Subgroups — C₁₆×C₃₂ #93663

Order 512.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₃₂	C₂	1	2	yes	maximal
2	C₁₆²	C₂	1	1	yes	maximal, characteristic
3	C₄×C₃₂	C₄	1	4	yes	—
4	C₈×C₁₆	C₄	1	2	yes	—
5	C₈×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₃₂	C₈	1	8	yes	—
7	C₄×C₁₆	C₈	1	4	yes	—
8	C₄×C₁₆	C₂×C₄	1	2	yes	—
9	C₈²	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₆	C₁₆	1	8	yes	—
11	C₂×C₁₆	C₂×C₈	1	4	yes	—
12	C₄×C₈	C₄²	1	1	yes	characteristic
13	C₄×C₈	C₂×C₈	1	2	yes	—
14	C₃₂	C₁₆	1	16	yes	direct product factor
15	C₂×C₈	C₄×C₈	1	2	yes	—
16	C₂×C₈	C₂×C₁₆	1	4	yes	—
17	C₄²	C₄×C₈	1	1	yes	characteristic
18	C₁₆	C₃₂	1	16	yes	direct product factor
19	C₁₆	C₂×C₁₆	1	8	yes	—
20	C₂×C₄	C₈²	1	1	yes	characteristic
21	C₂×C₄	C₄×C₁₆	1	2	yes	—
22	C₈	C₄×C₁₆	1	4	yes	—
23	C₈	C₂×C₃₂	1	8	yes	—
24	C₂²	C₈×C₁₆	1	1	yes	characteristic
25	C₄	C₈×C₁₆	1	2	yes	—
26	C₄	C₄×C₃₂	1	4	yes	—
27	C₂	C₁₆²	1	1	yes	characteristic
28	C₂	C₈×C₃₂	1	2	yes	—

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

N	H ≅ G/N	type
14. C₃₂	C₁₆	direct (N × H)
18. C₁₆	C₃₂	direct (N × H)

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

subgroup	index
C₈×C₃₂	2
C₁₆²	2