Subgroups — C₂⁶×D₁₃ #13129650

Order 1664.

58424 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, complemented
2	C₂⁵×D₁₃	C₂	1	126	yes	maximal, direct product factor
3	C₂⁵×C₁₃	C₂²	1	63	yes	complemented
4	C₂⁴×D₁₃	C₂²	1	2604	yes	direct product factor
5	C₂⁴×C₁₃	C₂³	1	651	yes	complemented
6	C₂³×D₁₃	C₂³	1	11160	yes	direct product factor
7	C₂⁷	—	13	1	no	maximal, Sylow
8	C₂³×C₁₃	C₂⁴	1	1395	yes	complemented
9	C₂²×D₁₃	C₂⁴	1	10416	yes	direct product factor
10	C₂⁶	—	13	126	no	—
11	C₂⁶	D₁₃	1	1	yes	characteristic, direct product factor
12	C₂²×C₁₃	C₂⁵	1	651	yes	complemented
13	C₂×D₁₃	C₂⁵	1	2016	yes	direct product factor
14	C₂⁵	—	13	2604	no	—
15	C₂⁵	C₂×D₁₃	1	63	yes	direct product factor
16	C₂×C₁₃	C₂⁶	1	63	yes	complemented
17	D₁₃	C₂⁶	1	64	yes	direct product factor
18	C₂⁴	—	13	11160	no	—
19	C₂⁴	C₂²×D₁₃	1	651	yes	direct product factor
20	C₁₃	C₂⁷	1	1	yes	characteristic, complemented, Sylow
21	C₂³	—	13	10416	no	—
22	C₂³	C₂³×D₁₃	1	1395	yes	direct product factor
23	C₂²	—	13	2016	no	—
24	C₂²	C₂⁴×D₁₃	1	651	yes	direct product factor
25	C₂	—	13	64	no	—
26	C₂	C₂⁵×D₁₃	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂⁷
Frattini	C₁	G
Fitting, socle	C₂⁶×C₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁶

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.