Subgroups — C₃×C₅×D₃₆₁⋊C₃ #44570434

Order 32490.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₃₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₃₆₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃₆₁⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×D₃₆₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₃₆₁⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₃₆₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₃₆₁	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₃₆₁⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×D₃₆₁	C₃×C₅	1	1	yes	characteristic, complemented
10	D₃₆₁⋊C₃	C₃×C₅	1	3	yes	direct product factor
11	C₅×C₃₆₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×D₁₉⋊C₃	—	19	1	no	maximal
13	C₃×C₃₆₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
14	C₃₆₁⋊C₃	C₂×C₃×C₅	1	3	yes	complemented
15	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
16	D₃₆₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×D₁₉	—	19	1	no	—
18	C₅×D₁₉⋊C₃	—	19	3	no	—
19	C₃₆₁	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
20	C₃×D₁₉⋊C₃	—	19	1	no	—
21	C₃×C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic
22	C₅×C₁₉⋊C₃	—	19	3	no	—
23	C₅×D₁₉	—	19	1	no	—
24	C₃×C₁₉⋊C₃	—	19	1	no	—
25	C₃×D₁₉	—	19	1	no	—
26	D₁₉⋊C₃	—	19	3	no	—
27	C₅×C₁₉	C₃×D₁₉⋊C₃	1	1	yes	characteristic
28	C₂×C₃²×C₅	—	361	1	no	Hall
29	C₃×C₁₉	C₅×D₁₉⋊C₃	1	1	yes	characteristic
30	C₁₉⋊C₃	—	19	3	no	—
31	C₃²×C₅	—	361	1	no	Hall
32	D₁₉	—	19	1	no	—
33	C₂×C₃×C₅	—	361	3	no	—
34	C₂×C₃×C₅	—	361	1	no	—
35	C₁₉	C₃×C₅×D₁₉⋊C₃	1	1	yes	characteristic
36	C₂×C₃²	—	361	1	no	Hall
37	C₃×C₅	—	361	3	no	—
38	C₃×C₅	D₃₆₁⋊C₃	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×D₃₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	361	3	no	—
45	C₃	C₅×D₃₆₁⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂	—	361	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₃₆₁⋊C₃
commutator, cosocle, hypocenter	C₃₆₁	C₂×C₃²×C₅
Frattini	C₁₉	C₃×C₅×D₁₉⋊C₃
Fitting	C₃×C₅×C₃₆₁	C₂×C₃
socle	C₃×C₅×C₁₉	D₁₉⋊C₃
LCS	G ▷ C₃₆₁
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₃₆₁⋊C₃	C₂	semidirect
2. C₃×C₅×D₃₆₁	C₃	semidirect
3. C₅×D₃₆₁⋊C₃	C₃	direct (N × H)
4. C₃×D₃₆₁⋊C₃	C₅	direct (N × H)
5. C₅×C₃₆₁⋊C₃	C₂×C₃	semidirect
6. C₃×C₅×C₃₆₁	C₂×C₃	semidirect
7. C₅×D₃₆₁	C₃²	semidirect
8. C₃×C₃₆₁⋊C₃	C₂×C₅	semidirect
9. C₃×D₃₆₁	C₃×C₅	semidirect
10. D₃₆₁⋊C₃	C₃×C₅	direct (N × H)
11. C₅×C₃₆₁	C₂×C₃²	semidirect
13. C₃×C₃₆₁	C₂×C₃×C₅	semidirect
14. C₃₆₁⋊C₃	C₂×C₃×C₅	semidirect
16. D₃₆₁	C₃²×C₅	semidirect
19. C₃₆₁	C₂×C₃²×C₅	semidirect
38. C₃×C₅	D₃₆₁⋊C₃	direct (N × H)
43. C₅	C₃×D₃₆₁⋊C₃	direct (N × H)
45. C₃	C₅×D₃₆₁⋊C₃	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×C₃₆₁⋊C₃	2
C₃×C₅×D₃₆₁	3
C₅×D₃₆₁⋊C₃	3
C₃×D₃₆₁⋊C₃	5
C₃×C₅×D₁₉⋊C₃	19

Subgroups — C3×C5×D361⋊C3 #44570434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₃₆₁⋊C₃ #44570434