Subgroups — #11746748

Order 960.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#672	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#3928	C₂	1	2	yes	maximal, complemented
3	#64877	—	3	1	no	maximal, Hall
4	C₂×C₃×C₅×C₈	C₄	1	1	yes	characteristic
5	C₃×#672	C₄	1	1	yes	characteristic
6	C₃×#672	C₂²	1	1	yes	characteristic
7	#4499	—	5	1	no	maximal, Hall
8	C₂×#672	D₃	1	1	yes	characteristic
9	#3928	—	3	2	no	—
10	C₂×C₃×C₄×C₅	C₈	1	1	yes	characteristic
11	C₃×C₅×C₈	C₈	1	1	yes	characteristic
12	C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₁₆	—	5	1	no	—
14	C₃⋊C₃₂	—	5	2	no	—
15	C₂×C₅×C₈	Dic₃	1	1	yes	characteristic
16	#672	Dic₃	1	1	yes	characteristic
17	#672	C₂×D₃	1	1	yes	characteristic
18	M₆₄	—	15	1	no	Sylow
19	C₂²×C₃×C₅	C₁₆	1	1	yes	characteristic
20	C₃×C₄×C₅	C₁₆	1	1	yes	characteristic
21	C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
22	C₂×C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
23	C₃×C₁₆	—	5	1	no	—
24	C₃×C₁₆	—	5	1	no	—
25	C₂×C₄×C₅	C₃⋊C₈	1	1	yes	characteristic
26	C₅×C₈	C₃⋊C₈	1	1	yes	characteristic
27	C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
28	C₂×C₁₆	—	5	1	no	—
29	C₃₂	—	15	2	no	—
30	C₂×C₃×C₅	—	2	1	no	—
31	C₂×C₃×C₅	C₂×C₁₆	1	1	yes	characteristic
32	C₂×C₃×C₄	#170	1	1	yes	characteristic
33	C₃×C₈	#170	1	1	yes	characteristic
34	C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
35	C₂²×C₅	C₃⋊C₁₆	1	1	yes	characteristic
36	C₄×C₅	C₃⋊C₁₆	1	1	yes	characteristic
37	C₄×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
38	C₂×C₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
39	C₁₆	—	5	1	no	—
40	C₁₆	—	5	1	no	—
41	C₃×C₅	M₆₄	1	1	yes	characteristic, complemented, Hall
42	C₂²×C₃	#674	1	1	yes	characteristic
43	C₃×C₄	#674	1	1	yes	characteristic
44	C₃×C₄	C₂×#170	1	1	yes	characteristic
45	C₂×C₅	—	2	1	no	—
46	C₂×C₅	C₂×C₃⋊C₁₆	1	1	yes	characteristic
47	C₂×C₄	C₃⋊#170	1	1	yes	characteristic
48	C₈	C₃⋊#170	1	1	yes	characteristic
49	C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
50	C₂×C₃	—	2	1	no	—
51	C₂×C₃	C₂×#674	1	1	yes	characteristic
52	C₅	#4499	1	1	yes	characteristic, complemented, Sylow
53	C₂²	C₃⋊#674	1	1	yes	characteristic
54	C₄	C₃⋊#674	1	1	yes	characteristic
55	C₄	C₂×C₃⋊#170	1	1	yes	characteristic
56	C₃	#64877	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	2	1	no	—
58	C₂	C₂×C₃⋊#674	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂×ΓL(1,𝔽₁₆)
commutator, socle	C₂×C₃×C₅	C₂×C₁₆
Fitting	C₂×C₃×C₅×C₈	C₄
prime radical	C₂²×C₃×C₅	C₁₆
cosocle	C₃×#672	C₂²
hypercenter	C₂×C₈	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	M₆₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₃⋊#3928	C₂	semidirect
41. C₃×C₅	M₆₄	semidirect
52. C₅	#4499	semidirect
56. C₃	#64877	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#672	2
C₃⋊#3928	2
#64877	3
#4499	5