Subgroups — C₃×C₅×#14524206 #44570580

Order 32490.

528 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#11762245	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₉⋊D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×#14524206	C₃	1	3	yes	maximal, direct product factor
4	C₃×#14524206	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×#11762245	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₁₉⋊D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×#11762245	C₂×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₉⋊D₁₉	C₃×C₅	1	1	yes	characteristic, complemented
10	#14524206	C₃×C₅	1	3	yes	direct product factor
11	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×D₁₉⋊C₃	—	19	20	no	maximal
13	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
14	#11762245	C₂×C₃×C₅	1	3	yes	complemented
15	C₃×C₅×C₁₉⋊C₃	—	19	20	no	—
16	C₁₉⋊D₁₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×D₁₉	—	19	20	no	—
18	C₅×D₁₉⋊C₃	—	19	60	no	—
19	C₁₉²	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
20	C₃×D₁₉⋊C₃	—	19	20	no	—
21	C₃×C₅×C₁₉	D₁₉⋊C₃	1	20	yes	complemented
22	C₅×C₁₉⋊C₃	—	19	60	no	—
23	C₅×D₁₉	—	19	20	no	—
24	C₃×C₁₉⋊C₃	—	19	20	no	—
25	C₃×D₁₉	—	19	20	no	—
26	D₁₉⋊C₃	—	19	60	no	—
27	C₅×C₁₉	C₃×D₁₉⋊C₃	1	20	yes	complemented
28	C₂×C₃²×C₅	—	361	1	no	Hall
29	C₃×C₁₉	C₅×D₁₉⋊C₃	1	20	yes	complemented
30	C₁₉⋊C₃	—	19	60	no	—
31	C₃²×C₅	—	361	1	no	Hall
32	D₁₉	—	19	20	no	—
33	C₂×C₃×C₅	—	361	3	no	—
34	C₂×C₃×C₅	—	361	1	no	—
35	C₁₉	C₃×C₅×D₁₉⋊C₃	1	20	yes	complemented
36	C₂×C₃²	—	361	1	no	Hall
37	C₃×C₅	—	361	3	no	—
38	C₃×C₅	#14524206	1	1	yes	characteristic, direct product factor
39	C₂×C₅	—	361	1	no	Hall
40	C₃²	—	361	1	no	Sylow
41	C₂×C₃	—	361	3	no	—
42	C₂×C₃	—	361	1	no	—
43	C₅	C₃×#14524206	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	361	3	no	—
45	C₃	C₅×#14524206	1	1	yes	characteristic, direct product factor
46	C₂	—	361	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	#14524206
commutator, cosocle, hypocenter	C₁₉²	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#11762245	C₂	semidirect
2. C₃×C₅×C₁₉⋊D₁₉	C₃	semidirect
3. C₅×#14524206	C₃	direct (N × H)
4. C₃×#14524206	C₅	direct (N × H)
5. C₅×#11762245	C₂×C₃	semidirect
6. C₃×C₅×C₁₉²	C₂×C₃	semidirect
7. C₅×C₁₉⋊D₁₉	C₃²	semidirect
8. C₃×#11762245	C₂×C₅	semidirect
9. C₃×C₁₉⋊D₁₉	C₃×C₅	semidirect
10. #14524206	C₃×C₅	direct (N × H)
11. C₅×C₁₉²	C₂×C₃²	semidirect
13. C₃×C₁₉²	C₂×C₃×C₅	semidirect
14. #11762245	C₂×C₃×C₅	semidirect
16. C₁₉⋊D₁₉	C₃²×C₅	semidirect
19. C₁₉²	C₂×C₃²×C₅	semidirect
21. C₃×C₅×C₁₉	D₁₉⋊C₃	semidirect
27. C₅×C₁₉	C₃×D₁₉⋊C₃	semidirect
29. C₃×C₁₉	C₅×D₁₉⋊C₃	semidirect
35. C₁₉	C₃×C₅×D₁₉⋊C₃	semidirect
38. C₃×C₅	#14524206	direct (N × H)
43. C₅	C₃×#14524206	direct (N × H)
45. C₃	C₅×#14524206	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#11762245	2
C₃×C₅×C₁₉⋊D₁₉	3
C₅×#14524206	3
C₃×#14524206	5
C₃×C₅×D₁₉⋊C₃	19

Subgroups — C3×C5×#14524206 #44570580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#14524206 #44570580