Subgroups — C₅×A₄×C₃₇⋊C₃ #20269112

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	2	yes	maximal, complemented
2	C₅×A₄×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×C₃₇⋊C₃	—	4	1	no	maximal, Hall
5	A₄×C₃₇⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₃₇⋊C₃	—	3	1	no	—
7	C₂²×C₅×C₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×C₃₇	—	4	1	no	—
9	C₅×C₃₇⋊C₃	—	4	2	no	—
10	C₅×C₃₇⋊C₃	A₄	1	1	yes	characteristic, direct product factor
11	C₂²⋊(C₃₇⋊C₃)	C₃×C₅	1	2	yes	complemented
12	A₄×C₃₇	C₃×C₅	1	1	yes	characteristic, complemented
13	C₂²×C₃₇⋊C₃	C₃×C₅	1	1	yes	characteristic, complemented
14	C₂×C₅×C₃₇	—	3	1	no	—
15	C₃×C₃₇⋊C₃	—	4	1	no	Hall
16	C₂×C₃₇⋊C₃	—	3	1	no	—
17	C₅×C₃₇	C₃×A₄	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×A₄	—	37	1	no	maximal, Hall
19	C₂²×C₃₇	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₃×C₃₇	—	4	1	no	—
21	C₃₇⋊C₃	—	4	2	no	—
22	C₃₇⋊C₃	C₅×A₄	1	1	yes	characteristic, direct product factor
23	C₂×C₃₇	—	3	1	no	—
24	C₂²×C₃×C₅	—	37	1	no	—
25	C₅×A₄	—	37	2	no	—
26	C₅×A₄	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
27	C₃²×C₅	—	148	1	no	Hall
28	C₃₇	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
29	C₃×A₄	—	37	1	no	Hall
30	C₂×C₃×C₅	—	111	1	no	—
31	C₂²×C₅	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₅	—	4	1	no	—
33	C₃×C₅	—	37	1	no	—
34	C₃×C₅	—	148	2	no	—
35	C₂²×C₃	—	37	1	no	—
36	A₄	—	37	2	no	—
37	A₄	C₅×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
38	C₂×C₅	—	3	1	no	—
39	C₃²	—	148	1	no	Sylow
40	C₂×C₃	—	111	1	no	—
41	C₅	A₄×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²	C₃×C₅×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	4	1	no	—
44	C₃	—	37	1	no	—
45	C₃	—	148	2	no	—
46	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅	A₄×C₃₇⋊C₃
commutator, hypocenter	C₂²×C₃₇	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₃₇	C₃²
LCS	G ▷ C₂²×C₃₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂²⋊(C₃₇⋊C₃)	C₃	semidirect
2. C₅×A₄×C₃₇	C₃	semidirect
3. C₂²×C₅×C₃₇⋊C₃	C₃	semidirect
5. A₄×C₃₇⋊C₃	C₅	direct (N × H)
7. C₂²×C₅×C₃₇	C₃²	semidirect
10. C₅×C₃₇⋊C₃	A₄	direct (N × H)
11. C₂²⋊(C₃₇⋊C₃)	C₃×C₅	semidirect
12. A₄×C₃₇	C₃×C₅	semidirect
13. C₂²×C₃₇⋊C₃	C₃×C₅	semidirect
17. C₅×C₃₇	C₃×A₄	semidirect
19. C₂²×C₃₇	C₃²×C₅	semidirect
22. C₃₇⋊C₃	C₅×A₄	direct (N × H)
26. C₅×A₄	C₃₇⋊C₃	direct (N × H)
28. C₃₇	C₃×C₅×A₄	semidirect
31. C₂²×C₅	C₃×C₃₇⋊C₃	semidirect
37. A₄	C₅×C₃₇⋊C₃	direct (N × H)
41. C₅	A₄×C₃₇⋊C₃	direct (N × H)
42. C₂²	C₃×C₅×C₃₇⋊C₃	semidirect

Subgroups — C5×A4×C37⋊C3 #20269112

Conjugacy classes of subgroups

Complements

Subgroups — C₅×A₄×C₃₇⋊C₃ #20269112