	C₃²×Dic₁₉	semidirect
51. C₃²×C₅	C₁₁×Dic₁₉	semidirect
55. C₃×C₁₁	C₃×C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
59. C₁₉	C₃²×C₁₁×AGL(1,𝔽₅)	semidirect
61. C₃×C₅	C₃×C₁₁×Dic₁₉	semidirect
63. C₁₁	C₃²×C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
65. C₃²	C₁₁×C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
67. C₅	C₃²×C₁₁×Dic₁₉	semidirect
69. C₃	C₃×C₁₁×C₁₉⋊AGL(1,𝔽₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₅×C₁₁×C₁₉	2
C₃×C₁₁×C₁₉⋊AGL(1,𝔽₅)	3
C₃²×C₁₁×Dic₁₉	5
C₃²×C₁₉⋊AGL(1,𝔽₅)	11
C₃²×C₁₁×AGL(1,𝔽₅)	19

Subgroups — C32×C11×C19⋊AGL(1,𝔽5) #49178659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₁×C₁₉⋊AGL(1,𝔽₅) #49178659