Subgroups — C₂×C₅×#15692437 #44570569

Order 32490.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692437	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₉×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₂×#15692437	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	#15692437	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	—	19	1	no	maximal
10	C₂×C₅×#4294	—	19	1	no	maximal
11	C₁₉×C₁₉⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic
12	C₅×#4296	—	19	1	no	—
13	C₅×#4294	—	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	C₁₉⋊C₃	1	1	yes	characteristic
17	C₁₉²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×#4296	—	19	1	no	—
19	C₂×#4294	—	19	1	no	—
20	C₃×C₅×C₁₉	—	19	1	no	—
21	C₅×C₁₉⋊C₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
22	C₂×C₅×C₁₉	—	9	2	no	—
23	C₂×C₅×C₁₉	#4294	1	1	yes	characteristic, complemented
24	C₂×C₅×C₁₉	#4296	1	1	yes	characteristic, complemented
25	#4296	—	19	1	no	—
26	#4294	—	19	1	no	—
27	C₂×C₃×C₁₉	—	19	1	no	—
28	C₂×C₁₉⋊C₃	C₅×C₁₉⋊C₃	1	1	yes	characteristic
29	C₅×C₁₉	—	9	2	no	—
30	C₅×C₁₉	C₂×#4294	1	1	yes	characteristic, complemented
31	C₅×C₁₉	C₂×#4296	1	1	yes	characteristic, complemented
32	C₂×C₅×C₉	—	361	1	no	Hall
33	C₃×C₁₉	—	19	1	no	—
34	C₁₉⋊C₃	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic
35	C₅×C₉	—	361	1	no	Hall
36	C₂×C₁₉	—	9	2	no	—
37	C₂×C₁₉	C₅×#4294	1	1	yes	characteristic, complemented
38	C₂×C₁₉	C₅×#4296	1	1	yes	characteristic, complemented
39	C₂×C₃×C₅	—	19	1	no	—
40	C₁₉	—	9	2	no	—
41	C₁₉	C₂×C₅×#4294	1	1	yes	characteristic, complemented
42	C₁₉	C₂×C₅×#4296	1	1	yes	characteristic, complemented
43	C₂×C₉	—	361	1	no	Hall
44	C₃×C₅	—	19	1	no	—
45	C₂×C₅	#15692437	1	1	yes	characteristic, direct product factor, Hall
46	C₉	—	361	1	no	Sylow
47	C₂×C₃	—	19	1	no	—
48	C₅	C₂×#15692437	1	1	yes	characteristic, direct product factor, Sylow
49	C₃	—	19	1	no	—
50	C₂	C₅×#15692437	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅	#15692437
commutator, hypocenter	C₁₉²	C₂×C₅×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉²	C₉
prime radical	C₂×C₅×C₁₉×C₁₉⋊C₃	C₃
cosocle	C₁₉×C₁₉⋊C₃	C₂×C₃×C₅
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#15692437	C₂	direct (N × H)
3. C₂×#15692437	C₅	direct (N × H)
5. C₂×C₅×C₁₉²	C₉	semidirect
6. #15692437	C₂×C₅	direct (N × H)
8. C₅×C₁₉²	C₂×C₉	semidirect
14. C₂×C₁₉²	C₅×C₉	semidirect
17. C₁₉²	C₂×C₅×C₉	semidirect
23. C₂×C₅×C₁₉	#4294	semidirect
24. C₂×C₅×C₁₉	#4296	semidirect
30. C₅×C₁₉	C₂×#4294	semidirect
31. C₅×C₁₉	C₂×#4296	semidirect
37. C₂×C₁₉	C₅×#4294	semidirect
38. C₂×C₁₉	C₅×#4296	semidirect
41. C₁₉	C₂×C₅×#4294	semidirect
42. C₁₉	C₂×C₅×#4296	semidirect
45. C₂×C₅	#15692437	direct (N × H)
48. C₅	C₂×#15692437	direct (N × H)
50. C₂	C₅×#15692437	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×#15692437	2
C₂×C₅×C₁₉×C₁₉⋊C₃	3
C₂×#15692437	5
C₂×C₅×#4296	19
C₂×C₅×#4294	19

Subgroups — C2×C5×#15692437 #44570569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#15692437 #44570569