Subgroups — #45656149

Order 32576.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654276	C₂	1	2	yes	maximal
2	#30654215	C₂	1	1	yes	maximal, characteristic
3	#22550870	—	2	2	no	—
4	C₂×Dic₁₀₁₈	C₄	1	1	yes	characteristic
5	C₂×Dic₁₀₁₈	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₅₀₉	—	2	2	no	—
7	C₄²×C₅₀₉	C₄	1	1	yes	characteristic
8	#16861332	—	4	2	no	—
9	Dic₁₀₁₈	—	4	1	no	—
10	Dic₁₀₁₈	—	4	1	no	—
11	C₂×Dic₅₀₉	—	2	1	no	—
12	C₂×Dic₅₀₉	D₄	1	2	yes	—
13	C₂×C₄×C₅₀₉	—	2	1	no	—
14	C₂×C₄×C₅₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₅₀₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₅₀₉	—	2	2	no	—
17	C₄×C₅₀₉	—	2	1	no	—
18	Dic₅₀₉	—	2	2	no	—
19	Dic₅₀₉	—	4	1	no	—
20	C₂×C₅₀₉	—	2	1	no	—
21	C₂×C₅₀₉	#99	1	1	yes	characteristic
22	C₅₀₉	#356	1	1	yes	characteristic, complemented, Sylow
23	#356	—	509	1	no	maximal, Sylow
24	C₄⋊Q₈	—	509	1	no	—
25	#101	—	509	2	no	—
26	C₂×Q₈	—	509	1	no	—
27	C₂×Q₈	—	509	1	no	—
28	M₁₆	—	1018	2	no	—
29	C₄⋊C₄	—	1018	2	no	—
30	C₄²	#14523266	1	1	yes	characteristic
31	Q₈	—	2036	1	no	—
32	Q₈	—	2036	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	1018	1	no	—
35	C₂×C₄	—	509	2	no	—
36	C₂×C₄	C₂×#14523266	1	1	yes	characteristic
37	C₈	—	2036	2	no	—
38	C₂²	C₂²⋊#14523266	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	2	1	no	—
41	C₄	—	2036	1	no	—
42	C₄	—	1018	2	no	—
43	C₂	—	2	1	no	—
44	C₂	#30654274	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₅₀₉	#356	semidirect

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