Subgroups — C₂⁷×C₄ #10587005

Order 512.

805186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁸	C₂	1	1	yes	maximal, characteristic
2	C₂⁶×C₄	C₂	1	254	yes	maximal, direct product factor
3	C₂⁷	C₄	1	128	yes	direct product factor
4	C₂⁷	C₂²	1	127	yes	—
5	C₂⁵×C₄	C₂²	1	10668	yes	direct product factor
6	C₂⁶	C₂×C₄	1	8128	yes	direct product factor
7	C₂⁶	C₂³	1	2667	yes	—
8	C₂⁴×C₄	C₂³	1	94488	yes	direct product factor
9	C₂⁵	C₂²×C₄	1	85344	yes	direct product factor
10	C₂⁵	C₂⁴	1	11811	yes	—
11	C₂³×C₄	C₂⁴	1	188976	yes	direct product factor
12	C₂⁴	C₂³×C₄	1	188976	yes	direct product factor
13	C₂⁴	C₂⁵	1	11811	yes	—
14	C₂²×C₄	C₂⁵	1	85344	yes	direct product factor
15	C₂³	C₂⁴×C₄	1	94488	yes	direct product factor
16	C₂³	C₂⁶	1	2667	yes	—
17	C₂×C₄	C₂⁶	1	8128	yes	direct product factor
18	C₂²	C₂⁵×C₄	1	10668	yes	direct product factor
19	C₂²	C₂⁷	1	127	yes	—
20	C₄	C₂⁷	1	128	yes	direct product factor
21	C₂	C₂⁶×C₄	1	254	yes	direct product factor
22	C₂	C₂⁸	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.

subgroup	index
C₂⁸	2
C₂⁶×C₄	2