Subgroups — D₅₀₉⋊C₃₂ #45656169

Order 32576.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654265	C₂	1	2	yes	maximal, complemented
2	C₁₆×D₅₀₉	C₂	1	1	yes	maximal, characteristic
3	C₈×D₅₀₉	C₄	1	1	yes	characteristic
4	#22550836	C₂²	1	1	yes	characteristic
5	C₁₆×C₅₀₉	C₄	1	1	yes	characteristic
6	C₄×D₅₀₉	C₈	1	1	yes	characteristic
7	#16861325	C₈	1	1	yes	characteristic
8	C₈×C₅₀₉	C₂×C₄	1	1	yes	characteristic
9	C₂×D₅₀₉	C₁₆	1	1	yes	characteristic
10	C₄×C₅₀₉	C₂×C₈	1	1	yes	characteristic
11	Dic₅₀₉	C₁₆	1	1	yes	characteristic
12	C₂×C₅₀₉	C₂×C₁₆	1	1	yes	characteristic
13	D₅₀₉	C₃₂	1	2	yes	complemented
14	C₅₀₉	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	509	1	no	maximal, Sylow
16	C₂×C₁₆	—	509	1	no	—
17	C₃₂	—	509	2	no	—
18	C₂×C₈	—	509	1	no	—
19	C₁₆	—	509	1	no	—
20	C₁₆	#14523266	1	1	yes	characteristic
21	C₂×C₄	—	509	1	no	—
22	C₈	—	509	1	no	—
23	C₈	C₂×#14523266	1	1	yes	characteristic
24	C₂²	—	509	1	no	—
25	C₄	—	509	1	no	—
26	C₄	D₅₀₉⋊C₈	1	1	yes	characteristic
27	C₂	—	509	2	no	—
28	C₂	D₅₀₉⋊C₁₆	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.