Subgroups — C₃×#1204 #67134

Order 360.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Dic₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₃²×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₃×Dic₁₀	—	3	1	no	maximal
5	#1204	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
7	C₃×Dic₆	—	5	1	no	maximal, Hall
8	C₃×C₄×C₅	—	3	1	no	—
9	Dic₁₅	C₂×C₃	1	1	yes	characteristic
10	C₃×Dic₅	—	2	1	no	—
11	C₃×Dic₅	—	3	1	no	—
12	C₃×Dic₅	D₃	1	1	yes	characteristic
13	C₃×Dic₅	C₂×C₃	1	1	yes	characteristic
14	C₅×Dic₃	C₂×C₃	1	1	yes	characteristic
15	C₃²×C₅	Q₈	1	1	yes	characteristic, complemented, Hall
16	Dic₁₀	—	3	1	no	Hall
17	C₃²×C₄	—	5	1	no	—
18	C₃×Dic₃	—	5	1	no	—
19	C₃×Dic₃	D₅	1	1	yes	characteristic
20	C₂×C₃×C₅	—	2	1	no	—
21	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic
22	C₂×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
23	C₃×Q₈	—	15	1	no	—
24	Dic₆	—	5	1	no	—
25	C₄×C₅	—	3	1	no	—
26	Dic₅	—	3	1	no	—
27	Dic₅	C₃×D₃	1	1	yes	characteristic
28	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
29	C₃×C₅	—	2	1	no	—
30	C₃×C₅	Dic₆	1	1	yes	characteristic, complemented
31	C₃×C₅	C₃×Q₈	1	1	yes	characteristic, complemented
32	C₃×C₄	—	3	1	no	—
33	C₃×C₄	—	5	1	no	—
34	C₃×C₄	—	5	1	no	—
35	C₃×C₄	—	10	1	no	—
36	C₃×C₄	—	15	1	no	—
37	Dic₃	—	5	1	no	—
38	Dic₃	C₃×D₅	1	1	yes	characteristic
39	C₂×C₅	C₂×C₃×D₃	1	1	yes	characteristic
40	C₃²	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
41	Q₈	—	15	1	no	Sylow
42	C₂×C₃	—	2	1	no	—
43	C₂×C₃	D₃×D₅	1	1	yes	characteristic
44	C₂×C₃	C₂×C₃×D₅	1	1	yes	characteristic
45	C₅	C₃×Dic₆	1	1	yes	characteristic, complemented, Sylow
46	C₄	—	3	1	no	—
47	C₄	—	5	1	no	—
48	C₄	—	15	1	no	—
49	C₃	—	2	1	no	—
50	C₃	#1204	1	1	yes	characteristic, direct product factor
51	C₃	C₃×Dic₁₀	1	1	yes	characteristic, complemented
52	C₂	C₃×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂²×C₃
Frattini	C₂	C₃×D₃×D₅
Fitting, socle, prime radical	C₂×C₃²×C₅	C₂²
hypocenter	C₃×C₅	C₃×Q₈
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
5. #1204	C₃	direct (N × H)
15. C₃²×C₅	Q₈	semidirect
30. C₃×C₅	Dic₆	semidirect
31. C₃×C₅	C₃×Q₈	semidirect
40. C₃²	Dic₁₀	semidirect
45. C₅	C₃×Dic₆	semidirect
50. C₃	#1204	direct (N × H)
51. C₃	C₃×Dic₁₀	semidirect

Maximal subgroups

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

subgroup	index
C₃×Dic₁₅	2
C₃×C₅×Dic₃	2
C₃²×Dic₅	2
C₃×Dic₁₀	3
#1204	3
C₃×Dic₆	5

Subgroups — C3×#1204 #67134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1204 #67134