Subgroups — #30654276

Order 16288.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550870	C₂	1	2	yes	maximal
2	C₂×Dic₁₀₁₈	C₂	1	1	yes	maximal, characteristic
3	#16861332	—	2	2	no	—
4	Dic₁₀₁₈	—	2	2	no	—
5	C₂×Dic₅₀₉	C₄	1	1	yes	characteristic
6	C₂×Dic₅₀₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅₀₉	C₄	1	1	yes	characteristic
8	C₂²×C₅₀₉	C₂×C₄	1	1	yes	characteristic
9	C₄×C₅₀₉	—	2	1	no	—
10	Dic₅₀₉	—	2	1	no	—
11	Dic₅₀₉	D₄	1	2	yes	—
12	C₂×C₅₀₉	—	2	1	no	—
13	C₂×C₅₀₉	C₂²⋊C₄	1	1	yes	characteristic
14	C₅₀₉	#101	1	1	yes	characteristic, complemented, Sylow
15	#101	—	509	1	no	maximal, Sylow
16	C₂×Q₈	—	509	1	no	—
17	M₁₆	—	509	2	no	—
18	Q₈	—	1018	2	no	—
19	C₂×C₄	—	509	1	no	—
20	C₂×C₄	—	509	1	no	—
21	C₂×C₄	#14523266	1	1	yes	characteristic
22	C₈	—	1018	2	no	—
23	C₂²	C₂×#14523266	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	—	1018	1	no	—
26	C₄	—	509	2	no	—
27	C₂	—	2	1	no	—
28	C₂	C₂²⋊#14523266	1	1	yes	characteristic

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

N	H ≅ G/N	type
14. C₅₀₉	#101	semidirect

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