Subgroups — C₅×C₃⋊D₃×C₃₆₁ #44570449

Order 32490.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₃₆₁	—	3	4	no	maximal
3	C₃⋊D₃×C₃₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₃₆₁	D₃	1	4	yes	complemented
5	C₂×C₅×C₃₆₁	—	9	1	no	Hall
6	C₃²×C₃₆₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₃×C₃₆₁	—	3	4	no	—
8	C₅×C₃₆₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₃⋊D₃×C₁₉	C₁₉	1	1	yes	maximal, characteristic
10	C₃×C₃₆₁	C₅×D₃	1	4	yes	complemented
11	C₃²×C₅×C₁₉	C₂×C₁₉	1	1	yes	characteristic
12	C₂×C₃₆₁	—	9	1	no	Hall
13	C₅×D₃×C₁₉	—	3	4	no	—
14	C₃₆₁	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₃⋊D₃×C₁₉	C₅×C₁₉	1	1	yes	characteristic
16	C₃×C₅×C₁₉	D₃×C₁₉	1	4	yes	—
17	C₂×C₅×C₁₉	—	9	1	no	—
18	C₃²×C₁₉	C₂×C₅×C₁₉	1	1	yes	characteristic
19	D₃×C₁₉	—	3	4	no	—
20	C₅×C₁₉	C₃⋊D₃×C₁₉	1	1	yes	characteristic
21	C₅×C₃⋊D₃	C₃₆₁	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₉	C₅×D₃×C₁₉	1	4	yes	—
23	C₃²×C₅	C₂×C₃₆₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₉	—	9	1	no	—
25	C₅×D₃	—	3	4	no	—
26	C₁₉	C₅×C₃⋊D₃×C₁₉	1	1	yes	characteristic
27	C₃⋊D₃	C₅×C₃₆₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	D₃×C₃₆₁	1	4	yes	complemented
29	C₂×C₅	—	9	1	no	Hall
30	C₃²	C₂×C₅×C₃₆₁	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3	4	no	—
32	C₅	C₃⋊D₃×C₃₆₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₅×D₃×C₃₆₁	1	4	yes	complemented
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₃₆₁	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₅×C₃₆₁
Frattini	C₁₉	C₅×C₃⋊D₃×C₁₉
Fitting	C₃²×C₅×C₃₆₁	C₂
socle	C₃²×C₅×C₁₉	C₂×C₁₉
prime radical	C₅×C₃⋊D₃×C₁₉	C₁₉
cosocle	C₃²×C₁₉	C₂×C₅×C₁₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₃₆₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₃₆₁	C₂	semidirect
3. C₃⋊D₃×C₃₆₁	C₅	direct (N × H)
4. C₃×C₅×C₃₆₁	D₃	semidirect
6. C₃²×C₃₆₁	C₂×C₅	semidirect
8. C₅×C₃₆₁	C₃⋊D₃	direct (N × H)
10. C₃×C₃₆₁	C₅×D₃	semidirect
14. C₃₆₁	C₅×C₃⋊D₃	direct (N × H)
21. C₅×C₃⋊D₃	C₃₆₁	direct (N × H)
23. C₃²×C₅	C₂×C₃₆₁	semidirect
27. C₃⋊D₃	C₅×C₃₆₁	direct (N × H)
28. C₃×C₅	D₃×C₃₆₁	semidirect
30. C₃²	C₂×C₅×C₃₆₁	semidirect
32. C₅	C₃⋊D₃×C₃₆₁	direct (N × H)
33. C₃	C₅×D₃×C₃₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₃₆₁	2
C₅×D₃×C₃₆₁	3
C₃⋊D₃×C₃₆₁	5
C₅×C₃⋊D₃×C₁₉	19

Subgroups — C5×C3⋊D3×C361 #44570449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊D₃×C₃₆₁ #44570449