Subgroups — C₃×#64889 #11746666

Order 960.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3998	C₂	1	2	yes	maximal
2	C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	#64889	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅×C₈	C₄	1	1	yes	characteristic
5	C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
6	C₂×C₃×#168	C₂²	1	1	yes	characteristic
7	C₃×#674	—	2	2	no	—
8	C₃×#364	—	5	1	no	maximal, Hall
9	#3998	C₂×C₃	1	2	yes	—
10	C₈×Dic₅	C₂×C₃	1	1	yes	characteristic
11	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×Dic₅	—	2	1	no	—
13	C₃×C₅×C₈	C₈	1	2	yes	—
14	C₃×#168	D₄	1	1	yes	characteristic
15	C₃×#168	Q₈	1	1	yes	characteristic
16	C₃×M₃₂	—	5	2	no	—
17	C₃×C₄×C₈	—	5	1	no	—
18	C₂×C₅×C₈	C₃×C₄	1	1	yes	characteristic
19	C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
20	C₂×#168	C₂²×C₃	1	1	yes	characteristic
21	#674	—	2	2	no	—
22	#364	—	5	1	no	Sylow
23	C₂²×C₃×C₅	M₁₆	1	1	yes	characteristic
24	C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
25	C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
26	C₃×Dic₅	—	2	2	no	—
27	C₂×C₃×C₈	—	5	1	no	—
28	C₂×C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₃×C₄²	—	5	1	no	—
30	C₃×C₁₆	—	10	2	no	—
31	C₂×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
32	C₂×Dic₅	—	2	1	no	—
33	C₅×C₈	C₃×C₈	1	2	yes	—
34	#168	C₃×D₄	1	1	yes	characteristic
35	#168	C₃×Q₈	1	1	yes	characteristic
36	M₃₂	—	5	2	no	—
37	C₄×C₈	—	5	1	no	—
38	C₂×C₃×C₅	—	2	1	no	—
39	C₂×C₃×C₅	C₄⋊C₈	1	1	yes	characteristic
40	C₂×C₃×C₄	—	10	1	no	—
41	C₂×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
42	C₃×C₈	—	5	1	no	—
43	C₃×C₈	—	5	1	no	—
44	C₃×C₈	#170	1	2	yes	—
45	C₂²×C₅	C₃×M₁₆	1	1	yes	characteristic
46	C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
47	C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
48	Dic₅	—	2	2	no	—
49	C₂×C₈	—	5	1	no	—
50	C₂×C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
51	C₄²	—	5	1	no	—
52	C₁₆	—	10	2	no	—
53	C₃×C₅	#364	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₃	#700	1	1	yes	characteristic
55	C₃×C₄	—	10	2	no	—
56	C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
57	C₃×C₄	C₂×#170	1	1	yes	characteristic
58	C₂×C₅	—	2	1	no	—
59	C₂×C₅	C₃×C₄⋊C₈	1	1	yes	characteristic
60	C₂×C₄	—	10	1	no	—
61	C₂×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
62	C₈	—	5	1	no	—
63	C₈	—	5	1	no	—
64	C₈	C₃×#170	1	2	yes	—
65	C₂×C₃	—	2	1	no	—
66	C₂×C₃	C₄⋊#170	1	1	yes	characteristic
67	C₅	C₃×#364	1	1	yes	characteristic, complemented, Sylow
68	C₂²	C₃×#700	1	1	yes	characteristic
69	C₄	—	10	2	no	—
70	C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
71	C₄	C₂×C₃×#170	1	1	yes	characteristic
72	C₃	#64889	1	1	yes	characteristic, direct product factor, Sylow
73	C₂	—	2	1	no	—
74	C₂	C₃×C₄⋊#170	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂×C₃×C₈
Frattini	C₂×C₄	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₄
socle	C₂×C₃×C₅	C₄⋊C₈
prime radical	C₂²×C₃×C₅	M₁₆
cosocle	C₂×#168	C₂²×C₃
hypercenter	C₂×C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#364
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
3. #64889	C₃	direct (N × H)
53. C₃×C₅	#364	semidirect
67. C₅	C₃×#364	semidirect
72. C₃	#64889	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×#3998	2
C₃×C₈×Dic₅	2
#64889	3
C₃×#364	5

Subgroups — C3×#64889 #11746666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#64889 #11746666