Subgroups — C₁₆×#674 #13013293

Order 1280.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#674	C₂	1	2	yes	maximal
2	C₁₆×#168	C₂	1	1	yes	maximal, characteristic
3	C₄×#674	C₄	1	4	yes	—
4	C₄×C₅×C₁₆	C₄	1	1	yes	characteristic
5	C₄×#672	C₄	1	1	yes	characteristic
6	C₈×#168	C₂²	1	1	yes	characteristic
7	C₁₆²	—	5	1	no	maximal, Sylow
8	C₂×#674	C₈	1	8	yes	—
9	C₂×C₅×C₁₆	C₈	1	2	yes	—
10	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
11	C₂×#672	C₈	1	2	yes	—
12	C₄×#168	C₂×C₄	1	2	yes	—
13	C₈×C₁₆	—	5	2	no	—
14	C₈×C₁₆	—	5	1	no	—
15	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
16	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₅	C₄²	1	1	yes	characteristic
18	C₂×#168	C₂×C₈	1	4	yes	—
19	#674	C₁₆	1	16	yes	direct product factor
20	C₅×C₁₆	C₁₆	1	4	yes	complemented
21	#672	C₁₆	1	4	yes	complemented
22	C₄×C₁₆	—	5	4	no	—
23	C₄×C₁₆	—	5	1	no	—
24	C₄×C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₈²	—	5	1	no	—
26	C₂×C₄×C₅	C₄×C₈	1	2	yes	—
27	C₂×C₄×C₅	C₄×C₈	1	1	yes	characteristic
28	C₅×C₈	C₂×C₁₆	1	2	yes	—
29	C₅×C₈	C₂×C₁₆	1	2	yes	—
30	#168	C₂×C₁₆	1	8	yes	—
31	C₂×C₁₆	—	5	8	no	—
32	C₂×C₁₆	—	5	2	no	—
33	C₂×C₁₆	#170	1	2	yes	—
34	C₄×C₈	—	5	2	no	—
35	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
36	C₂²×C₅	C₈²	1	1	yes	characteristic
37	C₄×C₅	C₄×C₁₆	1	4	yes	—
38	C₄×C₅	C₄×C₁₆	1	1	yes	characteristic
39	C₄×C₅	C₄×C₁₆	1	1	yes	characteristic
40	C₂×C₈	—	5	4	no	—
41	C₂×C₈	D₅⋊C₈	1	1	yes	characteristic
42	C₂×C₈	C₂×#170	1	1	yes	characteristic
43	C₄²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
44	C₁₆	—	5	16	no	—
45	C₁₆	—	5	4	no	—
46	C₁₆	#674	1	4	yes	direct product factor
47	C₂×C₅	C₈×C₁₆	1	1	yes	characteristic
48	C₂×C₅	C₈×C₁₆	1	2	yes	—
49	C₂×C₄	C₈×AGL(1,𝔽₅)	1	2	yes	—
50	C₂×C₄	C₄×#170	1	1	yes	characteristic
51	C₈	—	5	8	no	—
52	C₈	D₅⋊C₁₆	1	2	yes	—
53	C₈	C₂×#674	1	2	yes	—
54	C₅	C₁₆²	1	1	yes	characteristic, complemented, Sylow
55	C₂²	C₈×#170	1	1	yes	characteristic
56	C₄	C₁₆×AGL(1,𝔽₅)	1	4	yes	—
57	C₄	C₄×#674	1	1	yes	characteristic
58	C₄	#64885	1	1	yes	characteristic
59	C₂	C₈×#674	1	1	yes	characteristic
60	C₂	C₁₆×#170	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₁₆	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₁₆²
Frattini	C₄×C₈	C₂×AGL(1,𝔽₅)
Fitting	C₄×C₅×C₁₆	C₄
socle, prime radical	C₂²×C₅	C₈²
cosocle	C₈×#168	C₂²
LCS	G ▷ C₅
UCS	C₁ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
19. #674	C₁₆	direct (N × H)
20. C₅×C₁₆	C₁₆	semidirect
21. #672	C₁₆	semidirect
46. C₁₆	#674	direct (N × H)
54. C₅	C₁₆²	semidirect

Maximal subgroups

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

subgroup	index
C₈×#674	2
C₁₆×#168	2
C₁₆²	5

Subgroups — C16×#674 #13013293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×#674 #13013293