Subgroups — #11746756

Order 960.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊#674	C₂	1	2	yes	maximal
2	C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	#64885	—	3	1	no	maximal, 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	C₄	1	4	yes	complemented
8	C₄×C₃⋊C₁₆	—	5	1	no	maximal, Hall
9	C₂×#674	—	3	2	no	—
10	C₈×Dic₅	D₃	1	1	yes	characteristic
11	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×Dic₅	C₈	1	2	yes	—
13	C₃×C₅×C₈	C₈	1	2	yes	—
14	C₃×#168	C₂×C₄	1	2	yes	—
15	C₃×C₄×C₈	—	5	1	no	—
16	C₂×C₃⋊C₁₆	—	5	2	no	—
17	C₂×C₅×C₈	Dic₃	1	1	yes	characteristic
18	C₄×Dic₅	Dic₃	1	1	yes	characteristic
19	C₂×#168	C₂×D₃	1	1	yes	characteristic
20	#674	—	3	4	no	—
21	C₄×C₁₆	—	15	1	no	Sylow
22	C₂²×C₃×C₅	C₂×C₈	1	1	yes	characteristic
23	C₃×C₄×C₅	C₄²	1	1	yes	characteristic
24	C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
25	C₃×Dic₅	C₁₆	1	4	yes	complemented
26	C₂×C₃×C₈	—	5	1	no	—
27	C₂×C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₃×C₄²	—	5	1	no	—
29	C₃⋊C₁₆	—	5	4	no	—
30	C₂×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
31	C₂×Dic₅	C₃⋊C₈	1	2	yes	—
32	C₅×C₈	C₃⋊C₈	1	2	yes	—
33	#168	C₄×D₃	1	2	yes	—
34	C₂×C₁₆	—	15	2	no	—
35	C₄×C₈	—	5	1	no	—
36	C₂×C₃×C₅	C₄×C₈	1	1	yes	characteristic
37	C₂×C₃×C₅	C₂×C₁₆	1	2	yes	—
38	C₂×C₃×C₄	—	5	2	no	—
39	C₂×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₃×C₈	—	5	2	no	—
41	C₃×C₈	#170	1	2	yes	—
42	C₂²×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
43	C₄×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
44	C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
45	Dic₅	C₃⋊C₁₆	1	4	yes	complemented
46	C₂×C₈	—	5	1	no	—
47	C₂×C₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
48	C₄²	—	5	1	no	—
49	C₁₆	—	15	4	no	—
50	C₃×C₅	C₄×C₁₆	1	1	yes	characteristic, complemented, Hall
51	C₂²×C₃	D₅⋊C₈	1	1	yes	characteristic
52	C₃×C₄	—	5	4	no	—
53	C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
54	C₃×C₄	C₂×#170	1	1	yes	characteristic
55	C₂×C₅	C₄×C₃⋊C₈	1	1	yes	characteristic
56	C₂×C₅	C₂×C₃⋊C₁₆	1	2	yes	—
57	C₂×C₄	—	5	2	no	—
58	C₂×C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
59	C₈	—	5	2	no	—
60	C₈	C₃⋊#170	1	2	yes	—
61	C₂×C₃	D₅⋊C₁₆	1	2	yes	—
62	C₂×C₃	C₄×#170	1	1	yes	characteristic
63	C₅	C₄×C₃⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
64	C₂²	D₅⋊(C₃⋊C₈)	1	1	yes	characteristic
65	C₄	—	5	4	no	—
66	C₄	C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
67	C₄	C₂×C₃⋊#170	1	1	yes	characteristic
68	C₃	#64885	1	1	yes	characteristic, complemented, Sylow
69	C₂	D₅⋊(C₃⋊C₁₆)	1	2	yes	—
70	C₂	C₄×C₃⋊#170	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃×C₅	C₄×C₁₆
Frattini	C₂×C₄	C₂×ΓL(1,𝔽₁₆)
Fitting	C₂×C₃×C₅×C₈	C₄
socle, prime radical	C₂²×C₃×C₅	C₂×C₈
cosocle	C₂×C₃×#168	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
7. C₃⋊#674	C₄	semidirect
25. C₃×Dic₅	C₁₆	semidirect
45. Dic₅	C₃⋊C₁₆	semidirect
50. C₃×C₅	C₄×C₁₆	semidirect
63. C₅	C₄×C₃⋊C₁₆	semidirect
68. C₃	#64885	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊#674	2
C₃×C₈×Dic₅	2
#64885	3
C₄×C₃⋊C₁₆	5