Subgroups — C₂⁷×C₁₆₉ #72199169

Order 21632.

87636 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₁₆₉	C₂	1	127	yes	maximal, direct product factor
2	C₂⁵×C₁₆₉	C₂²	1	2667	yes	direct product factor
3	C₂⁴×C₁₆₉	C₂³	1	11811	yes	direct product factor
4	C₂⁷×C₁₃	C₁₃	1	1	yes	maximal, characteristic
5	C₂³×C₁₆₉	C₂⁴	1	11811	yes	direct product factor
6	C₂⁶×C₁₃	C₂×C₁₃	1	127	yes	—
7	C₂²×C₁₆₉	C₂⁵	1	2667	yes	direct product factor
8	C₂⁵×C₁₃	C₂²×C₁₃	1	2667	yes	—
9	C₂×C₁₆₉	C₂⁶	1	127	yes	direct product factor
10	C₂⁴×C₁₃	C₂³×C₁₃	1	11811	yes	—
11	C₁₆₉	C₂⁷	1	1	yes	characteristic, direct product factor, Sylow
12	C₂⁷	C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂³×C₁₃	C₂⁴×C₁₃	1	11811	yes	—
14	C₂⁶	C₂×C₁₆₉	1	127	yes	direct product factor
15	C₂²×C₁₃	C₂⁵×C₁₃	1	2667	yes	—
16	C₂⁵	C₂²×C₁₆₉	1	2667	yes	direct product factor
17	C₂×C₁₃	C₂⁶×C₁₃	1	127	yes	—
18	C₂⁴	C₂³×C₁₆₉	1	11811	yes	direct product factor
19	C₁₃	C₂⁷×C₁₃	1	1	yes	characteristic
20	C₂³	C₂⁴×C₁₆₉	1	11811	yes	direct product factor
21	C₂²	C₂⁵×C₁₆₉	1	2667	yes	direct product factor
22	C₂	C₂⁶×C₁₆₉	1	127	yes	direct product factor

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
C₂⁶×C₁₆₉	2
C₂⁷×C₁₃	13