Subgroups — #45656124

Order 32576.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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