Subgroups — #20266070

Order 6464.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692329	C₂	1	2	yes	maximal
2	#15692165	C₂	1	1	yes	maximal, characteristic
3	#13108077	C₄	1	4	yes	complemented
4	C₂×#11717579	C₂²	1	1	yes	characteristic
5	C₄×Dic₁₀₁	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₀₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₁₀₁	—	2	1	no	—
9	C₈×C₁₀₁	—	2	1	no	—
10	#11717579	C₂×C₄	1	2	yes	—
11	C₂²×C₁₀₁	M₁₆	1	1	yes	characteristic
12	C₄×C₁₀₁	C₄²	1	1	yes	characteristic
13	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
14	Dic₁₀₁	—	4	1	no	—
15	C₂×C₁₀₁	—	2	1	no	—
16	C₂×C₁₀₁	#97	1	1	yes	characteristic
17	C₁₀₁	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	101	1	no	maximal, Sylow
19	M₃₂	—	101	2	no	—
20	#97	—	101	1	no	—
21	C₂×C₈	—	101	1	no	—
22	C₂×C₈	#87938	1	1	yes	characteristic
23	C₄²	—	101	1	no	—
24	C₁₆	—	101	4	no	—
25	C₂×C₄	—	202	1	no	—
26	C₂×C₄	C₂×#87938	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	—	101	2	no	—
29	C₂²	#13108084	1	1	yes	characteristic
30	C₄	—	404	1	no	—
31	C₄	C₄×#87938	1	1	yes	characteristic
32	C₄	#13108083	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#15692310	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #13108077	C₄	semidirect
17. C₁₀₁	#347	semidirect