Subgroups — C₂×C₅×D₃×C₃₆₁ #36343113

Order 21660.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₃₆₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₃₆₁	—	3	1	no	maximal, Hall
4	C₃×C₅×C₃₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₃₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₃₆₁	—	3	2	no	—
7	C₂×C₅×C₃₆₁	D₃	1	1	yes	characteristic, direct product factor
8	D₃×C₃₆₁	C₂×C₅	1	2	yes	direct product factor
9	C₂×C₃×C₃₆₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×C₃₆₁	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₃₆₁	—	3	1	no	Hall
12	C₂×C₅×D₃×C₁₉	C₁₉	1	1	yes	maximal, characteristic
13	C₃×C₃₆₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃₆₁	—	3	2	no	—
15	C₂×C₃₆₁	C₅×D₃	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₅×C₁₉	C₂×C₁₉	1	1	yes	characteristic
17	C₅×D₃×C₁₉	C₂×C₁₉	1	2	yes	—
18	C₂²×C₅×C₁₉	—	3	1	no	—
19	C₃₆₁	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×C₅×C₁₉	C₂²×C₁₉	1	1	yes	characteristic
21	C₂×D₃×C₁₉	C₅×C₁₉	1	1	yes	characteristic
22	C₂×C₅×C₁₉	—	3	2	no	—
23	C₂×C₅×C₁₉	D₃×C₁₉	1	1	yes	characteristic
24	C₂×C₃×C₁₉	C₂×C₅×C₁₉	1	1	yes	characteristic
25	D₃×C₁₉	C₂×C₅×C₁₉	1	2	yes	—
26	C₅×C₁₉	C₂×D₃×C₁₉	1	1	yes	characteristic
27	C₂²×C₁₉	—	3	1	no	—
28	C₂×C₅×D₃	C₃₆₁	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₁₉	C₂²×C₅×C₁₉	1	1	yes	characteristic
30	C₂×C₁₉	—	3	2	no	—
31	C₂×C₁₉	C₅×D₃×C₁₉	1	1	yes	characteristic
32	C₂×C₃×C₅	C₂×C₃₆₁	1	1	yes	characteristic, complemented
33	C₅×D₃	C₂×C₃₆₁	1	2	yes	direct product factor
34	C₂²×C₅	—	3	1	no	Hall
35	C₁₉	C₂×C₅×D₃×C₁₉	1	1	yes	characteristic
36	C₃×C₅	C₂²×C₃₆₁	1	1	yes	characteristic, complemented, Hall
37	C₂×D₃	C₅×C₃₆₁	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₅	—	3	2	no	—
39	C₂×C₅	D₃×C₃₆₁	1	1	yes	characteristic, direct product factor
40	C₂×C₃	C₂×C₅×C₃₆₁	1	1	yes	characteristic, complemented
41	D₃	C₂×C₅×C₃₆₁	1	2	yes	direct product factor
42	C₅	C₂×D₃×C₃₆₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	3	1	no	Sylow
44	C₃	C₂²×C₅×C₃₆₁	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	3	2	no	—
46	C₂	C₅×D₃×C₃₆₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₃₆₁	D₃
commutator, hypocenter	C₃	C₂²×C₅×C₃₆₁
Frattini	C₁₉	C₂×C₅×D₃×C₁₉
Fitting	C₂×C₃×C₅×C₃₆₁	C₂
socle	C₂×C₃×C₅×C₁₉	C₂×C₁₉
prime radical	C₂×C₅×D₃×C₁₉	C₁₉
cosocle	C₃×C₁₉	C₂²×C₅×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₃₆₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×C₃₆₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₃₆₁	C₂	semidirect
4. C₃×C₅×C₃₆₁	C₂²	semidirect
5. C₂×D₃×C₃₆₁	C₅	direct (N × H)
7. C₂×C₅×C₃₆₁	D₃	direct (N × H)
8. D₃×C₃₆₁	C₂×C₅	direct (N × H)
9. C₂×C₃×C₃₆₁	C₂×C₅	semidirect
10. C₅×C₃₆₁	C₂×D₃	direct (N × H)
13. C₃×C₃₆₁	C₂²×C₅	semidirect
15. C₂×C₃₆₁	C₅×D₃	direct (N × H)
19. C₃₆₁	C₂×C₅×D₃	direct (N × H)
28. C₂×C₅×D₃	C₃₆₁	direct (N × H)
32. C₂×C₃×C₅	C₂×C₃₆₁	semidirect
33. C₅×D₃	C₂×C₃₆₁	direct (N × H)
36. C₃×C₅	C₂²×C₃₆₁	semidirect
37. C₂×D₃	C₅×C₃₆₁	direct (N × H)
39. C₂×C₅	D₃×C₃₆₁	direct (N × H)
40. C₂×C₃	C₂×C₅×C₃₆₁	semidirect
41. D₃	C₂×C₅×C₃₆₁	direct (N × H)
42. C₅	C₂×D₃×C₃₆₁	direct (N × H)
44. C₃	C₂²×C₅×C₃₆₁	semidirect
46. C₂	C₅×D₃×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
C₅×D₃×C₃₆₁	2
C₂×C₃×C₅×C₃₆₁	2
C₂²×C₅×C₃₆₁	3
C₂×D₃×C₃₆₁	5
C₂×C₅×D₃×C₁₉	19

Subgroups — C2×C5×D3×C361 #36343113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₃₆₁ #36343113