Subgroups — C₂⁵×C₈ #63071

Order 256.

7727 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₈	C₂	1	62	yes	maximal, direct product factor
3	C₂⁶	C₄	1	1	yes	characteristic
4	C₂⁴×C₄	C₄	1	31	yes	—
5	C₂⁴×C₄	C₂²	1	31	yes	—
6	C₂³×C₈	C₂²	1	620	yes	direct product factor
7	C₂⁵	C₈	1	32	yes	direct product factor
8	C₂⁵	C₂×C₄	1	31	yes	—
9	C₂³×C₄	C₂×C₄	1	465	yes	—
10	C₂³×C₄	C₂³	1	155	yes	—
11	C₂²×C₈	C₂³	1	1240	yes	direct product factor
12	C₂⁴	C₂×C₈	1	496	yes	direct product factor
13	C₂⁴	C₂²×C₄	1	155	yes	—
14	C₂²×C₄	C₂²×C₄	1	1085	yes	—
15	C₂²×C₄	C₂⁴	1	155	yes	—
16	C₂×C₈	C₂⁴	1	496	yes	direct product factor
17	C₂³	C₂²×C₈	1	1240	yes	direct product factor
18	C₂³	C₂³×C₄	1	155	yes	—
19	C₂×C₄	C₂³×C₄	1	465	yes	—
20	C₂×C₄	C₂⁵	1	31	yes	—
21	C₈	C₂⁵	1	32	yes	direct product factor
22	C₂²	C₂³×C₈	1	620	yes	direct product factor
23	C₂²	C₂⁴×C₄	1	31	yes	—
24	C₄	C₂⁴×C₄	1	31	yes	—
25	C₄	C₂⁶	1	1	yes	characteristic
26	C₂	C₂⁴×C₈	1	62	yes	direct product factor
27	C₂	C₂⁵×C₄	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
C₂⁵×C₄	2
C₂⁴×C₈	2