Subgroups — C₂×C₅×C₁₉×#4296 #44570568

Order 32490.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×#4296	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₉×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#4296	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅×C₁₉²	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉×#4296	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₉×C₁₉⋊C₃	C₃×C₅	1	1	yes	characteristic
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×#4296	C₁₉	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₅×C₉×C₁₉	—	19	1	no	maximal
11	C₁₉×C₁₉⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic
12	C₅×#4296	C₂×C₁₉	1	1	yes	characteristic, direct product factor
13	C₅×C₉×C₁₉	—	19	1	no	—
14	C₂×C₁₉²	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₉	—	19	1	no	—
16	C₂×C₅×C₁₉⋊C₃	C₃×C₁₉	1	1	yes	characteristic
17	C₁₉²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×#4296	C₅×C₁₉	1	1	yes	characteristic, direct product factor
19	C₂×C₉×C₁₉	—	19	1	no	—
20	C₃×C₅×C₁₉	—	19	1	no	—
21	C₅×C₁₉⋊C₃	C₂×C₃×C₁₉	1	1	yes	characteristic
22	C₂×C₅×C₁₉	—	9	2	no	—
23	C₂×C₅×C₁₉	C₉×C₁₉	1	1	yes	characteristic, complemented
24	C₂×C₅×C₁₉	#4296	1	1	yes	characteristic, direct product factor
25	#4296	C₂×C₅×C₁₉	1	1	yes	characteristic, direct product factor
26	C₉×C₁₉	—	19	1	no	—
27	C₂×C₃×C₁₉	—	19	1	no	—
28	C₂×C₁₉⋊C₃	C₃×C₅×C₁₉	1	1	yes	characteristic
29	C₅×C₁₉	—	9	2	no	—
30	C₅×C₁₉	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented
31	C₅×C₁₉	C₂×#4296	1	1	yes	characteristic, direct product factor
32	C₂×C₅×C₉	—	19	1	no	Hall
33	C₃×C₁₉	—	19	1	no	—
34	C₁₉⋊C₃	C₂×C₃×C₅×C₁₉	1	1	yes	characteristic
35	C₅×C₉	—	19	1	no	Hall
36	C₂×C₁₉	—	9	2	no	—
37	C₂×C₁₉	C₅×C₉×C₁₉	1	1	yes	characteristic, complemented
38	C₂×C₁₉	C₅×#4296	1	1	yes	characteristic, direct product factor
39	C₂×C₃×C₅	—	19	1	no	—
40	C₁₉	—	9	2	no	—
41	C₁₉	C₂×C₅×C₉×C₁₉	1	1	yes	characteristic, complemented
42	C₁₉	C₂×C₅×#4296	1	1	yes	characteristic, direct product factor
43	C₂×C₉	—	19	1	no	Hall
44	C₃×C₅	—	19	1	no	—
45	C₂×C₅	C₁₉×#4296	1	1	yes	characteristic, direct product factor, Hall
46	C₉	—	19	1	no	Sylow
47	C₂×C₃	—	19	1	no	—
48	C₅	C₂×C₁₉×#4296	1	1	yes	characteristic, direct product factor, Sylow
49	C₃	—	19	1	no	—
50	C₂	C₅×C₁₉×#4296	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	#4296
commutator, hypocenter	C₁₉	C₂×C₅×C₉×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉²	C₉
prime radical	C₂×C₅×C₁₉×C₁₉⋊C₃	C₃
cosocle	C₁₉⋊C₃	C₂×C₃×C₅×C₁₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×#4296	C₂	direct (N × H)
3. C₂×C₁₉×#4296	C₅	direct (N × H)
5. C₂×C₅×C₁₉²	C₉	semidirect
6. C₁₉×#4296	C₂×C₅	direct (N × H)
8. C₅×C₁₉²	C₂×C₉	semidirect
9. C₂×C₅×#4296	C₁₉	direct (N × H)
12. C₅×#4296	C₂×C₁₉	direct (N × H)
14. C₂×C₁₉²	C₅×C₉	semidirect
17. C₁₉²	C₂×C₅×C₉	semidirect
18. C₂×#4296	C₅×C₁₉	direct (N × H)
23. C₂×C₅×C₁₉	C₉×C₁₉	semidirect
24. C₂×C₅×C₁₉	#4296	direct (N × H)
25. #4296	C₂×C₅×C₁₉	direct (N × H)
30. C₅×C₁₉	C₂×C₉×C₁₉	semidirect
31. C₅×C₁₉	C₂×#4296	direct (N × H)
37. C₂×C₁₉	C₅×C₉×C₁₉	semidirect
38. C₂×C₁₉	C₅×#4296	direct (N × H)
41. C₁₉	C₂×C₅×C₉×C₁₉	semidirect
42. C₁₉	C₂×C₅×#4296	direct (N × H)
45. C₂×C₅	C₁₉×#4296	direct (N × H)
48. C₅	C₂×C₁₉×#4296	direct (N × H)
50. C₂	C₅×C₁₉×#4296	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₉×#4296	2
C₂×C₅×C₁₉×C₁₉⋊C₃	3
C₂×C₁₉×#4296	5
C₂×C₅×#4296	19
C₂×C₅×C₉×C₁₉	19

Subgroups — C2×C5×C19×#4296 #44570568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₉×#4296 #44570568