Subgroups — C₃²×C₁₉×#1044 #30685860

Order 17100.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×#1044	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×C₁₉×AGL(1,𝔽₅)	—	5	2	no	maximal
5	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	4	yes	—
6	C₁₉×#1044	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×D₅×C₁₉	—	5	2	no	—
8	C₃²×D₅×C₁₉	—	10	2	no	—
9	C₃×C₅²×C₁₉	C₃×C₄	1	4	yes	complemented
10	C₃×C₁₉×AGL(1,𝔽₅)	—	5	8	no	—
11	C₁₉×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
12	C₃²×#1044	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₅×C₁₉	—	2	2	no	—
14	C₃²×C₅×C₁₉	AGL(1,𝔽₅)	1	2	yes	complemented
15	C₃²×C₄×C₁₉	—	25	1	no	Hall
16	C₃×D₅×C₁₉	—	5	8	no	—
17	C₃×D₅×C₁₉	—	10	8	no	—
18	C₅²×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₅⋊D₅	C₂×C₁₉	1	1	yes	characteristic
20	C₁₉×AGL(1,𝔽₅)	—	5	2	no	—
21	C₂×C₃²×C₁₉	—	25	1	no	—
22	C₃×#1044	C₃×C₁₉	1	4	yes	direct product factor
23	C₃×C₅×C₁₉	—	2	8	no	—
24	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	8	yes	complemented
25	C₃×C₄×C₁₉	—	25	4	no	—
26	C₃²×C₅²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
27	D₅×C₁₉	—	5	2	no	—
28	D₅×C₁₉	—	10	2	no	—
29	C₃²×AGL(1,𝔽₅)	—	5	2	no	—
30	C₃²×C₁₉	#1044	1	1	yes	characteristic, direct product factor, Hall
31	C₃×C₅⋊D₅	C₂×C₃×C₁₉	1	4	yes	—
32	C₂×C₃×C₁₉	—	25	4	no	—
33	#1044	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
34	C₅×C₁₉	—	2	2	no	—
35	C₅×C₁₉	C₃²×AGL(1,𝔽₅)	1	2	yes	complemented
36	C₃²×D₅	—	5	2	no	—
37	C₃²×D₅	—	10	2	no	—
38	C₄×C₁₉	—	25	1	no	Hall
39	C₃×C₅²	C₃×C₄×C₁₉	1	4	yes	complemented
40	C₃×AGL(1,𝔽₅)	—	5	8	no	—
41	C₃×C₁₉	C₃×#1044	1	4	yes	direct product factor
42	C₅⋊D₅	C₂×C₃²×C₁₉	1	1	yes	characteristic
43	C₃²×C₅	—	2	2	no	—
44	C₃²×C₅	C₁₉×AGL(1,𝔽₅)	1	2	yes	complemented
45	C₂×C₁₉	—	25	1	no	—
46	C₃²×C₄	—	25	1	no	Hall
47	C₃×D₅	—	5	8	no	—
48	C₃×D₅	—	10	8	no	—
49	C₅²	C₃²×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
50	AGL(1,𝔽₅)	—	5	2	no	—
51	C₁₉	C₃²×#1044	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₃²	—	25	1	no	—
53	C₃×C₅	—	2	8	no	—
54	C₃×C₅	C₃×C₁₉×AGL(1,𝔽₅)	1	8	yes	complemented
55	C₃×C₄	—	25	4	no	—
56	D₅	—	5	2	no	—
57	D₅	—	10	2	no	—
58	C₃²	C₁₉×#1044	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₃	—	25	4	no	—
60	C₅	—	2	2	no	—
61	C₅	C₃²×C₁₉×AGL(1,𝔽₅)	1	2	yes	complemented
62	C₄	—	25	1	no	Sylow
63	C₃	C₃×C₁₉×#1044	1	4	yes	direct product factor
64	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₁₉	#1044
commutator, hypocenter	C₅²	C₃²×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₄
prime radical	C₃²×C₁₉×C₅⋊D₅	C₂
cosocle	C₅⋊D₅	C₂×C₃²×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃²×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₉×#1044	C₃	direct (N × H)
3. C₃²×C₅²×C₁₉	C₄	semidirect
6. C₁₉×#1044	C₃²	direct (N × H)
9. C₃×C₅²×C₁₉	C₃×C₄	semidirect
12. C₃²×#1044	C₁₉	direct (N × H)
14. C₃²×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
18. C₅²×C₁₉	C₃²×C₄	semidirect
22. C₃×#1044	C₃×C₁₉	direct (N × H)
24. C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
26. C₃²×C₅²	C₄×C₁₉	semidirect
30. C₃²×C₁₉	#1044	direct (N × H)
33. #1044	C₃²×C₁₉	direct (N × H)
35. C₅×C₁₉	C₃²×AGL(1,𝔽₅)	semidirect
39. C₃×C₅²	C₃×C₄×C₁₉	semidirect
41. C₃×C₁₉	C₃×#1044	direct (N × H)
44. C₃²×C₅	C₁₉×AGL(1,𝔽₅)	semidirect
49. C₅²	C₃²×C₄×C₁₉	semidirect
51. C₁₉	C₃²×#1044	direct (N × H)
54. C₃×C₅	C₃×C₁₉×AGL(1,𝔽₅)	semidirect
58. C₃²	C₁₉×#1044	direct (N × H)
61. C₅	C₃²×C₁₉×AGL(1,𝔽₅)	semidirect
63. C₃	C₃×C₁₉×#1044	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×C₁₉×C₅⋊D₅	2
C₃×C₁₉×#1044	3
C₃²×C₁₉×AGL(1,𝔽₅)	5
C₃²×#1044	19

Subgroups — C32×C19×#1044 #30685860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₉×#1044 #30685860