Subgroups — C₃²×D₅×C₃₆₁ #44570443

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	C₃×D₅×C₃₆₁	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₃₆₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₃₆₁	C₂×C₃	1	4	yes	complemented
5	D₅×C₃₆₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₃₆₁	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₃₆₁	—	5	4	no	—
8	C₅×C₃₆₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×D₅×C₁₉	C₁₉	1	1	yes	maximal, characteristic
10	C₃×C₃₆₁	C₃×D₅	1	4	yes	direct product factor
11	C₃²×C₅×C₁₉	C₂×C₁₉	1	1	yes	characteristic
12	C₂×C₃₆₁	—	5	1	no	Hall
13	C₃×D₅×C₁₉	C₃×C₁₉	1	4	yes	—
14	C₃₆₁	C₃²×D₅	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₃²×C₁₉	—	5	1	no	—
16	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	4	yes	—
17	D₅×C₁₉	C₃²×C₁₉	1	1	yes	characteristic
18	C₃²×C₁₉	D₅×C₁₉	1	1	yes	characteristic
19	C₂×C₃×C₁₉	—	5	4	no	—
20	C₅×C₁₉	C₂×C₃²×C₁₉	1	1	yes	characteristic
21	C₃²×D₅	C₃₆₁	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₉	C₃×D₅×C₁₉	1	4	yes	—
23	C₃²×C₅	C₂×C₃₆₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₉	—	5	1	no	—
25	C₃×D₅	C₃×C₃₆₁	1	4	yes	direct product factor
26	C₁₉	C₃²×D₅×C₁₉	1	1	yes	characteristic
27	C₂×C₃²	—	5	1	no	Hall
28	C₃×C₅	C₂×C₃×C₃₆₁	1	4	yes	complemented
29	D₅	C₃²×C₃₆₁	1	1	yes	characteristic, direct product factor, Hall
30	C₃²	D₅×C₃₆₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	5	4	no	—
32	C₅	C₂×C₃²×C₃₆₁	1	1	yes	characteristic, complemented, Sylow
33	C₃	C₃×D₅×C₃₆₁	1	4	yes	direct product factor
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₃₆₁	D₅
commutator, hypocenter	C₅	C₂×C₃²×C₃₆₁
Frattini	C₁₉	C₃²×D₅×C₁₉
Fitting	C₃²×C₅×C₃₆₁	C₂
socle	C₃²×C₅×C₁₉	C₂×C₁₉
prime radical	C₃²×D₅×C₁₉	C₁₉
cosocle	C₅×C₁₉	C₂×C₃²×C₁₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₃²×C₃₆₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₃₆₁	C₂	semidirect
2. C₃×D₅×C₃₆₁	C₃	direct (N × H)
4. C₃×C₅×C₃₆₁	C₂×C₃	semidirect
5. D₅×C₃₆₁	C₃²	direct (N × H)
6. C₃²×C₃₆₁	D₅	direct (N × H)
8. C₅×C₃₆₁	C₂×C₃²	semidirect
10. C₃×C₃₆₁	C₃×D₅	direct (N × H)
14. C₃₆₁	C₃²×D₅	direct (N × H)
21. C₃²×D₅	C₃₆₁	direct (N × H)
23. C₃²×C₅	C₂×C₃₆₁	semidirect
25. C₃×D₅	C₃×C₃₆₁	direct (N × H)
28. C₃×C₅	C₂×C₃×C₃₆₁	semidirect
29. D₅	C₃²×C₃₆₁	direct (N × H)
30. C₃²	D₅×C₃₆₁	direct (N × H)
32. C₅	C₂×C₃²×C₃₆₁	semidirect
33. C₃	C₃×D₅×C₃₆₁	direct (N × H)

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
C₃×D₅×C₃₆₁	3
C₂×C₃²×C₃₆₁	5
C₃²×D₅×C₁₉	19

Subgroups — C32×D5×C361 #44570443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₅×C₃₆₁ #44570443