Subgroups — C₃×#4065 #91636

Order 480.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#713	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#688	C₂	1	2	yes	maximal, complemented
4	C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#4065	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×Q₈	C₂²	1	2	yes	—
8	C₃×D₂₀	—	2	2	no	—
9	C₃×D₂₀	C₂²	1	2	yes	—
10	C₃×C₄×D₅	—	2	2	no	—
11	C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×#168	C₂²	1	1	yes	characteristic
14	C₃×#135	—	5	1	no	maximal, Hall
15	#713	C₂×C₃	1	2	yes	complemented
16	C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
17	#688	C₂×C₃	1	2	yes	complemented
18	D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
19	C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
20	C₂×C₃×D₅	—	2	2	no	—
21	C₂×C₃×D₅	D₄	1	1	yes	characteristic
22	C₃×C₄×C₅	—	2	2	no	—
23	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₃×Dic₅	D₄	1	1	yes	characteristic
25	C₃×#41	—	5	2	no	—
26	C₃×Q₁₆	D₅	1	1	yes	characteristic, complemented
27	C₃×SD₁₆	—	5	2	no	—
28	C₃×D₈	—	5	1	no	—
29	C₂×C₃×C₈	—	5	1	no	—
30	C₅×Q₈	C₂²×C₃	1	2	yes	—
31	D₂₀	—	2	2	no	—
32	D₂₀	C₂²×C₃	1	2	yes	—
33	C₄×D₅	—	2	2	no	—
34	C₄×D₅	C₂²×C₃	1	1	yes	characteristic
35	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
36	#168	C₂²×C₃	1	1	yes	characteristic
37	#135	—	5	1	no	Sylow
38	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
39	C₃×D₅	—	2	1	no	—
40	C₃×D₅	—	4	2	no	—
41	C₃×Q₈	C₂×D₅	1	2	yes	—
42	C₃×D₄	—	5	2	no	—
43	C₃×D₄	—	10	2	no	—
44	C₂×C₃×C₄	—	5	1	no	—
45	C₂×C₃×C₄	—	10	2	no	—
46	C₃×C₈	—	5	1	no	—
47	C₃×C₈	C₂×D₅	1	1	yes	characteristic
48	C₂×D₅	—	2	2	no	—
49	C₂×D₅	C₃×D₄	1	1	yes	characteristic
50	C₄×C₅	—	2	2	no	—
51	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
52	Dic₅	C₃×D₄	1	1	yes	characteristic
53	#41	—	5	2	no	—
54	Q₁₆	C₃×D₅	1	1	yes	characteristic, complemented
55	SD₁₆	—	5	2	no	—
56	D₈	—	5	1	no	—
57	C₂×C₈	—	5	1	no	—
58	C₃×C₅	#135	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₃	—	5	1	no	—
60	C₂²×C₃	—	10	2	no	—
61	C₃×C₄	—	2	2	no	—
62	C₃×C₄	—	5	1	no	—
63	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
64	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
65	D₅	—	2	1	no	—
66	D₅	—	4	2	no	—
67	Q₈	C₂×C₃×D₅	1	2	yes	—
68	D₄	—	5	2	no	—
69	D₄	—	10	2	no	—
70	C₂×C₄	—	5	1	no	—
71	C₂×C₄	—	10	2	no	—
72	C₈	—	5	1	no	—
73	C₈	C₂×C₃×D₅	1	1	yes	characteristic
74	C₂×C₃	—	10	1	no	—
75	C₂×C₃	—	20	2	no	—
76	C₂×C₃	D₄×D₅	1	1	yes	characteristic
77	C₅	C₃×#135	1	1	yes	characteristic, complemented, Sylow
78	C₂²	—	5	1	no	—
79	C₂²	—	10	2	no	—
80	C₄	—	2	2	no	—
81	C₄	—	5	1	no	—
82	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
83	C₃	#4065	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	10	1	no	—
85	C₂	—	20	2	no	—
86	C₂	C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×Q₁₆	C₂
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₃×Q₁₆	D₅
hypocenter	C₅	C₃×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×#713	C₂	semidirect
2. C₃×C₅×Q₁₆	C₂	semidirect
3. C₃×#688	C₂	semidirect
4. C₃×D₄₀	C₂	semidirect
5. C₃×C₈×D₅	C₂	semidirect
6. #4065	C₃	direct (N × H)
15. #713	C₂×C₃	semidirect
16. C₅×Q₁₆	C₂×C₃	semidirect
17. #688	C₂×C₃	semidirect
18. D₄₀	C₂×C₃	semidirect
19. C₈×D₅	C₂×C₃	semidirect
26. C₃×Q₁₆	D₅	semidirect
54. Q₁₆	C₃×D₅	semidirect
58. C₃×C₅	#135	semidirect
77. C₅	C₃×#135	semidirect
83. C₃	#4065	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×#713	2
C₃×C₅×Q₁₆	2
C₃×#688	2
C₃×D₄₀	2
C₃×C₈×D₅	2
#4065	3
C₃×#135	5

Subgroups — C3×#4065 #91636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4065 #91636