Subgroups — C₈×C₆₄ #94503

Order 512.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₆₄	C₂	1	2	yes	maximal
2	C₈×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₄	C₄	1	4	yes	—
4	C₄×C₃₂	C₄	1	1	yes	characteristic
5	C₄×C₃₂	C₂²	1	1	yes	characteristic
6	C₈×C₁₆	C₄	1	1	yes	characteristic
7	C₂×C₃₂	C₈	1	2	yes	—
8	C₂×C₃₂	C₂×C₄	1	2	yes	—
9	C₄×C₁₆	C₈	1	1	yes	characteristic
10	C₄×C₁₆	C₂×C₄	1	1	yes	characteristic
11	C₈²	C₈	1	1	yes	characteristic
12	C₆₄	C₈	1	8	yes	direct product factor
13	C₂×C₁₆	C₁₆	1	2	yes	—
14	C₂×C₁₆	C₄²	1	1	yes	characteristic
15	C₂×C₁₆	C₂×C₈	1	1	yes	characteristic
16	C₄×C₈	C₁₆	1	2	yes	—
17	C₄×C₈	C₂×C₈	1	1	yes	characteristic
18	C₃₂	C₁₆	1	4	yes	—
19	C₃₂	C₂×C₈	1	4	yes	—
20	C₂×C₈	C₃₂	1	4	yes	—
21	C₂×C₈	C₄×C₈	1	1	yes	characteristic
22	C₂×C₈	C₂×C₁₆	1	1	yes	characteristic
23	C₄²	C₂×C₁₆	1	1	yes	characteristic
24	C₁₆	C₃₂	1	4	yes	—
25	C₁₆	C₄×C₈	1	2	yes	—
26	C₁₆	C₂×C₁₆	1	2	yes	—
27	C₂×C₄	C₄×C₁₆	1	1	yes	characteristic
28	C₂×C₄	C₂×C₃₂	1	2	yes	—
29	C₈	C₆₄	1	8	yes	direct product factor
30	C₈	C₈²	1	1	yes	characteristic
31	C₈	C₄×C₁₆	1	1	yes	characteristic
32	C₈	C₂×C₃₂	1	2	yes	—
33	C₂²	C₄×C₃₂	1	1	yes	characteristic
34	C₄	C₈×C₁₆	1	1	yes	characteristic
35	C₄	C₄×C₃₂	1	1	yes	characteristic
36	C₄	C₂×C₆₄	1	4	yes	—
37	C₂	C₈×C₃₂	1	1	yes	characteristic
38	C₂	C₄×C₆₄	1	2	yes	—

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

N	H ≅ G/N	type
12. C₆₄	C₈	direct (N × H)
29. C₈	C₆₄	direct (N × H)

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

subgroup	index
C₄×C₆₄	2
C₈×C₃₂	2