Subgroups — C₂×C₃×#64665 #14279781

Order 1920.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3926	C₂	1	1	yes	maximal, characteristic
2	C₃×#64665	C₂	1	2	yes	maximal, direct product factor
3	C₂×#64665	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅×C₁₆	C₄	1	1	yes	characteristic
5	C₃×#3926	C₄	1	1	yes	characteristic
6	C₃×#3926	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₆₄	—	5	1	no	maximal, Hall
8	C₂×#3926	C₂×C₃	1	1	yes	characteristic
9	#64665	C₂×C₃	1	2	yes	direct product factor
10	C₂×C₃×C₅×C₈	C₈	1	1	yes	characteristic
11	C₃×C₅×C₁₆	C₈	1	1	yes	characteristic
12	C₃×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₃₂	—	5	1	no	—
14	C₃×C₆₄	—	5	2	no	—
15	C₂×C₅×C₁₆	C₃×C₄	1	1	yes	characteristic
16	#3926	C₃×C₄	1	1	yes	characteristic
17	#3926	C₂²×C₃	1	1	yes	characteristic
18	C₂×C₆₄	—	5	1	no	Sylow
19	C₂×C₃×C₄×C₅	C₁₆	1	1	yes	characteristic
20	C₃×C₅×C₈	C₁₆	1	1	yes	characteristic
21	C₃×C₅×C₈	C₂×C₈	1	1	yes	characteristic
22	C₂×C₃×C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
23	C₃×C₃₂	—	5	1	no	—
24	C₃×C₃₂	—	5	1	no	—
25	C₂×C₅×C₈	C₃×C₈	1	1	yes	characteristic
26	C₅×C₁₆	C₃×C₈	1	1	yes	characteristic
27	C₅×C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
28	C₂×C₃₂	—	5	1	no	—
29	C₆₄	—	5	2	no	—
30	C₂²×C₃×C₅	C₃₂	1	1	yes	characteristic
31	C₃×C₄×C₅	C₃₂	1	1	yes	characteristic
32	C₃×C₄×C₅	C₂×C₁₆	1	1	yes	characteristic
33	C₂×C₃×C₈	#170	1	1	yes	characteristic
34	C₃×C₁₆	#170	1	1	yes	characteristic
35	C₃×C₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
36	C₂×C₄×C₅	C₃×C₁₆	1	1	yes	characteristic
37	C₅×C₈	C₃×C₁₆	1	1	yes	characteristic
38	C₅×C₈	C₂×C₃×C₈	1	1	yes	characteristic
39	C₂×C₁₆	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₃₂	—	5	1	no	—
41	C₃₂	—	5	1	no	—
42	C₂×C₃×C₅	C₆₄	1	2	yes	complemented
43	C₂×C₃×C₅	C₂×C₃₂	1	1	yes	characteristic
44	C₂×C₃×C₄	#674	1	1	yes	characteristic
45	C₃×C₈	#674	1	1	yes	characteristic
46	C₃×C₈	C₂×#170	1	1	yes	characteristic
47	C₂²×C₅	C₃×C₃₂	1	1	yes	characteristic
48	C₄×C₅	C₃×C₃₂	1	1	yes	characteristic
49	C₄×C₅	C₂×C₃×C₁₆	1	1	yes	characteristic
50	C₂×C₈	C₃×#170	1	1	yes	characteristic
51	C₁₆	C₃×#170	1	1	yes	characteristic
52	C₁₆	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
53	C₃×C₅	C₂×C₆₄	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₃	#3928	1	1	yes	characteristic
55	C₃×C₄	#3928	1	1	yes	characteristic
56	C₃×C₄	C₂×#674	1	1	yes	characteristic
57	C₂×C₅	C₃×C₆₄	1	2	yes	complemented
58	C₂×C₅	C₂×C₃×C₃₂	1	1	yes	characteristic
59	C₂×C₄	C₃×#674	1	1	yes	characteristic
60	C₈	C₃×#674	1	1	yes	characteristic
61	C₈	C₂×C₃×#170	1	1	yes	characteristic
62	C₂×C₃	#64665	1	2	yes	direct product factor
63	C₂×C₃	C₂×#3928	1	1	yes	characteristic
64	C₅	C₂×C₃×C₆₄	1	1	yes	characteristic, complemented, Sylow
65	C₂²	C₃×#3928	1	1	yes	characteristic
66	C₄	C₃×#3928	1	1	yes	characteristic
67	C₄	C₂×C₃×#674	1	1	yes	characteristic
68	C₃	C₂×#64665	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	C₃×#64665	1	2	yes	direct product factor
70	C₂	C₂×C₃×#3928	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₆	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₂×C₃×C₆₄
Frattini	C₁₆	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₁₆	C₄
socle, prime radical	C₂²×C₃×C₅	C₃₂
cosocle	#3926	C₂²×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×#64665	C₂	direct (N × H)
3. C₂×#64665	C₃	direct (N × H)
9. #64665	C₂×C₃	direct (N × H)
42. C₂×C₃×C₅	C₆₄	semidirect
53. C₃×C₅	C₂×C₆₄	semidirect
57. C₂×C₅	C₃×C₆₄	semidirect
62. C₂×C₃	#64665	direct (N × H)
64. C₅	C₂×C₃×C₆₄	semidirect
68. C₃	C₂×#64665	direct (N × H)
69. C₂	C₃×#64665	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3926	2
C₃×#64665	2
C₂×#64665	3
C₂×C₃×C₆₄	5

Subgroups — C2×C3×#64665 #14279781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64665 #14279781