Subgroups — C₃×C₅×C₂²⋊(C₃₇⋊C₃) #20269171

Order 6660.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂²⋊(C₃₇⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₅×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₃₇⋊C₃	—	4	1	no	maximal, Hall
4	C₃×C₂²⋊(C₃₇⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₃₇	—	3	1	no	—
6	C₂²×C₅×C₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₃₇	A₄	1	1	yes	characteristic, complemented
8	C₅×C₃₇⋊C₃	—	4	3	no	—
9	C₂²×C₃×C₃₇	C₃×C₅	1	1	yes	characteristic, complemented
10	C₂²⋊(C₃₇⋊C₃)	C₃×C₅	1	3	yes	direct product factor
11	C₂×C₅×C₃₇	—	3	1	no	—
12	C₃×C₃₇⋊C₃	—	4	1	no	Hall
13	C₂×C₃×C₃₇	—	3	1	no	—
14	C₅×C₃₇	C₃×A₄	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×A₄	—	37	1	no	maximal, Hall
16	C₂²×C₃₇	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₃₇	C₅×A₄	1	1	yes	characteristic, complemented
18	C₃₇⋊C₃	—	4	3	no	—
19	C₂×C₃₇	—	3	1	no	—
20	C₂²×C₃×C₅	C₃₇⋊C₃	1	1	yes	characteristic, complemented
21	C₅×A₄	—	37	3	no	—
22	C₃²×C₅	—	148	1	no	Hall
23	C₃₇	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
24	C₃×A₄	—	37	1	no	Hall
25	C₂×C₃×C₅	—	3	1	no	—
26	C₂²×C₅	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₃×C₅	—	148	3	no	—
28	C₃×C₅	C₂²⋊(C₃₇⋊C₃)	1	1	yes	characteristic, direct product factor
29	C₂²×C₃	C₅×C₃₇⋊C₃	1	1	yes	characteristic, complemented
30	A₄	—	37	3	no	—
31	C₂×C₅	—	3	1	no	—
32	C₃²	—	148	1	no	Sylow
33	C₂×C₃	—	3	1	no	—
34	C₅	C₃×C₂²⋊(C₃₇⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	C₃×C₅×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	148	3	no	—
37	C₃	C₅×C₂²⋊(C₃₇⋊C₃)	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	C₂²⋊(C₃₇⋊C₃)
commutator, hypocenter	C₂²×C₃₇	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅×C₃₇	C₃
LCS	G ▷ C₂²×C₃₇
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂²⋊(C₃₇⋊C₃)	C₃	direct (N × H)
2. C₂²×C₃×C₅×C₃₇	C₃	semidirect
4. C₃×C₂²⋊(C₃₇⋊C₃)	C₅	direct (N × H)
6. C₂²×C₅×C₃₇	C₃²	semidirect
7. C₃×C₅×C₃₇	A₄	semidirect
9. C₂²×C₃×C₃₇	C₃×C₅	semidirect
10. C₂²⋊(C₃₇⋊C₃)	C₃×C₅	direct (N × H)
14. C₅×C₃₇	C₃×A₄	semidirect
16. C₂²×C₃₇	C₃²×C₅	semidirect
17. C₃×C₃₇	C₅×A₄	semidirect
20. C₂²×C₃×C₅	C₃₇⋊C₃	semidirect
23. C₃₇	C₃×C₅×A₄	semidirect
26. C₂²×C₅	C₃×C₃₇⋊C₃	semidirect
28. C₃×C₅	C₂²⋊(C₃₇⋊C₃)	direct (N × H)
29. C₂²×C₃	C₅×C₃₇⋊C₃	semidirect
34. C₅	C₃×C₂²⋊(C₃₇⋊C₃)	direct (N × H)
35. C₂²	C₃×C₅×C₃₇⋊C₃	semidirect
37. C₃	C₅×C₂²⋊(C₃₇⋊C₃)	direct (N × H)

Subgroups — C3×C5×C22⋊(C37⋊C3) #20269171

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅×C₂²⋊(C₃₇⋊C₃) #20269171