Finite Group Databasebeta

← C₂⁶×C₁₆₉ #72189385

Subgroups — C₂⁶×C₁₆₉ #72189385

Order 10816.

8475 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₁₆₉	C₂	1	63	yes	maximal, direct product factor
2	C₂⁴×C₁₆₉	C₂²	1	651	yes	direct product factor
3	C₂³×C₁₆₉	C₂³	1	1395	yes	direct product factor
4	C₂⁶×C₁₃	C₁₃	1	1	yes	maximal, characteristic
5	C₂²×C₁₆₉	C₂⁴	1	651	yes	direct product factor
6	C₂⁵×C₁₃	C₂×C₁₃	1	63	yes	—
7	C₂×C₁₆₉	C₂⁵	1	63	yes	direct product factor
8	C₂⁴×C₁₃	C₂²×C₁₃	1	651	yes	—
9	C₁₆₉	C₂⁶	1	1	yes	characteristic, direct product factor, Sylow
10	C₂³×C₁₃	C₂³×C₁₃	1	1395	yes	—
11	C₂⁶	C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₁₃	C₂⁴×C₁₃	1	651	yes	—
13	C₂⁵	C₂×C₁₆₉	1	63	yes	direct product factor
14	C₂×C₁₃	C₂⁵×C₁₃	1	63	yes	—
15	C₂⁴	C₂²×C₁₆₉	1	651	yes	direct product factor
16	C₁₃	C₂⁶×C₁₃	1	1	yes	characteristic
17	C₂³	C₂³×C₁₆₉	1	1395	yes	direct product factor
18	C₂²	C₂⁴×C₁₆₉	1	651	yes	direct product factor
19	C₂	C₂⁵×C₁₆₉	1	63	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₃	C₂⁶×C₁₃
socle, prime radical	C₂⁶×C₁₃	C₁₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₁₆₉	C₂	direct (N × H)
2. C₂⁴×C₁₆₉	C₂²	direct (N × H)
3. C₂³×C₁₆₉	C₂³	direct (N × H)
5. C₂²×C₁₆₉	C₂⁴	direct (N × H)
7. C₂×C₁₆₉	C₂⁵	direct (N × H)
9. C₁₆₉	C₂⁶	direct (N × H)
11. C₂⁶	C₁₆₉	direct (N × H)
13. C₂⁵	C₂×C₁₆₉	direct (N × H)
15. C₂⁴	C₂²×C₁₆₉	direct (N × H)
17. C₂³	C₂³×C₁₆₉	direct (N × H)
18. C₂²	C₂⁴×C₁₆₉	direct (N × H)
19. C₂	C₂⁵×C₁₆₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₁₆₉	2
C₂⁶×C₁₃	13