Subgroups — #45656125

Order 32576.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₀₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#14523266	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₅₀₉	C₂	1	1	yes	maximal, characteristic
4	D₅₀₉⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#14523266	C₄	1	1	yes	characteristic
6	#22550864	C₄	1	2	yes	complemented
7	C₈×D₅₀₉	C₂²	1	1	yes	characteristic
8	#22550836	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₅₀₉	C₄	1	1	yes	characteristic, complemented
10	C₂×#14523266	C₈	1	2	yes	—
11	#16861332	C₈	1	2	yes	—
12	C₄×D₅₀₉	C₂×C₄	1	1	yes	characteristic
13	#16861325	C₂×C₄	1	1	yes	characteristic
14	C₈×C₅₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂×D₅₀₉	C₂×C₈	1	1	yes	characteristic
16	#14523266	—	2	2	no	—
17	C₄×C₅₀₉	C₄²	1	1	yes	characteristic
18	Dic₅₀₉	C₂×C₈	1	1	yes	characteristic
19	C₂×C₅₀₉	C₄×C₈	1	1	yes	characteristic
20	D₅₀₉	M₃₂	1	2	yes	—
21	C₅₀₉	#346	1	1	yes	characteristic, complemented, Sylow
22	#346	—	509	1	no	maximal, Sylow
23	C₂×C₁₆	—	509	1	no	—
24	C₂×C₁₆	—	509	1	no	—
25	C₄×C₈	—	509	1	no	—
26	C₂×C₈	—	509	1	no	—
27	C₂×C₈	—	509	1	no	—
28	C₄²	—	509	1	no	—
29	C₁₆	—	509	2	no	—
30	C₁₆	—	509	1	no	—
31	C₁₆	#14523266	1	1	yes	characteristic, complemented
32	C₂×C₄	—	509	2	no	—
33	C₂×C₄	—	509	1	no	—
34	C₈	—	509	2	no	—
35	C₈	—	509	1	no	—
36	C₈	C₂×#14523266	1	1	yes	characteristic
37	C₂²	—	509	1	no	—
38	C₄	—	1018	2	no	—
39	C₄	—	509	1	no	—
40	C₄	C₄×#14523266	1	1	yes	characteristic
41	C₂	—	509	2	no	—
42	C₂	C₈×#14523266	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.