Subgroups — C₃×C₃⋊#672 #10623622

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⋊#672	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#672	—	3	1	no	maximal
4	C₃²×C₄×C₅	C₄	1	1	yes	characteristic
5	C₃×C₃⋊C₁₆	—	5	1	no	maximal, 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	#672	—	3	1	no	Hall
11	C₃²×C₈	D₅	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	—	15	1	no	—
16	C₃⋊C₁₆	—	5	1	no	—
17	C₃²×C₅	C₁₆	1	1	yes	characteristic, complemented, Hall
18	C₅×C₈	C₃×D₃	1	1	yes	characteristic
19	C₃²×C₄	Dic₅	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	C₃×D₅	1	1	yes	characteristic
25	C₃×C₈	D₁₅	1	1	yes	characteristic
26	C₄×C₅	C₃×Dic₃	1	1	yes	characteristic
27	C₂×C₃²	#168	1	1	yes	characteristic
28	C₁₆	—	15	1	no	Sylow
29	C₃×C₅	—	2	1	no	—
30	C₃×C₅	C₃⋊C₁₆	1	1	yes	characteristic, complemented
31	C₃×C₅	C₃×C₁₆	1	1	yes	characteristic, complemented
32	C₃×C₄	—	2	1	no	—
33	C₃×C₄	C₃×Dic₅	1	1	yes	characteristic
34	C₃×C₄	Dic₁₅	1	1	yes	characteristic
35	C₂×C₅	C₃×C₃⋊C₈	1	1	yes	characteristic
36	C₃²	#672	1	1	yes	characteristic, complemented, Sylow
37	C₈	C₃×D₁₅	1	1	yes	characteristic
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	C₃×#168	1	1	yes	characteristic
40	C₂×C₃	C₃⋊#168	1	1	yes	characteristic
41	C₅	C₃×C₃⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
42	C₄	C₃×Dic₁₅	1	1	yes	characteristic
43	C₃	—	2	1	no	—
44	C₃	C₃×#672	1	1	yes	characteristic, complemented
45	C₃	C₃⋊#672	1	1	yes	characteristic, direct product factor
46	C₂	C₃×C₃⋊#168	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₈	D₁₅
commutator, hypocenter	C₃×C₅	C₃×C₁₆
Frattini	C₈	C₃×D₁₅
Fitting	C₃²×C₅×C₈	C₂
socle, prime radical	C₂×C₃²×C₅	C₈
cosocle	C₃×C₅×C₈	C₂×C₃
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃⋊#672	C₃	direct (N × H)
17. C₃²×C₅	C₁₆	semidirect
30. C₃×C₅	C₃⋊C₁₆	semidirect
31. C₃×C₅	C₃×C₁₆	semidirect
36. C₃²	#672	semidirect
41. C₅	C₃×C₃⋊C₁₆	semidirect
44. C₃	C₃×#672	semidirect
45. C₃	C₃⋊#672	direct (N × H)

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⋊#672	3
C₃×#672	3
C₃×C₃⋊C₁₆	5

Subgroups — C3×C3⋊#672 #10623622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊#672 #10623622