Subgroups — C₃²×C₅×Dic₃ #10587421

Order 540.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×C₅	—	3	1	no	maximal
3	C₃×C₅×Dic₃	C₃	1	4	yes	maximal, direct product factor
4	C₃³×C₅	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃²×Dic₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃²×C₅	—	2	4	no	—
7	C₂×C₃²×C₅	D₃	1	1	yes	characteristic
8	C₂×C₃²×C₅	C₂×C₃	1	4	yes	—
9	C₃×C₄×C₅	—	3	4	no	—
10	C₅×Dic₃	C₃²	1	1	yes	characteristic, direct product factor
11	C₂×C₃³	C₂×C₅	1	1	yes	characteristic
12	C₃²×C₅	—	2	4	no	—
13	C₃²×C₅	Dic₃	1	1	yes	characteristic, direct product factor
14	C₃²×C₅	C₃×C₄	1	4	yes	complemented
15	C₃²×C₄	—	3	1	no	—
16	C₃×Dic₃	C₃×C₅	1	4	yes	direct product factor
17	C₂×C₃×C₅	—	2	4	no	—
18	C₂×C₃×C₅	C₃×D₃	1	4	yes	—
19	C₂×C₃×C₅	C₂×C₃²	1	1	yes	characteristic
20	C₃³	C₄×C₅	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₅	—	3	1	no	Hall
22	C₂×C₃²	—	2	4	no	—
23	C₂×C₃²	C₅×D₃	1	1	yes	characteristic
24	C₂×C₃²	C₂×C₃×C₅	1	4	yes	—
25	C₃×C₅	—	2	4	no	—
26	C₃×C₅	C₃×Dic₃	1	4	yes	direct product factor
27	C₃×C₅	C₃²×C₄	1	1	yes	characteristic, complemented
28	C₃×C₄	—	3	4	no	—
29	Dic₃	C₃²×C₅	1	1	yes	characteristic, direct product factor
30	C₂×C₅	C₃²×D₃	1	1	yes	characteristic
31	C₃²	—	2	4	no	—
32	C₃²	C₅×Dic₃	1	1	yes	characteristic, direct product factor
33	C₃²	C₃×C₄×C₅	1	4	yes	complemented
34	C₂×C₃	—	2	4	no	—
35	C₂×C₃	C₃×C₅×D₃	1	4	yes	—
36	C₂×C₃	C₂×C₃²×C₅	1	1	yes	characteristic
37	C₅	C₃²×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₄	—	3	1	no	Sylow
39	C₃	—	2	4	no	—
40	C₃	C₃×C₅×Dic₃	1	4	yes	direct product factor
41	C₃	C₃²×C₄×C₅	1	1	yes	characteristic, complemented
42	C₂	C₃²×C₅×D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅	D₃
commutator, hypocenter	C₃	C₃²×C₄×C₅
Frattini	C₂	C₃²×C₅×D₃
Fitting, socle, prime radical	C₂×C₃³×C₅	C₂
cosocle	C₂×C₃	C₂×C₃²×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×Dic₃	C₃	direct (N × H)
4. C₃³×C₅	C₄	semidirect
5. C₃²×Dic₃	C₅	direct (N × H)
10. C₅×Dic₃	C₃²	direct (N × H)
13. C₃²×C₅	Dic₃	direct (N × H)
14. C₃²×C₅	C₃×C₄	semidirect
16. C₃×Dic₃	C₃×C₅	direct (N × H)
20. C₃³	C₄×C₅	semidirect
26. C₃×C₅	C₃×Dic₃	direct (N × H)
27. C₃×C₅	C₃²×C₄	semidirect
29. Dic₃	C₃²×C₅	direct (N × H)
32. C₃²	C₅×Dic₃	direct (N × H)
33. C₃²	C₃×C₄×C₅	semidirect
37. C₅	C₃²×Dic₃	direct (N × H)
40. C₃	C₃×C₅×Dic₃	direct (N × H)
41. C₃	C₃²×C₄×C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃³×C₅	2
C₃²×C₄×C₅	3
C₃×C₅×Dic₃	3
C₃²×Dic₃	5

Subgroups — C32×C5×Dic3 #10587421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×Dic₃ #10587421