Subgroups — C₃×#4094 #91665

Order 480.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×#681	C₂	1	3	yes	maximal, complemented
3	C₂×C₃×#168	C₂	1	3	yes	maximal, complemented
4	#4094	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×Q₈	C₄	1	1	yes	characteristic
6	C₃×C₅×D₄	C₄	1	3	yes	—
7	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
8	C₃×#168	C₂²	1	1	yes	characteristic
9	C₃×#168	C₂²	1	3	yes	—
10	C₃×#131	—	5	1	no	maximal, Hall
11	C₅×#41	C₂×C₃	1	1	yes	characteristic
12	#681	C₂×C₃	1	3	yes	complemented
13	C₂×#168	C₂×C₃	1	3	yes	complemented
14	C₂²×C₃×C₅	C₂×C₄	1	3	yes	—
15	C₃×C₄×C₅	C₂×C₄	1	3	yes	—
16	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
17	C₃×#41	D₅	1	1	yes	characteristic
18	C₃×M₁₆	—	5	3	no	—
19	C₂×C₃×C₈	—	5	3	no	—
20	C₅×Q₈	C₃×C₄	1	1	yes	characteristic
21	C₅×D₄	C₃×C₄	1	3	yes	—
22	C₂×C₄×C₅	C₂²×C₃	1	3	yes	—
23	#168	C₂²×C₃	1	1	yes	characteristic
24	#168	C₂²×C₃	1	3	yes	—
25	#131	—	5	1	no	Sylow
26	C₂×C₃×C₅	—	2	3	no	—
27	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
28	C₃×Q₈	Dic₅	1	1	yes	characteristic
29	C₃×D₄	Dic₅	1	3	yes	—
30	C₂×C₃×C₄	C₂×D₅	1	3	yes	—
31	C₃×C₈	—	5	1	no	—
32	C₃×C₈	—	5	3	no	—
33	C₂²×C₅	C₂×C₃×C₄	1	3	yes	—
34	C₄×C₅	C₂×C₃×C₄	1	3	yes	—
35	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
36	#41	C₃×D₅	1	1	yes	characteristic
37	M₁₆	—	5	3	no	—
38	C₂×C₈	—	5	3	no	—
39	C₃×C₅	#131	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₃	C₂×Dic₅	1	3	yes	—
41	C₃×C₄	C₂×Dic₅	1	3	yes	—
42	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
43	C₂×C₅	—	2	3	no	—
44	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
45	Q₈	C₃×Dic₅	1	1	yes	characteristic
46	D₄	C₃×Dic₅	1	3	yes	—
47	C₂×C₄	C₂×C₃×D₅	1	3	yes	—
48	C₈	—	5	1	no	—
49	C₈	—	5	3	no	—
50	C₂×C₃	—	2	3	no	—
51	C₂×C₃	C₂²×Dic₅	1	1	yes	characteristic
52	C₅	C₃×#131	1	1	yes	characteristic, complemented, Sylow
53	C₂²	C₂×C₃×Dic₅	1	3	yes	—
54	C₄	C₂×C₃×Dic₅	1	3	yes	—
55	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
56	C₃	#4094	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	2	3	no	—
58	C₂	C₂²×C₃×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²×D₅
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₄	C₂²×C₃×D₅
Fitting, prime radical	C₃×C₅×#41	C₂
socle	C₂×C₃×C₅	C₂²×C₄
cosocle	C₄×C₅	C₂³×C₃
hypercenter	C₃×#41	D₅
hypocenter	C₅	C₃×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₃×#41

Complements

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

N	H ≅ G/N	type
2. C₃×#681	C₂	semidirect
3. C₂×C₃×#168	C₂	semidirect
4. #4094	C₃	direct (N × H)
12. #681	C₂×C₃	semidirect
13. C₂×#168	C₂×C₃	semidirect
39. C₃×C₅	#131	semidirect
52. C₅	C₃×#131	semidirect
56. C₃	#4094	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#41	2
C₃×#681	2
C₂×C₃×#168	2
#4094	3
C₃×#131	5

Subgroups — C3×#4094 #91665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4094 #91665