Subgroups — C₄×C₁₂₈ #94813

Order 512.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₈	C₂	1	2	yes	maximal
2	C₄×C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₄	C₄	1	1	yes	characteristic
4	C₂×C₆₄	C₂²	1	1	yes	characteristic
5	C₄×C₃₂	C₄	1	1	yes	characteristic
6	C₁₂₈	C₄	1	4	yes	direct product factor
7	C₂×C₃₂	C₈	1	1	yes	characteristic
8	C₂×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₄×C₁₆	C₈	1	1	yes	characteristic
10	C₆₄	C₈	1	2	yes	—
11	C₆₄	C₂×C₄	1	2	yes	—
12	C₂×C₁₆	C₁₆	1	1	yes	characteristic
13	C₂×C₁₆	C₂×C₈	1	1	yes	characteristic
14	C₄×C₈	C₁₆	1	1	yes	characteristic
15	C₃₂	C₁₆	1	2	yes	—
16	C₃₂	C₄²	1	1	yes	characteristic
17	C₃₂	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈	C₃₂	1	1	yes	characteristic
19	C₂×C₈	C₂×C₁₆	1	1	yes	characteristic
20	C₄²	C₃₂	1	1	yes	characteristic
21	C₁₆	C₃₂	1	2	yes	—
22	C₁₆	C₄×C₈	1	1	yes	characteristic
23	C₁₆	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₄	C₆₄	1	2	yes	—
25	C₂×C₄	C₂×C₃₂	1	1	yes	characteristic
26	C₈	C₆₄	1	2	yes	—
27	C₈	C₄×C₁₆	1	1	yes	characteristic
28	C₈	C₂×C₃₂	1	1	yes	characteristic
29	C₂²	C₂×C₆₄	1	1	yes	characteristic
30	C₄	C₁₂₈	1	4	yes	direct product factor
31	C₄	C₄×C₃₂	1	1	yes	characteristic
32	C₄	C₂×C₆₄	1	1	yes	characteristic
33	C₂	C₄×C₆₄	1	1	yes	characteristic
34	C₂	C₂×C₁₂₈	1	2	yes	—

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

N	H ≅ G/N	type
6. C₁₂₈	C₄	direct (N × H)
30. C₄	C₁₂₈	direct (N × H)

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

subgroup	index
C₂×C₁₂₈	2
C₄×C₆₄	2