Subgroups — C₃×C₅×C₃⋊C₁₆ #10623621

Order 720.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₁₆	—	3	1	no	maximal
3	C₅×C₃⋊C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃²×C₄×C₅	C₄	1	1	yes	characteristic
5	C₃×C₃⋊C₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₈	—	2	1	no	—
7	C₃×C₅×C₈	D₃	1	1	yes	characteristic
8	C₃×C₅×C₈	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃²×C₅	C₈	1	1	yes	characteristic
10	C₅×C₁₆	—	3	1	no	Hall
11	C₃²×C₈	C₂×C₅	1	1	yes	characteristic
12	C₃×C₄×C₅	—	2	1	no	—
13	C₃×C₄×C₅	Dic₃	1	1	yes	characteristic
14	C₃×C₄×C₅	C₃×C₄	1	1	yes	characteristic
15	C₃×C₁₆	—	3	1	no	—
16	C₃⋊C₁₆	C₃×C₅	1	1	yes	characteristic, direct product factor
17	C₃²×C₅	C₁₆	1	1	yes	characteristic, complemented, Hall
18	C₅×C₈	C₃×D₃	1	1	yes	characteristic
19	C₃²×C₄	C₄×C₅	1	1	yes	characteristic
20	C₂×C₃×C₅	—	2	1	no	—
21	C₂×C₃×C₅	C₃⋊C₈	1	1	yes	characteristic
22	C₂×C₃×C₅	C₃×C₈	1	1	yes	characteristic
23	C₃×C₈	—	2	1	no	—
24	C₃×C₈	C₅×D₃	1	1	yes	characteristic
25	C₃×C₈	C₂×C₃×C₅	1	1	yes	characteristic
26	C₄×C₅	C₃×Dic₃	1	1	yes	characteristic
27	C₂×C₃²	C₅×C₈	1	1	yes	characteristic
28	C₁₆	—	3	1	no	Sylow
29	C₃×C₅	—	2	1	no	—
30	C₃×C₅	C₃⋊C₁₆	1	1	yes	characteristic, direct product factor
31	C₃×C₅	C₃×C₁₆	1	1	yes	characteristic, complemented
32	C₃×C₄	—	2	1	no	—
33	C₃×C₄	C₅×Dic₃	1	1	yes	characteristic
34	C₃×C₄	C₃×C₄×C₅	1	1	yes	characteristic
35	C₂×C₅	C₃×C₃⋊C₈	1	1	yes	characteristic
36	C₃²	C₅×C₁₆	1	1	yes	characteristic, complemented, Sylow
37	C₈	C₃×C₅×D₃	1	1	yes	characteristic
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	C₅×C₃⋊C₈	1	1	yes	characteristic
40	C₂×C₃	C₃×C₅×C₈	1	1	yes	characteristic
41	C₅	C₃×C₃⋊C₁₆	1	1	yes	characteristic, direct product factor, Sylow
42	C₄	C₃×C₅×Dic₃	1	1	yes	characteristic
43	C₃	—	2	1	no	—
44	C₃	C₅×C₃⋊C₁₆	1	1	yes	characteristic, direct product factor
45	C₃	C₃×C₅×C₁₆	1	1	yes	characteristic, complemented
46	C₂	C₃×C₅×C₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₅×C₈	D₃
commutator, hypocenter	C₃	C₃×C₅×C₁₆
Frattini	C₈	C₃×C₅×D₃
Fitting	C₃²×C₅×C₈	C₂
socle, prime radical	C₂×C₃²×C₅	C₈
cosocle	C₃×C₈	C₂×C₃×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₅×C₈

Complements

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

N	H ≅ G/N	type
3. C₅×C₃⋊C₁₆	C₃	direct (N × H)
5. C₃×C₃⋊C₁₆	C₅	direct (N × H)
16. C₃⋊C₁₆	C₃×C₅	direct (N × H)
17. C₃²×C₅	C₁₆	semidirect
30. C₃×C₅	C₃⋊C₁₆	direct (N × H)
31. C₃×C₅	C₃×C₁₆	semidirect
36. C₃²	C₅×C₁₆	semidirect
41. C₅	C₃×C₃⋊C₁₆	direct (N × H)
44. C₃	C₅×C₃⋊C₁₆	direct (N × H)
45. C₃	C₃×C₅×C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₈	2
C₃×C₅×C₁₆	3
C₅×C₃⋊C₁₆	3
C₃×C₃⋊C₁₆	5

Subgroups — C3×C5×C3⋊C16 #10623621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₃⋊C₁₆ #10623621