Subgroups — C₈²×C₁₆₉ #72189372

Order 10816.

111 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₁₆₉	C₂	1	3	yes	maximal
2	C₄²×C₁₆₉	C₂²	1	1	yes	characteristic
3	C₂×C₈×C₁₆₉	C₄	1	6	yes	—
4	C₂×C₄×C₁₆₉	C₂×C₄	1	3	yes	—
5	C₈×C₁₆₉	C₈	1	12	yes	direct product factor
6	C₈²×C₁₃	C₁₃	1	1	yes	maximal, characteristic
7	C₂²×C₁₆₉	C₄²	1	1	yes	characteristic
8	C₄×C₁₆₉	C₂×C₈	1	6	yes	—
9	C₄×C₈×C₁₃	C₂×C₁₃	1	3	yes	—
10	C₂×C₁₆₉	C₄×C₈	1	3	yes	—
11	C₂×C₈×C₁₃	C₄×C₁₃	1	6	yes	—
12	C₄²×C₁₃	C₂²×C₁₃	1	1	yes	characteristic
13	C₁₆₉	C₈²	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₄×C₁₃	C₂×C₄×C₁₃	1	3	yes	—
15	C₈×C₁₃	C₈×C₁₃	1	12	yes	—
16	C₈²	C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂²×C₁₃	C₄²×C₁₃	1	1	yes	characteristic
18	C₄×C₁₃	C₂×C₈×C₁₃	1	6	yes	—
19	C₄×C₈	C₂×C₁₆₉	1	3	yes	—
20	C₂×C₁₃	C₄×C₈×C₁₃	1	3	yes	—
21	C₂×C₈	C₄×C₁₆₉	1	6	yes	—
22	C₄²	C₂²×C₁₆₉	1	1	yes	characteristic
23	C₁₃	C₈²×C₁₃	1	1	yes	characteristic
24	C₂×C₄	C₂×C₄×C₁₆₉	1	3	yes	—
25	C₈	C₈×C₁₆₉	1	12	yes	direct product factor
26	C₂²	C₄²×C₁₆₉	1	1	yes	characteristic
27	C₄	C₂×C₈×C₁₆₉	1	6	yes	—
28	C₂	C₄×C₈×C₁₆₉	1	3	yes	—

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
C₄×C₈×C₁₆₉	2
C₈²×C₁₃	13