Subgroups — M₅₁₂ #94845

Order 512.

25 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₂₅₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₆₄	C₄	1	1	yes	characteristic
4	C₁₂₈	C₄	1	1	yes	characteristic
5	C₁₂₈	C₂²	1	1	yes	characteristic
6	C₂×C₃₂	C₈	1	1	yes	characteristic
7	C₆₄	C₈	1	1	yes	characteristic
8	C₆₄	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆	C₁₆	1	1	yes	characteristic
10	C₃₂	C₁₆	1	1	yes	characteristic
11	C₃₂	C₂×C₈	1	1	yes	characteristic
12	C₂×C₈	C₃₂	1	1	yes	characteristic
13	C₁₆	C₃₂	1	1	yes	characteristic
14	C₁₆	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₄	C₆₄	1	1	yes	characteristic
16	C₈	C₆₄	1	1	yes	characteristic
17	C₈	C₂×C₃₂	1	1	yes	characteristic
18	C₂²	C₁₂₈	1	1	yes	characteristic
19	C₄	C₁₂₈	1	1	yes	characteristic
20	C₄	C₂×C₆₄	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×C₁₂₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂₅₆	C₂	semidirect

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

subgroup	index
C₂×C₁₂₈	2
C₂₅₆	2