Subgroups — C₂⁵×Dic₁₃ #13129626

Order 1664.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×Dic₁₃	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×C₁₃	C₄	1	32	yes	complemented
4	C₂⁵×C₁₃	C₂²	1	31	yes	—
5	C₂³×Dic₁₃	C₂²	1	620	yes	direct product factor
6	C₂⁴×C₁₃	C₂×C₄	1	496	yes	complemented
7	C₂⁴×C₁₃	C₂³	1	155	yes	—
8	C₂²×Dic₁₃	C₂³	1	1240	yes	direct product factor
9	C₂⁵×C₄	—	13	1	no	maximal, Sylow
10	C₂³×C₁₃	C₂²×C₄	1	1240	yes	complemented
11	C₂³×C₁₃	C₂⁴	1	155	yes	—
12	C₂×Dic₁₃	C₂⁴	1	496	yes	direct product factor
13	C₂⁶	D₁₃	1	1	yes	characteristic
14	C₂⁴×C₄	—	13	62	no	—
15	C₂²×C₁₃	C₂³×C₄	1	620	yes	complemented
16	C₂²×C₁₃	C₂⁵	1	31	yes	—
17	Dic₁₃	C₂⁵	1	32	yes	direct product factor
18	C₂⁵	Dic₁₃	1	32	yes	direct product factor
19	C₂⁵	C₂×D₁₃	1	31	yes	—
20	C₂³×C₄	—	13	620	no	—
21	C₂×C₁₃	C₂⁴×C₄	1	62	yes	complemented
22	C₂×C₁₃	C₂⁶	1	1	yes	characteristic
23	C₂⁴	C₂×Dic₁₃	1	496	yes	direct product factor
24	C₂⁴	C₂²×D₁₃	1	155	yes	—
25	C₂²×C₄	—	13	1240	no	—
26	C₁₃	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
27	C₂³	C₂²×Dic₁₃	1	1240	yes	direct product factor
28	C₂³	C₂³×D₁₃	1	155	yes	—
29	C₂×C₄	—	13	496	no	—
30	C₂²	C₂³×Dic₁₃	1	620	yes	direct product factor
31	C₂²	C₂⁴×D₁₃	1	31	yes	—
32	C₄	—	13	32	no	—
33	C₂	C₂⁴×Dic₁₃	1	62	yes	direct product factor
34	C₂	C₂⁵×D₁₃	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.