Subgroups — C₁₆×AGL(1,𝔽₅) #64843

Order 320.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	D₅⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄×AGL(1,𝔽₅)	C₄	1	1	yes	characteristic
5	D₅⋊C₈	C₄	1	1	yes	characteristic
6	C₈×D₅	C₂²	1	1	yes	characteristic
7	#674	C₄	1	2	yes	complemented
8	C₅×C₁₆	C₄	1	1	yes	characteristic, complemented
9	#672	C₄	1	1	yes	characteristic, complemented
10	C₄×C₁₆	—	5	1	no	maximal, Sylow
11	C₂×AGL(1,𝔽₅)	C₈	1	2	yes	—
12	C₄×D₅	C₂×C₄	1	1	yes	characteristic
13	#170	C₈	1	2	yes	—
14	C₅×C₈	C₂×C₄	1	1	yes	characteristic
15	#168	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆	—	5	1	no	—
17	C₂×C₁₆	—	5	1	no	—
18	C₄×C₈	—	5	1	no	—
19	C₂×D₅	C₂×C₈	1	1	yes	characteristic
20	AGL(1,𝔽₅)	C₁₆	1	4	yes	direct product factor
21	C₄×C₅	C₄²	1	1	yes	characteristic
22	Dic₅	C₂×C₈	1	1	yes	characteristic
23	C₂×C₈	—	5	1	no	—
24	C₂×C₈	—	5	1	no	—
25	C₄²	—	5	1	no	—
26	C₁₆	—	5	2	no	—
27	C₁₆	—	5	1	no	—
28	C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
29	C₂×C₅	C₄×C₈	1	1	yes	characteristic
30	D₅	C₂×C₁₆	1	2	yes	—
31	C₂×C₄	—	5	2	no	—
32	C₂×C₄	—	5	1	no	—
33	C₈	—	5	2	no	—
34	C₈	—	5	1	no	—
35	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
36	C₅	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
37	C₂²	—	5	1	no	—
38	C₄	—	5	4	no	—
39	C₄	—	5	1	no	—
40	C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
41	C₂	—	5	2	no	—
42	C₂	C₈×AGL(1,𝔽₅)	1	1	yes	characteristic

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

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