Subgroups — C₃×#14524206⋊C₅ #44570501

Order 32490.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11762245⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×(C₁₉⋊D₁₉)⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented
3	#14524206⋊C₅	C₃	1	3	yes	maximal, direct product factor
4	C₃×#14524206	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₁₉²⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
6	#11762245⋊C₅	C₂×C₃	1	3	yes	complemented
7	(C₁₉⋊D₁₉)⋊C₅	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	complemented
11	C₁₉²⋊C₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
13	#11762245	C₂×C₃×C₅	1	3	yes	complemented
14	C₁₉⋊D₁₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₁₉²	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₃×D₁₉⋊C₃	—	95	4	no	—
17	C₃×C₁₉⋊C₃	—	95	4	no	—
18	C₃×D₁₉	—	95	4	no	—
19	D₁₉⋊C₃	—	95	12	no	—
20	C₂×C₃²×C₅	—	361	1	no	maximal, Hall
21	C₃×C₁₉	—	5	4	no	—
22	C₁₉⋊C₃	—	95	12	no	—
23	C₃²×C₅	—	361	1	no	Hall
24	D₁₉	—	95	4	no	—
25	C₂×C₃×C₅	—	361	3	no	—
26	C₂×C₃×C₅	—	361	1	no	—
27	C₁₉	—	5	4	no	—
28	C₂×C₃²	—	361	1	no	Hall
29	C₃×C₅	—	361	3	no	—
30	C₃×C₅	—	361	1	no	—
31	C₂×C₅	—	361	1	no	Hall
32	C₃²	—	361	1	no	Sylow
33	C₂×C₃	—	361	3	no	—
34	C₂×C₃	—	361	1	no	—
35	C₅	—	361	1	no	Sylow
36	C₃	—	361	3	no	—
37	C₃	#14524206⋊C₅	1	1	yes	characteristic, direct product factor
38	C₂	—	361	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×#11762245⋊C₅	C₂	semidirect
2. C₃×(C₁₉⋊D₁₉)⋊C₅	C₃	semidirect
3. #14524206⋊C₅	C₃	direct (N × H)
4. C₃×#14524206	C₅	semidirect
5. C₃×C₁₉²⋊C₅	C₂×C₃	semidirect
6. #11762245⋊C₅	C₂×C₃	semidirect
7. (C₁₉⋊D₁₉)⋊C₅	C₃²	semidirect
8. C₃×#11762245	C₂×C₅	semidirect
9. C₃×C₁₉⋊D₁₉	C₃×C₅	semidirect
10. #14524206	C₃×C₅	semidirect
11. C₁₉²⋊C₅	C₂×C₃²	semidirect
12. C₃×C₁₉²	C₂×C₃×C₅	semidirect
13. #11762245	C₂×C₃×C₅	semidirect
14. C₁₉⋊D₁₉	C₃²×C₅	semidirect
15. C₁₉²	C₂×C₃²×C₅	semidirect
37. C₃	#14524206⋊C₅	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×#11762245⋊C₅	2
C₃×(C₁₉⋊D₁₉)⋊C₅	3
#14524206⋊C₅	3
C₃×#14524206	5
C₂×C₃²×C₅	361

Subgroups — C3×#14524206⋊C5 #44570501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#14524206⋊C₅ #44570501