Subgroups — C₃³×C₅×A₄ #13108561

Order 1620.

904 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×C₅	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₅×A₄	C₃	1	39	yes	maximal, direct product factor
3	C₃⁴×C₅	—	4	1	no	maximal, Hall
4	C₃³×A₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃³×C₅	—	3	1	no	—
6	C₂²×C₃²×C₅	C₃²	1	13	yes	complemented
7	C₃×C₅×A₄	C₃²	1	117	yes	direct product factor
8	C₃³×C₅	—	4	39	no	—
9	C₃³×C₅	A₄	1	1	yes	characteristic, direct product factor
10	C₂²×C₃³	C₃×C₅	1	1	yes	characteristic, complemented
11	C₃²×A₄	C₃×C₅	1	39	yes	direct product factor
12	C₂×C₃²×C₅	—	3	13	no	—
13	C₃⁴	—	4	1	no	Sylow
14	C₂²×C₃×C₅	C₃³	1	13	yes	complemented
15	C₅×A₄	C₃³	1	27	yes	direct product factor
16	C₂×C₃³	—	3	1	no	—
17	C₃²×C₅	—	4	117	no	—
18	C₃²×C₅	C₃×A₄	1	13	yes	direct product factor
19	C₂²×C₃²	C₃²×C₅	1	13	yes	complemented
20	C₃×A₄	C₃²×C₅	1	117	yes	direct product factor
21	C₂×C₃×C₅	—	3	13	no	—
22	C₃³	—	4	39	no	—
23	C₃³	C₅×A₄	1	1	yes	characteristic, direct product factor
24	C₂²×C₅	C₃⁴	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃²	—	3	13	no	—
26	C₃×C₅	—	4	27	no	—
27	C₃×C₅	C₃²×A₄	1	13	yes	direct product factor
28	C₂²×C₃	C₃³×C₅	1	13	yes	complemented
29	A₄	C₃³×C₅	1	27	yes	direct product factor
30	C₂×C₅	—	3	1	no	—
31	C₃²	—	4	117	no	—
32	C₃²	C₃×C₅×A₄	1	13	yes	direct product factor
33	C₂×C₃	—	3	13	no	—
34	C₅	C₃³×A₄	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	C₃⁴×C₅	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	4	27	no	—
37	C₃	C₃²×C₅×A₄	1	13	yes	direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃³×C₅	A₄
commutator, cosocle, hypocenter	C₂²	C₃⁴×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃³×C₅	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃³×C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×C₅	C₃	semidirect
2. C₃²×C₅×A₄	C₃	direct (N × H)
4. C₃³×A₄	C₅	direct (N × H)
6. C₂²×C₃²×C₅	C₃²	semidirect
7. C₃×C₅×A₄	C₃²	direct (N × H)
9. C₃³×C₅	A₄	direct (N × H)
10. C₂²×C₃³	C₃×C₅	semidirect
11. C₃²×A₄	C₃×C₅	direct (N × H)
14. C₂²×C₃×C₅	C₃³	semidirect
15. C₅×A₄	C₃³	direct (N × H)
18. C₃²×C₅	C₃×A₄	direct (N × H)
19. C₂²×C₃²	C₃²×C₅	semidirect
20. C₃×A₄	C₃²×C₅	direct (N × H)
23. C₃³	C₅×A₄	direct (N × H)
24. C₂²×C₅	C₃⁴	semidirect
27. C₃×C₅	C₃²×A₄	direct (N × H)
28. C₂²×C₃	C₃³×C₅	semidirect
29. A₄	C₃³×C₅	direct (N × H)
32. C₃²	C₃×C₅×A₄	direct (N × H)
34. C₅	C₃³×A₄	direct (N × H)
35. C₂²	C₃⁴×C₅	semidirect
37. C₃	C₃²×C₅×A₄	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃³×C₅	3
C₃²×C₅×A₄	3
C₃⁴×C₅	4
C₃³×A₄	5

Subgroups — C33×C5×A4 #13108561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₅×A₄ #13108561