Subgroups — C₃×#4047 #91618

Order 480.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#676	C₂	1	2	yes	maximal, complemented
5	C₃×C₈×D₅	C₂	1	2	yes	maximal, complemented
6	#4047	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₃×C₂²⋊D₅	C₄	1	2	yes	—
9	C₃×D₂₀	C₄	1	1	yes	characteristic
10	C₃×C₄×D₅	C₂²	1	2	yes	—
11	C₃×Dic₁₀	C₄	1	1	yes	characteristic
12	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×#168	C₂²	1	2	yes	—
15	C₃×#131	—	5	1	no	maximal, Hall
16	#709	C₂×C₃	1	1	yes	characteristic
17	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
18	#681	C₂×C₃	1	1	yes	characteristic, complemented
19	#676	C₂×C₃	1	2	yes	complemented
20	C₈×D₅	C₂×C₃	1	2	yes	complemented
21	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×D₅	C₂×C₄	1	2	yes	—
23	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
24	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₃×Dic₅	C₂×C₄	1	2	yes	—
26	C₃×#41	—	5	1	no	—
27	C₃×M₁₆	—	5	1	no	—
28	C₃×M₁₆	—	5	2	no	—
29	C₂×C₃×C₈	—	5	2	no	—
30	C₂×C₃×C₈	D₅	1	1	yes	characteristic, complemented
31	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
32	C₂²⋊D₅	C₃×C₄	1	2	yes	—
33	D₂₀	C₃×C₄	1	1	yes	characteristic
34	C₄×D₅	C₂²×C₃	1	2	yes	—
35	Dic₁₀	C₃×C₄	1	1	yes	characteristic
36	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
37	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
38	#168	C₂²×C₃	1	2	yes	—
39	#131	—	5	1	no	Sylow
40	C₂×C₃×C₅	—	2	1	no	—
41	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
42	C₃×D₅	—	2	2	no	—
43	C₃×Q₈	—	5	1	no	—
44	C₃×D₄	—	5	2	no	—
45	C₃×D₄	—	5	1	no	—
46	C₂×C₃×C₄	—	5	2	no	—
47	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
48	C₃×C₈	—	5	2	no	—
49	C₃×C₈	C₂×D₅	1	1	yes	characteristic
50	C₃×C₈	C₂×D₅	1	1	yes	characteristic
51	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
52	C₂×D₅	C₂×C₃×C₄	1	2	yes	—
53	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
54	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
55	Dic₅	C₂×C₃×C₄	1	2	yes	—
56	#41	—	5	1	no	—
57	M₁₆	—	5	1	no	—
58	M₁₆	—	5	2	no	—
59	C₂×C₈	—	5	2	no	—
60	C₂×C₈	C₃×D₅	1	1	yes	characteristic, complemented
61	C₃×C₅	#131	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₃	—	5	2	no	—
63	C₂²×C₃	C₄×D₅	1	1	yes	characteristic
64	C₃×C₄	—	5	2	no	—
65	C₃×C₄	C₄×D₅	1	1	yes	characteristic
66	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
67	C₂×C₅	—	2	1	no	—
68	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
69	D₅	—	2	2	no	—
70	Q₈	—	5	1	no	—
71	D₄	—	5	2	no	—
72	D₄	—	5	1	no	—
73	C₂×C₄	—	5	2	no	—
74	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
75	C₈	—	5	2	no	—
76	C₈	C₂×C₃×D₅	1	1	yes	characteristic
77	C₈	C₂×C₃×D₅	1	1	yes	characteristic
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	—	10	2	no	—
80	C₂×C₃	C₂×C₄×D₅	1	1	yes	characteristic
81	C₅	C₃×#131	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	5	2	no	—
83	C₂²	C₃×C₄×D₅	1	1	yes	characteristic
84	C₄	—	5	2	no	—
85	C₄	C₃×C₄×D₅	1	1	yes	characteristic
86	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
87	C₃	#4047	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	—	2	1	no	—
89	C₂	—	10	2	no	—
90	C₂	C₂×C₃×C₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₂×D₅
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle	C₂×C₃×C₅	C₂²×C₄
prime radical	C₃×#709	C₂
cosocle	C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₈	D₅
hypocenter	C₅	C₃×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₈ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₈	C₂	semidirect
3. C₃×#681	C₂	semidirect
4. C₃×#676	C₂	semidirect
5. C₃×C₈×D₅	C₂	semidirect
6. #4047	C₃	direct (N × H)
17. C₂×C₅×C₈	C₂×C₃	semidirect
18. #681	C₂×C₃	semidirect
19. #676	C₂×C₃	semidirect
20. C₈×D₅	C₂×C₃	semidirect
30. C₂×C₃×C₈	D₅	semidirect
60. C₂×C₈	C₃×D₅	semidirect
61. C₃×C₅	#131	semidirect
81. C₅	C₃×#131	semidirect
87. C₃	#4047	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×#709	2
C₂×C₃×C₅×C₈	2
C₃×#681	2
C₃×#676	2
C₃×C₈×D₅	2
#4047	3
C₃×#131	5

Subgroups — C3×#4047 #91618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4047 #91618