Subgroups — C₂×C₅×#15692430 #44570484

Order 32490.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692430	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅×C₁₉²	C₃	1	1	yes	maximal, characteristic
3	C₂×#15692430	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅×C₁₉²	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692430	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₁₉²	C₃×C₅	1	1	yes	characteristic
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×#4294	—	19	2	no	maximal
10	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic
11	C₅×#4294	—	19	2	no	—
12	C₂×C₁₉²	C₅×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₅×C₁₉	—	3	6	no	—
14	C₂×C₃×C₅×C₁₉	C₁₉⋊C₃	1	2	yes	—
15	C₁₉²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×#4294	—	19	2	no	—
17	C₃×C₅×C₁₉	—	3	6	no	—
18	C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	1	2	yes	—
19	C₂×C₅×C₁₉	—	3	6	no	—
20	C₂×C₅×C₁₉	#4294	1	2	yes	complemented
21	#4294	—	19	2	no	—
22	C₂×C₃×C₁₉	—	3	6	no	—
23	C₂×C₃×C₁₉	C₅×C₁₉⋊C₃	1	2	yes	—
24	C₅×C₁₉	—	3	6	no	—
25	C₅×C₁₉	C₂×#4294	1	2	yes	complemented
26	C₂×C₅×C₉	—	361	1	no	Hall
27	C₃×C₁₉	—	3	6	no	—
28	C₃×C₁₉	C₂×C₅×C₁₉⋊C₃	1	2	yes	—
29	C₅×C₉	—	361	1	no	Hall
30	C₂×C₁₉	—	3	6	no	—
31	C₂×C₁₉	C₅×#4294	1	2	yes	complemented
32	C₂×C₃×C₅	#11762246	1	1	yes	characteristic
33	C₁₉	—	3	6	no	—
34	C₁₉	C₂×C₅×#4294	1	2	yes	complemented
35	C₂×C₉	—	361	1	no	Hall
36	C₃×C₅	C₂×#11762246	1	1	yes	characteristic
37	C₂×C₅	#15692430	1	1	yes	characteristic, direct product factor, Hall
38	C₉	—	361	1	no	Sylow
39	C₂×C₃	C₅×#11762246	1	1	yes	characteristic
40	C₅	C₂×#15692430	1	1	yes	characteristic, direct product factor, Sylow
41	C₃	C₂×C₅×#11762246	1	1	yes	characteristic
42	C₂	C₅×#15692430	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	#11762246
commutator, hypocenter	C₁₉²	C₂×C₅×C₉
Frattini	C₃	C₂×C₅×#11762246
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₉²	C₃
cosocle	C₃×C₁₉²	C₂×C₃×C₅
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#15692430	C₂	direct (N × H)
3. C₂×#15692430	C₅	direct (N × H)
5. C₂×C₅×C₁₉²	C₉	semidirect
6. #15692430	C₂×C₅	direct (N × H)
8. C₅×C₁₉²	C₂×C₉	semidirect
12. C₂×C₁₉²	C₅×C₉	semidirect
15. C₁₉²	C₂×C₅×C₉	semidirect
20. C₂×C₅×C₁₉	#4294	semidirect
25. C₅×C₁₉	C₂×#4294	semidirect
31. C₂×C₁₉	C₅×#4294	semidirect
34. C₁₉	C₂×C₅×#4294	semidirect
37. C₂×C₅	#15692430	direct (N × H)
40. C₅	C₂×#15692430	direct (N × H)
42. C₂	C₅×#15692430	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×#15692430	2
C₂×C₃×C₅×C₁₉²	3
C₂×#15692430	5
C₂×C₅×#4294	19

Subgroups — C2×C5×#15692430 #44570484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#15692430 #44570484