Subgroups — #30654126

Order 16288.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861325	C₂	1	2	yes	maximal
2	C₄²×C₅₀₉	C₂	1	1	yes	maximal, characteristic
3	#16861325	C₄	1	4	yes	complemented
4	C₂×C₄×C₅₀₉	C₄	1	2	yes	—
5	C₂×C₄×C₅₀₉	C₂²	1	1	yes	characteristic
6	C₂²×C₅₀₉	C₂×C₄	1	1	yes	characteristic
7	C₄×C₅₀₉	—	2	2	no	—
8	C₄×C₅₀₉	C₂×C₄	1	2	yes	—
9	C₂×C₅₀₉	C₄²	1	1	yes	characteristic
10	C₂×C₅₀₉	M₁₆	1	2	yes	—
11	C₅₀₉	#97	1	1	yes	characteristic, complemented, Sylow
12	#97	—	509	1	no	maximal, Sylow
13	C₂×C₈	—	509	2	no	—
14	C₄²	D₅₀₉	1	1	yes	characteristic
15	C₂×C₄	Dic₅₀₉	1	2	yes	—
16	C₂×C₄	C₂×D₅₀₉	1	1	yes	characteristic
17	C₈	—	509	4	no	—
18	C₂²	C₂×Dic₅₀₉	1	1	yes	characteristic
19	C₄	—	2	2	no	—
20	C₄	C₄×D₅₀₉	1	2	yes	—
21	C₂	C₄×Dic₅₀₉	1	1	yes	characteristic
22	C₂	#22550845	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #16861325	C₄	semidirect
11. C₅₀₉	#97	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.